View Full Version : Most accurate measurements of particle position?
What experiments can nowadays be considered as the most precise
determinations of a single particle location in space?
Can one consider a limit of technology that would prohibit
determination of particle's location below a certain spatial extent?
I guess that extent would be well above the Plank distance but am
curious about exactly what kind of technological problems does one face
in attempting to localize the particle. If they involve energy what are
the approximate numbers, say in eVs?
Thanks,
Tony
Eugene Stefanovich
Oct12-06, 04:58 AM
"Tony" <tonkoj@gmail.com> wrote in message
news:1127632579.003189.233130@o13g2000cwo.googlegr oups.com...
> What experiments can nowadays be considered as the most precise
> determinations of a single particle location in space?
>
> Can one consider a limit of technology that would prohibit
> determination of particle's location below a certain spatial extent?
>
> I guess that extent would be well above the Plank distance but am
> curious about exactly what kind of technological problems does one face
> in attempting to localize the particle. If they involve energy what are
> the approximate numbers, say in eVs?
In my view, there are two separate issues. One is technological, another
is fundamental. From the technological point of view, I think, the best
you can achieve in direct measurements of particle position is somewhat
of the order of atomic size. I just cannot imagine how you can measure
position without your particle interacting with some macroscopic body
made of atoms, e.g., a crystal. The records in position measurements
were recently achieved with the use of scanning tunneling and atomic
force microscopes. These are fractions of an anstrom.
You can sometimes hear that with high accelerator energies we penetrate
deeper and deeper into electron/proton/pion/... probing distances of
many orders of magnitude smaller. But keep in mind, that these are not
direct measurements of position. These are just Fourier transforms of
momentum/energy data to the position space.
From the fundamental point of view, the situation is different. In
quantum mechanics there is no theoretical limit on how accurately the
position can be measured. The particle wavefunction can be represented
by a delta function in the position space. You can sometimes hear that
in relativistic quantum field theory, infinitely precise localization
of a single particle is impossible, because it requres infinite
uncertainty of momentum -> infinite uncertainty of energy -> uncertainty
in the number of particles. I don't think this is a valid argument,
because position operators of different particles commute with each
other and with the particle number operator. So, there is no problem in
having a single particle localized at a point.
Eugene.
Eugene Stefanovich
Oct12-06, 04:58 AM
"Tony" <tonkoj@gmail.com> wrote in message
news:1127632579.003189.233130@o13g2000cwo.googlegr oups.com...
> What experiments can nowadays be considered as the most precise
> determinations of a single particle location in space?
>
> Can one consider a limit of technology that would prohibit
> determination of particle's location below a certain spatial extent?
>
> I guess that extent would be well above the Plank distance but am
> curious about exactly what kind of technological problems does one face
> in attempting to localize the particle. If they involve energy what are
> the approximate numbers, say in eVs?
In my view, there are two separate issues. One is technological, another
is fundamental. From the technological point of view, I think, the best
you can achieve in direct measurements of particle position is somewhat
of the order of atomic size. I just cannot imagine how you can measure
position without your particle interacting with some macroscopic body
made of atoms, e.g., a crystal. The records in position measurements
were recently achieved with the use of scanning tunneling and atomic
force microscopes. These are fractions of an anstrom.
You can sometimes hear that with high accelerator energies we penetrate
deeper and deeper into electron/proton/pion/... probing distances of
many orders of magnitude smaller. But keep in mind, that these are not
direct measurements of position. These are just Fourier transforms of
momentum/energy data to the position space.
From the fundamental point of view, the situation is different. In
quantum mechanics there is no theoretical limit on how accurately the
position can be measured. The particle wavefunction can be represented
by a delta function in the position space. You can sometimes hear that
in relativistic quantum field theory, infinitely precise localization
of a single particle is impossible, because it requres infinite
uncertainty of momentum -> infinite uncertainty of energy -> uncertainty
in the number of particles. I don't think this is a valid argument,
because position operators of different particles commute with each
other and with the particle number operator. So, there is no problem in
having a single particle localized at a point.
Eugene.
Eugene Stefanovich
Oct12-06, 04:58 AM
"Tony" <tonkoj@gmail.com> wrote in message
news:1127632579.003189.233130@o13g2000cwo.googlegr oups.com...
> What experiments can nowadays be considered as the most precise
> determinations of a single particle location in space?
>
> Can one consider a limit of technology that would prohibit
> determination of particle's location below a certain spatial extent?
>
> I guess that extent would be well above the Plank distance but am
> curious about exactly what kind of technological problems does one face
> in attempting to localize the particle. If they involve energy what are
> the approximate numbers, say in eVs?
In my view, there are two separate issues. One is technological, another
is fundamental. From the technological point of view, I think, the best
you can achieve in direct measurements of particle position is somewhat
of the order of atomic size. I just cannot imagine how you can measure
position without your particle interacting with some macroscopic body
made of atoms, e.g., a crystal. The records in position measurements
were recently achieved with the use of scanning tunneling and atomic
force microscopes. These are fractions of an anstrom.
You can sometimes hear that with high accelerator energies we penetrate
deeper and deeper into electron/proton/pion/... probing distances of
many orders of magnitude smaller. But keep in mind, that these are not
direct measurements of position. These are just Fourier transforms of
momentum/energy data to the position space.
From the fundamental point of view, the situation is different. In
quantum mechanics there is no theoretical limit on how accurately the
position can be measured. The particle wavefunction can be represented
by a delta function in the position space. You can sometimes hear that
in relativistic quantum field theory, infinitely precise localization
of a single particle is impossible, because it requres infinite
uncertainty of momentum -> infinite uncertainty of energy -> uncertainty
in the number of particles. I don't think this is a valid argument,
because position operators of different particles commute with each
other and with the particle number operator. So, there is no problem in
having a single particle localized at a point.
Eugene.
Eugene Stefanovich
Oct12-06, 04:58 AM
"Tony" <tonkoj@gmail.com> wrote in message
news:1127632579.003189.233130@o13g2000cwo.googlegr oups.com...
> What experiments can nowadays be considered as the most precise
> determinations of a single particle location in space?
>
> Can one consider a limit of technology that would prohibit
> determination of particle's location below a certain spatial extent?
>
> I guess that extent would be well above the Plank distance but am
> curious about exactly what kind of technological problems does one face
> in attempting to localize the particle. If they involve energy what are
> the approximate numbers, say in eVs?
In my view, there are two separate issues. One is technological, another
is fundamental. From the technological point of view, I think, the best
you can achieve in direct measurements of particle position is somewhat
of the order of atomic size. I just cannot imagine how you can measure
position without your particle interacting with some macroscopic body
made of atoms, e.g., a crystal. The records in position measurements
were recently achieved with the use of scanning tunneling and atomic
force microscopes. These are fractions of an anstrom.
You can sometimes hear that with high accelerator energies we penetrate
deeper and deeper into electron/proton/pion/... probing distances of
many orders of magnitude smaller. But keep in mind, that these are not
direct measurements of position. These are just Fourier transforms of
momentum/energy data to the position space.
From the fundamental point of view, the situation is different. In
quantum mechanics there is no theoretical limit on how accurately the
position can be measured. The particle wavefunction can be represented
by a delta function in the position space. You can sometimes hear that
in relativistic quantum field theory, infinitely precise localization
of a single particle is impossible, because it requres infinite
uncertainty of momentum -> infinite uncertainty of energy -> uncertainty
in the number of particles. I don't think this is a valid argument,
because position operators of different particles commute with each
other and with the particle number operator. So, there is no problem in
having a single particle localized at a point.
Eugene.
Eugene Stefanovich
Oct12-06, 04:58 AM
"Tony" <tonkoj@gmail.com> wrote in message
news:1127632579.003189.233130@o13g2000cwo.googlegr oups.com...
> What experiments can nowadays be considered as the most precise
> determinations of a single particle location in space?
>
> Can one consider a limit of technology that would prohibit
> determination of particle's location below a certain spatial extent?
>
> I guess that extent would be well above the Plank distance but am
> curious about exactly what kind of technological problems does one face
> in attempting to localize the particle. If they involve energy what are
> the approximate numbers, say in eVs?
In my view, there are two separate issues. One is technological, another
is fundamental. From the technological point of view, I think, the best
you can achieve in direct measurements of particle position is somewhat
of the order of atomic size. I just cannot imagine how you can measure
position without your particle interacting with some macroscopic body
made of atoms, e.g., a crystal. The records in position measurements
were recently achieved with the use of scanning tunneling and atomic
force microscopes. These are fractions of an anstrom.
You can sometimes hear that with high accelerator energies we penetrate
deeper and deeper into electron/proton/pion/... probing distances of
many orders of magnitude smaller. But keep in mind, that these are not
direct measurements of position. These are just Fourier transforms of
momentum/energy data to the position space.
From the fundamental point of view, the situation is different. In
quantum mechanics there is no theoretical limit on how accurately the
position can be measured. The particle wavefunction can be represented
by a delta function in the position space. You can sometimes hear that
in relativistic quantum field theory, infinitely precise localization
of a single particle is impossible, because it requres infinite
uncertainty of momentum -> infinite uncertainty of energy -> uncertainty
in the number of particles. I don't think this is a valid argument,
because position operators of different particles commute with each
other and with the particle number operator. So, there is no problem in
having a single particle localized at a point.
Eugene.
Eugene Stefanovich
Oct12-06, 04:58 AM
"Tony" <tonkoj@gmail.com> wrote in message
news:1127632579.003189.233130@o13g2000cwo.googlegr oups.com...
> What experiments can nowadays be considered as the most precise
> determinations of a single particle location in space?
>
> Can one consider a limit of technology that would prohibit
> determination of particle's location below a certain spatial extent?
>
> I guess that extent would be well above the Plank distance but am
> curious about exactly what kind of technological problems does one face
> in attempting to localize the particle. If they involve energy what are
> the approximate numbers, say in eVs?
In my view, there are two separate issues. One is technological, another
is fundamental. From the technological point of view, I think, the best
you can achieve in direct measurements of particle position is somewhat
of the order of atomic size. I just cannot imagine how you can measure
position without your particle interacting with some macroscopic body
made of atoms, e.g., a crystal. The records in position measurements
were recently achieved with the use of scanning tunneling and atomic
force microscopes. These are fractions of an anstrom.
You can sometimes hear that with high accelerator energies we penetrate
deeper and deeper into electron/proton/pion/... probing distances of
many orders of magnitude smaller. But keep in mind, that these are not
direct measurements of position. These are just Fourier transforms of
momentum/energy data to the position space.
From the fundamental point of view, the situation is different. In
quantum mechanics there is no theoretical limit on how accurately the
position can be measured. The particle wavefunction can be represented
by a delta function in the position space. You can sometimes hear that
in relativistic quantum field theory, infinitely precise localization
of a single particle is impossible, because it requres infinite
uncertainty of momentum -> infinite uncertainty of energy -> uncertainty
in the number of particles. I don't think this is a valid argument,
because position operators of different particles commute with each
other and with the particle number operator. So, there is no problem in
having a single particle localized at a point.
Eugene.
Eugene Stefanovich
Oct12-06, 04:58 AM
"Tony" <tonkoj@gmail.com> wrote in message
news:1127632579.003189.233130@o13g2000cwo.googlegr oups.com...
> What experiments can nowadays be considered as the most precise
> determinations of a single particle location in space?
>
> Can one consider a limit of technology that would prohibit
> determination of particle's location below a certain spatial extent?
>
> I guess that extent would be well above the Plank distance but am
> curious about exactly what kind of technological problems does one face
> in attempting to localize the particle. If they involve energy what are
> the approximate numbers, say in eVs?
In my view, there are two separate issues. One is technological, another
is fundamental. From the technological point of view, I think, the best
you can achieve in direct measurements of particle position is somewhat
of the order of atomic size. I just cannot imagine how you can measure
position without your particle interacting with some macroscopic body
made of atoms, e.g., a crystal. The records in position measurements
were recently achieved with the use of scanning tunneling and atomic
force microscopes. These are fractions of an anstrom.
You can sometimes hear that with high accelerator energies we penetrate
deeper and deeper into electron/proton/pion/... probing distances of
many orders of magnitude smaller. But keep in mind, that these are not
direct measurements of position. These are just Fourier transforms of
momentum/energy data to the position space.
From the fundamental point of view, the situation is different. In
quantum mechanics there is no theoretical limit on how accurately the
position can be measured. The particle wavefunction can be represented
by a delta function in the position space. You can sometimes hear that
in relativistic quantum field theory, infinitely precise localization
of a single particle is impossible, because it requres infinite
uncertainty of momentum -> infinite uncertainty of energy -> uncertainty
in the number of particles. I don't think this is a valid argument,
because position operators of different particles commute with each
other and with the particle number operator. So, there is no problem in
having a single particle localized at a point.
Eugene.
Nick Maclaren
Oct12-06, 04:58 AM
In article <1127632579.003189.233130@o13g2000cwo.googlegroups. com>,
"Tony" <tonkoj@gmail.com> writes:
|> What experiments can nowadays be considered as the most precise
|> determinations of a single particle location in space?
|>
|> Can one consider a limit of technology that would prohibit
|> determination of particle's location below a certain spatial extent?
Well, if my ancient recollection of quantum mechanics is correct,
a precise location means an imprecise velocity. Now, as velocity
can be mapped to energy and hence mass, one might have a few
problems once that starts to produce a measurable gravitational
effect.
Regards,
Nick Maclaren.
Nick Maclaren
Oct12-06, 04:58 AM
In article <1127632579.003189.233130@o13g2000cwo.googlegroups. com>,
"Tony" <tonkoj@gmail.com> writes:
|> What experiments can nowadays be considered as the most precise
|> determinations of a single particle location in space?
|>
|> Can one consider a limit of technology that would prohibit
|> determination of particle's location below a certain spatial extent?
Well, if my ancient recollection of quantum mechanics is correct,
a precise location means an imprecise velocity. Now, as velocity
can be mapped to energy and hence mass, one might have a few
problems once that starts to produce a measurable gravitational
effect.
Regards,
Nick Maclaren.
Nick Maclaren
Oct12-06, 04:58 AM
In article <1127632579.003189.233130@o13g2000cwo.googlegroups. com>,
"Tony" <tonkoj@gmail.com> writes:
|> What experiments can nowadays be considered as the most precise
|> determinations of a single particle location in space?
|>
|> Can one consider a limit of technology that would prohibit
|> determination of particle's location below a certain spatial extent?
Well, if my ancient recollection of quantum mechanics is correct,
a precise location means an imprecise velocity. Now, as velocity
can be mapped to energy and hence mass, one might have a few
problems once that starts to produce a measurable gravitational
effect.
Regards,
Nick Maclaren.
Nick Maclaren
Oct12-06, 04:58 AM
In article <1127632579.003189.233130@o13g2000cwo.googlegroups. com>,
"Tony" <tonkoj@gmail.com> writes:
|> What experiments can nowadays be considered as the most precise
|> determinations of a single particle location in space?
|>
|> Can one consider a limit of technology that would prohibit
|> determination of particle's location below a certain spatial extent?
Well, if my ancient recollection of quantum mechanics is correct,
a precise location means an imprecise velocity. Now, as velocity
can be mapped to energy and hence mass, one might have a few
problems once that starts to produce a measurable gravitational
effect.
Regards,
Nick Maclaren.
Nick Maclaren
Oct12-06, 04:58 AM
In article <1127632579.003189.233130@o13g2000cwo.googlegroups. com>,
"Tony" <tonkoj@gmail.com> writes:
|> What experiments can nowadays be considered as the most precise
|> determinations of a single particle location in space?
|>
|> Can one consider a limit of technology that would prohibit
|> determination of particle's location below a certain spatial extent?
Well, if my ancient recollection of quantum mechanics is correct,
a precise location means an imprecise velocity. Now, as velocity
can be mapped to energy and hence mass, one might have a few
problems once that starts to produce a measurable gravitational
effect.
Regards,
Nick Maclaren.
Nick Maclaren
Oct12-06, 04:58 AM
In article <1127632579.003189.233130@o13g2000cwo.googlegroups. com>,
"Tony" <tonkoj@gmail.com> writes:
|> What experiments can nowadays be considered as the most precise
|> determinations of a single particle location in space?
|>
|> Can one consider a limit of technology that would prohibit
|> determination of particle's location below a certain spatial extent?
Well, if my ancient recollection of quantum mechanics is correct,
a precise location means an imprecise velocity. Now, as velocity
can be mapped to energy and hence mass, one might have a few
problems once that starts to produce a measurable gravitational
effect.
Regards,
Nick Maclaren.
Nick Maclaren
Oct12-06, 04:58 AM
In article <1127632579.003189.233130@o13g2000cwo.googlegroups. com>,
"Tony" <tonkoj@gmail.com> writes:
|> What experiments can nowadays be considered as the most precise
|> determinations of a single particle location in space?
|>
|> Can one consider a limit of technology that would prohibit
|> determination of particle's location below a certain spatial extent?
Well, if my ancient recollection of quantum mechanics is correct,
a precise location means an imprecise velocity. Now, as velocity
can be mapped to energy and hence mass, one might have a few
problems once that starts to produce a measurable gravitational
effect.
Regards,
Nick Maclaren.
So yuou are saying, if I understood correctly, that localizing a
particle beyond certain threshold can produce a black hole with some
non-negligible probability? But I wonder if there is any chance of
getting close to such values of standard deviation in measured energy
value, following Uncertainty Principle? Is a hardron holding
partons/quarks the best of nature's 'technology' of particle
containment? I can't think of nothing else, in addition to Eugene's
mention of electrons in a crystal lattice.
So yuou are saying, if I understood correctly, that localizing a
particle beyond certain threshold can produce a black hole with some
non-negligible probability? But I wonder if there is any chance of
getting close to such values of standard deviation in measured energy
value, following Uncertainty Principle? Is a hardron holding
partons/quarks the best of nature's 'technology' of particle
containment? I can't think of nothing else, in addition to Eugene's
mention of electrons in a crystal lattice.
So yuou are saying, if I understood correctly, that localizing a
particle beyond certain threshold can produce a black hole with some
non-negligible probability? But I wonder if there is any chance of
getting close to such values of standard deviation in measured energy
value, following Uncertainty Principle? Is a hardron holding
partons/quarks the best of nature's 'technology' of particle
containment? I can't think of nothing else, in addition to Eugene's
mention of electrons in a crystal lattice.
So yuou are saying, if I understood correctly, that localizing a
particle beyond certain threshold can produce a black hole with some
non-negligible probability? But I wonder if there is any chance of
getting close to such values of standard deviation in measured energy
value, following Uncertainty Principle? Is a hardron holding
partons/quarks the best of nature's 'technology' of particle
containment? I can't think of nothing else, in addition to Eugene's
mention of electrons in a crystal lattice.
So yuou are saying, if I understood correctly, that localizing a
particle beyond certain threshold can produce a black hole with some
non-negligible probability? But I wonder if there is any chance of
getting close to such values of standard deviation in measured energy
value, following Uncertainty Principle? Is a hardron holding
partons/quarks the best of nature's 'technology' of particle
containment? I can't think of nothing else, in addition to Eugene's
mention of electrons in a crystal lattice.
So yuou are saying, if I understood correctly, that localizing a
particle beyond certain threshold can produce a black hole with some
non-negligible probability? But I wonder if there is any chance of
getting close to such values of standard deviation in measured energy
value, following Uncertainty Principle? Is a hardron holding
partons/quarks the best of nature's 'technology' of particle
containment? I can't think of nothing else, in addition to Eugene's
mention of electrons in a crystal lattice.
So yuou are saying, if I understood correctly, that localizing a
particle beyond certain threshold can produce a black hole with some
non-negligible probability? But I wonder if there is any chance of
getting close to such values of standard deviation in measured energy
value, following Uncertainty Principle? Is a hardron holding
partons/quarks the best of nature's 'technology' of particle
containment? I can't think of nothing else, in addition to Eugene's
mention of electrons in a crystal lattice.
So yuou are saying, if I understood correctly, that localizing a
particle beyond certain threshold can produce a black hole with some
non-negligible probability? But I wonder if there is any chance of
getting close to such values of standard deviation in measured energy
value, following Uncertainty Principle? Is a hardron holding
partons/quarks the best of nature's 'technology' of particle
containment? I can't think of nothing else, in addition to Eugene's
mention of electrons in a crystal lattice.
Eugene Stefanovich
Oct12-06, 05:01 AM
Tony wrote:
> Is a hardron holding
> partons/quarks the best of nature's 'technology' of particle
> containment?
You simply know that quark is inside the hadron/nucleus.
However, this doesn't tell you the position of the quark in space.
You need to know (at least) the position of the nucleus in
your reference frame. I don't think this is possible without
your nucleus somehow interacting with a macroscopic object, e.g., a
crystal.
So, what concerns position measurement, you are still limited
to something of the order of interatomic distances.
The smallest size of particle's wave function is entirely
different matter. There is no theoretical limit on
how well-localized the particle can be.
Eugene.
Eugene Stefanovich
Oct12-06, 05:01 AM
Tony wrote:
> Is a hardron holding
> partons/quarks the best of nature's 'technology' of particle
> containment?
You simply know that quark is inside the hadron/nucleus.
However, this doesn't tell you the position of the quark in space.
You need to know (at least) the position of the nucleus in
your reference frame. I don't think this is possible without
your nucleus somehow interacting with a macroscopic object, e.g., a
crystal.
So, what concerns position measurement, you are still limited
to something of the order of interatomic distances.
The smallest size of particle's wave function is entirely
different matter. There is no theoretical limit on
how well-localized the particle can be.
Eugene.
Eugene Stefanovich
Oct12-06, 05:01 AM
Tony wrote:
> Is a hardron holding
> partons/quarks the best of nature's 'technology' of particle
> containment?
You simply know that quark is inside the hadron/nucleus.
However, this doesn't tell you the position of the quark in space.
You need to know (at least) the position of the nucleus in
your reference frame. I don't think this is possible without
your nucleus somehow interacting with a macroscopic object, e.g., a
crystal.
So, what concerns position measurement, you are still limited
to something of the order of interatomic distances.
The smallest size of particle's wave function is entirely
different matter. There is no theoretical limit on
how well-localized the particle can be.
Eugene.
Eugene Stefanovich
Oct12-06, 05:01 AM
Tony wrote:
> Is a hardron holding
> partons/quarks the best of nature's 'technology' of particle
> containment?
You simply know that quark is inside the hadron/nucleus.
However, this doesn't tell you the position of the quark in space.
You need to know (at least) the position of the nucleus in
your reference frame. I don't think this is possible without
your nucleus somehow interacting with a macroscopic object, e.g., a
crystal.
So, what concerns position measurement, you are still limited
to something of the order of interatomic distances.
The smallest size of particle's wave function is entirely
different matter. There is no theoretical limit on
how well-localized the particle can be.
Eugene.
Eugene Stefanovich
Oct12-06, 05:01 AM
Tony wrote:
> Is a hardron holding
> partons/quarks the best of nature's 'technology' of particle
> containment?
You simply know that quark is inside the hadron/nucleus.
However, this doesn't tell you the position of the quark in space.
You need to know (at least) the position of the nucleus in
your reference frame. I don't think this is possible without
your nucleus somehow interacting with a macroscopic object, e.g., a
crystal.
So, what concerns position measurement, you are still limited
to something of the order of interatomic distances.
The smallest size of particle's wave function is entirely
different matter. There is no theoretical limit on
how well-localized the particle can be.
Eugene.
Eugene Stefanovich
Oct12-06, 05:01 AM
Tony wrote:
> Is a hardron holding
> partons/quarks the best of nature's 'technology' of particle
> containment?
You simply know that quark is inside the hadron/nucleus.
However, this doesn't tell you the position of the quark in space.
You need to know (at least) the position of the nucleus in
your reference frame. I don't think this is possible without
your nucleus somehow interacting with a macroscopic object, e.g., a
crystal.
So, what concerns position measurement, you are still limited
to something of the order of interatomic distances.
The smallest size of particle's wave function is entirely
different matter. There is no theoretical limit on
how well-localized the particle can be.
Eugene.
Eugene Stefanovich
Oct12-06, 05:01 AM
Tony wrote:
> Is a hardron holding
> partons/quarks the best of nature's 'technology' of particle
> containment?
You simply know that quark is inside the hadron/nucleus.
However, this doesn't tell you the position of the quark in space.
You need to know (at least) the position of the nucleus in
your reference frame. I don't think this is possible without
your nucleus somehow interacting with a macroscopic object, e.g., a
crystal.
So, what concerns position measurement, you are still limited
to something of the order of interatomic distances.
The smallest size of particle's wave function is entirely
different matter. There is no theoretical limit on
how well-localized the particle can be.
Eugene.
Eugene Stefanovich
Oct12-06, 05:01 AM
Tony wrote:
> Is a hardron holding
> partons/quarks the best of nature's 'technology' of particle
> containment?
You simply know that quark is inside the hadron/nucleus.
However, this doesn't tell you the position of the quark in space.
You need to know (at least) the position of the nucleus in
your reference frame. I don't think this is possible without
your nucleus somehow interacting with a macroscopic object, e.g., a
crystal.
So, what concerns position measurement, you are still limited
to something of the order of interatomic distances.
The smallest size of particle's wave function is entirely
different matter. There is no theoretical limit on
how well-localized the particle can be.
Eugene.
Eugene Stefanovich
Oct12-06, 05:01 AM
Tony wrote:
> Is a hardron holding
> partons/quarks the best of nature's 'technology' of particle
> containment?
You simply know that quark is inside the hadron/nucleus.
However, this doesn't tell you the position of the quark in space.
You need to know (at least) the position of the nucleus in
your reference frame. I don't think this is possible without
your nucleus somehow interacting with a macroscopic object, e.g., a
crystal.
So, what concerns position measurement, you are still limited
to something of the order of interatomic distances.
The smallest size of particle's wave function is entirely
different matter. There is no theoretical limit on
how well-localized the particle can be.
Eugene.
Eugene Stefanovich wrote:
> The smallest size of particle's wave function is entirely
> different matter. There is no theoretical limit on
> how well-localized the particle can be.
Ok, I think I understand what you wrote about position operator
commuting with particle number operator. Formally, nothing prevents us
from using delta 'function' as particle function.
But can we ever *make it* (almost) such, at least in thought
experiment?
In classic example of harmonic oscillator lowest energy level is not 0
and wave function still has some spread because of Uncertainty
Principle. You casn consider confining potential as a measuring device.
One would think that, if 'confining potential' (like a microscopic
black hole) were sharply localized then we can expect the same for
particle wave function.
Of course, subnuclear-size black hole at rest in laboratory frame is
probably a fantasy even for a thought experiment. But it is hard not to
be curious about consequences of Uncertainty Principle on a particle
about to hit the singularity of a microscopic black hole. What happens
to the particle in loop gravity? It sits somewhere on a Planckian
surface and that is the best that Nature can do to localize it?
Eugene Stefanovich wrote:
> The smallest size of particle's wave function is entirely
> different matter. There is no theoretical limit on
> how well-localized the particle can be.
Ok, I think I understand what you wrote about position operator
commuting with particle number operator. Formally, nothing prevents us
from using delta 'function' as particle function.
But can we ever *make it* (almost) such, at least in thought
experiment?
In classic example of harmonic oscillator lowest energy level is not 0
and wave function still has some spread because of Uncertainty
Principle. You casn consider confining potential as a measuring device.
One would think that, if 'confining potential' (like a microscopic
black hole) were sharply localized then we can expect the same for
particle wave function.
Of course, subnuclear-size black hole at rest in laboratory frame is
probably a fantasy even for a thought experiment. But it is hard not to
be curious about consequences of Uncertainty Principle on a particle
about to hit the singularity of a microscopic black hole. What happens
to the particle in loop gravity? It sits somewhere on a Planckian
surface and that is the best that Nature can do to localize it?
Eugene Stefanovich wrote:
> The smallest size of particle's wave function is entirely
> different matter. There is no theoretical limit on
> how well-localized the particle can be.
Ok, I think I understand what you wrote about position operator
commuting with particle number operator. Formally, nothing prevents us
from using delta 'function' as particle function.
But can we ever *make it* (almost) such, at least in thought
experiment?
In classic example of harmonic oscillator lowest energy level is not 0
and wave function still has some spread because of Uncertainty
Principle. You casn consider confining potential as a measuring device.
One would think that, if 'confining potential' (like a microscopic
black hole) were sharply localized then we can expect the same for
particle wave function.
Of course, subnuclear-size black hole at rest in laboratory frame is
probably a fantasy even for a thought experiment. But it is hard not to
be curious about consequences of Uncertainty Principle on a particle
about to hit the singularity of a microscopic black hole. What happens
to the particle in loop gravity? It sits somewhere on a Planckian
surface and that is the best that Nature can do to localize it?
Eugene Stefanovich wrote:
> The smallest size of particle's wave function is entirely
> different matter. There is no theoretical limit on
> how well-localized the particle can be.
Ok, I think I understand what you wrote about position operator
commuting with particle number operator. Formally, nothing prevents us
from using delta 'function' as particle function.
But can we ever *make it* (almost) such, at least in thought
experiment?
In classic example of harmonic oscillator lowest energy level is not 0
and wave function still has some spread because of Uncertainty
Principle. You casn consider confining potential as a measuring device.
One would think that, if 'confining potential' (like a microscopic
black hole) were sharply localized then we can expect the same for
particle wave function.
Of course, subnuclear-size black hole at rest in laboratory frame is
probably a fantasy even for a thought experiment. But it is hard not to
be curious about consequences of Uncertainty Principle on a particle
about to hit the singularity of a microscopic black hole. What happens
to the particle in loop gravity? It sits somewhere on a Planckian
surface and that is the best that Nature can do to localize it?
Eugene Stefanovich wrote:
> The smallest size of particle's wave function is entirely
> different matter. There is no theoretical limit on
> how well-localized the particle can be.
Ok, I think I understand what you wrote about position operator
commuting with particle number operator. Formally, nothing prevents us
from using delta 'function' as particle function.
But can we ever *make it* (almost) such, at least in thought
experiment?
In classic example of harmonic oscillator lowest energy level is not 0
and wave function still has some spread because of Uncertainty
Principle. You casn consider confining potential as a measuring device.
One would think that, if 'confining potential' (like a microscopic
black hole) were sharply localized then we can expect the same for
particle wave function.
Of course, subnuclear-size black hole at rest in laboratory frame is
probably a fantasy even for a thought experiment. But it is hard not to
be curious about consequences of Uncertainty Principle on a particle
about to hit the singularity of a microscopic black hole. What happens
to the particle in loop gravity? It sits somewhere on a Planckian
surface and that is the best that Nature can do to localize it?
Eugene Stefanovich wrote:
> The smallest size of particle's wave function is entirely
> different matter. There is no theoretical limit on
> how well-localized the particle can be.
Ok, I think I understand what you wrote about position operator
commuting with particle number operator. Formally, nothing prevents us
from using delta 'function' as particle function.
But can we ever *make it* (almost) such, at least in thought
experiment?
In classic example of harmonic oscillator lowest energy level is not 0
and wave function still has some spread because of Uncertainty
Principle. You casn consider confining potential as a measuring device.
One would think that, if 'confining potential' (like a microscopic
black hole) were sharply localized then we can expect the same for
particle wave function.
Of course, subnuclear-size black hole at rest in laboratory frame is
probably a fantasy even for a thought experiment. But it is hard not to
be curious about consequences of Uncertainty Principle on a particle
about to hit the singularity of a microscopic black hole. What happens
to the particle in loop gravity? It sits somewhere on a Planckian
surface and that is the best that Nature can do to localize it?
Eugene Stefanovich wrote:
> The smallest size of particle's wave function is entirely
> different matter. There is no theoretical limit on
> how well-localized the particle can be.
Ok, I think I understand what you wrote about position operator
commuting with particle number operator. Formally, nothing prevents us
from using delta 'function' as particle function.
But can we ever *make it* (almost) such, at least in thought
experiment?
In classic example of harmonic oscillator lowest energy level is not 0
and wave function still has some spread because of Uncertainty
Principle. You casn consider confining potential as a measuring device.
One would think that, if 'confining potential' (like a microscopic
black hole) were sharply localized then we can expect the same for
particle wave function.
Of course, subnuclear-size black hole at rest in laboratory frame is
probably a fantasy even for a thought experiment. But it is hard not to
be curious about consequences of Uncertainty Principle on a particle
about to hit the singularity of a microscopic black hole. What happens
to the particle in loop gravity? It sits somewhere on a Planckian
surface and that is the best that Nature can do to localize it?
Eugene Stefanovich wrote:
> The smallest size of particle's wave function is entirely
> different matter. There is no theoretical limit on
> how well-localized the particle can be.
Ok, I think I understand what you wrote about position operator
commuting with particle number operator. Formally, nothing prevents us
from using delta 'function' as particle function.
But can we ever *make it* (almost) such, at least in thought
experiment?
In classic example of harmonic oscillator lowest energy level is not 0
and wave function still has some spread because of Uncertainty
Principle. You casn consider confining potential as a measuring device.
One would think that, if 'confining potential' (like a microscopic
black hole) were sharply localized then we can expect the same for
particle wave function.
Of course, subnuclear-size black hole at rest in laboratory frame is
probably a fantasy even for a thought experiment. But it is hard not to
be curious about consequences of Uncertainty Principle on a particle
about to hit the singularity of a microscopic black hole. What happens
to the particle in loop gravity? It sits somewhere on a Planckian
surface and that is the best that Nature can do to localize it?
Eugene Stefanovich wrote:
> The smallest size of particle's wave function is entirely
> different matter. There is no theoretical limit on
> how well-localized the particle can be.
Ok, I think I understand what you wrote about position operator
commuting with particle number operator. Formally, nothing prevents us
from using delta 'function' as particle function.
But can we ever *make it* (almost) such, at least in thought
experiment?
In classic example of harmonic oscillator lowest energy level is not 0
and wave function still has some spread because of Uncertainty
Principle. You casn consider confining potential as a measuring device.
One would think that, if 'confining potential' (like a microscopic
black hole) were sharply localized then we can expect the same for
particle wave function.
Of course, subnuclear-size black hole at rest in laboratory frame is
probably a fantasy even for a thought experiment. But it is hard not to
be curious about consequences of Uncertainty Principle on a particle
about to hit the singularity of a microscopic black hole. What happens
to the particle in loop gravity? It sits somewhere on a Planckian
surface and that is the best that Nature can do to localize it?
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