One-Way Speed of Light

[cianfa72]

The key is that if they are at mutual rest, you can take each component distance measure (laying out your ruler one and over) without reference to timing or simultaneity.

Sorry, what do you mean by "they are at mutual rest" ?

 

[PAllen]

Sorry, what do you mean by "they are at mutual rest" ?

See previous posts for various definitions.

 

[pervect]

Ok, if I understand what @pervect is getting at, it is that you can set up spatial coordinates in a physically realized inertial frame without using clocks (e.g. set up a network of bodies at mutual rest as define by no Doppler, and measure positions using a physical measuring body). Then proper velocity (a standard term, though not well chosen) can be measured for any test body (not light) with one clock on the body, distance determined by labels on the realized frame.

I claim that any such standard construction assumes isotropy (e.g., no Doppler = mutual rest, in all directions, implicitly assumes isotropy; so does the notion of Newtons laws holding in their simplest form).

But once you let isotropy slip in, there is simply no distinction between one way and two way speed, for light, or anything else. So, under assumption of isotropy, just measure two way speed of light with one clock and state it is also one way by assumption of isotropy.

I think we seem to be on the same page now, which is encouraging, but I do disagree with your conclusion. I do think you have a valid concern, and it's one I had myself. Is there some "hidden" assumptions equivalent to isotorpy in my formulation? I don't currently think there is one, but a discussion might help point out one if I'm wrong.

Currently, I don't think we need to make any assumptions about isotropy to work only with proper velocities. We need to introduce isotorpy if or when we introduce the usual notion of measuring velocity with two clocks, but not before.

In fact, I view comparing one-clock and two-clock measurements of velocity as a method of testing whether clocks are synchronized even in Newtonian theory. It is a method that is less abstract and more concrete than the usual discussions I recall about isotorpy. But the link with isotropy comes when we compare the two different formulations of velocities, it doesn't arise before that.

I still believe we don't have to worry about clock synchronization if we only have one clock (the clock we use to measure proper time). There's nothing we need to synchronize it with - yet.

It might be possible that the theory of special relativity implies that any notion of measuring distance implies there is some means of synchronizing clocks, but I haven't found one that doesn't require further assumptions yet. For instance, the idea that the Lorentz interval is equal to the distance only when clocks are synchronized requires an additional assumption that the quadratic form of the Lorentz interval is diagonal, i.e if we have ds^2 = -c^2 dt^2 + dx^2, we can conclude that if ds^2 = dx^2 then dt^2 = 0. But this is only true if we assume the quadratic form of the Lorentz interval has this specific form. The fact that I haven't thought of one doesn't necessarily mean that it doesn't exist however.

 

[PAllen]

I think we seem to be on the same page now, which is encouraging, but I do disagree with your conclusion. I do think you have a valid concern, and it's one I had myself. Is there some "hidden" assumptions equivalent to isotorpy in my formulation? I don't currently think there is one, but a discussion might help point out one if I'm wrong.

Currently, I don't think we need to make any assumptions about isotropy to work only with proper velocities. We need to introduce isotorpy if or when we introduce the usual notion of measuring velocity with two clocks, but not before.

In fact, I view comparing one-clock and two-clock measurements of velocity as a method of testing whether clocks are synchronized even in Newtonian theory. It is a method that is less abstract and more concrete than the usual discussions I recall about isotorpy. But the link with isotropy comes when we compare the two different formulations of velocities, it doesn't arise before that.

I still believe we don't have to worry about clock synchronization if we only have one clock (the clock we use to measure proper time). There's nothing we need to synchronize it with - yet.

It might be possible that the theory of special relativity implies that any notion of measuring distance implies there is some means of synchronizing clocks, but I haven't found one that doesn't require further assumptions yet. For instance, the idea that the Lorentz interval is equal to the distance only when clocks are synchronized requires an additional assumption that the quadratic form of the Lorentz interval is diagonal, i.e if we have ds^2 = -c^2 dt^2 + dx^2, we can conclude that if ds^2 = dx^2 then dt^2 = 0. But this is only true if we assume the quadratic form of the Lorentz interval has this specific form. The fact that I haven't thought of one doesn't necessarily mean that it doesn't exist however.

See the conversation following the quoted post of mine, and please comment as desired.