I Does Rest Mass Change if c Varies?

[jocarren]

I'd like to ask an specific question. If c changes (for whatever reason*), does the rest mass of a given particle changes, asuming E is conserved?

Let's say, for a given particle, the following initial condition:

• Placed in a vacuum**.
  
• Rest mass m₀.
  
• Particle's energy E.
• Propagation speed of light in vacuum c₀

We have that:

E = m₀c₀²

m₀=E/c₀²

If, for any given reason, the speed of light in the vacuum changes** from c₀ to c₁. Asuming E is conserved, for the same particle we have a new mass m₁:

m₁=E/c₁²

Then,

m₀ ≠ m₁

(*) The reason why c changes is beyond the scope of this question, as it is pure speculation and violates the rules of the forum. It could be a variation of the vacuum state, or any other hypothetical scenario.
(**) However, I am considering a variation of c as the propagation speed of light in vacuum, not in any given material medium. I am aware that the mass of an object does not change if it is immersed in a medium that also slows down the propagation of light. This particular scenario is beyond the scope of this question, since the slowing down of light in a material medium is a macroscopic phenomenon which, at a fundamental level, is also determined by the properties of vacuum (there is still vacuum between the atoms and fundamental particles of any material medium that refracts light).

 

[Dale]

The idea of c changing is physically meaningless. All it would mean is that your units are a function of time.

What you are probably actually asking is if the fine structure constant were changing.

 

[jocarren]

That is pretty much what I'm asking. I constrained it just to c, because changing the fine structure constant would affect many more things (actually, all of them) and I'm only interested in mass (and also, because I'm not a physicist and I get a lot of things wrong, I really thank you for trying to look for the core question beneath my misconceptions).

Also, I'm thinking no only in a variation over time, but a variation on space as well: could a different fine structure constant in another region of space "define" a different mass for the same particle?

 

[Dale]

That is pretty much what I'm asking. I constrained it just to c, because changing the fine structure constant would affect many more things (actually, all of them) and I'm only interested in mass

So let me explain a little bit of the issue I am addressing and then go on to answer your question as best as I can. The constants with units, like c and h, don’t actually provide any information about physics but only about our system of units. The information about physics is contained in dimensionless constants.

http://math.ucr.edu/home/baez/constants.html

So, now to answer your question, in SI units or in other similar systems there is the relationship $2h \alpha = \mu_0 e^2 c$. So you cannot change only one of these quantities, you must change at least two. Suppose, for example, that c were doubled and h were also doubled and all the rest unchanged. Even though c doubled, because the fine structure constant, $\alpha$, is unchanged the change in c would be completely undetectable. No measurement would detect any change in the physics, we would just use different numbers.

In contrast, suppose that c doubled and $\alpha$ doubled. Now, since $\alpha$ has changed there would be measurable physical differences. Physically, the electromagnetic force would be stronger. Electromagnets would produce stronger forces with the same current. Nuclei would hold electrons tighter. The repulsive EM forced in a nucleus would be stronger so different isotopes would now be radioactive, etc.

I'm thinking no only in a variation over time, but a variation on space as well:

Per Noether’s theorem, a universe in which the fine structure constant varied in time would not conserve energy. And a universe in which the fine structure constant varied in space would not conserve momentum.

 

[jocarren]

Thanks for your answer :)