So, what exactly is the role of stipulation, or convention, or definition, in the claim that the speed of light is always the same for every observer? Determining the average speed – or two-way speed - of a light signal moving in a straight line from A to B and back is clearly an empirical matter: all that is required is a single clock in A and the ability to determine the distance between A and B.
But what about the one-way speed, first from A to B and then from B to A? Is it necessarily the same on both legs of the journey? The question is relevant since, in some respects at least, light behaves like a wave, and the one-way speed between a wave and its source depends on the direction of travel of the wave if the source is in uniform motion relative to the medium in which the wave is travelling. That's a matter of empirical fact. Or is it?
In his 1905 article "On the Electrodynamics of Moving Bodies", Einstein argued that, in any coordinate system in which Newton's laws of mechanics hold, the question of whether or not the speed of light varies depending on the direction in which it travels is a matter of stipulation or definition rather than empirical fact.
Here's the relevant passage (p. 894):
'…so far we have only defined an "A time" [time at location A in a coordinate system in which Newton's laws of mechanics hold] and a "B time" [time at location B in the same coordinate system], but no "time" that is common to A and B. The latter time can now be defined by stipulating by definition that the time it takes for light to travel from A to B is the same as the time it takes for it to travel from B to A. For, let a ray of light leave A at "A time" tA in the direction of B, let it be reflected in B at "B time" tB in the direction of A and let it arrive back in A at "A time" t'A. The two clocks are defined to be synchronous if
tB – tA = t'A – tB. … '
In modern parlance, Einstein takes the view here that simultaneity is a matter of convention, and that we are free to define simultaneity by means of the Einstein synchronization procedure using light signals as outlined in the quote above. As a result of this definition, the one-way speed of light from A to B always turns out to be the same as from B to A. In this view, then, the equality of the speed of light in opposite directions in any coordinate system in which Newton's laws of mechanics hold is a matter of convention, too.
Do I agree with this conclusion? My provisional answer is "no", for three reasons:
1) It is true that it seems impossible to fully establish or even define the one-way speed of any signal without first defining simultaneity in different locations. However, certain findings about the one-way speeds of different signals, such as whether or not they are equal to or lower or higher than each other, can be obtained through experiment and observation without recourse to any definition of simultaneity in different locations. In conjunction with theories about how those signals propagate, which may also be based on experiment and observation, those findings may impose certain conditions on how simultaneity in different locations can be defined if what is being defined is to deserve the name of simultaneity.
2) The very notion of simultaneity implies a condition which any operational definition of simultaneity must meet if, again, what is being defined is to deserve the name of simultaneity, namely: if clocks in A and B are synchronized under the definition in question and if a signal that is sent from A at the time t1 arrives in B at the time t2, then t2 must be later than t1, i.e. t2 > t1.
3) On the basis of 1) and 2), I will show that applying the Einstein synchronization procedure to, for example, sound signals propagating through air does not yield a meaningful definition of simultaneity.
All of these points will be developed in greater detail in subsequent posts, in which I will also review what the physics texts mentioned in my first blog entry have to say about the issue. But even then I may not be in a position to say whether or not applying the Einstein synchronization procedure to light signals yields a meaningful definition of simultaneity. This is precisely because points 1) to 3) suggest that the answer depends on key theoretical and empirical findings relating to electromagnetic radiation, so ultimately I may well have to defer my final verdict until I have had a chance to review those. Whatever happens, I'm going to keep you posted.
