Yet another proposal for one-way speed of light measurement

Ahh, that one Veritasium video which has generated so many questions on this site!

Here’s my idea. I expect it won’t work, but since I’m a total layman in physics and don’t really grok even Special Relativity, I don’t understand why it won’t work. Also I didn’t see anything similar in the first page of search results. 🙂

So. All of the arguments I’ve seen center around our inability to synchronize clocks because speed of light itself affects it and cancels out the measurements. So what if we didn’t rely on it?

Let’s start by shooting out a pair of probes into space. After they’ve gained some distance from earth they separate and one of them gains some speed away from the other. After a while the engines are cut off. Now we have two probes, drifting away from each other at a constant speed. Both experience no acceleration and are thus purely inertial.

Now they start sending signals to each other. They both have these super-precise atomic clocks and can measure local time down to nanoseconds. So they send a little "bleep" to each other EXACTLY once every, say, 10 minutes. Now, since they are floating apart, the difference between two consecutive bleeps, as received by the other probe, will be slightly more than 10 minutes. The deviation would be small at the start, but accumulate over time. So by the time they got, say, about 5 light-minutes apart, the accumulated deviation would already be 5 minutes. And this can be measured by using nothing but the local clock. Simply start counting 10-minute intervals when you receive the first "bleep" and see how they drift away from actual received signals over time.

And here’s the kicker – if the speed of light is different in one direction than the other direction, the drift will happen at different rate for each probe. Take for example the extreme case where communication is instantaneous from A to B, but has the speed of c/2 from B to A. In that case B will see no drift at all and all the signals will arrive with precisely 10 minute intervals. While A will see a huge delay and when the probes are only 5 light-minutes apart, the count of received "bleeps" will already be off by 1.

Both probes can communicate this information and compare their drift rates. And send the results back to Earth too, of course.

Could relativity affect this? I… don’t know. After all the acceleration is done and both probes just drifting freely away from each other, I don’t think that time should pass faster in one probe than in the other. They are after all at that point completely symmetrical.

Or maybe it’s a problem that only one probe accelerated at their separation? Then have them both accelerate the same amount and in opposite directions before cutting off engines.

So… why wouldn’t this work? Please go easy on the formulas. I’m OK with math, but I know little beyond high school physics.