Changing speed of light.

[Petrel]

I'm not typically a math-oriented person, but I decided I ought to do some looking into the possibility of a varying speed of light. I found an interesting article which unfortunately is not going to be available on the web to everyone.

Ellis, George; Uzan, Jean-Philippe. "c is the speed of light, isn't it?" Am. J. Phys. 73 (3), March 2005, 240-247.

I'm sure that's not the proper reference format for physics, but it has all of the necessary information.

Basically a varying value of c is a popular idea among secular physicists as well as creationist scientists. This article examines the significance of varying c, starting with the question of "Which c is varying?" They describe four different types of c's:

cEM, the electromagnetism constant (speed of light in a vacuum)
cST, the spacetime constant (the actual c in E = mc^2)
cGW, the speed of gravitational waves in a vacuum--whoa! I didn't know there was an official consensus on this, but these authors say that typically cGW = cST according to general relativity, and if we change the value of c this relationship may change.
cE, the Einstein space-matter constant, which is equal to cST by general relativity, but will not be if c is changed.

If we wish to formulate a theory in which the speed of light is varying, the first step is to specify unambiguously which of the speeds that we have identified is varying, and then to propose a theoretical formulation, that is, a Lagrangian, to achieve this goal. There is no reason why after relaxing the property of constancy of the speed of light, the different facets of c described in this section will still coincide. It is important to clearly state which are the quantities that are kept fixed when one or another aspect of c is assumed to vary (see, for example, the discussion in Ref. 43).

We see from this example that when a constant becomes a dynamical field, we need to derive new equations of evolution. In particular a new equation describing the propagation of the new degree of freedom of the theory will have to be obtained. The best way to construct such a theory is to build a Lagrangian with a corresponding new degree of freedom included ab initio and derive field equations by means of a standard Lagrangian variation. In particular, such a formulation allows us (1) to determine the true degrees of freedom, (2) to check if there exists negative energies or acausal propagation of some modes in the theory, (3) to give a complete and self-consistent description of the dynamics by providing the dynamical equation for the new variable, and (4) to give a clear specification of what we call the stress-energy tensor (For instance, the example of the Appendix resulted in the appearance of both Tmn and T˜mn , whose physical meaning is now ambiguous, and it is very important not to decide a priori what we call energy, for example.) In addition, we can check if the equations are consistent, which will follow if they are all derived from the same Lagrangian by the standard universal method, which extremizes the specified Lagrangian under all small variations (in contrast to Refs. 7–10, where nonstandard variation schemes were used).

This is a list of very stringent criteria! No one has yet formulated a theory of a varying speed of light that is internally consistent in these ways. This is something that will need to be done if any of the c-decay based creationist models are to be taken seriously.

 

[Paul of Eugene]

On my own personal web site I have posted some illustrative material showing how astronomers are able to measure the rotation of galaxies:

http://www.epud.net/~richmond/science/grotate/grotate.htm

The material dates back to 1963! But the basic principles and findings have not changed since that time. The reason is, spectroscopice observation of galaxy rotation is actually a very easy thing to do. It also tells us something about the speed of light.

You all know what happens if a medium such as a record on a record player or a tape going through a tape recorder changes speed from the time it was recorded. Instantly the whole song or speech or whatever slows down or speeds up, exactly in agreement with the change in the speed of the medium! Well, exactly the same thing would happen if the light speed changed. In particular, if, as postulated by some, light speed changed so much as to allow for light to have once travelled so fast as to get here in just 6 to 10 thousand years, and then slowed down so that it is travelling now as if it would take 10 to 20 billion years to get here from there, then the physical processes shown by that light would also appear to have SLOWED DOWN. The light, you see, taking the place of the slowing down tape in a tape recorder or the record on the record player* .

Well, the rotation of the galaxies, being a kind of motion, would also appear to slow down.

Spectroscopic observations such as that posted above show that galactic rotation does not appear to be slowed down, no matter how far away we view the galaxies.

This observation places severe limits on how much the speed of light may have changed over the major part of the lifetime of the universe.

As you stated, physicists remain highly interested in testing the constants as we know them, hoping against hope they can find something that will make them famous or turn up some new phenomenon, but they don't have any successes to report on this issue.

* For the younger readers, a record player was an electronic device that mechanically spun a disk with a long spiral groove in it that would mechanically vibrate a small needle, and that needle's vibration would be amplified into sound, including speech and music. The standard speeds for the disks were 33 1/3 rpm or 45 rpm or 78 rpm, and it was a fun thing to do to play the record at the wrong speed.

 

[Paul of Eugene]

As long as one is talking about "changing the speed of light", let's ask - changing it in relation to what? What would it MEAN to have a different speed of light?

There are four known forces in the universe. Gravitation, Electro-Magnetic, Strong Nuclear, Weak Nuclear.

The Strong Nuclear force binds protons and neutrons (actually the constituent quarks) together to make the nucleii of atoms. It is opposed by the fact that like electric charges repel like electric charges. SO all those protons getting together repel each other yet attract each other. In today's world, the electric repulsion starts to really get the upper hand at about the size of the uranium atom, which explains why we can give that atom a nudge and have it split.

Light is propagated strictly by electromagnetic forces acting in space. If it becomes faster, then the electromagnetic force becomes stronger in relation to the other forces.

oops, there goes the stability of our atoms. We all blow apart. Hmmm. Better not do that . .

So we keep light and strong nuclear force together but vary them in relation to the gravitational force. Well, that would be equivalent to making gravity weaker. Hmmm - can't do that, we'll be falling off the earth, earth won't be held in its orbit, the sun won't hold itself together so tightly and will expand and go away . . .

Well, lets not go that route. Well, if all the forces stay the same strength in relation to each other, then light speed won't change.

The weak force? It is involved in some obscure kinds of radioactive decay, varying it up and down in relation to the three others would probably not make a lot of direct difference to us but it would not be interpreted as a change in the speed of light, rather a change in the way radioactive decay occurs.

 

[UTEOTW]

Paul

YOu are always more knowledgable than I am when it comes to relativity. I have a question.

I was poking around the other day and I came across something. I found something that said that the curvature of spacetime that defines an orbit is proportional to v/c where v is the velocity of the object in orbit.

Now Barry has always claimed that orbits would have been unaffected by a changing c. But if this is correct, it seems that they would have been altertered.

Here's the problem. First off, the reference was from Flandern who is a bit of a kook. Second, I don't know enough about this issue to judge. But you might or might be better at tracking down something like this.

 

[Paul of Eugene]

Well, I'm not all that great with relativity myself, especially when it comes to general relativity (which brings the gravity and space time curvature into the discussion) . . .

But I think most orbits we deal with are of objects orbiting at velocities low enough to not have a lot of variation that would matter for our purposes. For example, the recession of mercury's orbit would presumably be altered by a Setterfield type change in light speed velocity, but not the gross characteristics of the orbit itself.

On the other hand, relativity theory proposes that the bending of light by gravity is influenced by the speed of light. Specifically, Einstein's general theory of relativity proposes that light will bend in a gravity field exactly twice as much "as predicted by Newtonian physics", that is, twice as much as if one calculated with Newtonian physics how a PARTICLE would be deflected as it cruised by a gravitating object at c.

So Setterfield Physics, coupled with Einstein's theory of relativity, should predict a much smaller deflection in the lensing of light from galaxies than we see at this time, given that the light speed as the light cruised by the lensing galaxy was supposedly much higher at the time it cruised by.

 

[Magnetic Poles]

I am not a scientist, but no reputable scientist I know of accepts any change in the speed of light.

Since the relative speed of light is the same no matter how fast one is traveling, it would seem to me to be a constant. And as Paul has pointed out, there are numerous other problems that present themselves if you accept Mr. Setterfield's hypotheses.

 

[Petrel]

From my reading in varying speed of light (VSL) theories, the theories aren't proposed because of any experimental evidence showing a dropping speed of light, but because an initial very rapid speed of light that dropped immediately is an alternative means to the inflationary universe at solving the following problems (which I will link to because I don't understand them well enough to trust my explanation would be accurate!): the horizon problem, the flatness problem, and the monopole problem. It is also supposed to solve the cosmological constant problem, which the inflationary universe theory does not correct.

An article that I'm reading right now that I can barely understand at all

exposes some problems with VSL theories. The first problem is the isotropy problem (solved by rapid expansion in an inflationary universe) in which the VSL theories predict background radiation to not be constant in every direction.

There are several ways in which the VSL effects on anisotropy can be understood more physically. The naive VSL theories preserve the metric structure of spacetime so that gravitational-wave propagation still occurs at a maximum possible propagation speed. But light propagates with a variable speed that is less than or equal to the gravitational-wave propagation speed. Thus one can see that anisotropies that are carried by long-wavelength gravitational waves can avoid being made innocuous by a fall in the speed of light. The generic anisotropies at late time in ever-expanding Bianchi types that contain isotropic Friedmann universes are of this type.

~continued below~

 

[Petrel]

The second is the inhomogeneity problem, which involves the "spectrum of primordial fluctuations," the wavelengths seen in the background radiation.

In a finite time interval of c variation in a VSL theory that solves the flatness or lambda problems the expansion dynamics will be dominated by the usual Ma−3γ term. If the expansion is radiation dominated then no special inhomogeneity spectrum of the constant curvature form will be created by the VSL evolution. One way of imprinting a characteristic spectrum could be via the sudden phase transition model of VSL favoured by Moffat and Albrecht and Magueijo. Here, it would need to be shown that a constant curvature spectrum results. Again, this is a major challenge because the phase transition models of inflation achieve a constant curvature spectrum of fluctuations by virtue of their proximity to a de Sitter state in the vacuum state where the scalar field stops rolling.

The next is an interesting problem, the massive particle problem. Basically if a particle of mass M with a horizon ~ ct and a de Broglie wavelength lambda = Planck's constant/(M*c), under certain conditions the horizon may balloon out uncontrollably so the particle essentially becomes its own universe.

Note that this behaviour of massive particle states ceases when the VSL evolution ends and will not be going on in the universe today. Since the early universe may contain a population of massive states nside the horizon scale when VSL evolution begins, the ensuing evolution is not dissimilar to the self-reproducing inflationary universe. There small regions create eternal inflation due to the quantum evolution dominating the classical slow roll under fairly general conditions. The rapid expansion of many VSL regions would produce collisions that might lad to unacceptable levels of inhomogeneity when they subsequently re-enter the horizon if the amount of expansion was small. But if it was large then we could find ourselves inhabiting a single VSL pre-expanded domain. This scenario may repay further detailed analysis.

~continued below~

 

[Petrel]

There is a similar situation with primordial black holes, in which the black hole horizon grows faster than the particle horizon and the black hole turns into its own universe. There is also the possibility that varying c might prevent black holes from forming, or that if a black hole formed when c was constant it might not be affected by an outside change in c.

The final problem is in entropy, where calculations show in a VSL universe entropy might tend to decrease with time instead of increasing.

Thus the solution of the flatness an lambda problems can require this entropy measure to decrease with increasing time. The Bekenstein–Hawking entropy technically applies only to event horizons but many analogous measures of ‘gravitational entropy’ have been proposed and it is possible that the argument framed here will have application to any better-motivated measure of gravitational entropy. This worry also besets arguments like those of Davies et al. [35] which use black hole thermodynamics to assess whether the variation of certain constants are in accord with the second law of thermodynamics. The difficulty is that the required
black holes and their thermodynamic will only exist as particular solutions of a theory with varying constants—particular solutions in which those varying constants take constant values—and so the argument cannot be carried through.

All in all, VSL theories are a problematic proposal!

These quotes are from:

Barrow, John D. "Unusual features of varying speed of light cosmologies." Physics Letters B, 2003, 564, 1-7.

 

[Paul of Eugene]

I don't think it would be possible to have a changing speed of light scenario and still have a conservation of energy situation in physics. It is somewhat anologous to living in a situation where currencies fluctuated in relation to each other. If you know how they are going to fluctuate, you can time your currency exchanges just right and get rich just for swapping money from one dollars to (euros? pesos?) and back again at the right times. In the same way, if you know how the light speed is going to change, you might convert all your energy into electric charges on one occasion, potential gravitational energy on another, and play them off each other to gain free energy.