# Who first studied variable speed of light? - Einstein

1. Jul 6, 2013

### phys12345

Who first studied variable speed of light? --- Einstein

Variable speed of light is a hypothesis that states that the speed of light, usually denoted by c, may be a function of space and time. Einstein's first mentioned a variable speed of light in 1907, and he reconsidered the idea more thoroughly in 1911.
( http://en.wikipedia.org/wiki/Variable_speed_of_light )

As we know, Einstein developed his special theory of relativity, in which the constancy of light speed is a fundamental hypothesis. But I don't understand why he tried to set up the theory of variable speed of light. Does it not contradict the special theory of relativity?

2. Jul 6, 2013

### pervect

Staff Emeritus
Back in 1911, the meter bar was defined by a standard prototype, and the speed of light was measured, so it made more sense to talk about a "variable speed of light".

Today, the speed of light is defined as a constant,

See for example the Nist discussion of "c" and the meter. http://physics.nist.gov/cuu/Units/meter.html
So it doesn't make much sense to talk about a "variable speed of light". Occasionally people still try, but for the most part people are more careful and stick instead to talk about variations in unitless quantities, such as the fine structure constat.

We can still talk meaningfully to some extent about measuring variations in the length of meter prototpye bars, though it really simplifies things enormously to follow Duff's suggestion (see the FAQ) and talk about variations in the unitless fine structure constant instead.

Note that predictig a variation in said fine structure constant implies that one predicts the meter prototype bar length measured according to current standards would change. The change would be most easily understood as the result of changes in the atoms rather than changes in "c".

As far as what Einstein did in 1911, from the looks of the Wiki he was strugglign to come up with a theory of gravity - and this was one of his unsuccessful papers. I would suggest that while old unsuccessful theories (regardless of whether they were by Einstein or not)may be of some historical interest, they are not a high priority for people who actually want to learn how modern physics works.

Last edited by a moderator: May 6, 2017
3. Jul 6, 2013

### ShayanJ

Defining the speed of light as a constant and using it as a basis for a unit system,implicitly has in itself,the assumption that the speed of light is independent of the space and time!
If a theory comes up with the idea that speed of light does depend on space and time,then the system of units should be reconsidered...or at least redefined to say that speed of light at such a point and such a time is such a number!

And as a try for answering the question...I have read a paper in which it was suggested that the permeability and Permittivity of vacuum arise from the vacuum fluctuations predicted by QM...And...don't know...maybe that makes the speed of light variable
I also think I have read another paper suggesting sth similar but I remember non of them!sorry!

Another possibility is this...If one wants to consider electromagnetic fields in a curved space-time,they should change the Maxwell's equations for taking into account that curvature...And...again don't know..maybe that affects the speed of light!

4. Jul 6, 2013

### WannabeNewton

It is only locally that the speed of light is a frame invariant so there is no issue with regards to Maxwell's equations in curved space-time.

5. Jul 6, 2013

### ShayanJ

mmmm....could you explain it?
I somehow feel what you mean...but its just not clear...you know?!

6. Jul 6, 2013

### phys12345

But vacuum is not real vacuum, said in recent two papers in European Physical Journal D.
http://www.sciencedaily.com/releases/2013/03/130325111154.htm
http://arxiv.org/abs/1302.6165
http://arxiv.org/abs/1301.3923

Speed of Light May Not Be Fixed, Scientists Suggest; Ephemeral Vacuum Particles Induce Speed-Of-Light Fluctuations

"Two forthcoming European Physical Journal D papers challenge established wisdom about the nature of vacuum. In one paper, Marcel Urban from the University of Paris-Sud, located in Orsay, France and his colleagues identified a quantum level mechanism for interpreting vacuum as being filled with pairs of virtual particles with fluctuating energy values. As a result, the inherent characteristics of vacuum, like the speed of light, may not be a constant after all, but fluctuate.

Meanwhile, in another study, Gerd Leuchs and Luis L. Sánchez-Soto, from the Max Planck Institute for the Physics of Light in Erlangen, Germany, suggest that physical constants, such as the speed of light and the so-called impedance of free space, are indications of the total number of elementary particles in nature.

Vacuum is one of the most intriguing concepts in physics. When observed at the quantum level, vacuum is not empty. It is filled with continuously appearing and disappearing particle pairs such as electron-positron or quark-antiquark pairs. These ephemeral particles are real particles, but their lifetimes are extremely short. In their study, Urban and colleagues established, for the first time, a detailed quantum mechanism that would explain the magnetisation and polarisation of the vacuum, referred to as vacuum permeability and permittivity, and the finite speed of light. This finding is relevant because it suggests the existence of a limited number of ephemeral particles per unit volume in a vacuum.

As a result, there is a theoretical possibility that the speed of light is not fixed, as conventional physics has assumed. But it could fluctuate at a level independent of the energy of each light quantum, or photon, and greater than fluctuations induced by quantum level gravity. The speed of light would be dependent on variations in the vacuum properties of space or time."

(I am not sure if European Physical Journal D is a mainstream journal or not, sorry; non-mainstream journals are not allowed to cite according to the forum rules, but the rules don't say which are mainstream and which are not. I wrongly got a warning.)

7. Jul 6, 2013

### Staff: Mentor

This is not correct. The forum rules ( https://www.physicsforums.com/showthread.php?t=414380 ) clearly give a link to the list of journals which are generally considered mainstream. European Physical Journal D is on the list.

8. Jul 6, 2013

### Staff: Mentor

You have to be careful with your statements here. Einstein proposed that the speed of light is invariant. Invariance means that different reference frames agree on the value. This is a different concept from constant, which means that it is the same across time.

However, in science, when you have a theory that you want to test you cannot simply assume the theory and make measurements consistent with the theory, you must also assume that the theory might be wrong and make measurements to rule out alternative theories. The best way to do that is to make a test theory which has some parameters that allow it to vary between different competing theories. Then you devise experiments to measure that test theory.

So the best way to test the constancy or invariance of c is to make a theory where it is not constant or invariant and some parameter determines the degree of deviation from constancy or invariance. You then measure that parameter to put bounds on the variation.

9. Jul 6, 2013

### Agerhell

Eddington? The fact that light bends when sent through a gravitational field can be considered as a measurement of the variation of the speed of light in a gravitational field. Now the rate of time also varies in a gravitational field so that locally the speed of light will appear constant.

10. Jul 6, 2013

### Staff: Mentor

This runs into the same problem that pervect mentioned. The value of any dimensionful "fundamental" constant depends entirely on your choice of units and therefore "variations" can simply be attributed to variations in your units.

If you want to talk about the value of constants changing you must look at dimensionless parameters, like the fine structure constant. I like this page on the topic: http://math.ucr.edu/home/baez/constants.html

11. Jul 6, 2013

### phys12345

I know what you mean. In the special theory of relativity, usually a constant does not necessarily mean a Lorentz invariant; the simplest example is: the global energy for an isolated system is a constant, but it is not an Lorentz invariant. On the other side, a Lorentz invariant does not necessarily mean a constant; the simplest example is: the phase function for a plane wave is a Lorentz invariant, but it is not a constant because it changes with time and space. However the light speed in vacuum is a Lorentz invarinat and also is a constant.

If the light speed is assumed to be variable, then this assumption apparently contradicts the principle of relativity for Maxwell equations in free space, because from Maxwell equations, we directly know that the plane light wave propagates at a constant light speed, which holds in all inertial frames.

12. Jul 6, 2013

### Staff: Mentor

As far as we know this is true. However, the postulate of relativity only asserts that it is invariant.

No. It would just mean that Maxwell's equations (with constant coefficients in vacuum) are not exact laws of physics. Something similar happened with Newton's laws.

13. Jul 6, 2013

### WannabeNewton

This is incorrect. It can be shown that for any smooth 4-vector field $t^{\mu}$ of compact spatial support that satisfies $\partial_{\mu}t^{\mu} = 0$, the integral $I = \int t^{\mu}dS_{\mu}= \int t^{0}d^{3}x$ is a Lorentz invariant. The usual proof that $I$ is a constant, which uses Stokes' theorem, can be tweaked just a little bit in the interpretation to show that $I$ is a Lorentz invariant. See e.g. Panofsky and Phillips p.309 or Franklin p.399

14. Jul 6, 2013

### Bill_K

The global energy for an isolated system is the fourth component of a Lorentz vector. Your argument for integrating tμ is appropriate for electromagnetism, where tμ is the current density and the integral quantity is the total charge, but for gravity the integrand involves not a vector quantity but Tμν.

15. Jul 6, 2013

### WannabeNewton

The current being spoken of is $t^{\mu} = -T^{\mu\nu}\xi_{\nu}$ where $\xi^{\mu}$ is a time-like killing vector field. The total energy is then defined as $E = \int t^{\mu}dS_{\mu}$.

EDIT: Btw, this is how I interpreted the phrase "global energy". If some other notion of "global energy" was being used (e.g. Komar energy) then I apologize.

Last edited: Jul 6, 2013
16. Jul 6, 2013

### Samshorn

The concept of "speed" has meaning only in the context of physically meaningful measures of space and time. The original theory of special relativity asserted that the speed of light in vacuum is c when expressed in terms of a specific class of coordinate systems characterized by the homogeneity and isotropy of inertia. These are often called inertial coordinate systems. There was a tacit presumption that such a coordinate system could (in principle) be defined globally, covering all of space and time.

However, as Einstein tried to incorporate gravitation and the equivalence principle into this framework, he realized that this was not possible. The equivalence principle assures us that we can always define one of the special coordinate systems of special relativity (and Newtonian mechanics) locally, i.e., within a sufficiently small region of space and time, and the speed of light will have the value c in terms of those coordinates in that infinitesimal region, but such a coordinate system cannot be extended over a finite region in the presence of gravity, due to what Einstein conceived as the "curvature" of spacetime. (There are other interpretations, but they are operationally equivalent.)

Consequently, any coordinate system that extends over a finite region (in a gravitational field) cannot have the properties everywhere that characterize an inertial coordinate system as defined above. In particular, the speed of light expressed in terms of an extended coordinate system in a gravitational field cannot equal c everywhere. (Note well that this does not conflict with the fact stated above that the speed of light equals c everywhere in terms of a local inertial coordinate system.) In fact, the speed of light need not even have the same value in all directions at a given event. For example, the speed of light near a gravitating mass is non-isotropic when expressed in terms of Schwarzschild coordinates. (We can define coordinates in which it is isotropic, but it still varies in magnitude from place to place.)

Judging by some of the other comments in this thread, I think you may be confusing two very different subjects. When people talk (today) about possible variations in the speed of light (or the gravitational constant, etc.) due to cosmological evolution, changes in the properties of the vacuum, "deformed special relativity", or whatever, they are talking about local measures of the speed of light and putative secular or positional (or even random) deviations from the currently understood laws of physics. (Such variations would of course be manifested by changes in the dimensionless constants of physics.) This is totally unrelated to the variations in the numerical speed of light when expressed in terms of different coordinate systems, and the constraints placed by general relativity on the possible extended coordinate systems in a gravitational field, which is what Einstein was talking about in the 1907 and 1911 papers you mentioned. So, if your interest is in secular variations or vacuum fluctuations in the fundamental constants of physics, you're barking up the wrong tree by invoking the coordinate aspects due to the "curvature" of spacetime in general relativity. That's a completely different subject, and doesn't involve or imply any variations in the fundamental constants of nature.

I took the liberty of bolding the phrase that answers your question. The point is that, in a gravitational field in general relativity there do not exist extended inertial frames. Such frames can still be defined in any sufficiently small region of space and time, and the laws of physics - including the speed of light - will be consistent with special relativity when expressed in terms of that inertial frame, but we cannot generally extend that frame due to the curvature of spacetime, as explained above.

I notice that Duff's paper was rejected by the journal Nature, and it contains appendices in which the negative comments of Paul Davies, two referees, and some others are discussed. One of the referees says "Duff has already published his views on this issue in: M. J. Duff, L. B. Okun and G. Veneziano, JHEP 0203, 023 (2002). It is to be noted that the other two authors of this article do not appear to agree with Duff that it is 'operationally meaningless' to vary dimensional constants." In his response, Duff doesn't seem to dispute that his co-authors of the published paper disagree with him. (He simply points out that this doesn't imply he is necessarily wrong.) Since Duff's (rejected) paper is cited as the main reference for the FAQ, I assume it was eventually published somewhere, although I couldn't find it.

Duff's main thesis (the basis for his disagreement with Davies) is that there is no operationally meaningful distinction between increasing e or decreasing c, because only the change in the dimensionless constant alpha = e^2/hc is operationally meaningful. But in response to one of his critics Duff gives this example: "In Einstein-Maxwell-Dirac theory, for example, one could imagine units in which (at least) five dimensional constants, are changing in time: G,e,m,c,h..., but only two dimensionless combinations are necessary: μ^2 = Gm^2/hc and alpha = e^2/hc". (I've omitted some subscripts for typographical clarity.) But this seems to undermine Duff's claims, because if he grants that these two dimensionless constants are operationally meaningful, it would seem that changing c would be distinguishable from changing e, because c affects both of the dimensionless constants whereas e affects only one of them. So doesn't this imply that (contrary to Duff) we actually can distinguish between varying c and varying e? Of course, if we allow all five of the dimensional constants to vary, then any given changes in the two dimensionless constants could have a variety of explanations, but if we have it narrowed down to just changes in e and/or c, it looks like we could distinguish between them. Or am I missing something?

Last edited by a moderator: May 6, 2017
17. Jul 6, 2013

### phys12345

In "ON THE ELECTRODYNAMICS OF MOVING BODIES" by Einstein, there are the two hypotheses of his special theory of relativity, which are copied below

"1. The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of co-ordinates in uniform translatory motion.
2. Any ray of light moves in the “stationary” system of co-ordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body."

In my understanding, (i) any ray of light moves in the “stationary” system of co-ordinates with the determined velocity c, when the ray be emitted by a stationary body. ---- means the light speed is a constant in all directions (isotropic). (ii) any ray of light moves in the “stationary” system of co-ordinates with the determined velocity c, when the ray be emitted by any uniformly moving body. ---- means the light speed is a Lorentz invariant.

Therefore, in Einstein's second hypothesis the light speed is a Lorentz invariant constant.

18. Jul 6, 2013

### Staff: Mentor

I think you are misinterpreting it, but it certainly could be that I am. I cannot recall the subsequent derivation making obvious use of the constancy, only the invariance, but it could be something subtle I had missed.

In any case, there remain serious problems with attributing any meaning to the value of dimensionful constants.

19. Jul 6, 2013

### phys12345

In "§ 3. Theory of the Transformation of Co-ordinates and Times from a Stationary System to another System in Uniform Motion of Translation Relatively to the Former", to derive Lorentz transformation Einstein indicated in footnote 5 that

"The equations of the Lorentz transformation may be more simply deduced directly from the condition that in virtue of those equations the relation x2 + y2 + z2 = c2t2 shall have as its consequence the second relation ξ2 + η2 + ζ2 = c2τ2."

In both the moving and stationary frames, the same c is used, which means c is a Lorentz invariant constant.

20. Jul 6, 2013

### phys12345

They say that the global momentum and energy for an isolated system are conservative,which is a fundamental postulate in physics. According to the principle of relativity, the laws of physics are the same in all inertial frames of reference. So the conservation laws should be valid in all inertial frames.