# Speed of light in a comoving frame

1. Apr 20, 2004

### Peterdevis

The speed of light in vacuum is c in all frames, but is it also in comoving frames?

2. Apr 20, 2004

### turin

Does "all" include "comoving?"

3. Apr 21, 2004

### hemmul

I doubt there is no co-moving frame defined for light:
Reference Frame is defined as a material object, which is associated with the axes and so on... but there is no material object moving with c...

4. Apr 21, 2004

### Peterdevis

That's my question!

The frame I mend is not the lights frame.
Furthermore a reference frame is a matimatical object non material.

5. Apr 21, 2004

### JJ

You couldn't mesure c if you were going at c, since distance and time would be meaningless for you. And if you apply the Einstein Velocity Addition (which might not be suitable for this, I guess this is only for kicks), you get c if you're heading straight for the light and infinite if you're going in the same direction.

6. Apr 21, 2004

### hemmul

Which one then?
in any RF c is ~3e8 m/s

remember a picture of space-time involving light cone? boost makes t,x,y,z axes approach the surface of the cone. Roughly speaking when v==c, x and t axes merge each other. So the basis of 4d space is not orthogonal => in this case you can't speak about a proper RF...

hmm...

7. Apr 21, 2004

### turin

I think I get your question now.

c is NOT the same in all frames! It is the same in all inertial frames. A frame, K, moving at c wrt an inertial frame is not itself an inertial frame. Therefore, K does not contain the notion of a constant c.

8. Apr 21, 2004

### Eyesaw

Why not? The definition of inertial frames are frames that are moving at constant velocity relative to one another. Why should a frame moving at the constant velocity c not be an inertial frame? It's irrational to restrict apriori c as a limiting velocity for motion through space. Remember Einstein's "relativity of simultaneity" argument that the observer M' inside the train will detect the light from B earlier than the light from A, even though the lightning flashes at A and B happened simultaneously (Chapter 9 Special RElativity, read carefully). This of course cannot happen if relative to M's rest coordinates, light did not travel at c+v from B and c-v from A.

Last edited: Apr 21, 2004
9. Apr 21, 2004

### turin

Not true. The definition of an inertial frame is one in which massive objects move uniformly in straight lines in the absense of forces. It is quite an obscure definition in itself, but can be understood concretely.

Because it is not inertial. It is mathematically valid, but not physically realizable (as far as I know) from the rest frame of a massive object.

I agree. But this is not the state of affairs. After strong resistance by physicists in the 19th and early part of the 20th century (physicist for whom I indeed hold a distant repect) the inertial frame invariance of c has been repeatedly demonstrated. Are the demonstrations absolutely conclusively? Of course not.

Did you mean the translated and published work of Einstein, Relativity? If so, I suggest you do the same, while also carefully considering the context. Chapter 9 is by no means intended as a conclusion.

Last edited: Apr 21, 2004
10. Apr 21, 2004

### Peterdevis

Excuse me gentlemen,

I'm not interrested in a fight of Relativity is right or wrong.(There are a lot of threads where you can do that)

So I repeat my question "What is the velocity of light in a comoving frame"

Comoving frame = the frame in an expansional universe where a non moving object (wrt the frame) maintains the same metric coördinates throughout expansion.
for example the Robertson-Walker metric coördinates

11. Apr 21, 2004

### turin

.........
c

12. Apr 21, 2004

### Staff: Mentor

You didn't like the answer the last time it was explained to you - what is the point of asking again, other than possibly to hijack someone else's thread?

Guys - let him go.

Peterdevis: C. I'm still not exactly clear on the question though...

13. Apr 22, 2004

### Peterdevis

Ok let's use the balloon analogie. When you draw on the surface of a balloon coordinate axes and then blow up the balloon, the coordinates expands together with the balloon. This is what I call a comoving frame.
Since the universe is expanding you can define a comoving frame that moves togheter with the universe ( in this frame universe seems static).
So what is the speed of light in such a frame.

I hope my question is more clear now.

14. Apr 22, 2004

Staff Emeritus
I would say you are just asking what is the speed of light for an observer as close to "at rest" in an expanding universe as possible. And the speed of light (in a vacuum or course) for such an observer is c.

Some of the confusion is that comoving frame has a different meaning in SR, leading to the question "comoving wrt what?"

15. Apr 22, 2004

### turin

In your balloon analogy, let's say the balloon is rubber (naturally), and that you draw lines (curves) on it much like those on a globe with ink. Then, the balloon surface (the rubber) would be a 2-D space and the lines (ink) would be our artificial coordinate surfaces. Is this what you're talking about?

Two flaws with the balloon analogy:
1) As it expands, the rubber only stretches, it does not actually increase. The surface area of the rubber increases, and, from here on, when I refer to the rubber, I will mean the 2-D volume (surface area on the balloon) of the rubber, not the mass or 3-D volume of the rubber. This will make the analogy more consistent.
2) The rubber seems rather ethereal. I can't think of a way around this while maintaining a meaningful balloon analogy. So, this actually does not address the question, but, it addresses the issue of the expansion and how it affects local measurements.

Then when the balloon expands, this essnetially effects more rubber distance (space distance) between our ink lines (coordinates). Imagine an ant crawling on the surface in a straight line (great circle/geodesic). It would take the ant longer to crawl from one ink line to another if the balloon is expanding than if it is not, but that doesn't mean the ant is going slower, even with respect to the coordinate system. The metric of the coordinate system changes in time. At one point the ant may be approaching an ink line; at another point, the ant may be receeding from an ink line (in terms of the amount of rubber), but the any is moving its legs just as quickly as always, and thus pushing just as much rubber behind it as always. At whatever point the any wishes to determine its speed, it can simply leave, let's say, an ant dropping behind at that moment, and what how quickly the dropping flies behind. Of course, this will appear to speed up as time goes on, but the ant has only to leave another dropping to determine its speed at any time, and does not rely on the past droppings to determine its speed.

I don't think I like the balloon analogy any more.

Last edited: Apr 22, 2004
16. Apr 23, 2004

### Peterdevis

Yes , i noticed that there are two interpretations of comoving frames:
In SR : the frame that moves togheter with a particle
in Robertson- walker metric : the frame of the used coördinates in the Robertson- walker metric.

Yes, that's the way

I think that is the right meaning of the balloon analogy

When you described space itself as an "ether" with the properties of the metric, I don't think there is an analogy problem

When i see it right : when the metric change in time, also the measurement of distance change in relation to the coördinates?

17. Apr 23, 2004

### turin

That's how I see it.