Re: deriving fundamental constants - only dimensionless ones! [Archive]

Thomas Dent

Jun30-04, 05:40 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>alistair@goforit64.fsnet.co.uk (alistair) wrote\n\n> An ultimate theory of physics would be one in which fundamental\n> constants like\n> planck\'s constant and the gravitational constant could all be\n> predicted without any experimental data being used to deduce the value\n> of the constants.But,in principle,can such a theory exist?\n> Constants tend to be composed of units of length, time, speed etc.\n> Units are not independent of one another: a metre can be defined as\n> the length of a certain piece of metal that has a particular\n> cross-sectional area, density and temperature at a particular\n> pressure.These variables amount to a set of criteria that are fixed by\n> a process of measurement - by gathering experimental data.It is\n> therefore difficult to see how a fundamental constant could be be\n> predicted independently of experimental data.\n> Can anyone think of a way of bypassing experimental data, that would\n> allow a fundamental constant to be predicted ?\n\n\nAlistair, you are making rapid progress! In fact, the only things that\ncould be predicted by a fundamental theory are *dimensionless\nnumbers*. Things like the fine structure constant e^2/4 pi h c ~\n1/137. Or, the ratio of the electron mass to the proton mass m_e/m_p ~\n1/1836. Anything else depends on the arbitrary choice of units.\n\nThis is why it\'s somewhat nonsensical to talk about the speed of light\nchanging, since you can always define units where the speed of light\nis constant. (Despite which, some people still write down theories\nwhere c is supposed to vary.)\n\nAlso, when an experiment is done, the results are all really\n*dimensionless numbers*. For example when you measure a time interval,\nwhat you are really doing (because of the definition of the second) is\nfinding the ratio of the time you are measuring to the time for 1\noscillation of the light in a particular transition of the cesium\natom.\n\nhttp://physics.nist.gov/GenInt/Time/atomic.html\nhttp://tycho.usno.navy.mil/cesium.html\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>alistair@goforit64.fsnet.co.uk (alistair) wrote

> An ultimate theory of physics would be one in which fundamental
> constants like
> planck's constant and the gravitational constant could all be
> predicted without any experimental data being used to deduce the value
> of the constants.But,in principle,can such a theory exist?
> Constants tend to be composed of units of length, time, speed etc.
> Units are not independent of one another: a metre can be defined as
> the length of a certain piece of metal that has a particular
> cross-sectional area, density and temperature at a particular
> pressure.These variables amount to a set of criteria that are fixed by
> a process of measurement - by gathering experimental data.It is
> therefore difficult to see how a fundamental constant could be be
> predicted independently of experimental data.
> Can anyone think of a way of bypassing experimental data, that would
> allow a fundamental constant to be predicted ?

Alistair, you are making rapid progress! In fact, the only things that
could be predicted by a fundamental theory are *dimensionless
numbers*. Things like the fine structure constant e^2/4 \pi h c ~1/137. Or, the ratio of the electron mass to the proton mass m_e/m_p ~1/1836. Anything else depends on the arbitrary choice of units.

This is why it's somewhat nonsensical to talk about the speed of light
changing, since you can always define units where the speed of light
is constant. (Despite which, some people still write down theories
where c is supposed to vary.)

Also, when an experiment is done, the results are all really
*dimensionless numbers*. For example when you measure a time interval,
what you are really doing (because of the definition of the second) is
finding the ratio of the time you are measuring to the time for 1
oscillation of the light in a particular transition of the cesium
atom.

http://physics.nist.gov/GenInt/Time/atomic.html
http://tycho.usno.navy.mil/cesium.html

Frank Hellmann

Jul2-04, 04:32 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\ntdent@auth.gr (Thomas Dent) wrote in message news:<cb504c2c.0406300312.5d420cdc@posting.google. com>...\n> alistair@goforit64.fsnet.co.uk (alistair) wrote\n>\n> > An ultimate theory of physics would be one in which fundamental\n> > constants like\n> > planck\'s constant and the gravitational constant could all be\n> > predicted without any experimental data being used to deduce the value\n> > of the constants.But,in principle,can such a theory exist?\n> > Constants tend to be composed of units of length, time, speed etc.\n> > Units are not independent of one another: a metre can be defined as\n> > the length of a certain piece of metal that has a particular\n> > cross-sectional area, density and temperature at a particular\n> > pressure.These variables amount to a set of criteria that are fixed by\n> > a process of measurement - by gathering experimental data.It is\n> > therefore difficult to see how a fundamental constant could be be\n> > predicted independently of experimental data.\n> > Can anyone think of a way of bypassing experimental data, that would\n> > allow a fundamental constant to be predicted ?\n>\n>\n> Alistair, you are making rapid progress! In fact, the only things that\n> could be predicted by a fundamental theory are *dimensionless\n> numbers*. Things like the fine structure constant e^2/4 pi h c ~\n> 1/137. Or, the ratio of the electron mass to the proton mass m_e/m_p ~\n> 1/1836. Anything else depends on the arbitrary choice of units.\n>\n> This is why it\'s somewhat nonsensical to talk about the speed of light\n> changing, since you can always define units where the speed of light\n> is constant. (Despite which, some people still write down theories\n> where c is supposed to vary.)\n>\n> Also, when an experiment is done, the results are all really\n> *dimensionless numbers*. For example when you measure a time interval,\n> what you are really doing (because of the definition of the second) is\n> finding the ratio of the time you are measuring to the time for 1\n> oscillation of the light in a particular transition of the cesium\n> atom.\n>\n> http://physics.nist.gov/GenInt/Time/atomic.html\n> http://tycho.usno.navy.mil/cesium.html\n\nIsn\'t that just shifting around the question?\nThe meter has to be defined in some way. Let\'s assume it\'s something\nlike 10^10 time the diameter of some particle according to some good\ndefinition. Now Plancks constant supposedly features in the radius.\nIf we choose units such that h equals one the question simply becomes\nwhat a meter is.\nYes the size of the constants depends on an arbitrary choice of units,\njust as the velocity of an object depends upon an arbitrary frame of\nreference used to view it. Doesn\'t mean we can\'t calculate it from\nfirst principles if we know which frame of reference (definition of\nunits) we are talking about.\n\n---\n\nfrank.\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>tdent@auth.gr (Thomas Dent) wrote in message news:<cb504c2c.0406300312.5d420cdc@posting.google.com>...
> alistair@goforit64.fsnet.co.uk (alistair) wrote
>
> > An ultimate theory of physics would be one in which fundamental
> > constants like
> > planck's constant and the gravitational constant could all be
> > predicted without any experimental data being used to deduce the value
> > of the constants.But,in principle,can such a theory exist?
> > Constants tend to be composed of units of length, time, speed etc.
> > Units are not independent of one another: a metre can be defined as
> > the length of a certain piece of metal that has a particular
> > cross-sectional area, density and temperature at a particular
> > pressure.These variables amount to a set of criteria that are fixed by
> > a process of measurement - by gathering experimental data.It is
> > therefore difficult to see how a fundamental constant could be be
> > predicted independently of experimental data.
> > Can anyone think of a way of bypassing experimental data, that would
> > allow a fundamental constant to be predicted ?
>
>
> Alistair, you are making rapid progress! In fact, the only things that
> could be predicted by a fundamental theory are *dimensionless
> numbers*. Things like the fine structure constant e^2/4 \pi h c ~
> 1/137. Or, the ratio of the electron mass to the proton mass m_e/m_p ~
> 1/1836. Anything else depends on the arbitrary choice of units.
>
> This is why it's somewhat nonsensical to talk about the speed of light
> changing, since you can always define units where the speed of light
> is constant. (Despite which, some people still write down theories
> where c is supposed to vary.)
>
> Also, when an experiment is done, the results are all really
> *dimensionless numbers*. For example when you measure a time interval,
> what you are really doing (because of the definition of the second) is
> finding the ratio of the time you are measuring to the time for 1
> oscillation of the light in a particular transition of the cesium
> atom.
>
> http://physics.nist.gov/GenInt/Time/atomic.html
> http://tycho.usno.navy.mil/cesium.html

Isn't that just shifting around the question?
The meter has to be defined in some way. Let's assume it's something
like 10^10 time the diameter of some particle according to some good
definition. Now Plancks constant supposedly features in the radius.
If we choose units such that h equals one the question simply becomes
what a meter is.
Yes the size of the constants depends on an arbitrary choice of units,
just as the velocity of an object depends upon an arbitrary frame of
reference used to view it. Doesn't mean we can't calculate it from
first principles if we know which frame of reference (definition of
units) we are talking about.

---

frank.

Thomas Dent

Jul9-04, 03:49 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nCerthas@gmail.com (Frank Hellmann) wrote in message\n\n> > Also, when an experiment is done, the results are all really\n> > *dimensionless numbers*. For example when you measure a time interval,\n> > what you are really doing (because of the definition of the second) is\n> > finding the ratio of the time you are measuring to the time for 1\n> > oscillation of the light in a particular transition of the cesium\n> > atom.\n> >\n> > http://physics.nist.gov/GenInt/Time/atomic.html\n> > http://tycho.usno.navy.mil/cesium.html\n>\n> Isn\'t that just shifting around the question?\n> The meter has to be defined in some way. Let\'s assume it\'s something\n> like 10^10 time the diameter of some particle according to some good\n> definition. Now Plancks constant supposedly features in the radius.\n> If we choose units such that h equals one the question simply becomes\n> what a meter is.\n> Yes the size of the constants depends on an arbitrary choice of units,\n> just as the velocity of an object depends upon an arbitrary frame of\n> reference used to view it. Doesn\'t mean we can\'t calculate it from\n> first principles if we know which frame of reference (definition of\n> units) we are talking about.\n>\n\nIf you define enough things then some things become measurable and/or\nderivable, I suppose.\n\nBut it\'s not enough to define the value of hbar to be able to\nderive/measure the metre.\n\nThe dimensions of hbar are [ML^2T^-1]\n\nso we *also* need to define a mass (dimension [M]) and a speed\n(dimension [LT-1]) before we can calculate or measure what a metre (or\nan atomic radius) is.\n\nSuppose then we use the electron mass m_e and the speed of light c.\nThen we form\n\nhbar/m_e with dimensions [L^2T^-1] and\n\nhbar/m_e c with dimensions [L] - the Compton wavelength of the\nelectron. So we have a unit of length.\n\nSo now we can (in principle) predict the atomic radius and go on to\nconstruct a metre made up of X atoms laid end to end. But all we are\nreally doing is finding the *dimensionless ratio* of an atomic radius\nto hbar/m_e c. In other words, the real unit of length, whose value is\n*defined* is now hbar/m_e c.\n\nIn the current system of units, one can measure, and try to predict\nfrom fundamental theory, the electron\'s mass and Compton wavelength;\nbut the metre cannot be measured since it is *defined*. In the new\n"electron" system, the metre can be measured and predicted, but the\nelectron\'s Compton wavelength cannot be measured since it is\n*defined*.\n\nSo, there is always at least one defined unit of length, time, action,\netc. which cannot be measured or predicted. Of course, the value of\nsuch a unit disappears from all physically meaningful expressions.\n\nThomas\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Certhas@gmail.com (Frank Hellmann) wrote in message

> > Also, when an experiment is done, the results are all really
> > *dimensionless numbers*. For example when you measure a time interval,
> > what you are really doing (because of the definition of the second) is
> > finding the ratio of the time you are measuring to the time for 1
> > oscillation of the light in a particular transition of the cesium
> > atom.
> >
> > http://physics.nist.gov/GenInt/Time/atomic.html
> > http://tycho.usno.navy.mil/cesium.html
>
> Isn't that just shifting around the question?
> The meter has to be defined in some way. Let's assume it's something
> like 10^10 time the diameter of some particle according to some good
> definition. Now Plancks constant supposedly features in the radius.
> If we choose units such that h equals one the question simply becomes
> what a meter is.
> Yes the size of the constants depends on an arbitrary choice of units,
> just as the velocity of an object depends upon an arbitrary frame of
> reference used to view it. Doesn't mean we can't calculate it from
> first principles if we know which frame of reference (definition of
> units) we are talking about.
>

If you define enough things then some things become measurable and/or
derivable, I suppose.

But it's not enough to define the value of \hbar to be able to
derive/measure the metre.

The dimensions of \hbar are [ML^2T^-1]

so we *also* need to define a mass (dimension [M]) and a speed
(dimension [LT-1]) before we can calculate or measure what a metre (or
an atomic radius) is.

Suppose then we use the electron mass m_e and the speed of light c.
Then we form

\hbar/m_e[/itex] with dimensions [L^{2T}^-1] and

\hbar/m_e c with dimensions [L] - the Compton wavelength of the
electron. So we have a unit of length.

So now we can (in principle) predict the atomic radius and go on to
construct a metre made up of X atoms laid end to end. But all we are
really doing is finding the *dimensionless ratio* of an atomic radius
to \hbar/m_e c. In other words, the real unit of length, whose value is
*defined* is now [itex]\hbar/m_e c.

In the current system of units, one can measure, and try to predict
from fundamental theory, the electron's mass and Compton wavelength;
but the metre cannot be measured since it is *defined*. In the new
"electron" system, the metre can be measured and predicted, but the
electron's Compton wavelength cannot be measured since it is
*defined*.

So, there is always at least one defined unit of length, time, action,
etc. which cannot be measured or predicted. Of course, the value of
such a unit disappears from all physically meaningful expressions.

Thomas

Frank Hellmann

Jul9-04, 10:32 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n> So, there is always at least one defined unit of length, time, action,\n> etc. which cannot be measured or predicted. Of course, the value of\n> such a unit disappears from all physically meaningful expressions.\n>\n> Thomas\n\nWell yes, units can not be meassured or predicted they are defined,\nbut then it becomes viable to ask if, given this definitions one can\npredict, from the underlying theory the size of the natural constants,\nisn\'t it?\n\nAnd by saying that we can define things in such a way that those\nconstants (or at least some of them) become one you do not say\nanything because then we don\'t know the system of meassurement we are\nin. You don\'t know how this system you define thus relates to the\nother defined systems.\n\nNow a physical meassurement you say is a ratio but I take that to be\nthe meaning of Units in the first place.\n5 meters is just like saying 5 times the wavelength of a photon\nemitted in this particular experiment.\n5 meters means the ratio between the length meassured and the\nexperiment that defines the meter.\n\nAnd if we define the meter and the second we can speculate that c\nchanges over time, if we define the second and c we can speculate that\na meter changes over time.\nThe only thing that makes no sense speculating at all is if our theory\nis invariant under rescaling of a certain thing. But then, for that\nparticular reason we don\'t usually have units and constants associated\nwith it to begin with.\nBefore there was a constant of action h in the theory the theory was\ninvariant under rescaling of the action.\n\nI feel like I\'m probably reiterating a discussion that has already\nhappened, I\'m gonna read through the earlier threads on this once I\'ve\ngot the time.\n\n----\nfrank\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>So, there is always at least one defined unit of length, time, action,
> etc. which cannot be measured or predicted. Of course, the value of
> such a unit disappears from all physically meaningful expressions.
>
> Thomas

Well yes, units can not be meassured or predicted they are defined,
but then it becomes viable to ask if, given this definitions one can
predict, from the underlying theory the size of the natural constants,
isn't it?

And by saying that we can define things in such a way that those
constants (or at least some of them) become one you do not say
anything because then we don't know the system of meassurement we are
in. You don't know how this system you define thus relates to the
other defined systems.

Now a physical meassurement you say is a ratio but I take that to be
the meaning of Units in the first place.
5 meters is just like saying 5 times the wavelength of a photon
emitted in this particular experiment.
5 meters means the ratio between the length meassured and the
experiment that defines the meter.

And if we define the meter and the second we can speculate that c
changes over time, if we define the second and c we can speculate that
a meter changes over time.
The only thing that makes no sense speculating at all is if our theory
is invariant under rescaling of a certain thing. But then, for that
particular reason we don't usually have units and constants associated
with it to begin with.
Before there was a constant of action h in the theory the theory was
invariant under rescaling of the action.

I feel like I'm probably reiterating a discussion that has already
happened, I'm gonna read through the earlier threads on this once I've
got the time.

----
frank