# Varying constants in special relativity [closed]

The first thing you learn in special relativity is:

1. All "inertial" frames of reference are equivalent.

2. There is a frame - invariant speed limit, usually called speed of "light."

So, geometry is a very useful way to think about relativity. Wheeler even coined the term "geometrodynamics." My real question is, is it possible to change special relativity ever so slightly so that the 2nd postulate, the frame-invariant speed limit, is a consequence of the spacetime itself? And if this is true, would the frame-invariant speed be dynamic if spacetime itself was expanding?

Edit: I'm not making the rooky mistake of attaching a frame of reference to light, apologies if i didn't make that clear enough.

## closed as unclear what you're asking by Ben Crowell, Mike, Buzz, WillO, John RennieJan 19 at 7:08

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• The latest experimental evidence suggests that neutrinos do have mass (a very small one). – Lewis Miller Jan 18 at 19:16
• What about a scale - invariant mass generating mechanism? – Liam Wasserman Jan 18 at 19:21
• When you go to general relativity, you learn that because (presumably) everything has mass, there is no such thing as a perfect inertial frame of reference. What do you mean by this? Neutrinos do have mass, and in any case massless objects don't have frames of reference associated with them, so this doesn't make much sense. BTW, your user icon is currently mired in a political cesspool, so IMO it's a bad choice. – Ben Crowell Jan 18 at 20:02
• I second everything Ben says, including the last part. Also, the second point is not correct; there is an invariant speed limit, but there is no associated frame. – Mike Jan 18 at 20:20
• What is a "perfect inertial frame of reference"? – WillO Jan 19 at 6:42

A few quick clarifications here. Frame-invariance is a property held by constants, not by reference frames themselves. It means that, from any inertial reference frame, that constant or value is observed to be the same. I see light moving with the same speed (in a vacuum, of course) as someone traveling at half the speed of light relative to myself. Some other constants, such as the charge of the electron, are also invariant to the "boosts" described in relativity.

There are also plenty of things that do not have mass, in the inertial sense. Photons do not, as well as gluons (okay, that's two, not plenty. Sorry.). But neutrinos do. This has been experimentally confirmed because they oscillate as they travel (a complex phenomenon that I am not the one to explain). If they do this, they experience time. And if they experience time, they have mass.

Now it's important to note that an object's mass does not preclude it from experiencing an inertial reference frame! In fact, some will argue that having mass (and thus travelling slower than light speed) is necessary to have an inertial reference frame. Anything not being acted upon by a force (recall that gravity does not count here) is in an inertial reference frame. I'm not sure what you mean by a "perfect" reference frame, but these are certainly as good as any other.

If you want a solid resource to learn SR in more depth, I highly recommend a text such as Taylor's and Wheeler's Spacetime Physics.

Please feel free, anyone more experienced with GR, to correct any mistakes I have made.

• Yes I know.. I’m not saying that light is a frame of reference, I’m saying that the constant varies depending on the geometry of space and time, which happens to be a de - Sitter space for us. – Liam Wasserman Jan 18 at 21:14
• @LiamWasserman Ah, my apologies. I was not trying to insinuate that you had said that lightspeed was a valid frame of reference. I haven't encountered variation in the speed of light before; perhaps you could direct me towards a source? I'd love to fill in the gaps in my own knowledge. Otherwise, I hope that my response has helped answer at least some parts of your query. – BillyTheSquid Jan 18 at 21:21
• No, I’m sorry for being rash... people were getting confused about me saying that light is a valid reference... I think a few mathematicians have had this idea before? I’m not sure – Liam Wasserman Jan 18 at 21:36
• @LiamWasserman People are harsh sometimes. At least your question is still up, I got told to delete my first one within two hours of posting. My apologies, and better luck next time. – BillyTheSquid Jan 18 at 21:44

(presumably) everything has mass, there is no such thing as a perfect inertial frame of reference

This isn't right. "There isn't generally a perfectly flat co-ordinate system" does not imply everything has mass, and being an inertial reference frame has nothing to do with the associated observer's mass (in fact, the Lorentz transformation associated with a photon's "co-ordinate system" is singular, so there isn't really a co-ordinate system/reference frame associated with it).

I guess your concern is with the fact that photons are affected by spacetime curvature -- this is true, but the/a point of general relativity is that this doesn't imply anything about the mass.

• Yeah, that’s a way better way to word my question, I think people are getting upset at the (admittedly) really horrible way I phrased this question. Sorry, I’m just getting really into the whole modern physics thing. Also, about my profile pic, my little brother changed it to that without me being aware. – Liam Wasserman Jan 18 at 20:49
• I didn't complain about your profile pic. – Abhimanyu Pallavi Sudhir Jan 18 at 23:45

Neutrinos do have mass (although you are right, initially it was thought that they didn't) just an incredibly small one, when compared to the mass of a proton, for instance.

There are only (as far as we know) two massless particles: photons and gluons. But since gluons are always confined within other particles (hadrons, such as the proton and the neutron) we can't observe their behaviour as free particles. As for photons, they don't come with any rest frame, according to special relativity itself, so they don't "break the rules". In fact, they make the rules.

If you still want to know more about this topic, take a look at: Is a photon really massless? and related posts.

Hope I helped!

I see problem with used terminology 'There is a frame - invariant speed limit, usually called speed of "light."' Sorry, speed of light is not a frame. Perhaps you should reformulate the question.

What might help to find the answer is the following fact: any massless object is bound to move with a speed of light, therefore changing frames for them does not do much - it'll keep moving with the same velocity...

• I specified frame - invariant though? I thought that’s how you say “it’s not a frame.” – Liam Wasserman Jan 18 at 20:47
• @LiamWasserman To the best of my knowledge, the term "frame-invariant" in special relativity means that the speed of light, as calculated by anyone in any inertial reference frame, is the same. The charge of the electron is also frame-invariant, alongside a few other quantities. – BillyTheSquid Jan 18 at 20:59
• What i’m Trying to say is that the “speed of light” is dependent on the geometry of space and time. We live in a de - sitter space with a positive cosmological constant, which means that the “speed of light” is very very slightly changing over time. – Liam Wasserman Jan 18 at 21:03
• @LiamWasserman The speed of light does not change in deSitter space, or in any other spacetime, at least not according to General Relativity. At every point in spacetime (other than a singularity), spacetime looks locally like Minkowski space. – G. Smith Jan 18 at 22:29
• The path a “particle” takes according to the principle of stationary action is should be affected by space time geometry, if the geometry is changing the optimal path is changing, right? – Liam Wasserman Jan 18 at 23:15

A single massless particle does not have a frame. However a system of two (or more) massless particles (with non-colinear trajectories) do have an inertial frame and invariant mass. It is a bit counterintuitive, but the combined mass of two massless particles generally is not zero.

Note that this frame does not move with the speed of light.