[Kryptid (OP)]

For those who are unaware, the Australian dipole is the reported measurement that the fine-structure constant varies from one part of the Universe to another: https://en.wikipedia.org/wiki/Fine-structure_constant#Spatial_variation_%E2%80%93_Australian_dipole

The results have not been confirmed, as some attempts to look for such a variation have failed to find it. Let's say, for the sake of argument, that the dipole really is there. Wouldn't this be a potential method to determine objectively whether one is moving or is sitting still? If you had a very precise experiment aboard a spacecraft that was capable of continuously measuring the local value of the fine-structure constant, wouldn't a moving spacecraft measure a changing constant while a stationary one would not?

[Halc]

Wouldn't this be a potential method to determine objectively whether one is moving or is sitting still?

One can already do that now by measuring CMB isotropy. So the ability to do so doesn't particularly shake relativity.
It would still have interesting consequences. Fly your ship too far and its atoms can't exist anymore.

[Eternal Student]

Hi.

   I think Halc has said most of what is likely to apply.

   However, the fine structure constant influences electromagnetic force and this relationship seems to hold:
      the fine structure constant =

So that if some other properties like e (the fundamental electronic charge) are assumed to hold constant,  then c (the speed of light) must change.   Technically this isn't possible because of the way the S.I. metre is defined.   A metre is the distance light would travel in about 1/(3x10⁸)   of a second,  whatever that might be.   So if light "slows down" then what is officially happening is that the metre is getting shorter or the second is getting longer (but light is still covering the same number of metres per second).
   Anyway, if  the fine structure constant isn't constant across the universe then distances and/or times in SI units aren't what we thought they were.    This may force an adjustment to the formulae used in special relativity (but presumably also to many other formulae in common use).
    However, the old idea that special relativity implies that you can't tell the difference between two inertial reference frames is now recognised as being greatly exagerated and not at all necessary.   Special relativity implies (and therefore requires to be true or else SR is falsified) only that "the laws of physics" are the same in any two inertial reference frames.

   As Halc mentioned, the existance of a CMB rest frame at every point in space,  where the CMB would look isotropic as opposed to having some dipole,  can already be used to pick out one frame as being different from the others.

 - - - - -  What is a law of Physics?   -----
   I don't know....
   Deciding what is "a law of physics" as opposed to just a specific observation about how something looks in your frame of reference is an issue that could be debated.  For example, planet earth is round in some frames of reference but would be quite flat and disc like in some other frames of reference.  That sort of thing is just a specific observation, it's not a law of physics that the planet earth must be round.   To formalise the notion of what is a "law of physics" we could insist that they are always statements expressed in a covariant form.   So you could get away with saying that planet earth is a sphere in its own rest frame because that is something we can write an equation for in covariant form.   If you were using a different co-ordinate system perhaps derived from some other frame of reference then you would have to transform your co-ordinates and thus the shape of the planet you observe (and all being well, the law will then hold).   
    Many laws of physics are expressed with mathematical statements and it is reasonably possible to write these statements as equations in a covariant form  BUT not all principles of physics are like this.   It gets worse as you move further away from standard Physics to fringe areas like Chemistry.   By the time you're talking about Biology, well forget it.   I don't think you can express the priciples of evolution in equations let alone getting them in a covarant form.   So although "the laws of physics" is ideally understood to mean all scienitifc principles,  in reality many principles of science are just connections between two sets of observations that are extremely specific to one co-ordinate choice (and usually to one location in the universe - here on planet earth).
   Let's give one concrete example:   In Biology we know that some types of moss tend to grow on only one side of a tree.   This is explained by things like prevailing wind direction etc.   On a Cosmic scale there is a wind of particles from the CMB.  In some frames of reference the anisotropy of the CMB would be pronounced.   This means the wavelength of e-m radition from one direction could be harmful to life.  Could you change the side of a planet-like object that some life has developed on just by changing your own motion?    Anyway, hopefully you see what I mean.   It is not difficult to imagine that the anisotropy of the CMB radiation is potentially very important in developing some science and explaining the apparent connection between things.  However, any scientific principle based on this would be at best a law of science in THEIR frame only and nature would be under no obligation to follow the principle or law in some other frame.   So, for planet earth and where we deliberately look at the North and South pole (so that we can ignore the rotation of earth around it's own axis which prevents one side from always facing into the CMB wind),  then maybe you really CAN change the history of evolution and the distribition of life on the planet just by changing your own motion.

Best Wishes.

[paul cotter]

Fascinating ideas, Eternal Student, you should have been a theoretical physicist as opposed to a mathematician! Don't get me wrong, I'm not knocking maths.

[alancalverd]

- - - - -  What is a law of Physics? 

It's a statement about the observable universe that appears to be true in all cases. Unlike statute law, it is descriptive not prescriptive, but like statute law it can evolve in the light of experience.

Just as a matter of interest, why did you include π in your equation for α? ħ = h/2π. I thought mathematicians liked to reduce equations to their simplest form!

[Eternal Student]

Hi.

Just as a matter of interest, why did you include π in your equation for α?

   Lazy.   I just took the equation from the first source that came to hand.

There are many others that could have come to hand.   If you take the ratio of any two things that are relevant to electrons,  there is fair chance that is .   See this Wikipedia entry for examples:   https://en.wikipedia.org/wiki/Fine-structure_constant#Physical_interpretations

Best Wishes.

[SeanB]

If true then it will mean that SR is, like Newtonian physics, just a subset of a larger and more complex set of equations, with the large equations simplifying to SR when one of the components of it is either very large or very small, and thus dropping almost entirely into measurement noise of the experiments used to determine them.

After all F=MA is correct with small masses and small accelerations, but has a component related to C when either mass or the acceleration becomes a significant portion of C.

[Eternal Student]

Hi.

..... it will mean that SR is, like Newtonian physics, just a subset of a larger and more complex set of equations, with the large equations simplifying to SR when .......

     The spirit of this is fine.  It is almost certainly true and precisely what most scientists assume (with or without the Australian dipole observation).  I'm just not sure this particular observation brings many new concerns to the table.

Best Wishes.

[Bored chemist]

Fly your ship too far and its atoms can't exist anymore.

That raises an interesting point.
If there aren't atoms then what are we looking at?
Can we assume that it behaves like the atoms we are familiar with?
If not, how can we be sure that the observations  we make of these "not atoms" are actually telling us what we think they are?
But, if we can't be sure of that, we can't be sure they are telling us that alpha has changed.

Any experiment that tells us that alpha is (sufficiently) different elsewhere also tells us that we can't measure alpha at that position because we don't know what matter there is like.

[yor_on]

There are several things with the idea of the fine-structure constant varying. It builds on the speed of light, the charge on the electron, Planck’s constant, and the permittivity of free space. If one want to prove it astronomically it would be good to also define which of them, or combination of, that would be the instigator.  All of those mentioned are fundamental constants as far as I know, that we sort of found without having a explanation for why they must exist. The speed of light is what special relativity builds on so if that one varied with space or time, or both, it would become a problem in a 'global representation'. Even if, locally defined, still holding.

But it doesn't seem to be that way.

https://www.science.org/doi/10.1126/sciadv.aay9672

=

Thinking of it, it do become a problem as soon as you leave the local definition, so it's already here :)  It's a tricky one as one then first will have to define what a 'global speed restriction is', before stating that it have changed with 'time'. Because it's after all already a local definition, the speed of light in a vacuum.

A simple example is a far away observer, of a black hole, finding its 'clock' to 'tick slower'. If it does it also implies that the speed of light, according to that observer, must vary with his local definition. Or you can use NIST and GR for it.

I think it becomes a good argument for 'field theory' and possibly about dimensions, those we find and those that might 'exist', or 'not exist', aka the holographic model..