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

[lugita15]

What is special is Einstein's idea that the two principles (the principle of relativity and the principle of the constancy of the speed of light) were not incompatible with each other (like everyone else believed at the time) and could be raised to the level of postulates (assumed to be true without proof) and shown to be mutually consistent in his Theory of Special Relativity. Once you accept both principles as postulates, there is only one synchronization convention possible, the one Einstein outlined.

But why would you make accept the postulate in the first place that the speed of light is constant? As Ohanian says, you could just as well stipulate that the speed of sound is constant, and then you could make a simultaneity convention exactly analogous to Einstein's, just replacing the word light with sound. How do you decide which postulate to use, or which simultaneity convention to use? What seems natural is to experimentally determine the simultaneity defined by slow transport, and from there infer that the one-way speed of light is constant.

 

[lugita15]

I would say that it is a).

The point is that synchronization is a convention. We can think of synchronizing clocks using Einstein's convention, but we can also think of other conventions. For example we could think of synchronizing our clocks by using some master clock which broadcasts the current time and the distant clocks simply set their time to coincide with the master clock. In that case the "outward" speed of light would be infinite and the "inward" speed of light would be 1/2 c. We could re-write Maxwell's equations in terms of this synchronization convention and get a theory which agrees with all of the experimental results. In particular, the round-trip (aka two way) speed of light would be isotropic and equal to c.

How exactly would you change Maxwell's equations in order to fit any particular simultaneity convention?

 

[rede96]

But why would you make accept the postulate in the first place that the speed of light is constant? As Ohanian says, you could just as well stipulate that the speed of sound is constant, and then you could make a simultaneity convention exactly analogous to Einstein's, just replacing the word light with sound.

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.

So you could substitute sound, or anything else for that matter. (As I understood it, the Lorentz transformation was derived by representing the speed of light as a single unit anyway.) But as there are known speeds greater than sound, you would run into problems when doing the transformations where you had velocities greater than the constant that you set. Time would be going backwards for example if we exceeded the speed of sound.

But as I said, I’m still learning this stuff.

 

[ghwellsjr]

But why would you make accept the postulate in the first place that the speed of light is constant? As Ohanian says, you could just as well stipulate that the speed of sound is constant, and then you could make a simultaneity convention exactly analogous to Einstein's, just replacing the word light with sound. How do you decide which postulate to use, or which simultaneity convention to use? What seems natural is to experimentally determine the simultaneity defined by slow transport, and from there infer that the one-way speed of light is constant.

As I said in the thread you linked to in post #27:

Every inertial observer will experience exactly the same things that an observer at rest in an absolute ether frame would experience. One of those things is that the one-way speed of light is the same in all directions. This is Einstein's second postulate which cannot be tested, measured or proven. Einstein made it very clear in his 1905 paper and in subsequent papers that the assignment of one-way light speed being a constant is arbitrary. In SR, when a frame of reference is selected, the one-way speed of light is not the same in all directions for other inertial observers that are not at rest in that frame of reference, although even for those other observers, they will still experience the same things they would if they were at rest in an absolute ether rest frame.

The choice isn't between light and sound, it's between the postulates that the speed of light is constant in space or constant in ether.

Prior to Einstein, experiments showed that every inertial observer appears to be at rest in the ether. The problem is to come up with a theory that would explain that fact and the fact that another inertial observer moving with respect to the first one, and therefore moving in the ether, would also appear to be at rest in the ether. The explanations at the time affirmed the existence of an absolute immovable ether, an absolute space, an absolute time, and an absolute speed of light only in that ether. All other states of motion had things like length contractions and slowing down of clocks as adjustments to explain the experimental facts, and they could even explain why the slow transport of moving clocks would appear to have the same times on them, even though they were moving through the ether and didn't keep track of the real absolute time as defined by the ether. This is the Lorentz Ether Theory and it posutates a different timing convention that Einstein's.

You could hold to LET but then you would have the added problem of identifying the rest state of the ether. Giving up the concepts of absolute space and time allows you to accept the speed of light to be constant in space and produces a much simpler theory. It's a philosophical choice, not one demanded by nature.

 

[DrGreg]

But why would you make accept the postulate in the first place that the speed of light is constant? As Ohanian says, you could just as well stipulate that the speed of sound is constant, and then you could make a simultaneity convention exactly analogous to Einstein's, just replacing the word light with sound. How do you decide which postulate to use, or which simultaneity convention to use? What seems natural is to experimentally determine the simultaneity defined by slow transport, and from there infer that the one-way speed of light is constant.

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.

 

[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.