Reichenbach on SR: Conventional Element & One-Way Speed of Light

[phellen]

What do people think about the conventional element of SR? Is the assumption that the one way speed of light is always the same (for any rf) justified (as opposed the the two way speed of light)?

 

[pervect]

What do people think about the conventional element of SR? Is the assumption that the one way speed of light is always the same (for any rf) justified (as opposed the the two way speed of light)?

Personally, I suggest (conceptually) reformulating the two-clock concept of velocity to the one-clock concept concept of proper velocity (also called celerity).

There's some discussion of the definition of this in http://arxiv.org/abs/physics/0608040 though they do not suggest exactly what I am suggesting as far as using this concept.

Sometimes, one single quantity in a theory splits into sever al distinct quantities in the
generalised theory. One example is the velocity in classical mechanics. In the widest sense,
velocity or speed means the covered distance divided by the time needed to cover it. This is
uncritical in classical physics, where time and distance are well defined operational concepts
that are independent of the frame of reference, in which they are measured. In Special
Relativity, these concepts depend on the frame of referencein which they are defined, if the
frames are not at rest with respect to each other. This makes it necessary to distinguish
between the different possibilities regarding the frame of reference in which the spatial and
the temporal intervals are measured. This is best illustrated with a common situation of
measuring the velocity of a rolling car. Firstly, the velocity of the car can be measured
by driving past kilometer posts and reading the time at the moment of passing the post
on synchronized watches mounted on the posts. Secondly, the driver can also measure the
velocity by reading the corresponding times on a clock which is traveling with the car.
Thirdly, a person with clock standing beside the street can measure the times on his clock
at the moments, when the front and the rear ends of the car are p assing him. The travelled
distance is then taken from a measurement of the length of the car in the frame of reference of
the car. A fourth possibility measures the velocity of the car up to an arbitrary constant by
measuring its acceleration using an accelerometer traveling with the car, e.g. by measuring
a force and using Newtons Second Law, and integrates the measured acceleration over the
time measured with a clock, also traveling with the car.

In classical mechanics, all four measurements are equivalent and give the same value for
the velocity. In Special Relativity, the first possiblility gives the coordinate velocity, which
is often referred to as the genuine velocity. The second and third possibilities are equivalent,
but are hybrid definitions of the speed. The temporal and spatial intervals are measured
in different frames of reference. This speed is sometimes called celerity, or proper
velocity.

I regard the definition of velocity using two clocks as being mainly inspired by the experimental difficulties in realizing accurate clocks that move along with the object whose velocity we wish to measure.

However, if we regard the concept of velocity as something that could be measured by one clock, that's carried along with the object whose velocity we wish to measure, we no longer have to worry about synchronization issues. Though we do need to note that celerity is numerically not the same as velocity, it's related only on a philosophical / conceptual level as being another way to measure "speed".

Thus, rather than dealing with all the synch issues, my suggestion is to reformulate the problem in terms of clocks that measure proper time, by using the concept of celerity to replace the concept of velocity.

This won't really answer issues related to the "one-way speed of light", because in this model the celerity of any object approaching the speed of light appraoches infinity. But I think it's more productive than agonizing over the synchronization issues, in the belief that they are fundamental and unavoidable. I believe that this prescription allows one to avoid the synchronization issues and reveals them to be actually non-fundamental.

 

[WannabeNewton]

Is the assumption that the one way speed of light is always the same (for any rf) justified (as opposed the the two way speed of light)?

Well Malament proved under certain assumptions that there is a preferred and natural synchronization convention for inertial frames defined by the causal structure and this is the one in which the one-way speed of light is isotropic; this convention also agrees with slow-clock transport. So in that sense it is clear that the $\varepsilon = 1$ convention holds a special place.

Of course this is still not the only possible convention as one can still freely choose other synchronization conventions for inertial frames even if they are very unnatural. Malament's argument was that nature naturally picks out $\varepsilon = 1$ in inertial frames so it is not only justified but also preferred. Other conventions would of course also be justified but they would the calculations, amongst other things, intractable due to global time functions built out of more complicated synchronization prescriptions.