# Could a non-relativistic universe be logically consistent?

As I understand it, the principle of relativity was accepted from Galileo until Maxwell, whereupon the equations which predict constant speed of light imply a preferred reference frame in a Euclidian space, suddenly making relativity testable.

The Michelson–Morley experiment showed that light speed was constant in all reference frames, ergo Maxwell, relativity, or Euclidian space had to be wrong.

As it turns out Euclidian space is what broke, and moving the equations of physics to Minkowski space allowed us to preserve constant light speed and the principle of relativity (although relativity implies some surprising things in Minkowski space, nevertheless it's merely a logical consequence of the geometry).

Suppose we changed something else instead?

Would physics still make sense if the Michaelson-Morley experiment had shown that light speed was not constant in all reference frames?

• i.e. would everything else still be logically consistent, perhaps with some tweaks, and hence the universe would have a sense of absolute space and time? What would be the consequences of this?

I guess another model universe could have no preferred reference frame but that would imply non-constant lightspeed. Is this a logically consistent hypothetical physics?

• I imagine that would imply a change in the assumptions underlying Maxwell's equations, but my physics isn't good enough to follow this line of reasoning through. What would we have to adjust to make this work, or is it nonsense?
• Related (and possible duplicate) – overactor Jan 11 '15 at 19:44
• Are you asking if it we could have a have a consistent theory of electromagnetism and classical physics if we dropped the principle of relativity, and assumed Maxwell's equations are only correct in a preferred frame and have to be modified by a Galilei transformation in other frames? If so the answer is yes, this is just the luminiferous ether theory. But if you're asking if we could preserve relativity but have a non-constant light speed, I think the answer is no. – Hypnosifl Mar 10 '16 at 13:35
• I discovered I could write down valid kinematics in which this is true; but the headaches are real. Maxwell holds if you assume that it's valid in the source reference frame rather than the observation reference frame. The uglyness comes in elsewhere. – Joshua Sep 21 '16 at 21:47

From what I have been lead to believe, there was a non relativistic universe model which we used after Maxwell. It had a large number of "correction" terms which resulted in varying speeds of light. The proving power of Minkowski space was not that it was "more correct," but that it baked all of those correction terms into the space. It was found that this was a more convenient way of thinking about the problem, so we ran with it. Our universe is not defined to be a Minkowski space, but rather we have found the laws to be simplest if we map our models into a Minkowski space. This is the same argument for saying "the Earth was never flat, but we found the laws of navigation to be simplest if we map our models onto a flat surface."

As for a world where there actually is a "preferred" frame of reference for light, it would likely have little impact on the world. Given that we could not measure the speed of light until Maxwell's era, and the fact that the universe doesn't even seem to be very dependent on this speed, I would not expect much to change.

As technology advances however, this ether like behavior might have a large effect. As we become more and more enamored with things that move at the speed of light, being able to measure things with precise timing would be an issue. Atomic clocks would have to synchronize to account for their rotation within the ether. There would be a preference for building structures in the ether frame whenever possible, making calculations easier. Eventually there could be a galactic building crunch, as everyone tries to align themselves with the ether.

• A bit of a nitpick, but mapping from the surface of a sphere to a plane makes some things more complicated. Distances get distorted, and the shortest path between two points is usually not a straight line. But I suppose this could actually extend the analogy, since it works well enough on "everyday" scales, just like classical mechanics. – KSmarts Jan 13 '15 at 16:56
• "we could not measure the speed of light until Maxwell's era" Not true, Ole Rømer measured (with limited accuracy, of course) the speed of light almost 200 years before Maxwell's Laws, and even before Galileo had proposed an experiment to measure it – Bosoneando May 2 '15 at 14:01
• @KSmarts yes, it does make things more complicated, in cases where your process pushes the model to the limit, which is true of any model which is designed to be simpler than reality. If it seems more accessable, I might instead change that to talking about rotating vs. fixed frames which is probably a hair closer to a "similar" situation. I just felt maps were more accessible than explaining the Coreolis effect. – Cort Ammon May 2 '15 at 17:32
• @Bosoneando From what I understand, it was not understood that the speed of light was constant in all reference frames until roughly 1900, which is the strange behavior that lead those like Einstein towards a relativistic model. If I add verbiage to point towards this being the special part, will that help clarify what you are seeing? – Cort Ammon May 2 '15 at 17:35
• @CortAmmon Having the ability to measure the speed of light and knowing that is constant in all reference frames are two completely different things, and you seem to mix them up. And in its 1905 paper, Einstein talked only about thought experiments, he didn't reference any experimental results. It is not clear if he knew the Michelson-Morley experiment and was inluenced by it. – Bosoneando May 2 '15 at 18:04

By "non-relativistic" I assume you mean Galilean relativity. That is, a universe with no weird high-speed effects, where changing reference frames is as simple as adding velocities and there is only one universal time.

The reason Galilean relativity was the prevailing theory at one time was that it is an extremely close approximation to reality at the low speeds we deal with. In order to make it exactly true, then all speeds must be small compared to the speed of light. In other words, the speed of light is infinite.

Just take all our physical laws, and take the limit as $c$ goes to infinity. Then the factor $\beta=v/c$ is always zero, and the factor $\gamma=1/\sqrt{1-\beta^2}$ is always 1. This means there is no time dilation or length contraction.

This universe is logically consistent, but due to the infinite speed of light there would be no electromagnetic radiation as we know it. I'm not sure what implications this has, but you can probably handwave those problems away.

## Details (Update)

Maxwell's equations implicitly involve the speed of light (they must, since they are what govern electromagnetic radiation i.e. light). The key one to consider is Ampere's law:

$$\nabla\times\mathbf{B}=\mu_0\epsilon_0\frac{\partial\mathbf{E}}{\partial t}$$

It so happens that the product of the constants in that equation is related to the speed of light:

$$\nabla\times\mathbf{B}=\frac{1}{c^2}\frac{\partial\mathbf{E}}{\partial t}$$

This means that if $c$ is infinite, this equation becomes:

$$\nabla\times\mathbf{B}=0$$

That is to say, instead of electrodynamics we have magnetostatics, under which conditions no waves exist.

Another way to think of this is with the relationship between frequency and wavelength:

$$\lambda f=c$$

If $c$ is infinite, this equation can only be satisfied is if the frequency or wavelength (or both) are infinite. Since infinite frequency makes no physical sense, we must conclude that all waves are infinitely long: that is, that there are no waves at all.

• Why do you say "no electromagnetic radiation" and not "infinitely fast electromagnetic radiation"? – spraff Apr 24 '15 at 16:41
• @spraff Does that help? – 2012rcampion Apr 24 '15 at 17:08
• That would imply that mass has infinite energy by e = mc^2. It seems like that might result in... interesting side effects to the output of fission and fusion. – Dan Smolinske Apr 24 '15 at 17:25
• @Dan or it might imply that all matter has zero mass. Either way, I bet the same sort of troubles would happen with the strong force, so there may not even be composite baryons like protons and neutrons. Setting an infinite speed of light breaks all known physics. But the question was about whether it could be logically consistent, not consistent with our current models of physics, so I left those points alone initially. – 2012rcampion Apr 24 '15 at 17:29
• @DanSmolinske Fission and fusion? You get mass loss even with chemical reactions! – Loren Pechtel Apr 24 '15 at 22:56