Freethought & Rationalism Archive

Friar Bellows · 08-15-2002, 12:00 AM

Drawing from the intriguing <a href="http://arxiv.org/abs/astro-ph/0012539" target="_blank">observational results</a> of astronomer John Webb, a group of theorists guided by science-popularist Paul Davies <a href="http://news.ninemsn.com.au/Sci_Tech/story_36933.asp" target="_blank">recently speculated</a> that the so-called fundamental constant, c (i.e. the speed of light), may not be constant after all. Au contraire, claims physicist Mike Duff. In a <a href="http://arxiv.org/abs/hep-th/0208093" target="_blank">short paper</a> (see references therein for more explanation), Duff argues that Davies' conclusion is wrong and/or meaningless because the speed of light is not a fundamental constant. Actually, he points out, it is a factor to convert from one system of units to another -- a mere human convention. As he puts it: "Asking whether c has varied over cosmic history, a question unfortunately appearing on the front page of the New York Times and on CNN, is like asking whether the number of liters to the gallon has varied."

Or in other words:

Davies: The fundamental constant, c, is not so constant!
Duff: The fundamental constant, c, is not so fundamental!

Not all (many? most?) scientists agree with Duff's ideas about what is and what isn't a fundamental constant. A <a href="http://arxiv.org/abs/physics/0110060" target="_blank">recent trialogue</a> involving Duff should satisfy your curiosity on the subject.

[ August 15, 2002: Message edited by: Friar Bellows ]

fando · 08-15-2002, 12:38 AM

I haven't followed this controversy deeply, but what strikes me as odd is how Webb, et al, arrived at time variation in c from time variation in the fine structure constant alpha. I don't understand the reasoning behind that leap, and if you ask me, it's a pretty large one. Enough to invoke Sagan's adage that extraordinary claims require extraordinary evidence. It's likely that something else is going on, possibly something in the standard model rather than in the macroscopic relationship between space and time. Whatever the case may be, it's important that the questions are being asked. New insights might arise in the process, and Science shall advance another step forward.

Anyhoo, thanks for the journal links. I'm going to delve a little deeper.

beausoleil · 08-15-2002, 05:35 AM

Since the fine structure constant = 2*Pi * e^2/(h * c), if it varies, either pi, the charge on the electron, planck's constant or the speed of light (or, I suppose, 2) must vary. Any one of them varying would be extraordinary. Or am I missing something?

The evidence looks reasonable to me - Sagan's adage is overused anyway. It' feels to me like another way of saying 'Once I've made my mind up it's hard to make me change it' mixed in with some natural professional jealousy.

ohwilleke · 08-15-2002, 07:57 AM

Duff's argument that c is just a unit of conversion baffles me. You can measure it experimentally in any units you choose. For instance while the usual way of mathematically stating c is almost 3 x 10^8 meters per second, this result which contains human created dimension units, can be converted into any set of units you like. For example, you can also say that the speed of light is 186,000 miles per second, give or take. Or, 1,594,286 leagues per minute.

The number in the dimensional constant isn't sacred to be sure. But, any combination of number, length unit and time unit that describes the constant must be equal.

[ August 15, 2002: Message edited by: ohwilleke ]

fando · 08-15-2002, 02:56 PM

Quote:

Originally posted by beausoleil:
 Any one of them varying would be extraordinary. Or am I missing something?

That formula is not the only thing that gives rise to alpha. It's one of several arguably distinct sources, which should suggest more to the story. Check <a href="http://www.geocities.com/Area51/Nebula/3735/fine.html" target="_blank">this </a> out and especially <a href="http://www.btinternet.com/~ugah174/" target="_blank">this interpretation</a> inspired by Feynman.

What I suspect is that there is something deeper that gives rise to alpha and all this talk will eventually lead us to that knowledge. Then again, it might simply be time variation in e, c, G, hbar or what have you.

beausoleil · 08-15-2002, 04:14 PM

Well, as it happens I looked at both those sites yesterday. And to quote one of them:

Attention, student! Don't read!
The theory, proposed here, does not coincide to the generally adopted views in the modern physics.

Surely the fine structure constant still has to be equal to the formula given above. It expresses the relationship that holds among those quantities - that's what it is. If it was different in the early universe slightly, then the relationship among them was slightly different, meaning one or more of them was different.

See for instance

<a href="http://www.physicscentral.com/action/action-02-2.html" target="_blank">http://www.physicscentral.com/action/action-02-2.html</a>

From a theory you may be able to predict a value of the fine structure constant from something like the geometry of space time (I really don't know) - but that would then be compared with the formula.

Pi is also a dimensionless number. It seems to me as if you're saying that pi was different in the early universe but the ratio of a circle's circumeference to its radius was the same as it is today.

But once again, I may be missing something.

fando · 08-16-2002, 02:02 AM

It seems to me as if you're saying that pi was different in the early universe but the ratio of a circle's circumeference to its radius was the same as it is today.

Just for kicks, I'll eleaborate a bit. If alpha has something to do with the geometry of space-time, then this is a distinct possibility. The value of pi depends on the curvature of the surface that the circle lives on. The canonical value of pi is as would be measured on an Euclidean plane, or 3.14159... etc. As far as we're concerned, that's the everyday value of pi. However, it might very well be that the laws of nature behave according to the local non-Euclidean value of pi, or pi as measured on a curved surface. (Pi measured at an event horizon would be 0.) If this kind of pi is related to alpha, then it could mean that the time variance of alpha is a manifestation of a change in local curvature over time.

Aside from space-time curvature, another way that a local pi can vary is through approximation of circular motion. A pure circle of exact roundness might exist in the world of mathematics, but it is practically impossible to trace a pure circle in reality. An electron in a uniform magnetic field might travel in a circle, but it might deviate a bit here and there due to influences from external noise or quantum uncertainties. The rough circle its path describes could be related to alpha in some fundamental way. If this were so, then a changing alpha could mean that the roughness of the circular path is changing with time.

If I knew anything about quantum field theory and the standard model, I'd probably comment on a few other possibilities for time varying alpha in those specialties. In particular, I recall reading something that said a time variation in alpha can be explained by adjusting the standard model in such and such a way. Alas, all I know is general relativity, so I can't really add much more detail.

[ August 16, 2002: Message edited by: fando ]

beausoleil · 08-16-2002, 07:22 AM

It was a poor analogy, but what I meant was that pi is the ratio between the perimeter and diameter of a circle. The ratio may change in different geometries, but pi can't change and the ratio stay the same.

As I say, it's a poor analogy. But the fine structure constant is the result of measurements. Theory predicts it is related to the charge of the electron and the speed of light, which we think of as constants. If it varied, either the theory is incorrect (at least slightly) or e or c must have been different in the past. That is to say, the interactions governed by the fine structure constant must depend on something in addition to the charge on the electron and the speed of light that we are currently overlooking.

Turning to the link 'based on' Feynmann's work...

<a href="http://www.btinternet.com/~ugah174/" target="_blank">http://www.btinternet.com/~ugah174/</a>

He notes that the fine structure constant is predicted by...

a = a(137,29) = 29cos(p/137)tan(p/(137�29))/p = 0.00729735253186...

which is...

a(n1,n2) = n2cos(pi/n1)tan(pi/(n1� n2))/pi

with n1 =137 and n2 =29.

Now this is odd. Why 137 and 29 I ask myself? I decided to investigate the function. Here for instance are the values for n1=137 and n2 as given...

n2.... fomula
28...7.29735264244E-03
29...7.29735253186E-03
30...7.29735243216E-03
fsc..7.297352533e-3
err..0.000000027e-3

In effect, the function samples the number line in that region so regularly that agreement within the uncertainty in measured alpha for some value of n1, n2 by chance alone is hardly unexpected.

This formula is superficially more impressive since it approximates pi at n1=137

a(n1) = cos(pi/n1)/n1.

But then cos(pi/137) is approximately 1 (=0.9997 to 4 dp), and 1/137 is known to be approximately the fine structure constant.

So that page smacks of numerology to me, unless there is some other reason for choosing 137 and 29.

08-15-2002, 12:00 AM	#1
Friar Bellows Veteran Member Join Date: Apr 2001 Location: arse-end of the world Posts: 2,305	Fundamental constants and the speed of light Drawing from the intriguing <a href="http://arxiv.org/abs/astro-ph/0012539" target="_blank">observational results</a> of astronomer John Webb, a group of theorists guided by science-popularist Paul Davies <a href="http://news.ninemsn.com.au/Sci_Tech/story_36933.asp" target="_blank">recently speculated</a> that the so-called fundamental constant, c (i.e. the speed of light), may not be constant after all. Au contraire, claims physicist Mike Duff. In a <a href="http://arxiv.org/abs/hep-th/0208093" target="_blank">short paper</a> (see references therein for more explanation), Duff argues that Davies' conclusion is wrong and/or meaningless because the speed of light is not a fundamental constant. Actually, he points out, it is a factor to convert from one system of units to another -- a mere human convention. As he puts it: "Asking whether c has varied over cosmic history, a question unfortunately appearing on the front page of the New York Times and on CNN, is like asking whether the number of liters to the gallon has varied." Or in other words: Davies: The fundamental constant, c, is not so constant! Duff: The fundamental constant, c, is not so fundamental! Not all (many? most?) scientists agree with Duff's ideas about what is and what isn't a fundamental constant. A <a href="http://arxiv.org/abs/physics/0110060" target="_blank">recent trialogue</a> involving Duff should satisfy your curiosity on the subject. [ August 15, 2002: Message edited by: Friar Bellows ]</p>

08-15-2002, 07:57 AM	#4
ohwilleke Veteran Member Join Date: Jun 2000 Location: Denver, Colorado, USA Posts: 4,834	Duff's argument that c is just a unit of conversion baffles me. You can measure it experimentally in any units you choose. For instance while the usual way of mathematically stating c is almost 3 x 10^8 meters per second, this result which contains human created dimension units, can be converted into any set of units you like. For example, you can also say that the speed of light is 186,000 miles per second, give or take. Or, 1,594,286 leagues per minute. The number in the dimensional constant isn't sacred to be sure. But, any combination of number, length unit and time unit that describes the constant must be equal. [ August 15, 2002: Message edited by: ohwilleke ]</p>

08-16-2002, 02:02 AM	#7
fando Veteran Member Join Date: Sep 2001 Location: Los Angeles Area Posts: 1,372	It seems to me as if you're saying that pi was different in the early universe but the ratio of a circle's circumeference to its radius was the same as it is today. Just for kicks, I'll eleaborate a bit. If alpha has something to do with the geometry of space-time, then this is a distinct possibility. The value of pi depends on the curvature of the surface that the circle lives on. The canonical value of pi is as would be measured on an Euclidean plane, or 3.14159... etc. As far as we're concerned, that's the everyday value of pi. However, it might very well be that the laws of nature behave according to the local non-Euclidean value of pi, or pi as measured on a curved surface. (Pi measured at an event horizon would be 0.) If this kind of pi is related to alpha, then it could mean that the time variance of alpha is a manifestation of a change in local curvature over time. Aside from space-time curvature, another way that a local pi can vary is through approximation of circular motion. A pure circle of exact roundness might exist in the world of mathematics, but it is practically impossible to trace a pure circle in reality. An electron in a uniform magnetic field might travel in a circle, but it might deviate a bit here and there due to influences from external noise or quantum uncertainties. The rough circle its path describes could be related to alpha in some fundamental way. If this were so, then a changing alpha could mean that the roughness of the circular path is changing with time. If I knew anything about quantum field theory and the standard model, I'd probably comment on a few other possibilities for time varying alpha in those specialties. In particular, I recall reading something that said a time variation in alpha can be explained by adjusting the standard model in such and such a way. Alas, all I know is general relativity, so I can't really add much more detail. [ August 16, 2002: Message edited by: fando ]</p>

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08-15-2002, 12:38 AM	#2
fando Veteran Member Join Date: Sep 2001 Location: Los Angeles Area Posts: 1,372	I haven't followed this controversy deeply, but what strikes me as odd is how Webb, et al, arrived at time variation in c from time variation in the fine structure constant alpha. I don't understand the reasoning behind that leap, and if you ask me, it's a pretty large one. Enough to invoke Sagan's adage that extraordinary claims require extraordinary evidence. It's likely that something else is going on, possibly something in the standard model rather than in the macroscopic relationship between space and time. Whatever the case may be, it's important that the questions are being asked. New insights might arise in the process, and Science shall advance another step forward. Anyhoo, thanks for the journal links. I'm going to delve a little deeper.

08-15-2002, 05:35 AM	#3
beausoleil Senior Member Join Date: May 2002 Location: US and UK Posts: 846	Since the fine structure constant = 2Pi e^2/(h * c), if it varies, either pi, the charge on the electron, planck's constant or the speed of light (or, I suppose, 2) must vary. Any one of them varying would be extraordinary. Or am I missing something? The evidence looks reasonable to me - Sagan's adage is overused anyway. It' feels to me like another way of saying 'Once I've made my mind up it's hard to make me change it' mixed in with some natural professional jealousy.

08-15-2002, 04:14 PM	#6
beausoleil Senior Member Join Date: May 2002 Location: US and UK Posts: 846	Well, as it happens I looked at both those sites yesterday. And to quote one of them: Attention, student! Don't read! The theory, proposed here, does not coincide to the generally adopted views in the modern physics. Surely the fine structure constant still has to be equal to the formula given above. It expresses the relationship that holds among those quantities - that's what it is. If it was different in the early universe slightly, then the relationship among them was slightly different, meaning one or more of them was different. See for instance <a href="http://www.physicscentral.com/action/action-02-2.html" target="_blank">http://www.physicscentral.com/action/action-02-2.html</a> From a theory you may be able to predict a value of the fine structure constant from something like the geometry of space time (I really don't know) - but that would then be compared with the formula. Pi is also a dimensionless number. It seems to me as if you're saying that pi was different in the early universe but the ratio of a circle's circumeference to its radius was the same as it is today. But once again, I may be missing something.

08-16-2002, 07:22 AM	#8
beausoleil Senior Member Join Date: May 2002 Location: US and UK Posts: 846	It was a poor analogy, but what I meant was that pi is the ratio between the perimeter and diameter of a circle. The ratio may change in different geometries, but pi can't change and the ratio stay the same. As I say, it's a poor analogy. But the fine structure constant is the result of measurements. Theory predicts it is related to the charge of the electron and the speed of light, which we think of as constants. If it varied, either the theory is incorrect (at least slightly) or e or c must have been different in the past. That is to say, the interactions governed by the fine structure constant must depend on something in addition to the charge on the electron and the speed of light that we are currently overlooking. Turning to the link 'based on' Feynmann's work... <a href="http://www.btinternet.com/~ugah174/" target="_blank">http://www.btinternet.com/~ugah174/</a> He notes that the fine structure constant is predicted by... a = a(137,29) = 29cos(p/137)tan(p/(137�29))/p = 0.00729735253186... which is... a(n1,n2) = n2cos(pi/n1)tan(pi/(n1� n2))/pi with n1 =137 and n2 =29. Now this is odd. Why 137 and 29 I ask myself? I decided to investigate the function. Here for instance are the values for n1=137 and n2 as given... n2.... fomula 28...7.29735264244E-03 29...7.29735253186E-03 30...7.29735243216E-03 fsc..7.297352533e-3 err..0.000000027e-3 In effect, the function samples the number line in that region so regularly that agreement within the uncertainty in measured alpha for some value of n1, n2 by chance alone is hardly unexpected. This formula is superficially more impressive since it approximates pi at n1=137 a(n1) = cos(pi/n1)/n1. But then cos(pi/137) is approximately 1 (=0.9997 to 4 dp), and 1/137 is known to be approximately the fine structure constant. So that page smacks of numerology to me, unless there is some other reason for choosing 137 and 29.

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