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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.

Qmechanic
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Liam Wasserman
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5 Answers5

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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.

BillyTheSquid
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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, and since special relativity is contructed around this preposition, they don't break the rules - 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.

Rye
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(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.

Abhimanyu Pallavi Sudhir
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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...

Alex
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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.

See: The rest mass of a system of two photons

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

safesphere
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