# Proper time=0 is nonsense?

It looks to be related, but there's only so far you can push the comparison. Bell's Spaceship paradox is at heart a relativity of simultaneity problem within a flat local region; this cosmological question is about comparisons of coordinates across non-locally curved regions.
Thanks. That caution makes sense to me (I'm glad).

Hope it's okay to clarify my understanding in context. Is it correct to say the curvature between coordinates in the cosmological question is described, accounted for, by the second term of the FLRW solution to the GR field equations, an equation taken as a model of the shape of the our 4d universe?

${ -c }^{ 2 }d{ \tau }^{ 2 }={ -c }^{ 2 }d{ t }^{ 2 }+a{ \left( t \right) }^{ 2 }d{ \Sigma }^{ 2 }$

And is t in that FLRW equation the coordinate time of a frame co-moving (at rest) with respect to the CMB? Or rather, what is that t?

 Sorry, maybe that should be a separate thread. I just wouldn't have the question if I wasn't trying to follow this one.

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ghwellsjr
Gold Member
Along the same lines as the OP, I've wondered if some sources object to the application of proper time to a photon because of these definitions:

a photon follows a light like path,

proper time is the time of an inertial clock along the path of an object,

"In relativity, proper time is the elapsed time between two events as measured by a clock that passes through both events.... [Wikipedia] [In fact I thought the clock had to travel the path of the object.]

and these definitions conflict?

That is, you can't have a massive clock travel at light speed.

Or is there a way around the apparent conflict?
Wikipedia's article on Proper Time makes it clear that the clock has to follow the world line, that is, it has to travel the path of the object, so I don't know where you are seeing a possible conflict. Where did you get that quote?

Just so I dont open another thread.

If the photon doesnt have a referential frame, and relativity says the laws of physics are the same in all referential frames, cant one say that the laws of physics are ...not...the same for the photon ?

Just so I dont open another thread.

If the photon doesnt have a referential frame, and relativity says the laws of physics are the same in all referential frames, cant one say that the laws of physics are ...not...the same for the photon ?
the photon doesnt have a referential frame is a law of physics.

jbriggs444
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the photon doesnt have a referential frame is a law of physics.
That's pithy but does not ring true. Maybe it's just my mathematical background showing through.

The principle of relativity seems to be a kind of "second order" law of physics. First order laws are valid within a particular frame of reference and specify the behavior of objects and phenomenon referenced against such a frame. But the term "frame of reference" is not even part of the first order language of physics. It is a second order concept.

Asking that the principle of relativity apply to second order concepts brings in the possibility of self-reference which is probably better avoided.

From what I know, the laws of physics being the same in all referential frames is usually interpreted with specific examples where if in one frame a rope breaks that means that it must break in all other reference frames, so I'm trying to understand how does a non-existing referential frame agree with the fact that in our reference frame the photon has certain laws.

jbriggs444
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From what I know, the laws of physics being the same in all referential frames is usually interpreted with specific examples where if in one frame a rope breaks that means that it must break in all other reference frames, so I'm trying to understand how does a non-existing referential frame agree with the fact that in our reference frame the photon has certain laws.
The claim that "the laws of physics are the same in all inertial reference frames" entails no prediction whatsoever about what the laws of physics are like in non-existent reference frames.

entails no prediction whatsoever about what the laws of physics are like in non-existent reference frames.
So then how come we from our frame of reference know or are so convinced that our laws of the photon are true ? (I sense maybe its a stupid question but I had to do it)

Ibix
The principle of relativity itself implies an invariant speed. If that speed is infinite you get Newtonian physics. If it is finite you get relativistic physics.

See http://arxiv.org/abs/physics/0302045.

jbriggs444
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So then how come we from our frame of reference know or are so convinced that our laws of the photon are true ? (I sense maybe its a stupid question but I had to do it)
Our laws are our laws. They apply to all objects, including photons. How a hypothetical photon would make up a hypothetical law of physics to hypothetically describe how things look from its hypothetical point of view is irrelevant. The photon is not telling us what it sees.

Nugatory
Mentor
Just so I dont open another thread.

If the photon doesnt have a referential frame, and relativity says the laws of physics are the same in all referential frames, cant one say that the laws of physics are ...not...the same for the photon ?

No, because when someone says "the laws of physics are the same in all reference frames", they are being a bit sloppy with the English language. It would be more accurate (but sounds clumsier, which is why we don't often say it this way) to say "The law of physics produce the same results no matter what reference frame you use to assign times and positions to events". Phrased this way, it is clear that the aws of physics apply to everything, whether we can find a reference frame in which it is at rest or not.

Ibix