Discrepancy regarding time measurement

[wizrdofvortex]

Here's a quote from Einstein's 1905 paper regarding evaluation of times of events occurring at places remote from the observer :

We might, of course, content ourselves with time values determined by an observer stationed together with the watch at the origin of the co-ordinates, and coordinating the corresponding positions of the hands with light signals, given out by every event to be timed, and reaching him through empty space. But this co-ordination has the disadvantage that it is not independent of the standpoint of the observer with the watch or clock, as we know from experience.

Please explain the meaning of that last sentence. I mean, where and why does the disadvantage of using the above method arise?

 

[ghwellsjr]

It's because, although we can measure the round-trip speed of light, we cannot know if the two halves of the trip take an equal amount of time. In other words, we cannot measure the one-way speed of light without making some arbitrary assumptions (like, it is the same as the average of the two-way speed of light). The observers that Einstein is taliking about are moving at different constant speeds with respect to each other. Einstein's second postulate is that for each of them, they can make the assumption that the two halves of their measured round-trip will take the same amount of time and it will be consistent with the First Postulate that all the laws of physics look the same to all observers no matter what constant speed they are traveling at.

 

[wizrdofvortex]

It's because, although we can measure the round-trip speed of light, we cannot know if the two halves of the trip take an equal amount of time. In other words, we cannot measure the one-way speed of light without making some arbitrary assumptions (like, it is the same as the average of the two-way speed of light). The observers that Einstein is taliking about are moving at different constant speeds with respect to each other. Einstein's second postulate is that for each of them, they can make the assumption that the two halves of their measured round-trip will take the same amount of time and it will be consistent with the First Postulate that all the laws of physics look the same to all observers no matter what constant speed they are traveling at.

I'm sorry but I don't quite follow. I understood your latter point about the consistency between two inertial frames and that they can assume the two halves to be of the same duration. But could you please elaborate on how the necessity of measuring the time of the two halves of a round-trip come into the picture? I mean, how is this relevant to the method of measuring the time of an event I mentioned in my first post quote?

(Apologies if I'm being obtuse)

 

[ghwellsjr]

In his 1905 paper, Einstein described the normal method of measuring the round-trip speed of light by placing a mirror a measured distance away and timing how long it takes the light to go from the source, to the mirror, and reflect back to the source. Then he shows the formula for calculating the average speed of light. (He doesn't describe all the details because he assumes the reader is already familiar with this process but if you read it with this in mind, you can see that this is what he is talking about.)

He then points out that it is impossible to know what time the light actually hit the mirror (a distant event) or any other distant event with respect to the timer (or clock) that was used at the source to measure the round-trip speed of light. If you read his paper again carefully with this understanding in mind, you will see that this is exactly what he is talking about.

So now comes his postulate. Just define both halves of the round-trip to take the same amount of time. Now you can use this technique to synchronize any distant clock that is at rest with respect to the first clock/timer and mirror, etc. This process allows an observer to define a system of co-ordinates involving three dimensions of space and one dimension of time in a consistent way.

You have to keep in mind that the problem that Einstein is solving is how to describe the transmission of light when it proves impossible to determine the rest state of the "luminiferous ether" which is the only frame in which the two-halves of the measured round-trip speed of light actually take the same amount of time. He points out that two observers in relative inertial motion can both presume that they are each at rest in the presumed absolute ether rest frame and by using his techinique of establishing a co-ordinate system, all the laws of physics will be the same for each of them. In other words, it is not necessary to be concerned about identifying an actual ether rest frame.

 

[wizrdofvortex]

Understood, thanks a lot...