# Constancy of the speed of light (locally)

1. Jun 21, 2010

### Passionflower

Which statement is (more) true?

A. because lengths contract and clocks slow down the speed of light (measured locally) is always c.

B. because the speed of light (measured locally) is always c lengths contract and clocks slow down.

Personally I think it is a "which comes first the chicken or the egg" question.

2. Jun 21, 2010

### Tomsk

You could say both happen because spacetime has Lorentzian symmetry.

3. Jun 21, 2010

### Austin0

Hi Regarding A. As far as local measurements in a GR context it seems like length contraction and clock dilation combined with an actual slowdown of light in lower potential locales is sufficient to explain the constancy of local c.
Regrding the measured invariance in inertial frames of varying relative velocities it doesn't seem like contraction [length] and dilation [time] together, are at all an adequate explanation.
Certainly not to explain the isotropic invariance in any frame.
I.e. That the measured speed of light moving in the direction of system motion is the same as the speed of light moving counter to the direction of the system.
If you have some explantion for how how these factors can account for this I would like to hear it.
My own personal explanation is that relative simultaneity is at the core of the phenomena.
Thanks

4. Jun 21, 2010

### weaselman

Well, in a way "A" is "true", because the constancy of c is postulated in SR, and the length and time contraction is deduced from it.

If you are rather talking about the "cause and effect" when you say "because", then both statements are wrong. Constancy of the speed of light does not cause the lengths to contract.

Like Tomsk said, these two things - the constancy of c and the contraction of lenghts and times - are both properties of the space-time geometry, they don't cause each other in any way.

A more or less equivalent question to ask about the Eucledian 3-space would be something like this - what is more true:
A: The sum of two sides of a triangle is always longer than the third side because the interval between two points always has the same length in any reference frame or
B: The interval between two points is identical in all reference frames because two sides of a triangle are always longer than the third.

5. Jun 21, 2010

### GRDixon

Because the clocks distributed in an IRF are synchronized on the premise that light propagates with the one speed, c, in all directions relative to that frame, the light speed is always MEASURED to be c, using the clocks and grid of that frame.

6. Jun 21, 2010

### Mentz114

This is not completely correct. The clocks are synchronised on the assumption of isotropy but the actual speed is irrelevant.

7. Jun 22, 2010

### Austin0

Originally Posted by G.R.Dixon
Because the clocks distributed in an IRF are synchronized on the premise that light propagates with the one speed, c, in all directions relative to that frame, the light speed is always MEASURED to be c, using the clocks and grid of that frame.

Isn't it true that the synchronization procedure, whether it is one way or reflected always sets the clocks based on the time interval calculated by the distance of separation divided by c ??? SO yes, the initial assignment of any metric is arbitrary but if you used a different value for the speed of light to synch your clocks , wouldn't this render them inaccurate for clocking all other phenomena? In effect require the recalibration of the whole coordinate system?

8. Jun 22, 2010

### Ich

No. For reflection, you set t(reflection) = (t(emission) + t(absorption))/2. The value of c is irrelevant.