# B Calculating c in Thought Experiments

1. Mar 22, 2016

### Ian432

Let's say that, for the purpose of a thought experiment, I want to use the following as a calculation of the speed of light. Assume the following scene is an inertial, non-accelerated frame.
1. I have two clocks, A and B, which start out one millimeter from each other, and are perfectly synchronized.
2. I slowly displace clock B until it is 10 km away from clock A.
3. I shine a light beam from clock A to clock B.
4. I compute time T as the difference between the time the beam was shone from clock A, to the time the beam hits clock B.
5. I compute the speed of light as (10 km) / T.

Q1. Would the physics community consider the calculation in step 5 to be a legitimate calculation of the speed of light (for the purposes of a thought experiment)?
Q2: Is there any inertial, non-accelerated frame of reference in which the above calculation would NOT be considered a legitimate calculation of the speed of light?

I am setting the stage for future questions, but first I want to make sure I have a basic understanding of the way c can be "thought-calculated."

2. Mar 22, 2016

### Staff: Mentor

I assume you also bring clock B to rest relative to clock A at this distance, correct?

I assume you mean by this that you compute the difference between the reading on clock A when the beam is emitted, and the reading on clock B when the beam is received, correct?

A legitimate approximate calculation of the one-way speed of light. But only approximate; there will be some error involved because you moved clock B. The error can be made small by moving B slowly, but it cannot be made zero; there is always some measurement accuracy at which the difference becomes detectable. It is impossible to make a perfectly accurate measurement of the one-way speed of light by this method.

The comments I made above are valid for any inertial frame.

3. Mar 23, 2016

### Staff: Mentor

This is called slow transport synchronization. It turns out that it is equivalent to Einstein click synchronization.
It is the same as Einstein synchronization, so it would only be legitimate in the frame in which they are synchronized. In all other frames the clocks would be desynchronized and the distance contracted, so the calculation would be wrong, even though the errors cancel out.

4. Mar 23, 2016

### Vitro

Also, you'd need to use a pre-1983 definition for the meter since now it is defined based on the speed of light so it would be circular to measure the speed of light as distance / time with the current definition.

5. Mar 23, 2016

### Ian432

PeterDonis, both of your assumptions are correct.
Dale, you've pointed me in an interesting direction--by searching on the term "slow transport synchronization" I find that event synchronization is a ripe area of study dating back at least to Augustine in the 4th century. I will need to do some further reading, and will come back to this post after I do so.

Many thanks to all of you for these thoughtful replies.

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