View Full Version : where does newtons laws fail
iam really searching for the answer where does newtons laws fail.i came
to know that in some cases without the application of force there may
be change in the momentum of the particle.how can this happen .can any
one quote the example.
what is a virtual work and how could it be possible.
thaks for ur valuable time
Uncle Al
Oct12-06, 04:16 AM
jaan wrote:
>
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Newton fails whenever c=infinity and/or h=0 are poor approximations.
GPS, for example, or accurate clocks on commercial aircraft,
<http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html>
<http://metrologyforum.tm.agilent.com/pdf/flying_clock_math.pdf>
http://metrologyforum.tm.agilent.com/cesium.shtml
http://arxiv.org/abs/physics/0008012
Hafele-Keating Experiment
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
Uncle Al
Oct12-06, 04:16 AM
jaan wrote:
>
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Newton fails whenever c=infinity and/or h=0 are poor approximations.
GPS, for example, or accurate clocks on commercial aircraft,
<http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html>
<http://metrologyforum.tm.agilent.com/pdf/flying_clock_math.pdf>
http://metrologyforum.tm.agilent.com/cesium.shtml
http://arxiv.org/abs/physics/0008012
Hafele-Keating Experiment
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
Uncle Al
Oct12-06, 04:16 AM
jaan wrote:
>
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Newton fails whenever c=infinity and/or h=0 are poor approximations.
GPS, for example, or accurate clocks on commercial aircraft,
<http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html>
<http://metrologyforum.tm.agilent.com/pdf/flying_clock_math.pdf>
http://metrologyforum.tm.agilent.com/cesium.shtml
http://arxiv.org/abs/physics/0008012
Hafele-Keating Experiment
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
Uncle Al
Oct12-06, 04:16 AM
jaan wrote:
>
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Newton fails whenever c=infinity and/or h=0 are poor approximations.
GPS, for example, or accurate clocks on commercial aircraft,
<http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html>
<http://metrologyforum.tm.agilent.com/pdf/flying_clock_math.pdf>
http://metrologyforum.tm.agilent.com/cesium.shtml
http://arxiv.org/abs/physics/0008012
Hafele-Keating Experiment
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
Uncle Al
Oct12-06, 04:16 AM
jaan wrote:
>
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Newton fails whenever c=infinity and/or h=0 are poor approximations.
GPS, for example, or accurate clocks on commercial aircraft,
<http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html>
<http://metrologyforum.tm.agilent.com/pdf/flying_clock_math.pdf>
http://metrologyforum.tm.agilent.com/cesium.shtml
http://arxiv.org/abs/physics/0008012
Hafele-Keating Experiment
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
Uncle Al
Oct12-06, 04:16 AM
jaan wrote:
>
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Newton fails whenever c=infinity and/or h=0 are poor approximations.
GPS, for example, or accurate clocks on commercial aircraft,
<http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html>
<http://metrologyforum.tm.agilent.com/pdf/flying_clock_math.pdf>
http://metrologyforum.tm.agilent.com/cesium.shtml
http://arxiv.org/abs/physics/0008012
Hafele-Keating Experiment
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
Uncle Al
Oct12-06, 04:16 AM
jaan wrote:
>
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Newton fails whenever c=infinity and/or h=0 are poor approximations.
GPS, for example, or accurate clocks on commercial aircraft,
<http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html>
<http://metrologyforum.tm.agilent.com/pdf/flying_clock_math.pdf>
http://metrologyforum.tm.agilent.com/cesium.shtml
http://arxiv.org/abs/physics/0008012
Hafele-Keating Experiment
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
Uncle Al
Oct12-06, 04:16 AM
jaan wrote:
>
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Newton fails whenever c=infinity and/or h=0 are poor approximations.
GPS, for example, or accurate clocks on commercial aircraft,
<http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html>
<http://metrologyforum.tm.agilent.com/pdf/flying_clock_math.pdf>
http://metrologyforum.tm.agilent.com/cesium.shtml
http://arxiv.org/abs/physics/0008012
Hafele-Keating Experiment
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
Uncle Al
Oct12-06, 04:16 AM
jaan wrote:
>
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Newton fails whenever c=infinity and/or h=0 are poor approximations.
GPS, for example, or accurate clocks on commercial aircraft,
<http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html>
<http://metrologyforum.tm.agilent.com/pdf/flying_clock_math.pdf>
http://metrologyforum.tm.agilent.com/cesium.shtml
http://arxiv.org/abs/physics/0008012
Hafele-Keating Experiment
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
Uncle Al
Oct12-06, 04:16 AM
jaan wrote:
>
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Newton fails whenever c=infinity and/or h=0 are poor approximations.
GPS, for example, or accurate clocks on commercial aircraft,
<http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html>
<http://metrologyforum.tm.agilent.com/pdf/flying_clock_math.pdf>
http://metrologyforum.tm.agilent.com/cesium.shtml
http://arxiv.org/abs/physics/0008012
Hafele-Keating Experiment
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
Uncle Al
Oct12-06, 04:16 AM
jaan wrote:
>
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Newton fails whenever c=infinity and/or h=0 are poor approximations.
GPS, for example, or accurate clocks on commercial aircraft,
<http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html>
<http://metrologyforum.tm.agilent.com/pdf/flying_clock_math.pdf>
http://metrologyforum.tm.agilent.com/cesium.shtml
http://arxiv.org/abs/physics/0008012
Hafele-Keating Experiment
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
Uncle Al
Oct12-06, 04:16 AM
jaan wrote:
>
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Newton fails whenever c=infinity and/or h=0 are poor approximations.
GPS, for example, or accurate clocks on commercial aircraft,
<http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html>
<http://metrologyforum.tm.agilent.com/pdf/flying_clock_math.pdf>
http://metrologyforum.tm.agilent.com/cesium.shtml
http://arxiv.org/abs/physics/0008012
Hafele-Keating Experiment
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
Uncle Al
Oct12-06, 04:16 AM
jaan wrote:
>
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Newton fails whenever c=infinity and/or h=0 are poor approximations.
GPS, for example, or accurate clocks on commercial aircraft,
<http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html>
<http://metrologyforum.tm.agilent.com/pdf/flying_clock_math.pdf>
http://metrologyforum.tm.agilent.com/cesium.shtml
http://arxiv.org/abs/physics/0008012
Hafele-Keating Experiment
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
Uncle Al
Oct12-06, 04:16 AM
jaan wrote:
>
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Newton fails whenever c=infinity and/or h=0 are poor approximations.
GPS, for example, or accurate clocks on commercial aircraft,
<http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html>
<http://metrologyforum.tm.agilent.com/pdf/flying_clock_math.pdf>
http://metrologyforum.tm.agilent.com/cesium.shtml
http://arxiv.org/abs/physics/0008012
Hafele-Keating Experiment
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
Uncle Al
Oct12-06, 04:16 AM
jaan wrote:
>
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Newton fails whenever c=infinity and/or h=0 are poor approximations.
GPS, for example, or accurate clocks on commercial aircraft,
<http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html>
<http://metrologyforum.tm.agilent.com/pdf/flying_clock_math.pdf>
http://metrologyforum.tm.agilent.com/cesium.shtml
http://arxiv.org/abs/physics/0008012
Hafele-Keating Experiment
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
Uncle Al
Oct12-06, 04:16 AM
jaan wrote:
>
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Newton fails whenever c=infinity and/or h=0 are poor approximations.
GPS, for example, or accurate clocks on commercial aircraft,
<http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html>
<http://metrologyforum.tm.agilent.com/pdf/flying_clock_math.pdf>
http://metrologyforum.tm.agilent.com/cesium.shtml
http://arxiv.org/abs/physics/0008012
Hafele-Keating Experiment
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
Uncle Al
Oct12-06, 04:16 AM
jaan wrote:
>
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Newton fails whenever c=infinity and/or h=0 are poor approximations.
GPS, for example, or accurate clocks on commercial aircraft,
<http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html>
<http://metrologyforum.tm.agilent.com/pdf/flying_clock_math.pdf>
http://metrologyforum.tm.agilent.com/cesium.shtml
http://arxiv.org/abs/physics/0008012
Hafele-Keating Experiment
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
Gerry Quinn
Oct12-06, 04:17 AM
In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
imsphy9@gmail.com says...
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Probably you are being confused by some poor quality explanation of
some part of physics (could be one of several fields as far as I can
see) that is using terms without explaining them properly, or how they
relate to other theories.
I *think* the discussion is probably about forces being explained by
the exchange of virtual bosons. This doesn't actually mean Newton's
law - or definition - f=ma fails at some point. It means it's being
explained by a different model of how forces work. [I will also point
out that a relativistic version of f=ma is still built into the new
theory, even if strange things are done with it.]
Let me give a simple example: I say "water doesn't evaporate, the
faster atoms escape from the liquid". Am I saying that the ordinary
theory of evaporation "added heat converts water into vapour with a
certain latent heat of evaporation" is wrong or fails at some point?
No - I'm explaining the same phenomenon in a different way.
The term 'virtual work' actually indicates a bad jumble of unrelated
concepts - we don't need the term work unless we are operating on a
scale above that of virtual particle interactions. We can talk about
momentum of virtual particles, but the only need for the term work is
in the context of energy and entropy in thermodynamics, which is
precisely to do with the scale in which the interference effects of
virtual particles have been cancelled out, and real particles have been
measured. And any real particle you measure will honour f=ma very
well, allowing for a little residual quantum uncertainty that
definitely can't be harnessed to do actual work.
- Gerry Quinn
Gerry Quinn
Oct12-06, 04:17 AM
In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
imsphy9@gmail.com says...
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Probably you are being confused by some poor quality explanation of
some part of physics (could be one of several fields as far as I can
see) that is using terms without explaining them properly, or how they
relate to other theories.
I *think* the discussion is probably about forces being explained by
the exchange of virtual bosons. This doesn't actually mean Newton's
law - or definition - f=ma fails at some point. It means it's being
explained by a different model of how forces work. [I will also point
out that a relativistic version of f=ma is still built into the new
theory, even if strange things are done with it.]
Let me give a simple example: I say "water doesn't evaporate, the
faster atoms escape from the liquid". Am I saying that the ordinary
theory of evaporation "added heat converts water into vapour with a
certain latent heat of evaporation" is wrong or fails at some point?
No - I'm explaining the same phenomenon in a different way.
The term 'virtual work' actually indicates a bad jumble of unrelated
concepts - we don't need the term work unless we are operating on a
scale above that of virtual particle interactions. We can talk about
momentum of virtual particles, but the only need for the term work is
in the context of energy and entropy in thermodynamics, which is
precisely to do with the scale in which the interference effects of
virtual particles have been cancelled out, and real particles have been
measured. And any real particle you measure will honour f=ma very
well, allowing for a little residual quantum uncertainty that
definitely can't be harnessed to do actual work.
- Gerry Quinn
Gerry Quinn
Oct12-06, 04:17 AM
In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
imsphy9@gmail.com says...
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Probably you are being confused by some poor quality explanation of
some part of physics (could be one of several fields as far as I can
see) that is using terms without explaining them properly, or how they
relate to other theories.
I *think* the discussion is probably about forces being explained by
the exchange of virtual bosons. This doesn't actually mean Newton's
law - or definition - f=ma fails at some point. It means it's being
explained by a different model of how forces work. [I will also point
out that a relativistic version of f=ma is still built into the new
theory, even if strange things are done with it.]
Let me give a simple example: I say "water doesn't evaporate, the
faster atoms escape from the liquid". Am I saying that the ordinary
theory of evaporation "added heat converts water into vapour with a
certain latent heat of evaporation" is wrong or fails at some point?
No - I'm explaining the same phenomenon in a different way.
The term 'virtual work' actually indicates a bad jumble of unrelated
concepts - we don't need the term work unless we are operating on a
scale above that of virtual particle interactions. We can talk about
momentum of virtual particles, but the only need for the term work is
in the context of energy and entropy in thermodynamics, which is
precisely to do with the scale in which the interference effects of
virtual particles have been cancelled out, and real particles have been
measured. And any real particle you measure will honour f=ma very
well, allowing for a little residual quantum uncertainty that
definitely can't be harnessed to do actual work.
- Gerry Quinn
Gerry Quinn
Oct12-06, 04:17 AM
In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
imsphy9@gmail.com says...
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Probably you are being confused by some poor quality explanation of
some part of physics (could be one of several fields as far as I can
see) that is using terms without explaining them properly, or how they
relate to other theories.
I *think* the discussion is probably about forces being explained by
the exchange of virtual bosons. This doesn't actually mean Newton's
law - or definition - f=ma fails at some point. It means it's being
explained by a different model of how forces work. [I will also point
out that a relativistic version of f=ma is still built into the new
theory, even if strange things are done with it.]
Let me give a simple example: I say "water doesn't evaporate, the
faster atoms escape from the liquid". Am I saying that the ordinary
theory of evaporation "added heat converts water into vapour with a
certain latent heat of evaporation" is wrong or fails at some point?
No - I'm explaining the same phenomenon in a different way.
The term 'virtual work' actually indicates a bad jumble of unrelated
concepts - we don't need the term work unless we are operating on a
scale above that of virtual particle interactions. We can talk about
momentum of virtual particles, but the only need for the term work is
in the context of energy and entropy in thermodynamics, which is
precisely to do with the scale in which the interference effects of
virtual particles have been cancelled out, and real particles have been
measured. And any real particle you measure will honour f=ma very
well, allowing for a little residual quantum uncertainty that
definitely can't be harnessed to do actual work.
- Gerry Quinn
Gerry Quinn
Oct12-06, 04:17 AM
In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
imsphy9@gmail.com says...
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Probably you are being confused by some poor quality explanation of
some part of physics (could be one of several fields as far as I can
see) that is using terms without explaining them properly, or how they
relate to other theories.
I *think* the discussion is probably about forces being explained by
the exchange of virtual bosons. This doesn't actually mean Newton's
law - or definition - f=ma fails at some point. It means it's being
explained by a different model of how forces work. [I will also point
out that a relativistic version of f=ma is still built into the new
theory, even if strange things are done with it.]
Let me give a simple example: I say "water doesn't evaporate, the
faster atoms escape from the liquid". Am I saying that the ordinary
theory of evaporation "added heat converts water into vapour with a
certain latent heat of evaporation" is wrong or fails at some point?
No - I'm explaining the same phenomenon in a different way.
The term 'virtual work' actually indicates a bad jumble of unrelated
concepts - we don't need the term work unless we are operating on a
scale above that of virtual particle interactions. We can talk about
momentum of virtual particles, but the only need for the term work is
in the context of energy and entropy in thermodynamics, which is
precisely to do with the scale in which the interference effects of
virtual particles have been cancelled out, and real particles have been
measured. And any real particle you measure will honour f=ma very
well, allowing for a little residual quantum uncertainty that
definitely can't be harnessed to do actual work.
- Gerry Quinn
Gerry Quinn
Oct12-06, 04:17 AM
In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
imsphy9@gmail.com says...
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Probably you are being confused by some poor quality explanation of
some part of physics (could be one of several fields as far as I can
see) that is using terms without explaining them properly, or how they
relate to other theories.
I *think* the discussion is probably about forces being explained by
the exchange of virtual bosons. This doesn't actually mean Newton's
law - or definition - f=ma fails at some point. It means it's being
explained by a different model of how forces work. [I will also point
out that a relativistic version of f=ma is still built into the new
theory, even if strange things are done with it.]
Let me give a simple example: I say "water doesn't evaporate, the
faster atoms escape from the liquid". Am I saying that the ordinary
theory of evaporation "added heat converts water into vapour with a
certain latent heat of evaporation" is wrong or fails at some point?
No - I'm explaining the same phenomenon in a different way.
The term 'virtual work' actually indicates a bad jumble of unrelated
concepts - we don't need the term work unless we are operating on a
scale above that of virtual particle interactions. We can talk about
momentum of virtual particles, but the only need for the term work is
in the context of energy and entropy in thermodynamics, which is
precisely to do with the scale in which the interference effects of
virtual particles have been cancelled out, and real particles have been
measured. And any real particle you measure will honour f=ma very
well, allowing for a little residual quantum uncertainty that
definitely can't be harnessed to do actual work.
- Gerry Quinn
Gerry Quinn
Oct12-06, 04:17 AM
In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
imsphy9@gmail.com says...
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Probably you are being confused by some poor quality explanation of
some part of physics (could be one of several fields as far as I can
see) that is using terms without explaining them properly, or how they
relate to other theories.
I *think* the discussion is probably about forces being explained by
the exchange of virtual bosons. This doesn't actually mean Newton's
law - or definition - f=ma fails at some point. It means it's being
explained by a different model of how forces work. [I will also point
out that a relativistic version of f=ma is still built into the new
theory, even if strange things are done with it.]
Let me give a simple example: I say "water doesn't evaporate, the
faster atoms escape from the liquid". Am I saying that the ordinary
theory of evaporation "added heat converts water into vapour with a
certain latent heat of evaporation" is wrong or fails at some point?
No - I'm explaining the same phenomenon in a different way.
The term 'virtual work' actually indicates a bad jumble of unrelated
concepts - we don't need the term work unless we are operating on a
scale above that of virtual particle interactions. We can talk about
momentum of virtual particles, but the only need for the term work is
in the context of energy and entropy in thermodynamics, which is
precisely to do with the scale in which the interference effects of
virtual particles have been cancelled out, and real particles have been
measured. And any real particle you measure will honour f=ma very
well, allowing for a little residual quantum uncertainty that
definitely can't be harnessed to do actual work.
- Gerry Quinn
Gerry Quinn
Oct12-06, 04:17 AM
In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
imsphy9@gmail.com says...
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Probably you are being confused by some poor quality explanation of
some part of physics (could be one of several fields as far as I can
see) that is using terms without explaining them properly, or how they
relate to other theories.
I *think* the discussion is probably about forces being explained by
the exchange of virtual bosons. This doesn't actually mean Newton's
law - or definition - f=ma fails at some point. It means it's being
explained by a different model of how forces work. [I will also point
out that a relativistic version of f=ma is still built into the new
theory, even if strange things are done with it.]
Let me give a simple example: I say "water doesn't evaporate, the
faster atoms escape from the liquid". Am I saying that the ordinary
theory of evaporation "added heat converts water into vapour with a
certain latent heat of evaporation" is wrong or fails at some point?
No - I'm explaining the same phenomenon in a different way.
The term 'virtual work' actually indicates a bad jumble of unrelated
concepts - we don't need the term work unless we are operating on a
scale above that of virtual particle interactions. We can talk about
momentum of virtual particles, but the only need for the term work is
in the context of energy and entropy in thermodynamics, which is
precisely to do with the scale in which the interference effects of
virtual particles have been cancelled out, and real particles have been
measured. And any real particle you measure will honour f=ma very
well, allowing for a little residual quantum uncertainty that
definitely can't be harnessed to do actual work.
- Gerry Quinn
Gerry Quinn
Oct12-06, 04:17 AM
In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
imsphy9@gmail.com says...
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Probably you are being confused by some poor quality explanation of
some part of physics (could be one of several fields as far as I can
see) that is using terms without explaining them properly, or how they
relate to other theories.
I *think* the discussion is probably about forces being explained by
the exchange of virtual bosons. This doesn't actually mean Newton's
law - or definition - f=ma fails at some point. It means it's being
explained by a different model of how forces work. [I will also point
out that a relativistic version of f=ma is still built into the new
theory, even if strange things are done with it.]
Let me give a simple example: I say "water doesn't evaporate, the
faster atoms escape from the liquid". Am I saying that the ordinary
theory of evaporation "added heat converts water into vapour with a
certain latent heat of evaporation" is wrong or fails at some point?
No - I'm explaining the same phenomenon in a different way.
The term 'virtual work' actually indicates a bad jumble of unrelated
concepts - we don't need the term work unless we are operating on a
scale above that of virtual particle interactions. We can talk about
momentum of virtual particles, but the only need for the term work is
in the context of energy and entropy in thermodynamics, which is
precisely to do with the scale in which the interference effects of
virtual particles have been cancelled out, and real particles have been
measured. And any real particle you measure will honour f=ma very
well, allowing for a little residual quantum uncertainty that
definitely can't be harnessed to do actual work.
- Gerry Quinn
Gerry Quinn
Oct12-06, 04:17 AM
In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
imsphy9@gmail.com says...
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Probably you are being confused by some poor quality explanation of
some part of physics (could be one of several fields as far as I can
see) that is using terms without explaining them properly, or how they
relate to other theories.
I *think* the discussion is probably about forces being explained by
the exchange of virtual bosons. This doesn't actually mean Newton's
law - or definition - f=ma fails at some point. It means it's being
explained by a different model of how forces work. [I will also point
out that a relativistic version of f=ma is still built into the new
theory, even if strange things are done with it.]
Let me give a simple example: I say "water doesn't evaporate, the
faster atoms escape from the liquid". Am I saying that the ordinary
theory of evaporation "added heat converts water into vapour with a
certain latent heat of evaporation" is wrong or fails at some point?
No - I'm explaining the same phenomenon in a different way.
The term 'virtual work' actually indicates a bad jumble of unrelated
concepts - we don't need the term work unless we are operating on a
scale above that of virtual particle interactions. We can talk about
momentum of virtual particles, but the only need for the term work is
in the context of energy and entropy in thermodynamics, which is
precisely to do with the scale in which the interference effects of
virtual particles have been cancelled out, and real particles have been
measured. And any real particle you measure will honour f=ma very
well, allowing for a little residual quantum uncertainty that
definitely can't be harnessed to do actual work.
- Gerry Quinn
Gerry Quinn
Oct12-06, 04:17 AM
In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
imsphy9@gmail.com says...
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Probably you are being confused by some poor quality explanation of
some part of physics (could be one of several fields as far as I can
see) that is using terms without explaining them properly, or how they
relate to other theories.
I *think* the discussion is probably about forces being explained by
the exchange of virtual bosons. This doesn't actually mean Newton's
law - or definition - f=ma fails at some point. It means it's being
explained by a different model of how forces work. [I will also point
out that a relativistic version of f=ma is still built into the new
theory, even if strange things are done with it.]
Let me give a simple example: I say "water doesn't evaporate, the
faster atoms escape from the liquid". Am I saying that the ordinary
theory of evaporation "added heat converts water into vapour with a
certain latent heat of evaporation" is wrong or fails at some point?
No - I'm explaining the same phenomenon in a different way.
The term 'virtual work' actually indicates a bad jumble of unrelated
concepts - we don't need the term work unless we are operating on a
scale above that of virtual particle interactions. We can talk about
momentum of virtual particles, but the only need for the term work is
in the context of energy and entropy in thermodynamics, which is
precisely to do with the scale in which the interference effects of
virtual particles have been cancelled out, and real particles have been
measured. And any real particle you measure will honour f=ma very
well, allowing for a little residual quantum uncertainty that
definitely can't be harnessed to do actual work.
- Gerry Quinn
Gerry Quinn
Oct12-06, 04:17 AM
In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
imsphy9@gmail.com says...
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Probably you are being confused by some poor quality explanation of
some part of physics (could be one of several fields as far as I can
see) that is using terms without explaining them properly, or how they
relate to other theories.
I *think* the discussion is probably about forces being explained by
the exchange of virtual bosons. This doesn't actually mean Newton's
law - or definition - f=ma fails at some point. It means it's being
explained by a different model of how forces work. [I will also point
out that a relativistic version of f=ma is still built into the new
theory, even if strange things are done with it.]
Let me give a simple example: I say "water doesn't evaporate, the
faster atoms escape from the liquid". Am I saying that the ordinary
theory of evaporation "added heat converts water into vapour with a
certain latent heat of evaporation" is wrong or fails at some point?
No - I'm explaining the same phenomenon in a different way.
The term 'virtual work' actually indicates a bad jumble of unrelated
concepts - we don't need the term work unless we are operating on a
scale above that of virtual particle interactions. We can talk about
momentum of virtual particles, but the only need for the term work is
in the context of energy and entropy in thermodynamics, which is
precisely to do with the scale in which the interference effects of
virtual particles have been cancelled out, and real particles have been
measured. And any real particle you measure will honour f=ma very
well, allowing for a little residual quantum uncertainty that
definitely can't be harnessed to do actual work.
- Gerry Quinn
Gerry Quinn
Oct12-06, 04:17 AM
In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
imsphy9@gmail.com says...
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Probably you are being confused by some poor quality explanation of
some part of physics (could be one of several fields as far as I can
see) that is using terms without explaining them properly, or how they
relate to other theories.
I *think* the discussion is probably about forces being explained by
the exchange of virtual bosons. This doesn't actually mean Newton's
law - or definition - f=ma fails at some point. It means it's being
explained by a different model of how forces work. [I will also point
out that a relativistic version of f=ma is still built into the new
theory, even if strange things are done with it.]
Let me give a simple example: I say "water doesn't evaporate, the
faster atoms escape from the liquid". Am I saying that the ordinary
theory of evaporation "added heat converts water into vapour with a
certain latent heat of evaporation" is wrong or fails at some point?
No - I'm explaining the same phenomenon in a different way.
The term 'virtual work' actually indicates a bad jumble of unrelated
concepts - we don't need the term work unless we are operating on a
scale above that of virtual particle interactions. We can talk about
momentum of virtual particles, but the only need for the term work is
in the context of energy and entropy in thermodynamics, which is
precisely to do with the scale in which the interference effects of
virtual particles have been cancelled out, and real particles have been
measured. And any real particle you measure will honour f=ma very
well, allowing for a little residual quantum uncertainty that
definitely can't be harnessed to do actual work.
- Gerry Quinn
Gerry Quinn
Oct12-06, 04:17 AM
In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
imsphy9@gmail.com says...
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Probably you are being confused by some poor quality explanation of
some part of physics (could be one of several fields as far as I can
see) that is using terms without explaining them properly, or how they
relate to other theories.
I *think* the discussion is probably about forces being explained by
the exchange of virtual bosons. This doesn't actually mean Newton's
law - or definition - f=ma fails at some point. It means it's being
explained by a different model of how forces work. [I will also point
out that a relativistic version of f=ma is still built into the new
theory, even if strange things are done with it.]
Let me give a simple example: I say "water doesn't evaporate, the
faster atoms escape from the liquid". Am I saying that the ordinary
theory of evaporation "added heat converts water into vapour with a
certain latent heat of evaporation" is wrong or fails at some point?
No - I'm explaining the same phenomenon in a different way.
The term 'virtual work' actually indicates a bad jumble of unrelated
concepts - we don't need the term work unless we are operating on a
scale above that of virtual particle interactions. We can talk about
momentum of virtual particles, but the only need for the term work is
in the context of energy and entropy in thermodynamics, which is
precisely to do with the scale in which the interference effects of
virtual particles have been cancelled out, and real particles have been
measured. And any real particle you measure will honour f=ma very
well, allowing for a little residual quantum uncertainty that
definitely can't be harnessed to do actual work.
- Gerry Quinn
Gerry Quinn
Oct12-06, 04:17 AM
In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
imsphy9@gmail.com says...
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Probably you are being confused by some poor quality explanation of
some part of physics (could be one of several fields as far as I can
see) that is using terms without explaining them properly, or how they
relate to other theories.
I *think* the discussion is probably about forces being explained by
the exchange of virtual bosons. This doesn't actually mean Newton's
law - or definition - f=ma fails at some point. It means it's being
explained by a different model of how forces work. [I will also point
out that a relativistic version of f=ma is still built into the new
theory, even if strange things are done with it.]
Let me give a simple example: I say "water doesn't evaporate, the
faster atoms escape from the liquid". Am I saying that the ordinary
theory of evaporation "added heat converts water into vapour with a
certain latent heat of evaporation" is wrong or fails at some point?
No - I'm explaining the same phenomenon in a different way.
The term 'virtual work' actually indicates a bad jumble of unrelated
concepts - we don't need the term work unless we are operating on a
scale above that of virtual particle interactions. We can talk about
momentum of virtual particles, but the only need for the term work is
in the context of energy and entropy in thermodynamics, which is
precisely to do with the scale in which the interference effects of
virtual particles have been cancelled out, and real particles have been
measured. And any real particle you measure will honour f=ma very
well, allowing for a little residual quantum uncertainty that
definitely can't be harnessed to do actual work.
- Gerry Quinn
Gerry Quinn
Oct12-06, 04:17 AM
In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
imsphy9@gmail.com says...
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Probably you are being confused by some poor quality explanation of
some part of physics (could be one of several fields as far as I can
see) that is using terms without explaining them properly, or how they
relate to other theories.
I *think* the discussion is probably about forces being explained by
the exchange of virtual bosons. This doesn't actually mean Newton's
law - or definition - f=ma fails at some point. It means it's being
explained by a different model of how forces work. [I will also point
out that a relativistic version of f=ma is still built into the new
theory, even if strange things are done with it.]
Let me give a simple example: I say "water doesn't evaporate, the
faster atoms escape from the liquid". Am I saying that the ordinary
theory of evaporation "added heat converts water into vapour with a
certain latent heat of evaporation" is wrong or fails at some point?
No - I'm explaining the same phenomenon in a different way.
The term 'virtual work' actually indicates a bad jumble of unrelated
concepts - we don't need the term work unless we are operating on a
scale above that of virtual particle interactions. We can talk about
momentum of virtual particles, but the only need for the term work is
in the context of energy and entropy in thermodynamics, which is
precisely to do with the scale in which the interference effects of
virtual particles have been cancelled out, and real particles have been
measured. And any real particle you measure will honour f=ma very
well, allowing for a little residual quantum uncertainty that
definitely can't be harnessed to do actual work.
- Gerry Quinn
Gerry Quinn
Oct12-06, 04:17 AM
In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
imsphy9@gmail.com says...
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Probably you are being confused by some poor quality explanation of
some part of physics (could be one of several fields as far as I can
see) that is using terms without explaining them properly, or how they
relate to other theories.
I *think* the discussion is probably about forces being explained by
the exchange of virtual bosons. This doesn't actually mean Newton's
law - or definition - f=ma fails at some point. It means it's being
explained by a different model of how forces work. [I will also point
out that a relativistic version of f=ma is still built into the new
theory, even if strange things are done with it.]
Let me give a simple example: I say "water doesn't evaporate, the
faster atoms escape from the liquid". Am I saying that the ordinary
theory of evaporation "added heat converts water into vapour with a
certain latent heat of evaporation" is wrong or fails at some point?
No - I'm explaining the same phenomenon in a different way.
The term 'virtual work' actually indicates a bad jumble of unrelated
concepts - we don't need the term work unless we are operating on a
scale above that of virtual particle interactions. We can talk about
momentum of virtual particles, but the only need for the term work is
in the context of energy and entropy in thermodynamics, which is
precisely to do with the scale in which the interference effects of
virtual particles have been cancelled out, and real particles have been
measured. And any real particle you measure will honour f=ma very
well, allowing for a little residual quantum uncertainty that
definitely can't be harnessed to do actual work.
- Gerry Quinn
Gerry Quinn
Oct12-06, 04:17 AM
In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
imsphy9@gmail.com says...
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Probably you are being confused by some poor quality explanation of
some part of physics (could be one of several fields as far as I can
see) that is using terms without explaining them properly, or how they
relate to other theories.
I *think* the discussion is probably about forces being explained by
the exchange of virtual bosons. This doesn't actually mean Newton's
law - or definition - f=ma fails at some point. It means it's being
explained by a different model of how forces work. [I will also point
out that a relativistic version of f=ma is still built into the new
theory, even if strange things are done with it.]
Let me give a simple example: I say "water doesn't evaporate, the
faster atoms escape from the liquid". Am I saying that the ordinary
theory of evaporation "added heat converts water into vapour with a
certain latent heat of evaporation" is wrong or fails at some point?
No - I'm explaining the same phenomenon in a different way.
The term 'virtual work' actually indicates a bad jumble of unrelated
concepts - we don't need the term work unless we are operating on a
scale above that of virtual particle interactions. We can talk about
momentum of virtual particles, but the only need for the term work is
in the context of energy and entropy in thermodynamics, which is
precisely to do with the scale in which the interference effects of
virtual particles have been cancelled out, and real particles have been
measured. And any real particle you measure will honour f=ma very
well, allowing for a little residual quantum uncertainty that
definitely can't be harnessed to do actual work.
- Gerry Quinn
EF Ferrari
Oct12-06, 04:18 AM
Gerry Quinn wrote:
> In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
> imsphy9@gmail.com says...
> > iam really searching for the answer where does newtons laws fail.i came
> > to know that in some cases without the application of force there may
> > be change in the momentum of the particle.how can this happen .can any
> > one quote the example.
> > what is a virtual work and how could it be possible.
> > thaks for ur valuable time
>
> Probably you are being confused by some poor quality explanation of
> some part of physics (could be one of several fields as far as I can
> see) that is using terms without explaining them properly, or how they
> relate to other theories.
>
> I *think* the discussion is probably about forces being explained by
> the exchange of virtual bosons. This doesn't actually mean Newton's
> law - or definition - f=ma fails at some point. It means it's being
> explained by a different model of how forces work. [I will also point
> out that a relativistic version of f=ma is still built into the new
> theory, even if strange things are done with it.]
>
> Let me give a simple example: I say "water doesn't evaporate, the
> faster atoms escape from the liquid". Am I saying that the ordinary
> theory of evaporation "added heat converts water into vapour with a
> certain latent heat of evaporation" is wrong or fails at some point?
> No - I'm explaining the same phenomenon in a different way.
>
> The term 'virtual work' actually indicates a bad jumble of unrelated
> concepts - we don't need the term work unless we are operating on a
> scale above that of virtual particle interactions. We can talk about
> momentum of virtual particles, but the only need for the term work is
> in the context of energy and entropy in thermodynamics, which is
> precisely to do with the scale in which the interference effects of
> virtual particles have been cancelled out, and real particles have been
> measured. And any real particle you measure will honour f=ma very
> well, allowing for a little residual quantum uncertainty that
> definitely can't be harnessed to do actual work.
>
> - Gerry Quinn
Is the question about the D'Alembert's Principle, isn't it?
Alain J. Brizard wrote a nice Introduction to Lagrangian and
Hamiltonian
mechanics:
http://academics.smcvt.edu/abrizard/Classical_Mechanics/CM.htm
EF Ferrari
Oct12-06, 04:18 AM
Gerry Quinn wrote:
> In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
> imsphy9@gmail.com says...
> > iam really searching for the answer where does newtons laws fail.i came
> > to know that in some cases without the application of force there may
> > be change in the momentum of the particle.how can this happen .can any
> > one quote the example.
> > what is a virtual work and how could it be possible.
> > thaks for ur valuable time
>
> Probably you are being confused by some poor quality explanation of
> some part of physics (could be one of several fields as far as I can
> see) that is using terms without explaining them properly, or how they
> relate to other theories.
>
> I *think* the discussion is probably about forces being explained by
> the exchange of virtual bosons. This doesn't actually mean Newton's
> law - or definition - f=ma fails at some point. It means it's being
> explained by a different model of how forces work. [I will also point
> out that a relativistic version of f=ma is still built into the new
> theory, even if strange things are done with it.]
>
> Let me give a simple example: I say "water doesn't evaporate, the
> faster atoms escape from the liquid". Am I saying that the ordinary
> theory of evaporation "added heat converts water into vapour with a
> certain latent heat of evaporation" is wrong or fails at some point?
> No - I'm explaining the same phenomenon in a different way.
>
> The term 'virtual work' actually indicates a bad jumble of unrelated
> concepts - we don't need the term work unless we are operating on a
> scale above that of virtual particle interactions. We can talk about
> momentum of virtual particles, but the only need for the term work is
> in the context of energy and entropy in thermodynamics, which is
> precisely to do with the scale in which the interference effects of
> virtual particles have been cancelled out, and real particles have been
> measured. And any real particle you measure will honour f=ma very
> well, allowing for a little residual quantum uncertainty that
> definitely can't be harnessed to do actual work.
>
> - Gerry Quinn
Is the question about the D'Alembert's Principle, isn't it?
Alain J. Brizard wrote a nice Introduction to Lagrangian and
Hamiltonian
mechanics:
http://academics.smcvt.edu/abrizard/Classical_Mechanics/CM.htm
EF Ferrari
Oct12-06, 04:18 AM
Gerry Quinn wrote:
> In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
> imsphy9@gmail.com says...
> > iam really searching for the answer where does newtons laws fail.i came
> > to know that in some cases without the application of force there may
> > be change in the momentum of the particle.how can this happen .can any
> > one quote the example.
> > what is a virtual work and how could it be possible.
> > thaks for ur valuable time
>
> Probably you are being confused by some poor quality explanation of
> some part of physics (could be one of several fields as far as I can
> see) that is using terms without explaining them properly, or how they
> relate to other theories.
>
> I *think* the discussion is probably about forces being explained by
> the exchange of virtual bosons. This doesn't actually mean Newton's
> law - or definition - f=ma fails at some point. It means it's being
> explained by a different model of how forces work. [I will also point
> out that a relativistic version of f=ma is still built into the new
> theory, even if strange things are done with it.]
>
> Let me give a simple example: I say "water doesn't evaporate, the
> faster atoms escape from the liquid". Am I saying that the ordinary
> theory of evaporation "added heat converts water into vapour with a
> certain latent heat of evaporation" is wrong or fails at some point?
> No - I'm explaining the same phenomenon in a different way.
>
> The term 'virtual work' actually indicates a bad jumble of unrelated
> concepts - we don't need the term work unless we are operating on a
> scale above that of virtual particle interactions. We can talk about
> momentum of virtual particles, but the only need for the term work is
> in the context of energy and entropy in thermodynamics, which is
> precisely to do with the scale in which the interference effects of
> virtual particles have been cancelled out, and real particles have been
> measured. And any real particle you measure will honour f=ma very
> well, allowing for a little residual quantum uncertainty that
> definitely can't be harnessed to do actual work.
>
> - Gerry Quinn
Is the question about the D'Alembert's Principle, isn't it?
Alain J. Brizard wrote a nice Introduction to Lagrangian and
Hamiltonian
mechanics:
http://academics.smcvt.edu/abrizard/Classical_Mechanics/CM.htm
EF Ferrari
Oct12-06, 04:18 AM
Gerry Quinn wrote:
> In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
> imsphy9@gmail.com says...
> > iam really searching for the answer where does newtons laws fail.i came
> > to know that in some cases without the application of force there may
> > be change in the momentum of the particle.how can this happen .can any
> > one quote the example.
> > what is a virtual work and how could it be possible.
> > thaks for ur valuable time
>
> Probably you are being confused by some poor quality explanation of
> some part of physics (could be one of several fields as far as I can
> see) that is using terms without explaining them properly, or how they
> relate to other theories.
>
> I *think* the discussion is probably about forces being explained by
> the exchange of virtual bosons. This doesn't actually mean Newton's
> law - or definition - f=ma fails at some point. It means it's being
> explained by a different model of how forces work. [I will also point
> out that a relativistic version of f=ma is still built into the new
> theory, even if strange things are done with it.]
>
> Let me give a simple example: I say "water doesn't evaporate, the
> faster atoms escape from the liquid". Am I saying that the ordinary
> theory of evaporation "added heat converts water into vapour with a
> certain latent heat of evaporation" is wrong or fails at some point?
> No - I'm explaining the same phenomenon in a different way.
>
> The term 'virtual work' actually indicates a bad jumble of unrelated
> concepts - we don't need the term work unless we are operating on a
> scale above that of virtual particle interactions. We can talk about
> momentum of virtual particles, but the only need for the term work is
> in the context of energy and entropy in thermodynamics, which is
> precisely to do with the scale in which the interference effects of
> virtual particles have been cancelled out, and real particles have been
> measured. And any real particle you measure will honour f=ma very
> well, allowing for a little residual quantum uncertainty that
> definitely can't be harnessed to do actual work.
>
> - Gerry Quinn
Is the question about the D'Alembert's Principle, isn't it?
Alain J. Brizard wrote a nice Introduction to Lagrangian and
Hamiltonian
mechanics:
http://academics.smcvt.edu/abrizard/Classical_Mechanics/CM.htm
EF Ferrari
Oct12-06, 04:18 AM
Gerry Quinn wrote:
> In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
> imsphy9@gmail.com says...
> > iam really searching for the answer where does newtons laws fail.i came
> > to know that in some cases without the application of force there may
> > be change in the momentum of the particle.how can this happen .can any
> > one quote the example.
> > what is a virtual work and how could it be possible.
> > thaks for ur valuable time
>
> Probably you are being confused by some poor quality explanation of
> some part of physics (could be one of several fields as far as I can
> see) that is using terms without explaining them properly, or how they
> relate to other theories.
>
> I *think* the discussion is probably about forces being explained by
> the exchange of virtual bosons. This doesn't actually mean Newton's
> law - or definition - f=ma fails at some point. It means it's being
> explained by a different model of how forces work. [I will also point
> out that a relativistic version of f=ma is still built into the new
> theory, even if strange things are done with it.]
>
> Let me give a simple example: I say "water doesn't evaporate, the
> faster atoms escape from the liquid". Am I saying that the ordinary
> theory of evaporation "added heat converts water into vapour with a
> certain latent heat of evaporation" is wrong or fails at some point?
> No - I'm explaining the same phenomenon in a different way.
>
> The term 'virtual work' actually indicates a bad jumble of unrelated
> concepts - we don't need the term work unless we are operating on a
> scale above that of virtual particle interactions. We can talk about
> momentum of virtual particles, but the only need for the term work is
> in the context of energy and entropy in thermodynamics, which is
> precisely to do with the scale in which the interference effects of
> virtual particles have been cancelled out, and real particles have been
> measured. And any real particle you measure will honour f=ma very
> well, allowing for a little residual quantum uncertainty that
> definitely can't be harnessed to do actual work.
>
> - Gerry Quinn
Is the question about the D'Alembert's Principle, isn't it?
Alain J. Brizard wrote a nice Introduction to Lagrangian and
Hamiltonian
mechanics:
http://academics.smcvt.edu/abrizard/Classical_Mechanics/CM.htm
EF Ferrari
Oct12-06, 04:18 AM
Gerry Quinn wrote:
> In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
> imsphy9@gmail.com says...
> > iam really searching for the answer where does newtons laws fail.i came
> > to know that in some cases without the application of force there may
> > be change in the momentum of the particle.how can this happen .can any
> > one quote the example.
> > what is a virtual work and how could it be possible.
> > thaks for ur valuable time
>
> Probably you are being confused by some poor quality explanation of
> some part of physics (could be one of several fields as far as I can
> see) that is using terms without explaining them properly, or how they
> relate to other theories.
>
> I *think* the discussion is probably about forces being explained by
> the exchange of virtual bosons. This doesn't actually mean Newton's
> law - or definition - f=ma fails at some point. It means it's being
> explained by a different model of how forces work. [I will also point
> out that a relativistic version of f=ma is still built into the new
> theory, even if strange things are done with it.]
>
> Let me give a simple example: I say "water doesn't evaporate, the
> faster atoms escape from the liquid". Am I saying that the ordinary
> theory of evaporation "added heat converts water into vapour with a
> certain latent heat of evaporation" is wrong or fails at some point?
> No - I'm explaining the same phenomenon in a different way.
>
> The term 'virtual work' actually indicates a bad jumble of unrelated
> concepts - we don't need the term work unless we are operating on a
> scale above that of virtual particle interactions. We can talk about
> momentum of virtual particles, but the only need for the term work is
> in the context of energy and entropy in thermodynamics, which is
> precisely to do with the scale in which the interference effects of
> virtual particles have been cancelled out, and real particles have been
> measured. And any real particle you measure will honour f=ma very
> well, allowing for a little residual quantum uncertainty that
> definitely can't be harnessed to do actual work.
>
> - Gerry Quinn
Is the question about the D'Alembert's Principle, isn't it?
Alain J. Brizard wrote a nice Introduction to Lagrangian and
Hamiltonian
mechanics:
http://academics.smcvt.edu/abrizard/Classical_Mechanics/CM.htm
EF Ferrari
Oct12-06, 04:18 AM
Gerry Quinn wrote:
> In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
> imsphy9@gmail.com says...
> > iam really searching for the answer where does newtons laws fail.i came
> > to know that in some cases without the application of force there may
> > be change in the momentum of the particle.how can this happen .can any
> > one quote the example.
> > what is a virtual work and how could it be possible.
> > thaks for ur valuable time
>
> Probably you are being confused by some poor quality explanation of
> some part of physics (could be one of several fields as far as I can
> see) that is using terms without explaining them properly, or how they
> relate to other theories.
>
> I *think* the discussion is probably about forces being explained by
> the exchange of virtual bosons. This doesn't actually mean Newton's
> law - or definition - f=ma fails at some point. It means it's being
> explained by a different model of how forces work. [I will also point
> out that a relativistic version of f=ma is still built into the new
> theory, even if strange things are done with it.]
>
> Let me give a simple example: I say "water doesn't evaporate, the
> faster atoms escape from the liquid". Am I saying that the ordinary
> theory of evaporation "added heat converts water into vapour with a
> certain latent heat of evaporation" is wrong or fails at some point?
> No - I'm explaining the same phenomenon in a different way.
>
> The term 'virtual work' actually indicates a bad jumble of unrelated
> concepts - we don't need the term work unless we are operating on a
> scale above that of virtual particle interactions. We can talk about
> momentum of virtual particles, but the only need for the term work is
> in the context of energy and entropy in thermodynamics, which is
> precisely to do with the scale in which the interference effects of
> virtual particles have been cancelled out, and real particles have been
> measured. And any real particle you measure will honour f=ma very
> well, allowing for a little residual quantum uncertainty that
> definitely can't be harnessed to do actual work.
>
> - Gerry Quinn
Is the question about the D'Alembert's Principle, isn't it?
Alain J. Brizard wrote a nice Introduction to Lagrangian and
Hamiltonian
mechanics:
http://academics.smcvt.edu/abrizard/Classical_Mechanics/CM.htm
EF Ferrari
Oct12-06, 04:18 AM
Gerry Quinn wrote:
> In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
> imsphy9@gmail.com says...
> > iam really searching for the answer where does newtons laws fail.i came
> > to know that in some cases without the application of force there may
> > be change in the momentum of the particle.how can this happen .can any
> > one quote the example.
> > what is a virtual work and how could it be possible.
> > thaks for ur valuable time
>
> Probably you are being confused by some poor quality explanation of
> some part of physics (could be one of several fields as far as I can
> see) that is using terms without explaining them properly, or how they
> relate to other theories.
>
> I *think* the discussion is probably about forces being explained by
> the exchange of virtual bosons. This doesn't actually mean Newton's
> law - or definition - f=ma fails at some point. It means it's being
> explained by a different model of how forces work. [I will also point
> out that a relativistic version of f=ma is still built into the new
> theory, even if strange things are done with it.]
>
> Let me give a simple example: I say "water doesn't evaporate, the
> faster atoms escape from the liquid". Am I saying that the ordinary
> theory of evaporation "added heat converts water into vapour with a
> certain latent heat of evaporation" is wrong or fails at some point?
> No - I'm explaining the same phenomenon in a different way.
>
> The term 'virtual work' actually indicates a bad jumble of unrelated
> concepts - we don't need the term work unless we are operating on a
> scale above that of virtual particle interactions. We can talk about
> momentum of virtual particles, but the only need for the term work is
> in the context of energy and entropy in thermodynamics, which is
> precisely to do with the scale in which the interference effects of
> virtual particles have been cancelled out, and real particles have been
> measured. And any real particle you measure will honour f=ma very
> well, allowing for a little residual quantum uncertainty that
> definitely can't be harnessed to do actual work.
>
> - Gerry Quinn
Is the question about the D'Alembert's Principle, isn't it?
Alain J. Brizard wrote a nice Introduction to Lagrangian and
Hamiltonian
mechanics:
http://academics.smcvt.edu/abrizard/Classical_Mechanics/CM.htm
EF Ferrari
Oct12-06, 04:18 AM
Gerry Quinn wrote:
> In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
> imsphy9@gmail.com says...
> > iam really searching for the answer where does newtons laws fail.i came
> > to know that in some cases without the application of force there may
> > be change in the momentum of the particle.how can this happen .can any
> > one quote the example.
> > what is a virtual work and how could it be possible.
> > thaks for ur valuable time
>
> Probably you are being confused by some poor quality explanation of
> some part of physics (could be one of several fields as far as I can
> see) that is using terms without explaining them properly, or how they
> relate to other theories.
>
> I *think* the discussion is probably about forces being explained by
> the exchange of virtual bosons. This doesn't actually mean Newton's
> law - or definition - f=ma fails at some point. It means it's being
> explained by a different model of how forces work. [I will also point
> out that a relativistic version of f=ma is still built into the new
> theory, even if strange things are done with it.]
>
> Let me give a simple example: I say "water doesn't evaporate, the
> faster atoms escape from the liquid". Am I saying that the ordinary
> theory of evaporation "added heat converts water into vapour with a
> certain latent heat of evaporation" is wrong or fails at some point?
> No - I'm explaining the same phenomenon in a different way.
>
> The term 'virtual work' actually indicates a bad jumble of unrelated
> concepts - we don't need the term work unless we are operating on a
> scale above that of virtual particle interactions. We can talk about
> momentum of virtual particles, but the only need for the term work is
> in the context of energy and entropy in thermodynamics, which is
> precisely to do with the scale in which the interference effects of
> virtual particles have been cancelled out, and real particles have been
> measured. And any real particle you measure will honour f=ma very
> well, allowing for a little residual quantum uncertainty that
> definitely can't be harnessed to do actual work.
>
> - Gerry Quinn
Is the question about the D'Alembert's Principle, isn't it?
Alain J. Brizard wrote a nice Introduction to Lagrangian and
Hamiltonian
mechanics:
http://academics.smcvt.edu/abrizard/Classical_Mechanics/CM.htm
EF Ferrari
Oct12-06, 04:18 AM
Gerry Quinn wrote:
> In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
> imsphy9@gmail.com says...
> > iam really searching for the answer where does newtons laws fail.i came
> > to know that in some cases without the application of force there may
> > be change in the momentum of the particle.how can this happen .can any
> > one quote the example.
> > what is a virtual work and how could it be possible.
> > thaks for ur valuable time
>
> Probably you are being confused by some poor quality explanation of
> some part of physics (could be one of several fields as far as I can
> see) that is using terms without explaining them properly, or how they
> relate to other theories.
>
> I *think* the discussion is probably about forces being explained by
> the exchange of virtual bosons. This doesn't actually mean Newton's
> law - or definition - f=ma fails at some point. It means it's being
> explained by a different model of how forces work. [I will also point
> out that a relativistic version of f=ma is still built into the new
> theory, even if strange things are done with it.]
>
> Let me give a simple example: I say "water doesn't evaporate, the
> faster atoms escape from the liquid". Am I saying that the ordinary
> theory of evaporation "added heat converts water into vapour with a
> certain latent heat of evaporation" is wrong or fails at some point?
> No - I'm explaining the same phenomenon in a different way.
>
> The term 'virtual work' actually indicates a bad jumble of unrelated
> concepts - we don't need the term work unless we are operating on a
> scale above that of virtual particle interactions. We can talk about
> momentum of virtual particles, but the only need for the term work is
> in the context of energy and entropy in thermodynamics, which is
> precisely to do with the scale in which the interference effects of
> virtual particles have been cancelled out, and real particles have been
> measured. And any real particle you measure will honour f=ma very
> well, allowing for a little residual quantum uncertainty that
> definitely can't be harnessed to do actual work.
>
> - Gerry Quinn
Is the question about the D'Alembert's Principle, isn't it?
Alain J. Brizard wrote a nice Introduction to Lagrangian and
Hamiltonian
mechanics:
http://academics.smcvt.edu/abrizard/Classical_Mechanics/CM.htm
EF Ferrari
Oct12-06, 04:18 AM
Gerry Quinn wrote:
> In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
> imsphy9@gmail.com says...
> > iam really searching for the answer where does newtons laws fail.i came
> > to know that in some cases without the application of force there may
> > be change in the momentum of the particle.how can this happen .can any
> > one quote the example.
> > what is a virtual work and how could it be possible.
> > thaks for ur valuable time
>
> Probably you are being confused by some poor quality explanation of
> some part of physics (could be one of several fields as far as I can
> see) that is using terms without explaining them properly, or how they
> relate to other theories.
>
> I *think* the discussion is probably about forces being explained by
> the exchange of virtual bosons. This doesn't actually mean Newton's
> law - or definition - f=ma fails at some point. It means it's being
> explained by a different model of how forces work. [I will also point
> out that a relativistic version of f=ma is still built into the new
> theory, even if strange things are done with it.]
>
> Let me give a simple example: I say "water doesn't evaporate, the
> faster atoms escape from the liquid". Am I saying that the ordinary
> theory of evaporation "added heat converts water into vapour with a
> certain latent heat of evaporation" is wrong or fails at some point?
> No - I'm explaining the same phenomenon in a different way.
>
> The term 'virtual work' actually indicates a bad jumble of unrelated
> concepts - we don't need the term work unless we are operating on a
> scale above that of virtual particle interactions. We can talk about
> momentum of virtual particles, but the only need for the term work is
> in the context of energy and entropy in thermodynamics, which is
> precisely to do with the scale in which the interference effects of
> virtual particles have been cancelled out, and real particles have been
> measured. And any real particle you measure will honour f=ma very
> well, allowing for a little residual quantum uncertainty that
> definitely can't be harnessed to do actual work.
>
> - Gerry Quinn
Is the question about the D'Alembert's Principle, isn't it?
Alain J. Brizard wrote a nice Introduction to Lagrangian and
Hamiltonian
mechanics:
http://academics.smcvt.edu/abrizard/Classical_Mechanics/CM.htm
EF Ferrari
Oct12-06, 04:18 AM
Gerry Quinn wrote:
> In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
> imsphy9@gmail.com says...
> > iam really searching for the answer where does newtons laws fail.i came
> > to know that in some cases without the application of force there may
> > be change in the momentum of the particle.how can this happen .can any
> > one quote the example.
> > what is a virtual work and how could it be possible.
> > thaks for ur valuable time
>
> Probably you are being confused by some poor quality explanation of
> some part of physics (could be one of several fields as far as I can
> see) that is using terms without explaining them properly, or how they
> relate to other theories.
>
> I *think* the discussion is probably about forces being explained by
> the exchange of virtual bosons. This doesn't actually mean Newton's
> law - or definition - f=ma fails at some point. It means it's being
> explained by a different model of how forces work. [I will also point
> out that a relativistic version of f=ma is still built into the new
> theory, even if strange things are done with it.]
>
> Let me give a simple example: I say "water doesn't evaporate, the
> faster atoms escape from the liquid". Am I saying that the ordinary
> theory of evaporation "added heat converts water into vapour with a
> certain latent heat of evaporation" is wrong or fails at some point?
> No - I'm explaining the same phenomenon in a different way.
>
> The term 'virtual work' actually indicates a bad jumble of unrelated
> concepts - we don't need the term work unless we are operating on a
> scale above that of virtual particle interactions. We can talk about
> momentum of virtual particles, but the only need for the term work is
> in the context of energy and entropy in thermodynamics, which is
> precisely to do with the scale in which the interference effects of
> virtual particles have been cancelled out, and real particles have been
> measured. And any real particle you measure will honour f=ma very
> well, allowing for a little residual quantum uncertainty that
> definitely can't be harnessed to do actual work.
>
> - Gerry Quinn
Is the question about the D'Alembert's Principle, isn't it?
Alain J. Brizard wrote a nice Introduction to Lagrangian and
Hamiltonian
mechanics:
http://academics.smcvt.edu/abrizard/Classical_Mechanics/CM.htm
EF Ferrari
Oct12-06, 04:18 AM
Gerry Quinn wrote:
> In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
> imsphy9@gmail.com says...
> > iam really searching for the answer where does newtons laws fail.i came
> > to know that in some cases without the application of force there may
> > be change in the momentum of the particle.how can this happen .can any
> > one quote the example.
> > what is a virtual work and how could it be possible.
> > thaks for ur valuable time
>
> Probably you are being confused by some poor quality explanation of
> some part of physics (could be one of several fields as far as I can
> see) that is using terms without explaining them properly, or how they
> relate to other theories.
>
> I *think* the discussion is probably about forces being explained by
> the exchange of virtual bosons. This doesn't actually mean Newton's
> law - or definition - f=ma fails at some point. It means it's being
> explained by a different model of how forces work. [I will also point
> out that a relativistic version of f=ma is still built into the new
> theory, even if strange things are done with it.]
>
> Let me give a simple example: I say "water doesn't evaporate, the
> faster atoms escape from the liquid". Am I saying that the ordinary
> theory of evaporation "added heat converts water into vapour with a
> certain latent heat of evaporation" is wrong or fails at some point?
> No - I'm explaining the same phenomenon in a different way.
>
> The term 'virtual work' actually indicates a bad jumble of unrelated
> concepts - we don't need the term work unless we are operating on a
> scale above that of virtual particle interactions. We can talk about
> momentum of virtual particles, but the only need for the term work is
> in the context of energy and entropy in thermodynamics, which is
> precisely to do with the scale in which the interference effects of
> virtual particles have been cancelled out, and real particles have been
> measured. And any real particle you measure will honour f=ma very
> well, allowing for a little residual quantum uncertainty that
> definitely can't be harnessed to do actual work.
>
> - Gerry Quinn
Is the question about the D'Alembert's Principle, isn't it?
Alain J. Brizard wrote a nice Introduction to Lagrangian and
Hamiltonian
mechanics:
http://academics.smcvt.edu/abrizard/Classical_Mechanics/CM.htm
EF Ferrari
Oct12-06, 04:18 AM
Gerry Quinn wrote:
> In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
> imsphy9@gmail.com says...
> > iam really searching for the answer where does newtons laws fail.i came
> > to know that in some cases without the application of force there may
> > be change in the momentum of the particle.how can this happen .can any
> > one quote the example.
> > what is a virtual work and how could it be possible.
> > thaks for ur valuable time
>
> Probably you are being confused by some poor quality explanation of
> some part of physics (could be one of several fields as far as I can
> see) that is using terms without explaining them properly, or how they
> relate to other theories.
>
> I *think* the discussion is probably about forces being explained by
> the exchange of virtual bosons. This doesn't actually mean Newton's
> law - or definition - f=ma fails at some point. It means it's being
> explained by a different model of how forces work. [I will also point
> out that a relativistic version of f=ma is still built into the new
> theory, even if strange things are done with it.]
>
> Let me give a simple example: I say "water doesn't evaporate, the
> faster atoms escape from the liquid". Am I saying that the ordinary
> theory of evaporation "added heat converts water into vapour with a
> certain latent heat of evaporation" is wrong or fails at some point?
> No - I'm explaining the same phenomenon in a different way.
>
> The term 'virtual work' actually indicates a bad jumble of unrelated
> concepts - we don't need the term work unless we are operating on a
> scale above that of virtual particle interactions. We can talk about
> momentum of virtual particles, but the only need for the term work is
> in the context of energy and entropy in thermodynamics, which is
> precisely to do with the scale in which the interference effects of
> virtual particles have been cancelled out, and real particles have been
> measured. And any real particle you measure will honour f=ma very
> well, allowing for a little residual quantum uncertainty that
> definitely can't be harnessed to do actual work.
>
> - Gerry Quinn
Is the question about the D'Alembert's Principle, isn't it?
Alain J. Brizard wrote a nice Introduction to Lagrangian and
Hamiltonian
mechanics:
http://academics.smcvt.edu/abrizard/Classical_Mechanics/CM.htm
EF Ferrari
Oct12-06, 04:18 AM
Gerry Quinn wrote:
> In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
> imsphy9@gmail.com says...
> > iam really searching for the answer where does newtons laws fail.i came
> > to know that in some cases without the application of force there may
> > be change in the momentum of the particle.how can this happen .can any
> > one quote the example.
> > what is a virtual work and how could it be possible.
> > thaks for ur valuable time
>
> Probably you are being confused by some poor quality explanation of
> some part of physics (could be one of several fields as far as I can
> see) that is using terms without explaining them properly, or how they
> relate to other theories.
>
> I *think* the discussion is probably about forces being explained by
> the exchange of virtual bosons. This doesn't actually mean Newton's
> law - or definition - f=ma fails at some point. It means it's being
> explained by a different model of how forces work. [I will also point
> out that a relativistic version of f=ma is still built into the new
> theory, even if strange things are done with it.]
>
> Let me give a simple example: I say "water doesn't evaporate, the
> faster atoms escape from the liquid". Am I saying that the ordinary
> theory of evaporation "added heat converts water into vapour with a
> certain latent heat of evaporation" is wrong or fails at some point?
> No - I'm explaining the same phenomenon in a different way.
>
> The term 'virtual work' actually indicates a bad jumble of unrelated
> concepts - we don't need the term work unless we are operating on a
> scale above that of virtual particle interactions. We can talk about
> momentum of virtual particles, but the only need for the term work is
> in the context of energy and entropy in thermodynamics, which is
> precisely to do with the scale in which the interference effects of
> virtual particles have been cancelled out, and real particles have been
> measured. And any real particle you measure will honour f=ma very
> well, allowing for a little residual quantum uncertainty that
> definitely can't be harnessed to do actual work.
>
> - Gerry Quinn
Is the question about the D'Alembert's Principle, isn't it?
Alain J. Brizard wrote a nice Introduction to Lagrangian and
Hamiltonian
mechanics:
http://academics.smcvt.edu/abrizard/Classical_Mechanics/CM.htm
EF Ferrari
Oct12-06, 04:18 AM
Gerry Quinn wrote:
> In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
> imsphy9@gmail.com says...
> > iam really searching for the answer where does newtons laws fail.i came
> > to know that in some cases without the application of force there may
> > be change in the momentum of the particle.how can this happen .can any
> > one quote the example.
> > what is a virtual work and how could it be possible.
> > thaks for ur valuable time
>
> Probably you are being confused by some poor quality explanation of
> some part of physics (could be one of several fields as far as I can
> see) that is using terms without explaining them properly, or how they
> relate to other theories.
>
> I *think* the discussion is probably about forces being explained by
> the exchange of virtual bosons. This doesn't actually mean Newton's
> law - or definition - f=ma fails at some point. It means it's being
> explained by a different model of how forces work. [I will also point
> out that a relativistic version of f=ma is still built into the new
> theory, even if strange things are done with it.]
>
> Let me give a simple example: I say "water doesn't evaporate, the
> faster atoms escape from the liquid". Am I saying that the ordinary
> theory of evaporation "added heat converts water into vapour with a
> certain latent heat of evaporation" is wrong or fails at some point?
> No - I'm explaining the same phenomenon in a different way.
>
> The term 'virtual work' actually indicates a bad jumble of unrelated
> concepts - we don't need the term work unless we are operating on a
> scale above that of virtual particle interactions. We can talk about
> momentum of virtual particles, but the only need for the term work is
> in the context of energy and entropy in thermodynamics, which is
> precisely to do with the scale in which the interference effects of
> virtual particles have been cancelled out, and real particles have been
> measured. And any real particle you measure will honour f=ma very
> well, allowing for a little residual quantum uncertainty that
> definitely can't be harnessed to do actual work.
>
> - Gerry Quinn
Is the question about the D'Alembert's Principle, isn't it?
Alain J. Brizard wrote a nice Introduction to Lagrangian and
Hamiltonian
mechanics:
http://academics.smcvt.edu/abrizard/Classical_Mechanics/CM.htm
EF Ferrari
Oct12-06, 04:18 AM
Gerry Quinn wrote:
> In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
> imsphy9@gmail.com says...
> > iam really searching for the answer where does newtons laws fail.i came
> > to know that in some cases without the application of force there may
> > be change in the momentum of the particle.how can this happen .can any
> > one quote the example.
> > what is a virtual work and how could it be possible.
> > thaks for ur valuable time
>
> Probably you are being confused by some poor quality explanation of
> some part of physics (could be one of several fields as far as I can
> see) that is using terms without explaining them properly, or how they
> relate to other theories.
>
> I *think* the discussion is probably about forces being explained by
> the exchange of virtual bosons. This doesn't actually mean Newton's
> law - or definition - f=ma fails at some point. It means it's being
> explained by a different model of how forces work. [I will also point
> out that a relativistic version of f=ma is still built into the new
> theory, even if strange things are done with it.]
>
> Let me give a simple example: I say "water doesn't evaporate, the
> faster atoms escape from the liquid". Am I saying that the ordinary
> theory of evaporation "added heat converts water into vapour with a
> certain latent heat of evaporation" is wrong or fails at some point?
> No - I'm explaining the same phenomenon in a different way.
>
> The term 'virtual work' actually indicates a bad jumble of unrelated
> concepts - we don't need the term work unless we are operating on a
> scale above that of virtual particle interactions. We can talk about
> momentum of virtual particles, but the only need for the term work is
> in the context of energy and entropy in thermodynamics, which is
> precisely to do with the scale in which the interference effects of
> virtual particles have been cancelled out, and real particles have been
> measured. And any real particle you measure will honour f=ma very
> well, allowing for a little residual quantum uncertainty that
> definitely can't be harnessed to do actual work.
>
> - Gerry Quinn
Is the question about the D'Alembert's Principle, isn't it?
Alain J. Brizard wrote a nice Introduction to Lagrangian and
Hamiltonian
mechanics:
http://academics.smcvt.edu/abrizard/Classical_Mechanics/CM.htm
EF Ferrari
Oct12-06, 04:18 AM
Gerry Quinn wrote:
> In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
> imsphy9@gmail.com says...
> > iam really searching for the answer where does newtons laws fail.i came
> > to know that in some cases without the application of force there may
> > be change in the momentum of the particle.how can this happen .can any
> > one quote the example.
> > what is a virtual work and how could it be possible.
> > thaks for ur valuable time
>
> Probably you are being confused by some poor quality explanation of
> some part of physics (could be one of several fields as far as I can
> see) that is using terms without explaining them properly, or how they
> relate to other theories.
>
> I *think* the discussion is probably about forces being explained by
> the exchange of virtual bosons. This doesn't actually mean Newton's
> law - or definition - f=ma fails at some point. It means it's being
> explained by a different model of how forces work. [I will also point
> out that a relativistic version of f=ma is still built into the new
> theory, even if strange things are done with it.]
>
> Let me give a simple example: I say "water doesn't evaporate, the
> faster atoms escape from the liquid". Am I saying that the ordinary
> theory of evaporation "added heat converts water into vapour with a
> certain latent heat of evaporation" is wrong or fails at some point?
> No - I'm explaining the same phenomenon in a different way.
>
> The term 'virtual work' actually indicates a bad jumble of unrelated
> concepts - we don't need the term work unless we are operating on a
> scale above that of virtual particle interactions. We can talk about
> momentum of virtual particles, but the only need for the term work is
> in the context of energy and entropy in thermodynamics, which is
> precisely to do with the scale in which the interference effects of
> virtual particles have been cancelled out, and real particles have been
> measured. And any real particle you measure will honour f=ma very
> well, allowing for a little residual quantum uncertainty that
> definitely can't be harnessed to do actual work.
>
> - Gerry Quinn
Is the question about the D'Alembert's Principle, isn't it?
Alain J. Brizard wrote a nice Introduction to Lagrangian and
Hamiltonian
mechanics:
http://academics.smcvt.edu/abrizard/Classical_Mechanics/CM.htm
EF Ferrari
Oct12-06, 04:18 AM
Gerry Quinn wrote:
> In article <1125735134.153451.18680@g43g2000cwa.googlegroups.c om>,
> imsphy9@gmail.com says...
> > iam really searching for the answer where does newtons laws fail.i came
> > to know that in some cases without the application of force there may
> > be change in the momentum of the particle.how can this happen .can any
> > one quote the example.
> > what is a virtual work and how could it be possible.
> > thaks for ur valuable time
>
> Probably you are being confused by some poor quality explanation of
> some part of physics (could be one of several fields as far as I can
> see) that is using terms without explaining them properly, or how they
> relate to other theories.
>
> I *think* the discussion is probably about forces being explained by
> the exchange of virtual bosons. This doesn't actually mean Newton's
> law - or definition - f=ma fails at some point. It means it's being
> explained by a different model of how forces work. [I will also point
> out that a relativistic version of f=ma is still built into the new
> theory, even if strange things are done with it.]
>
> Let me give a simple example: I say "water doesn't evaporate, the
> faster atoms escape from the liquid". Am I saying that the ordinary
> theory of evaporation "added heat converts water into vapour with a
> certain latent heat of evaporation" is wrong or fails at some point?
> No - I'm explaining the same phenomenon in a different way.
>
> The term 'virtual work' actually indicates a bad jumble of unrelated
> concepts - we don't need the term work unless we are operating on a
> scale above that of virtual particle interactions. We can talk about
> momentum of virtual particles, but the only need for the term work is
> in the context of energy and entropy in thermodynamics, which is
> precisely to do with the scale in which the interference effects of
> virtual particles have been cancelled out, and real particles have been
> measured. And any real particle you measure will honour f=ma very
> well, allowing for a little residual quantum uncertainty that
> definitely can't be harnessed to do actual work.
>
> - Gerry Quinn
Is the question about the D'Alembert's Principle, isn't it?
Alain J. Brizard wrote a nice Introduction to Lagrangian and
Hamiltonian
mechanics:
http://academics.smcvt.edu/abrizard/Classical_Mechanics/CM.htm
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:44 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:45 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:45 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:45 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
markwh04@yahoo.com
Oct12-06, 04:46 AM
jaan wrote:
> iam really searching for the answer where does newtons laws fail.
The infrastructure underlying Newton's Laws fails -- that is: the
structure of its spacetime.
Use the word "event" in the following to denote that which is
characterized by a position and time -- a point-instant.
Newton's laws presume a spacetime amongst whose features includes the
following ones of significance:
* Spacetime has the form of a sequence of 3-dimensional snapshots, each
representing "space" at a given "time"
* The past of any event is ALL of space on all the snapshots preceding
that which the event lies on
* The future of any event is ALL of space on all the snapshots
preceding that which the event lies on
* A hypothetical object travelling at an infinite speed in one frame of
reference would be doing so in all frames of reference. Infinity is an
invariant speed. All finite speeds are relative.
* To say the same thing another way: two events simultaneous in one
frame of reference are simultaneous in all frames of reference.
* To say the same thing a third way: for a given event, the
neither-past-nor-future of the event comprises a 3-dimensional space --
namely, the snapshot the event lies on.
* To say the same thing a fourth way: if A, B, C are events and A is
neither past nor future of B, B is neither past nor future of C, then A
is neither past nor future of C.
The contrast to Relativity is this:
* The past of any event is a sphere (and its inside) that contracts
down at light speed to the event, itself -- the past light cone of the
event.
* The future of the event is a sphere (and its inside) that expands at
light speed from the event, itself -- the future light cone of the
event.
* The invariant speed is FINITE. Not all finite speeds are relative,
which makes the name "Relativity" of the theory entirely inappropriate,
as Einstein pointed out early on.
* Infinity is NOT an invariant speed, it's relative.
* The neither-past-nor-future of a given event is a FOUR dimensional
continuum -- namely the outside of the past and future light cones of
the event.
* It is possible for A, B, C to be events with A neither before nor
after
B, B neither before nor after C, but A before C. (Example: A = the
Earth at a specific time, C = the Earth 1 second later; B = the Moon at
one of a specific range of times within the approximate 2 second window
of its existence that lies outside the light cones of A and C).
The two spacetimes are known, respectively, as Galilean and Minkowski
spacetime.
In the process of trying to retrofit Newton's Laws to Minkowski
spacetime, this forces the concepts of energy and momentum to be
unified into a single entity -- the 4-momentum. The law of inertia has
to be suitably modified and extended; with the additional condition
that a quantity, U, of energy must be associated with a mass equal to
U/c^2, where c is light speed.
In Newtonian spacetime, the two separate concepts of kinetic energy
(Lagrangian and Hamiltonian) for a body are equal, the equivalence
expressed by L = H; where L and H are related by the Legendre transform
H = pv - L, and the momentum and velocity by the relation p = mv.
This implies that L = mv^2/2; H = p^2/2m.
In Relativity, these two concepts split. The Hamiltonian is larger
than the Lagrangian, since it also includes the contribution provided
by the mass equivalent of the total energy of the Hamiltonian, itself.
So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
of the body.
Likewise, the momentum carries this additional contribution: p = (m +
H/c^2) v.
Since L and H are related by the Legendre transform, H = pv - L, this
implies that
H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
whose solution is
L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
= mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
H = p^2/((p/c)^2 + m^2)^{1/2} + m)
= mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
So, it's natural to identify mc^2 as the rest energy of the body and
equate the total kinetic energy to H + mc^2, which is
E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
The momentum is thus
p = mv/(1 - (v/c)^2)^{1/2}
and (E, p) form the components of the momentum 4-vector.
jaan wrote:
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Newton's laws fails for very fast objects. For example, it cannot tell
us why muons which have a very short lifetime at rest can survive for a
long enough journey from the upper atmosphere to the surface of the
earth.
Newton's law fails for very heavy objects. For example, it cannot tell
us why the orbit of Mercury precesses.
Newton's law fails for very small objects. For example, it cannot tell
us why the spectrum of the hydrogen atom is the way it is.
And of course, when a daily scale phenomenon, such as the specific heat
capacity of gases, involves phenomena from any of the above, Newton's
law fails to explain that as well.
There are hundreds of such examples in each of the above four
categories which will make any physicist reading this post will say
"Oh, why doesn't he mention that?!". However, those are the basic
regimes where Newton's laws start to give.
Cheers,
Souvik
jaan wrote:
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Newton's laws fails for very fast objects. For example, it cannot tell
us why muons which have a very short lifetime at rest can survive for a
long enough journey from the upper atmosphere to the surface of the
earth.
Newton's law fails for very heavy objects. For example, it cannot tell
us why the orbit of Mercury precesses.
Newton's law fails for very small objects. For example, it cannot tell
us why the spectrum of the hydrogen atom is the way it is.
And of course, when a daily scale phenomenon, such as the specific heat
capacity of gases, involves phenomena from any of the above, Newton's
law fails to explain that as well.
There are hundreds of such examples in each of the above four
categories which will make any physicist reading this post will say
"Oh, why doesn't he mention that?!". However, those are the basic
regimes where Newton's laws start to give.
Cheers,
Souvik
jaan wrote:
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Newton's laws fails for very fast objects. For example, it cannot tell
us why muons which have a very short lifetime at rest can survive for a
long enough journey from the upper atmosphere to the surface of the
earth.
Newton's law fails for very heavy objects. For example, it cannot tell
us why the orbit of Mercury precesses.
Newton's law fails for very small objects. For example, it cannot tell
us why the spectrum of the hydrogen atom is the way it is.
And of course, when a daily scale phenomenon, such as the specific heat
capacity of gases, involves phenomena from any of the above, Newton's
law fails to explain that as well.
There are hundreds of such examples in each of the above four
categories which will make any physicist reading this post will say
"Oh, why doesn't he mention that?!". However, those are the basic
regimes where Newton's laws start to give.
Cheers,
Souvik
jaan wrote:
> iam really searching for the answer where does newtons laws fail.i came
> to know that in some cases without the application of force there may
> be change in the momentum of the particle.how can this happen .can any
> one quote the example.
> what is a virtual work and how could it be possible.
> thaks for ur valuable time
Newton's laws fails for very fast objects. For example, it cannot tell
us why muons which have a very short lifetime at rest can survive for a
long enough journey from the upper atmosphere to the surface of the
earth.
Newton's law fails for very heavy objects. For example, it cannot tell
us why the orbit of Mercury precesses.
Newton's law fails for very small objects. For example, it cannot tell
us why the spectrum of the hydrogen atom is the way it is.
And of course, when a daily scale phenomenon, such as the specific heat
capacity of gases, involves phenomena from any of the above, Newton's
law fails to explain that as well.
There are hundreds of such examples in each of the above four
categories which will make any physicist reading this post will say
"Oh, why doesn't he mention that?!". However, those are the basic
regimes where Newton's laws start to give.
Cheers,
Souvik
markwh04@yahoo.com
Oct12-06, 04:56 AM
Harry wrote:
> > The infrastructure underlying Newton's Laws fails -- that is: the
> > structure of its spacetime.
> I'm not sure what is meant above with "Newton's spacetime",
That's precisely what the rest of the article you're replying to
described in detail; so your reply doesn't make much sense unless you
simply jumped the gun.
More commonly, it is known as Galilean spacetime, the corresponding
principle of relativity as Galilean Relativity, and the symmetry group
analogous to the Poincare' symmetry group as the Galilean symmetry
group.
> About his laws:
> With the post-Einstein concept of relativistic mass increase it's [sic]
> not necessary to retrofit Newton's force law F=d(m*v)/dt to Minkowski spacetime,
> as with m=gamma*m_0 it works fine as it stands
... which is precisely what is entailed by the retrofit, as explained
in the article. Again, the reply doesn't make sense since it directly
preceded the very thing you're reiterating ... unless you jumped the
gun.
markwh04@yahoo.com
Oct12-06, 04:56 AM
Harry wrote:
> > The infrastructure underlying Newton's Laws fails -- that is: the
> > structure of its spacetime.
> I'm not sure what is meant above with "Newton's spacetime",
That's precisely what the rest of the article you're replying to
described in detail; so your reply doesn't make much sense unless you
simply jumped the gun.
More commonly, it is known as Galilean spacetime, the corresponding
principle of relativity as Galilean Relativity, and the symmetry group
analogous to the Poincare' symmetry group as the Galilean symmetry
group.
> About his laws:
> With the post-Einstein concept of relativistic mass increase it's [sic]
> not necessary to retrofit Newton's force law F=d(m*v)/dt to Minkowski spacetime,
> as with m=gamma*m_0 it works fine as it stands
... which is precisely what is entailed by the retrofit, as explained
in the article. Again, the reply doesn't make sense since it directly
preceded the very thing you're reiterating ... unless you jumped the
gun.
markwh04@yahoo.com
Oct12-06, 04:56 AM
Harry wrote:
> > The infrastructure underlying Newton's Laws fails -- that is: the
> > structure of its spacetime.
> I'm not sure what is meant above with "Newton's spacetime",
That's precisely what the rest of the article you're replying to
described in detail; so your reply doesn't make much sense unless you
simply jumped the gun.
More commonly, it is known as Galilean spacetime, the corresponding
principle of relativity as Galilean Relativity, and the symmetry group
analogous to the Poincare' symmetry group as the Galilean symmetry
group.
> About his laws:
> With the post-Einstein concept of relativistic mass increase it's [sic]
> not necessary to retrofit Newton's force law F=d(m*v)/dt to Minkowski spacetime,
> as with m=gamma*m_0 it works fine as it stands
... which is precisely what is entailed by the retrofit, as explained
in the article. Again, the reply doesn't make sense since it directly
preceded the very thing you're reiterating ... unless you jumped the
gun.
markwh04@yahoo.com
Oct12-06, 04:56 AM
Harry wrote:
> > The infrastructure underlying Newton's Laws fails -- that is: the
> > structure of its spacetime.
> I'm not sure what is meant above with "Newton's spacetime",
That's precisely what the rest of the article you're replying to
described in detail; so your reply doesn't make much sense unless you
simply jumped the gun.
More commonly, it is known as Galilean spacetime, the corresponding
principle of relativity as Galilean Relativity, and the symmetry group
analogous to the Poincare' symmetry group as the Galilean symmetry
group.
> About his laws:
> With the post-Einstein concept of relativistic mass increase it's [sic]
> not necessary to retrofit Newton's force law F=d(m*v)/dt to Minkowski spacetime,
> as with m=gamma*m_0 it works fine as it stands
... which is precisely what is entailed by the retrofit, as explained
in the article. Again, the reply doesn't make sense since it directly
preceded the very thing you're reiterating ... unless you jumped the
gun.
markwh04@yahoo.com
Oct12-06, 04:56 AM
Harry wrote:
> > The infrastructure underlying Newton's Laws fails -- that is: the
> > structure of its spacetime.
> I'm not sure what is meant above with "Newton's spacetime",
That's precisely what the rest of the article you're replying to
described in detail; so your reply doesn't make much sense unless you
simply jumped the gun.
More commonly, it is known as Galilean spacetime, the corresponding
principle of relativity as Galilean Relativity, and the symmetry group
analogous to the Poincare' symmetry group as the Galilean symmetry
group.
> About his laws:
> With the post-Einstein concept of relativistic mass increase it's [sic]
> not necessary to retrofit Newton's force law F=d(m*v)/dt to Minkowski spacetime,
> as with m=gamma*m_0 it works fine as it stands
... which is precisely what is entailed by the retrofit, as explained
in the article. Again, the reply doesn't make sense since it directly
preceded the very thing you're reiterating ... unless you jumped the
gun.
<markwh04@yahoo.com> wrote in message
news:1127767092.916343.156150@g14g2000cwa.googlegr oups.com...
> Harry wrote:
> > > The infrastructure underlying Newton's Laws fails -- that is: the
> > > structure of its spacetime.
> > I'm not sure what is meant above with "Newton's spacetime",
>
> That's precisely what the rest of the article you're replying to
> described in detail; so your reply doesn't make much sense unless you
> simply jumped the gun.
I replied to your reply to a question about Newton's laws; that posting
has not appeared in my newsreader but it's the subject header. From your
full reply I wasn't sure if you you meant Newton's concepts of Space and
Time, or his assumption that Galilean transformation rules are valid for
all speeds. As I indicated, what has failed was his accompanying
assumption (based on observation of that time) that speed has no effect
on objects. With Lorentz' relativistic corrections, there is no problem
with the structure of Newton's Space and Time. Text books often mislead
people into thinking that Newton's Space and Time concepts failed (or
they don't even mention it), and that his concepts must be replaced by
Minkowski's Spacetime. See also the recent threads "logical
inconsistency in Lorentz' theory" and Ilja's comments in "why isn't the
mathematician Henri Poincare acknowledged as the true discoverer of
special relativity?".
> More commonly, it is known as Galilean spacetime, the corresponding
> principle of relativity as Galilean Relativity, and the symmetry group
> analogous to the Poincare' symmetry group as the Galilean symmetry
> group.
I didn't know that Galileo had such Newtonian concepts. If so, Newton
was misleading his readers when he claimed in his introduction of the
Principia:
"I do not define time, space, place and motion, as being well known to
all."
I suppose that Newton was truthful, and that common jargon is
misleading. But if someone has a quote of Galileo that shows the
contrary, I'll be glad to see it.
> > About his laws:
> > With the post-Einstein concept of relativistic mass increase it's [sic]
> > not necessary to retrofit Newton's force law F=d(m*v)/dt to Minkowski
spacetime,
>
> > as with m=gamma*m_0 it works fine as it stands
>
> .. which is precisely what is entailed by the retrofit, as explained
> in the article. Again, the reply doesn't make sense since it directly
> preceded the very thing you're reiterating ... unless you jumped the
> gun.
We agree on the math. However, the difference between Minkowski's
Spacetime and Newton's Space and Time is conceptual (metaphysical) and
not mathematical (physics). You seemed to suggest that one has to use
the first in order to do correct physics calculations. Sorry if I
misunderstood you. Still, many people confuse those things so that it is
useful to point it out now and then.
Cheers,
Harald
<markwh04@yahoo.com> wrote in message
news:1127767092.916343.156150@g14g2000cwa.googlegr oups.com...
> Harry wrote:
> > > The infrastructure underlying Newton's Laws fails -- that is: the
> > > structure of its spacetime.
> > I'm not sure what is meant above with "Newton's spacetime",
>
> That's precisely what the rest of the article you're replying to
> described in detail; so your reply doesn't make much sense unless you
> simply jumped the gun.
I replied to your reply to a question about Newton's laws; that posting
has not appeared in my newsreader but it's the subject header. From your
full reply I wasn't sure if you you meant Newton's concepts of Space and
Time, or his assumption that Galilean transformation rules are valid for
all speeds. As I indicated, what has failed was his accompanying
assumption (based on observation of that time) that speed has no effect
on objects. With Lorentz' relativistic corrections, there is no problem
with the structure of Newton's Space and Time. Text books often mislead
people into thinking that Newton's Space and Time concepts failed (or
they don't even mention it), and that his concepts must be replaced by
Minkowski's Spacetime. See also the recent threads "logical
inconsistency in Lorentz' theory" and Ilja's comments in "why isn't the
mathematician Henri Poincare acknowledged as the true discoverer of
special relativity?".
> More commonly, it is known as Galilean spacetime, the corresponding
> principle of relativity as Galilean Relativity, and the symmetry group
> analogous to the Poincare' symmetry group as the Galilean symmetry
> group.
I didn't know that Galileo had such Newtonian concepts. If so, Newton
was misleading his readers when he claimed in his introduction of the
Principia:
"I do not define time, space, place and motion, as being well known to
all."
I suppose that Newton was truthful, and that common jargon is
misleading. But if someone has a quote of Galileo that shows the
contrary, I'll be glad to see it.
> > About his laws:
> > With the post-Einstein concept of relativistic mass increase it's [sic]
> > not necessary to retrofit Newton's force law F=d(m*v)/dt to Minkowski
spacetime,
>
> > as with m=gamma*m_0 it works fine as it stands
>
> .. which is precisely what is entailed by the retrofit, as explained
> in the article. Again, the reply doesn't make sense since it directly
> preceded the very thing you're reiterating ... unless you jumped the
> gun.
We agree on the math. However, the difference between Minkowski's
Spacetime and Newton's Space and Time is conceptual (metaphysical) and
not mathematical (physics). You seemed to suggest that one has to use
the first in order to do correct physics calculations. Sorry if I
misunderstood you. Still, many people confuse those things so that it is
useful to point it out now and then.
Cheers,
Harald
<markwh04@yahoo.com> wrote in message
news:1127767092.916343.156150@g14g2000cwa.googlegr oups.com...
> Harry wrote:
> > > The infrastructure underlying Newton's Laws fails -- that is: the
> > > structure of its spacetime.
> > I'm not sure what is meant above with "Newton's spacetime",
>
> That's precisely what the rest of the article you're replying to
> described in detail; so your reply doesn't make much sense unless you
> simply jumped the gun.
I replied to your reply to a question about Newton's laws; that posting
has not appeared in my newsreader but it's the subject header. From your
full reply I wasn't sure if you you meant Newton's concepts of Space and
Time, or his assumption that Galilean transformation rules are valid for
all speeds. As I indicated, what has failed was his accompanying
assumption (based on observation of that time) that speed has no effect
on objects. With Lorentz' relativistic corrections, there is no problem
with the structure of Newton's Space and Time. Text books often mislead
people into thinking that Newton's Space and Time concepts failed (or
they don't even mention it), and that his concepts must be replaced by
Minkowski's Spacetime. See also the recent threads "logical
inconsistency in Lorentz' theory" and Ilja's comments in "why isn't the
mathematician Henri Poincare acknowledged as the true discoverer of
special relativity?".
> More commonly, it is known as Galilean spacetime, the corresponding
> principle of relativity as Galilean Relativity, and the symmetry group
> analogous to the Poincare' symmetry group as the Galilean symmetry
> group.
I didn't know that Galileo had such Newtonian concepts. If so, Newton
was misleading his readers when he claimed in his introduction of the
Principia:
"I do not define time, space, place and motion, as being well known to
all."
I suppose that Newton was truthful, and that common jargon is
misleading. But if someone has a quote of Galileo that shows the
contrary, I'll be glad to see it.
> > About his laws:
> > With the post-Einstein concept of relativistic mass increase it's [sic]
> > not necessary to retrofit Newton's force law F=d(m*v)/dt to Minkowski
spacetime,
>
> > as with m=gamma*m_0 it works fine as it stands
>
> .. which is precisely what is entailed by the retrofit, as explained
> in the article. Again, the reply doesn't make sense since it directly
> preceded the very thing you're reiterating ... unless you jumped the
> gun.
We agree on the math. However, the difference between Minkowski's
Spacetime and Newton's Space and Time is conceptual (metaphysical) and
not mathematical (physics). You seemed to suggest that one has to use
the first in order to do correct physics calculations. Sorry if I
misunderstood you. Still, many people confuse those things so that it is
useful to point it out now and then.
Cheers,
Harald
<markwh04@yahoo.com> wrote in message
news:1127767092.916343.156150@g14g2000cwa.googlegr oups.com...
> Harry wrote:
> > > The infrastructure underlying Newton's Laws fails -- that is: the
> > > structure of its spacetime.
> > I'm not sure what is meant above with "Newton's spacetime",
>
> That's precisely what the rest of the article you're replying to
> described in detail; so your reply doesn't make much sense unless you
> simply jumped the gun.
I replied to your reply to a question about Newton's laws; that posting
has not appeared in my newsreader but it's the subject header. From your
full reply I wasn't sure if you you meant Newton's concepts of Space and
Time, or his assumption that Galilean transformation rules are valid for
all speeds. As I indicated, what has failed was his accompanying
assumption (based on observation of that time) that speed has no effect
on objects. With Lorentz' relativistic corrections, there is no problem
with the structure of Newton's Space and Time. Text books often mislead
people into thinking that Newton's Space and Time concepts failed (or
they don't even mention it), and that his concepts must be replaced by
Minkowski's Spacetime. See also the recent threads "logical
inconsistency in Lorentz' theory" and Ilja's comments in "why isn't the
mathematician Henri Poincare acknowledged as the true discoverer of
special relativity?".
> More commonly, it is known as Galilean spacetime, the corresponding
> principle of relativity as Galilean Relativity, and the symmetry group
> analogous to the Poincare' symmetry group as the Galilean symmetry
> group.
I didn't know that Galileo had such Newtonian concepts. If so, Newton
was misleading his readers when he claimed in his introduction of the
Principia:
"I do not define time, space, place and motion, as being well known to
all."
I suppose that Newton was truthful, and that common jargon is
misleading. But if someone has a quote of Galileo that shows the
contrary, I'll be glad to see it.
> > About his laws:
> > With the post-Einstein concept of relativistic mass increase it's [sic]
> > not necessary to retrofit Newton's force law F=d(m*v)/dt to Minkowski
spacetime,
>
> > as with m=gamma*m_0 it works fine as it stands
>
> .. which is precisely what is entailed by the retrofit, as explained
> in the article. Again, the reply doesn't make sense since it directly
> preceded the very thing you're reiterating ... unless you jumped the
> gun.
We agree on the math. However, the difference between Minkowski's
Spacetime and Newton's Space and Time is conceptual (metaphysical) and
not mathematical (physics). You seemed to suggest that one has to use
the first in order to do correct physics calculations. Sorry if I
misunderstood you. Still, many people confuse those things so that it is
useful to point it out now and then.
Cheers,
Harald
<markwh04@yahoo.com> wrote in message
news:1127767092.916343.156150@g14g2000cwa.googlegr oups.com...
> Harry wrote:
> > > The infrastructure underlying Newton's Laws fails -- that is: the
> > > structure of its spacetime.
> > I'm not sure what is meant above with "Newton's spacetime",
>
> That's precisely what the rest of the article you're replying to
> described in detail; so your reply doesn't make much sense unless you
> simply jumped the gun.
I replied to your reply to a question about Newton's laws; that posting
has not appeared in my newsreader but it's the subject header. From your
full reply I wasn't sure if you you meant Newton's concepts of Space and
Time, or his assumption that Galilean transformation rules are valid for
all speeds. As I indicated, what has failed was his accompanying
assumption (based on observation of that time) that speed has no effect
on objects. With Lorentz' relativistic corrections, there is no problem
with the structure of Newton's Space and Time. Text books often mislead
people into thinking that Newton's Space and Time concepts failed (or
they don't even mention it), and that his concepts must be replaced by
Minkowski's Spacetime. See also the recent threads "logical
inconsistency in Lorentz' theory" and Ilja's comments in "why isn't the
mathematician Henri Poincare acknowledged as the true discoverer of
special relativity?".
> More commonly, it is known as Galilean spacetime, the corresponding
> principle of relativity as Galilean Relativity, and the symmetry group
> analogous to the Poincare' symmetry group as the Galilean symmetry
> group.
I didn't know that Galileo had such Newtonian concepts. If so, Newton
was misleading his readers when he claimed in his introduction of the
Principia:
"I do not define time, space, place and motion, as being well known to
all."
I suppose that Newton was truthful, and that common jargon is
misleading. But if someone has a quote of Galileo that shows the
contrary, I'll be glad to see it.
> > About his laws:
> > With the post-Einstein concept of relativistic mass increase it's [sic]
> > not necessary to retrofit Newton's force law F=d(m*v)/dt to Minkowski
spacetime,
>
> > as with m=gamma*m_0 it works fine as it stands
>
> .. which is precisely what is entailed by the retrofit, as explained
> in the article. Again, the reply doesn't make sense since it directly
> preceded the very thing you're reiterating ... unless you jumped the
> gun.
We agree on the math. However, the difference between Minkowski's
Spacetime and Newton's Space and Time is conceptual (metaphysical) and
not mathematical (physics). You seemed to suggest that one has to use
the first in order to do correct physics calculations. Sorry if I
misunderstood you. Still, many people confuse those things so that it is
useful to point it out now and then.
Cheers,
Harald
<markwh04@yahoo.com> wrote in message
news:1127767092.916343.156150@g14g2000cwa.googlegr oups.com...
> Harry wrote:
> > > The infrastructure underlying Newton's Laws fails -- that is: the
> > > structure of its spacetime.
> > I'm not sure what is meant above with "Newton's spacetime",
>
> That's precisely what the rest of the article you're replying to
> described in detail; so your reply doesn't make much sense unless you
> simply jumped the gun.
I replied to your reply to a question about Newton's laws; that posting
has not appeared in my newsreader but it's the subject header. From your
full reply I wasn't sure if you you meant Newton's concepts of Space and
Time, or his assumption that Galilean transformation rules are valid for
all speeds. As I indicated, what has failed was his accompanying
assumption (based on observation of that time) that speed has no effect
on objects. With Lorentz' relativistic corrections, there is no problem
with the structure of Newton's Space and Time. Text books often mislead
people into thinking that Newton's Space and Time concepts failed (or
they don't even mention it), and that his concepts must be replaced by
Minkowski's Spacetime. See also the recent threads "logical
inconsistency in Lorentz' theory" and Ilja's comments in "why isn't the
mathematician Henri Poincare acknowledged as the true discoverer of
special relativity?".
> More commonly, it is known as Galilean spacetime, the corresponding
> principle of relativity as Galilean Relativity, and the symmetry group
> analogous to the Poincare' symmetry group as the Galilean symmetry
> group.
I didn't know that Galileo had such Newtonian concepts. If so, Newton
was misleading his readers when he claimed in his introduction of the
Principia:
"I do not define time, space, place and motion, as being well known to
all."
I suppose that Newton was truthful, and that common jargon is
misleading. But if someone has a quote of Galileo that shows the
contrary, I'll be glad to see it.
> > About his laws:
> > With the post-Einstein concept of relativistic mass increase it's [sic]
> > not necessary to retrofit Newton's force law F=d(m*v)/dt to Minkowski
spacetime,
>
> > as with m=gamma*m_0 it works fine as it stands
>
> .. which is precisely what is entailed by the retrofit, as explained
> in the article. Again, the reply doesn't make sense since it directly
> preceded the very thing you're reiterating ... unless you jumped the
> gun.
We agree on the math. However, the difference between Minkowski's
Spacetime and Newton's Space and Time is conceptual (metaphysical) and
not mathematical (physics). You seemed to suggest that one has to use
the first in order to do correct physics calculations. Sorry if I
misunderstood you. Still, many people confuse those things so that it is
useful to point it out now and then.
Cheers,
Harald
<markwh04@yahoo.com> wrote in message
news:1127767092.916343.156150@g14g2000cwa.googlegr oups.com...
> Harry wrote:
> > > The infrastructure underlying Newton's Laws fails -- that is: the
> > > structure of its spacetime.
> > I'm not sure what is meant above with "Newton's spacetime",
>
> That's precisely what the rest of the article you're replying to
> described in detail; so your reply doesn't make much sense unless you
> simply jumped the gun.
I replied to your reply to a question about Newton's laws; that posting
has not appeared in my newsreader but it's the subject header. From your
full reply I wasn't sure if you you meant Newton's concepts of Space and
Time, or his assumption that Galilean transformation rules are valid for
all speeds. As I indicated, what has failed was his accompanying
assumption (based on observation of that time) that speed has no effect
on objects. With Lorentz' relativistic corrections, there is no problem
with the structure of Newton's Space and Time. Text books often mislead
people into thinking that Newton's Space and Time concepts failed (or
they don't even mention it), and that his concepts must be replaced by
Minkowski's Spacetime. See also the recent threads "logical
inconsistency in Lorentz' theory" and Ilja's comments in "why isn't the
mathematician Henri Poincare acknowledged as the true discoverer of
special relativity?".
> More commonly, it is known as Galilean spacetime, the corresponding
> principle of relativity as Galilean Relativity, and the symmetry group
> analogous to the Poincare' symmetry group as the Galilean symmetry
> group.
I didn't know that Galileo had such Newtonian concepts. If so, Newton
was misleading his readers when he claimed in his introduction of the
Principia:
"I do not define time, space, place and motion, as being well known to
all."
I suppose that Newton was truthful, and that common jargon is
misleading. But if someone has a quote of Galileo that shows the
contrary, I'll be glad to see it.
> > About his laws:
> > With the post-Einstein concept of relativistic mass increase it's [sic]
> > not necessary to retrofit Newton's force law F=d(m*v)/dt to Minkowski
spacetime,
>
> > as with m=gamma*m_0 it works fine as it stands
>
> .. which is precisely what is entailed by the retrofit, as explained
> in the article. Again, the reply doesn't make sense since it directly
> preceded the very thing you're reiterating ... unless you jumped the
> gun.
We agree on the math. However, the difference between Minkowski's
Spacetime and Newton's Space and Time is conceptual (metaphysical) and
not mathematical (physics). You seemed to suggest that one has to use
the first in order to do correct physics calculations. Sorry if I
misunderstood you. Still, many people confuse those things so that it is
useful to point it out now and then.
Cheers,
Harald
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