Wanting to understand the one-way speed of light problem in more detail please

[harrylin]

I'd be interested in the answer to this, as it was one of things I was still trying to understand.
The laymen conclusion I came to was that might have something to do with light being the natural speed limit of the universe. [..]

That's correct: Maxwell's theory models light as a wave with universal speed c, thus isotropic and independent of the speed of the source. Lots of experiments had been done in earlier years which not only strongly supported that theory, but which also suggested that this theory is perfectly valid in any inertial frame.

Lorentz discovered in 1904 that by combining his earlier theory of electrons (which was based on Maxwel's theory) with Poincare's relativity principle, the speed of light becomes the maximum speed of the universe. And as you read in "the measure of time", Poincare had already made the synchronisation convention popular, which fitted perfectly with Lorentz's "local time". All those pieces fit very well together, for the synchronisation convention becomes perfectly self-consistent with SR.

Einstein's development one year later followed from the same model, as he explained in 1907:

"We [...] assume that the clocks can be adjusted in such a way that
the propagation velocity of every light ray in vacuum - measured by
means of these clocks - becomes everywhere equal to a universal
constant c, provided that the coordinate system is not accelerated.
[..this] "principle of the constancy of the velocity of light," is at
least for a coordinate system in a certain state of motion [..] made
plausible by the confirmation through experiment of the Lorentz theory
[1895], which is based on the assumption of an ether that is
absolutely at rest".

 

[PhilDSP]

That's correct: Maxwell's theory models light as a wave with universal speed c, thus isotropic and independent of the speed of the source. Lots of experiments had been done in earlier years which not only strongly supported that theory, but which also suggested that this theory is perfectly valid in any inertial frame.

But we should remember that the Maxwell equations (containing the factors that in a vacuum conspire to make c observable) are strictly speaking not applicable to moving media (as we know the equations today). Hence the need for the whole ruckus about relativity. Differential equations require one to specify both initial conditions and boundary conditions to produce a proper result. It's those conditions that allow one to actually apply the equations to realistic-experimental problems to generate values that can be observed.

Lorentz partly understood the need for specifying initial conditions and spent a great deal of time developing the means for manipulating those initial conditions to synthetically produce answers for moving media. Einstein apparently didn't consider at all initial or boundary conditions but abstracted them into the concepts of reference and inertial frames. Was that actually Poincare's initiative? Poincare apparently only meagerly considered the mathematics behind initial and boundary conditions.

 

[lugita15]

Postulating that the 1-way speed of light is constant implies that the 2-way speed of light is also constant, which is something we can test experimentally and is observed to be true. The 2-way speed of sound can be experimentally demonstrated not to be constant, so it's impossible to synchronise clocks to make the 1-way speed of sound constant under all possible wind conditions.

But what would happen if you synchronized clocks by exhanging sound, exactly analogous to Einstein synchronization? Wouldn't you then find by definition that the one-way speed of sound from A to B is the same as the speed from B to A?

 

[grav-universe]

But what would happen if you synchronized clocks by exhanging sound, exactly analogous to Einstein synchronization? Wouldn't you then find by definition that the one-way speed of sound from A to B is the same as the speed from B to A?

You cannot replace sound with light in SR or LET and gain the same results.

In SR, bodies contract in the line of motion and clocks are time dilated by sqrt(1 - (v/c)^2), where c is the universal constant, the speed of light. We cannot then change c to the speed of sound 's' and have a body contracted both by sqrt(1 - (v/c)^2) and sqrt(1 - (v/s)^2) at the same time, it can only be one or the other, so there can only be one maximum universal speed. A body moving through air at v will still be contracted by sqrt(1 - (v/c)^2), whereas a contraction of sqrt(1 - (v/s)^2) would be required to measure the speed of sound isotropically.

In LET, "rigid" bodies are held together electromagnetically by light carried through a medium, so not by sound of course. We postulate that there exists at least one homogeneous frame. A body in this frame is in electromagnetic equilibrium and impulse waves are measured isotropically when the frame is properly synchronized. When a body is accelerated from this frame to another, it will readjust itself until electromagnetic forces are once again in equilibrium (rigid bodies aren't so rigid), whereby the body remains stable, and when synchronized accordingly, the electromagnetic impulses are measured isotropically. This effectively makes all frames homogeneous in this manner and is thereafter postulated similarly to SR to gain the same mathematical results, but where length contraction and time dilation are no longer coordinate effects, distortions of space and time, but a real physical slowing of clocks and contraction of bodies in the line of motion.

 

[harrylin]

But what would happen if you synchronized clocks by exhanging sound, exactly analogous to Einstein synchronization? Wouldn't you then find by definition that the one-way speed of sound from A to B is the same as the speed from B to A?

Yes, it works the same with sound if you do it with sound: "Einstein synchronization" makes the one-way speed between A and B isotropic by definition, by mathematical necessity.
More elaborated:

The one-way speeds between A and B are defined as:
v1 = (x2-x1)/(t2-t1) and
v2 = (x2-x1)/(t3-t2)
The two-way speed is defined as:
v3 = 2*(x2-x1)/(t3-t1)

The path length (x2-x1) is fixed and is half the two-way length.
If you define (t2-t1) = 1/2 * (t3-t1), then you get:
v1 = v2 = v3

Cheers,
Harald

 

[grav-universe]

Yes, it works the same with sound if you do it with sound: "Einstein synchronization" makes the one-way speed between A and B isotropic by definition, by mathematical necessity.
More elaborated:

The one-way speeds between A and B are defined as:
v1 = (x2-x1)/(t2-t1) and
v2 = (x2-x1)/(t3-t2)
The two-way speed is defined as:
v3 = 2*(x2-x1)/(t3-t1)

The path length (x2-x1) is fixed and is half the two-way length.
If you define (t2-t1) = 1/2 * (t3-t1), then you get:
v1 = v2 = v3

Cheers,
Harald

That only works along a single linear direction, not isotropically in all directions. If a frame stationary to the medium measures sound speed s isotropically, in order for another frame moving through the medium at v to measure sound speed isotropically in all directions, bodies and rulers within that frame would have to contract in the line of motion by sqrt(1 - (v/s)^2).

 

[DrGreg]

But what would happen if you synchronized clocks by exhanging sound, exactly analogous to Einstein synchronization? Wouldn't you then find by definition that the one-way speed of sound from A to B is the same as the speed from B to A?

Yes it would, but it might not mean that the one-way speed of sound from A to C was the same as the one-way speed of sound from A to B for some point C in a different direction from B (relative to A); nor would two different observers agree on the value of the speed of sound; and as soon as the wind velocity changed you would need to resynchronise all your clocks.

 

[harrylin]

That only works along a single linear direction, not isotropically in all directions.[..].

Indeed, only for opposite directions as is the case here, with the definition: I already explained that in message #18.
Therefore I also repeated here "between A and B".

 

[harrylin]

[..] as soon as the wind velocity changed you would need to resynchronise all your clocks.

Note that the same is true for radio waves if one changes the velocity of a physical reference frame: also after that, a resynchronisation is required.

 

[Agrippa2]

Hey rede96. I'm new to the forums, but I think I have a very similar interest to you about isotropy/anisotropy of light. I was going to post something about it tomorrow, but I just wanted to poke in and say hi for now. Maybe you can check out my new thread tomorrow.