# Questions about Varying Speed of Light (VSL)

#### dand5

I realize this should be in the Theory forum, but I don't seem to have "permission" to post there, so I am posting here. Moderators, please move this thread there if you get the chance. Thanks.

Though I find VSL sort of troubling, I have a hard time understanding why it is so easily dismissed by some. So I just have a few questions for both VSL haters and lovers (I do not know that much about the theory).

According to VSL, the speed of light nowadays is decreasing pretty slowly, so doesn't that imply that the constancy of light is an excellent approximation to VSL nowadays?

Similarly, wouldn't VSL reduce to GR in any local spatial slice of spacetime?

With this in mind, how does the fact that experiments have shown c to be constant during the past couple of centuries prove that it is a universal constant?

Does anyone know if, according to VSL, c is actually approaching some
constant value (besides 0)?

Thanks a lot for any replies.

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#### arildno

Homework Helper
Gold Member
Dearly Missed
Now, I know next to nothing about this, but this is how I've been given a rough explanation:

"c" appears in the GR equations not typically isolated, but in some product with another term (don't ask me).
VSL then lets "c" vary, but they haven't really motivated why it is "c" in that product which should be variable, rather than the other.

That is, as yet VSL has been unable to come up with any sort of solid motivation for this non-standard choice; if a VSL-theorist manages to come off with a TESTABLE PREDICTION in which his prediction will differ from more standard predictions, then an experiment will most likely be performed in order to settle the matter.

(I believe that the current view is that VSL is an unnecessary complication, and, hence, uninteresting)

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#### dand5

I believe the other option was for "h" to vary. But the varying "c" seemed to solve certain cosmological "puzzles," (something about homogeniety of the universe on large scales, and the flatness problem) which I am fairly sure varying h did not.

There were some other constants that could vary as well I think.

In any case, thanks for the reply; I can see how VSL would be a nasty complication.

#### rbj

dand5 said:
I have a hard time understanding why it is so easily dismissed by some. So I just have a few questions for both VSL haters and lovers
count me among the former. VSL is cold fusion. possibly the best single paper to read detracting from the proposal is Duff:

http://arxiv.org/PS_cache/hep-th/pdf/0208/0208093.pdf [Broken]
http://xxx.lanl.gov/pdf/physics/0110060

Duff isn't picking solely on VSL, but he reminds us that the only quantities that we ultimately measure in physical experiments or in our perception of reality are dimensionless numbers. (When one commonly measures a length with a ruler or tape-measure, that person is actually counting tick marks on a given standard or is measuring the length relative to that given standard, which is a dimensionless value. It is no different for physical experiments, all physical quantities are measured relative to some other like dimensioned values.) We can notice a difference if some dimensionless physical quantity such as the fine-structure contant or the proton/electron mass ratio changes (atomic structures would change) but if all dimensionless physical quantities remained constant, we could not tell if a dimensionful quantity, such as the speed of light, c, has changed.

in the first paper above, he shows that, assuming that there is a bona fide variation of the fine-structure constant, alpha, once you strip away the dimensionful expression of entropy of a black hole, that the proposition that measuring such entropy would shed light on whether it is c changing or e changing falls flat. he shows that it only depends on what set of units you use and when i look at the math, it really only reiterates that alpha has changed. so you measure that alpha may have changed at Oklo, and then when you look at black holes it might show there that alpha has changed. big deal (unless the two experiments conflict and show alpha changing in different directions or amounts).

assuming that you use a bar standard for a meter (rather than the current SI standard which effectively defines c to be 299792458 m/s, so there is no way you can use that standard for length and come to a VSL result) and some clock and measure c to be different, you have to ask: is it c that is different or your meter stick or your clock? saying one of those changing is reasonable but the other is preposterous is mistaken.

r b-j

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#### Kea

counterpoint

New varying speed of light theories
Joao Magueijo
http://arxiv.org/abs/astro-ph/0305457

This paper has a very nice discussion about what it means to talk about varying dimensionful quantities.

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#### Integral

Staff Emeritus
Gold Member
WARNING!
I would like to see this thread develop into a discussion of Joao Magueijo's paper. I believe that that his the only viable VSL work that has been done. I am going to be absolutely ruthless in deleting posts which contain personal theories of VSL and relativity in general. The minimum requirement for participating in this discussion will be reading paper linked above. If you are unable to understand the contents of that paper feel free to ask questions but, please, keep extraneous opinions to yourself.

I WILL delete crackpottery!

#### rbj

Kea said:
New varying speed of light theories
Joao Magueijo
http://arxiv.org/abs/astro-ph/0305457

This paper has a very nice discussion about what it means to talk about varying dimensionful quantities.
I would still like it if someone would respond to the points of Duff (or my paraphrase of them) rather than just say "look at this paper".

I am reading through the paper and I can take issue with a couple of points he makes in the context of Duff's paper. "At the end of the day, even if all dimensionless parameters were running wild, one would still want to set up quantum mechanics using Planck’s “constant”, or electrodynamics using the speed of light. Dimensional quantities would still play a role," I think I disagree with this statement. With Planck Units, you can do quantum mechanics without any mention of Planck's constant, or do electrodynamics or SR or GR without any mention of the speed of light (or speed of propagation of gravity) or even G. All those go away. The elementary charge, e, does not go away (however, its value becomes dimensionless because it is expressed in terms of the Planck charge, sqrt(h_bar*c*4*pi*epsilon_0)), but those universal "constants" (or non-constants, if you so choose) such as c, G, h_bar, epsilon_0, Boltzmann, *do* go away. And I think all other dimensional quantities go away also, when using Planck Units.

I think I agree with this:

"We need units and dimensional parameters to set up physics. Dimensional parameters or quantities are a necessary evil in physics. For the most part they are tautological and meaningless; still within the whole construction one gleans operationally meaningful statements, which are indeed dimensionless. But it’s easier to get there by means of constructions which are purely human conventions. These conventions amount to a prescription for defining units of mass, time, and length (and temperature if required). In the context of varying dimensionless constants, that choice translates into a statement on which dimensional constants are varying."

... but I would reiterate that the physics of reality does not give a rat's ass what choice of units we use, so to say that something meaningful is varying, the factuality of that cannot depend on the choice of units we eventually choose.

r b-j

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#### russ_watters

Mentor
I think a clarification may be in order (I'm by no means an expert on VSL theories):

From the abstract of the paper Integral linked:
We then summarize the main VSL mechanisms proposed so far: hard breaking of Lorentz invariance; bimetric theories (where the speeds of gravity and light are not the same); locally Lorentz invariant VSL theories; theories exhibiting a color dependent speed of light; varying $c$ induced by extra dimensions (e.g. in the brane-world scenario); and field theories where VSL results from vacuum polarization or CPT violation.
There are several different types of VSL theories with varying levels of scientific validity. My perception is that most of the hard-core crackpottery is associated with the idea that C isn't contstant today, ie, the M-M experiment really did find the ether, we're just at the center of it. Most of the possibly scientifically valid (but still kinda fringe) ideas are associated with the idea that C has varied slightly with the aging of the universe.

#### Kea

sorry

rbj said:
I would still like it if someone would respond to the points of Duff (or my paraphrase of them) rather than just say "look at this paper".

I think I disagree with this statement. With Planck Units, you can do quantum mechanics without any mention of Planck's constant, or do electrodynamics or SR or GR without any mention of the speed of light (or speed of propagation of gravity) or even G. All those go away.
Well, I'm not a VSL person either. Actually, all the alternatives discussed really bother me because he keeps referring to 'the early universe' and nice smooth metrics whilst at the same time clearly motivating much of this research from the point of view of quantum gravity. Having said this, your favourite VSL theory is capable of making testable predictions, and there isn't much out there that does that.

But I think his points about dimensional quantities are very valid. Planck's constant is important in QM. Of course it doesn't matter at all what actual numerical value it has, but its dimensions are crucial for 'comparing' position and momentum operators. Similarly for other dimensional quantities in physics.

As Magueijo says:
Poincare clearly implies that matters as fundamental as the uniformity of time, and by consequence the law of inertia and the theorem of energy conservation, are not provable by experiment. Experiment is dimensionless, but these statements 'have units', eg. depend on the definition of the unit of time, which is nothing but a convention. And yet that definition is not a subjective choice. One particular unit of time - that which renders the laws of classical mechanics simple - objectively stands out.

#### rbj

Kea said:
...
But I think his points about dimensional quantities are very valid. Planck's constant is important in QM. Of course it doesn't matter at all what actual numerical value it has, but its dimensions are crucial for 'comparing' position and momentum operators. Similarly for other dimensional quantities in physics.
...
being an engineer, i have found myself arguing your point regarding dimensions with real hard-core physikers on sci.physics.research ("Mathematicians routinely ignore units, but engineers do so at their peril."). those guys insist that dimensions of physical quantity itself is a human construct. i would tend to agree that we humans have created the concept of dimensions of physical stuff to be able to wrap our brain around the concepts of what that stuff is. however, i disagree with these heavyweights that length is the same species of animal that time is or mass or electric charge. i think some things are the same animal (basically, by definition): force and the time derivative of momentum. absolute temperature and the energy per particle per degree of freedom (so i look at Boltzmann's constant or Advogadro's constant as being less fundamental as h_bar or G or c or even epsilon_0).

but just as we can define the unit force so that Newton's 2nd law has no conversion factor in it or the unit temperature so that Boltzmann's constant goes away, we can define our unit time, length, and mass so that G, c, and h_bar go away (the only difference is now we have 3 equations and 3 unknowns rather than 1 eq. and 1 unknown). then we can define our unit charge so that the Coulomb's force constant goes to one also (as they do for electrostatic cgs units). here we made those definitions without refering to any particular particle or object or "thing" in the universe. no reference to any kilogram prototype, any bar of platinum, or even some particular element's radiation.

so really, all h_bar, G, c, and epsilon_0 are, are indirect indications of where Nature has put her tick marks on her meter stick, her clock, her scale, and her electroscope. using those units, there is no h_bar, G, c, or epsilon_0 (and, consequently, no mu_0 nor Z_0). our units of scale are different (much bigger), but if all dimensionless quantities of measure remain constant (and dimensionless quantities are the only ones we can measure in any physical experiment), our units of scale, indeed our perception of scale remains proportional to those Planck units by unchanging constants. saying this is a tautology. but to argue with it is like disagreeing with "5=5" or "x=x".

http://en.wikipedia.org/wiki/Planck_units

in the interest of full disclosure, i'll admit that i contributed a large portion to the article, but it has survived editing, indicating, i beleive, that it isn't too unorthodox. personally, i think the part that deals with the dimensionful scaling issue (which is my only objection to the VSL theory, but one that suffices to discredit it) is really just a tautology or perhaps a truism. it's true but it doesn't really say much (like saying 5=5 or x=x) which is why i'm just incredulous that people disagree with it.

there is another wikipedian that has recently created an article

http://en.wikipedia.org/wiki/Variable_speed_of_light

of which i have taken great exception to. rather than repeat the blow-by-blow here, just take a look at the Discussion page for that article. as best as i can read the english language, the supporters of VSL do not address what Duff is saying. perhaps the speed of light is changing (as well as the Planck length, Planck time, Planck mass, and Planck charge), but we will never know the difference. a theist could claim that God (however he/she understands God) might know the difference, but whether bars or atomic clocks are used to measure c, if c alone changes, then our means for measuring c will change in exactly the same way so that, as far as we can tell, c ostensibly remains at 299792458 m/s. now if that is not true, then there is some dimensionless quantity, a ratio of two like dimensioned quantities that has changed, and that is the salient measure.

you should check out the Duff article at:

http://arxiv.org/PS_cache/hep-th/pdf/0208/0208093.pdf [Broken]

and the Duff, Veneziano, and Okun "Trialogue" article at

http://xxx.lanl.gov/pdf/physics/0110060

and one refutation by Moffat at

http://arxiv.org/pdf/hep-th/0208109

and judge for yourself.

Kea said:
...
Having said this, your favourite VSL theory is capable of making testable predictions, ...
i think, as best as i can read the lit, that Duff accurately destroyed that notion. these guys claimed that the change in alpha inferred at Oklo coupled with the change in the entropy of a non-rotating black hole together indicated that it's c that is changing, not e. but Duff showed that, in both experiments, the salient quantity that would be changing is simply alpha, the fine-structure "constant". and that is in keeping with his central premise. a change in the dimensionless fine-structure constant is meaningful. a change in the dimensionless proton/electron mass ratio is meaningful. a change in c or h_bar or G is not. we (and our measuring apparatus) could not tell the difference.

Kea said:
As Magueijo says:
Poincare clearly implies that matters as fundamental as the uniformity of time, and by consequence the law of inertia and the theorem of energy conservation, are not provable by experiment. Experiment is dimensionless, but these statements 'have units', eg. depend on the definition of the unit of time, which is nothing but a convention. And yet that definition is not a subjective choice. One particular unit of time - that which renders the laws of classical mechanics simple - objectively stands out.
just curious, what unit of time is that?

r b-j

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#### Kea

rbj said:
you should check out the Duff article at:

http://arxiv.org/PS_cache/hep-th/pdf/0208/0208093.pdf [Broken]
I looked at the Duff article. He completely misses the point. He begins by discussing the Davies et al. paper, which I agree is bad. We agree that one could take $c$ to be constant, or varying, as one pleases by selecting units appropriately.

When Duff discusses entropy and mass and so on he is talking about quantities for which the definition is well established. VSL theories address a qualitatively new cosmology, and so they are forced to consider what sort of dimensional quantities might make this new physics easy to write down. Thus their discussion of varying $c$ is far from pointless.

As for units for time: the question isn't whether one should use Krypton light or the seconds on your grandfather's watch, but whether or not something that behaves like $t$ in one's equations is an appropriate choice of quantity with which to discuss the physics in question.

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#### Wave's_Hand_Particle

dand5 said:
I realize this should be in the Theory forum, but I don't seem to have "permission" to post there, so I am posting here. Moderators, please move this thread there if you get the chance. Thanks.

Though I find VSL sort of troubling, I have a hard time understanding why it is so easily dismissed by some. So I just have a few questions for both VSL haters and lovers (I do not know that much about the theory).

According to VSL, the speed of light nowadays is decreasing pretty slowly, so doesn't that imply that the constancy of light is an excellent approximation to VSL nowadays?

Similarly, wouldn't VSL reduce to GR in any local spatial slice of spacetime?

With this in mind, how does the fact that experiments have shown c to be constant during the past couple of centuries prove that it is a universal constant?

Does anyone know if, according to VSL, c is actually approaching some
constant value (besides 0)?

Thanks a lot for any replies.

This paper is quite interesting:http://arxiv.org/abs/astro-ph/9811018

there is reference to John Moffats early work on VSL, any mentor who knows who John Moffat is would not be so eager to assign a crackpot tag relative inquiries.

This paper:http://arxiv.org/abs/astro-ph/0004321

relays not all doom and gloom.

and this paper is highly cited, and it is really an interesting paper, if one takes the time to read and understand some of its consequences:http://arxiv.org/abs/hep-th/0112090

#### rbj

Kea said:
I looked at the Duff article. He completely misses the point. He begins by discussing the Davies et al. paper, which I agree is bad. We agree that one could take $c$ to be constant, or varying, as one pleases by selecting units appropriately.

When Duff discusses entropy and mass and so on he is talking about quantities for which the definition is well established. VSL theories address a qualitatively new cosmology, and so they are forced to consider what sort of dimensional quantities might make this new physics easy to write down. Thus their discussion of varying $c$ is far from pointless.
no, it still appears to me that Magueijo has done nothing to refute Duff's main argument. in fact Duff revised his paper to respond to Magueijo. Duff basically says that Magueijo is "not wrong" but still does not address his point. in fact, since Magueijo puts forth the same black hole entropy equation (not "shorn" of its unit dependence) and repeats the same fallacy that the equation can differentiate between varying $c$ and and varying $e$ theories, i think that Magueijo is missing the point. that is a factually incorrect statement. the black hole entropy equation, "shorn of its irrelevant unit dependence" is a function of alpha and the mass and charge of the black hole normalized to the Planck mass and Planck charge. there is no $c$ in it at all.

Kea said:
As for units for time: the question isn't whether one should use Krypton light or the seconds on your grandfather's watch, but whether or not something that behaves like $t$ in one's equations is an appropriate choice of quantity with which to discuss the physics in question.

again, rather than just say "read the article" (which i have, being a EE i do not know all of the physics of cosmology, but i do understand dimension of physical quantity, units, and the experimental method), please persuade me with some physics.

r b-j

#### Kea

rbj said:
in fact, since Magueijo puts forth the same black hole entropy equation (not "shorn" of its unit dependence) and repeats the same fallacy
If you read the paragraph below the appearance of the entropy equation you will see that Magueijo is in fact criticising it. Anyway, once again, I agree with you for the most part.

However, you appear to be living in a Newtonian universe. Now I'm sorry, but I don't have the time to explain elementary relativity to you. There are a number of good textbooks on the subject: for instance Carroll.

#### rbj

Magueijo says:

"Indeed if the black hole entropy is still given by

S = (k*pi*G)/(h_bar*c) [M + sqrt(M^2 + Q^2/G) ]^2

and if h_bar, G, and, M remain constant, there is a clear difference between varying c and varying e theories."

Duff has it with a minus sign in front of the Q^2/G. i dunno which one is right, but Duff's version makes sense with the argument that Davies was making.

i guess Magueijo does put in a qualifier ("if"), but, as i read it, he repeats the fallacy and does not fix it to be not unit dependant as Duff does. That's the main basis for the refutation of the point that Davies makes. Davies says that decreasing c increases S while increasing e decreases S, and he is wrong about that because he fails to express this in terms without human constructs.

Kea said:
... you appear to be living in a Newtonian universe. Now I'm sorry, but I don't have the time to explain elementary relativity to you.
how about testing me on SR? if that is the "elementary relativity", i'm pretty comfortable there.

i won't claim to be particularly good at GR, but i understand the fundamental concepts like the equivalence principle. i sorta understand the tutorial by Baez and Bunn http://arxiv.org/pdf/gr-qc/0103044 [Broken] but Carroll's tutorial at http://pancake.uchicago.edu/~carroll/notes/grtinypdf.pdf is more difficult for me. i sorta understand how they go from Einstien's equation to the GEM equations (looks just like Maxwell's equations with 1/(4*pi*G) substituted for epsilon_0) for reasonably flat space-time.

i know that because of the equivalence principle that where gravity is strong (equivalent to highly accelerated frame of reference) that c is measured to be different.

anyway, i guess it's fine to patronize, but i just would like to see someone who supports VSL seriously and effectively dispose with Duff's point. if they can't then Duff's point stands and a varying c (in inertial frames of reference) is something we would never know the difference of. and if we can't tell the difference, i fail to understand what its "meaning" (of VSL) would be, whatever the theory.

r b-j

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#### Kea

Hi rbj

rbj said:
How about testing me on SR?
All right. Please explain SR to us without using $c$. Now you are not permitted to set $c$ to 1, because units are completely arbitrary, as you have nicely pointed out.

#### rbj

Kea said:
All right. Please explain SR to us without using $c$. Now you are not permitted to set $c$ to 1, because units are completely arbitrary, as you have nicely pointed out.
that's "elementary relativity"? if i can't say that $c$ is 1, how do i say that the speed of light is observed to be the same for all inertial reference frames? if i can't say that $c$ is 1, can i use $$\beta$$ for the velocity of one observer relative to the "primary" observer? is your intent that i describe all velocities as relative to light? i s'pose i can copy a chapter in Beiser (an old Elementary Modern Physics text) replace every $v$ with $$\beta$$, delete every reference to $c$, and refer to every mention of velocity as the "velocity normalized to the speed of light".

what does this do for the issue at hand?

i asked for someone who supports VSL (i don't think that's you, if i take you for your word) to refute Duff with their own words rather than just say "read Moffat" or whoever. i understands Duff's point sufficiently that i can make it and defend it myself. i want someone to explain to me why he's wrong (or "completely misses the point") without copping out to some other author.

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#### Kea

Hi rbj

I must say, I'm surprised that no real VSL supporter has come forward. I'm a little tired of defending it. PF sees plenty of String bashing (from myself also), which makes one wonder just which aspects of quantum gravity people do support.

Anyhow....consider the Planck length

$$l_{p} = \sqrt{\frac{G \hbar}{c^{3}}}$$

We all agree that this is a natural length scale. But the consequences of this depend very much on the theory that one is working with. In String theory, for instance, one wants dimensionless string tension and $c = 1$ and dimensionless $G$. In this case one cannot have $\hbar = 1$.

So without a complete theory of quantum gravity in which we really understand Planck units, work such as VSL is very worthwhile even despite its faults.

#### rbj

Kea said:
\consider the Planck length

$$l_{p} = \sqrt{\frac{G \hbar}{c^{3}}}$$

We all agree that this is a natural length scale.
but it ain't the only natural unit of length. i like it the best since it does not refer to any particle, object, or "thing" for its definition.

But the consequences of this depend very much on the theory that one is working with. In String theory, for instance, one wants dimensionless string tension and $c = 1$ and dimensionless $G$. In this case one cannot have $\hbar = 1$.
i can see that. i dunno anything about string theory other than what they put up on Nova (The Elegant Universe). why is it that "one" wants the string tension to be dimensionless? does it have to be 1 or do different strings have different tensions. suppose they set $$\hbar$$ to 1, what would be the dimension (and value) of the string tension? just a curiousity.

i have had disagreements with real physicists about what they choose for elegance. i think that Planck should have normalized $$4 \pi G$$ instead of $$G$$ and likewize they should define the unit charge to normalize $$\epsilon_0$$ instead of $$4 \pi \epsilon_0$$ and put those $$4 \pi$$ factors where they belong, in the geometry of a physical problem being analyzed instead of in the field equations.

So without a complete theory of quantum gravity in which we really understand Planck units, work such as VSL is very worthwhile even despite its faults.
i'm sure there are other consequences of Planck units, but i just see them as the units that naturally kill off "extraneous" factors in the fundamental field equations.

thought experiments regarding VSL and cosmology are fine, but until someone can convince me that we could actually measure such variation, it seems to me to be without meaning. what $$G$$ and $$c$$ and $$\hbar$$ and $$\epsilon_0$$ do for us (or me) is to simply define where Nature has put her tick marks on her ruler, clock, scale, and electroscope. we define our own tick marks (m s kg C) and we get non-unity values for $$G$$ and $$c$$ and $$\hbar$$ and $$\epsilon_0$$.

that's my only sense about Planck units. if the Planck length turns out to be important to other theories, sounds good to me, but the Planck units have theoretical value even before that.

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