You have two clocks. They each measure “something” on the far end of each of their respective journeys. What, exactly, are they measuring, when you cannot establish the distance they travel except by relying on the two-way measurement you are trying to avoid? Two clocks doubles, not halves, the problem.
ETA: That is - the distance ‘measured’ can itself be anisotropic and dependent on an anisotropic speed of light. But we couldn’t tell because the clocks would measure the same number of ‘ticks’ either way. Assuming ‘distance’ is some globally consistent isotropic constant is itself an assumption we can’t make in such a thought experiment.
We are slowly measuring the distance with a yardstick or string. On earth we can estimate how much it changes worst case as temperature changes and crusts move. Yes, the length depends on velocity. But we know the possible error. Depending on the speed of light c/2 or infinite. I hear what you’re saying. I think I have expressed one problem with assuming light is isotropic, before you attempt to measure that same thing. There may be more that you are aware of.
And how do you know the length of that yardstick or string? It’s turtles all the way down
That’s kind of the point of relativity. The measurement of that distance - whether 1 yard, 1 meter, or 1 light-year - depends on the speed of light itself. How ‘slowly’ you lay out the yardstick or string doesn’t really matter.
There is no global reference for a meter like there used to be, because we know (because of relativity) that it is does not make sense to have one. Distances are now defined as a function of time and the speed of light - the very thing we’re trying to measure
Note, this isn’t just for the meter. Even the kilogram has been redefined because we recognize there are issues with using a cylinder of platinum-iridium. A kilogram is now defined, not by comparison to a chunk of metal, but itself partly as a function of the speed of light.
Likewise, a ‘second’ is no longer defined by rotations of astronomic bodies but by atomic transition frequencies.
If the speed is isotropic, then none of this is a problem. So let’s say it’s not, worst case. I’m really trying to understand the basics, before I move on. Seems we’ve gone down a rabbit hole that I’m certain is related to my question. Take a piece of non-stretchy string. If you try to measure distance with the round trip time of light. It would work consistently in every direction, even if non-isotropic. It would match the length of the string. We are within an inertial frame of reference. The velocity vector is not changing. Why would the length of the string change? Depending on how it’s oriented? Even if you rapidly moved it miles, then stopped. It’s still the same inertial frame, and the same length. It was only temporarily longer.
Let me try again. The speed of light is constant. In every direction. You must read Einstein. ROUND TRIP. The clock is constant. Since it’s not moving at all. Measuring round trip. Speed=d/t. Neither are depending on isotropic speed. Nothing is moving, except the photons. I must be missing something very basic.
I think you’re messing with me. You can measure the length in a parking lot in one direction with TOF Round trip. Put a pin in the ground. Move your test equipment, move your mirror to opposite sides. You’d get the same result. You can do the same with a string. It’s the same in both directions. N,S,E,W. I thought you said it would change? In theory? It cannot.
The ‘measured’ distance would look the same but there’s no way to know that’s the same ‘distance’ if measured in a different direction. The way you see it will change but you couldn’t tell that in a one-way measurement.
Everything you measure will look consistent, even if the speed of light is anisotropic - the amount of time and the measurement of distance you see will both be consistent and match the local speed of light. But there’s no outside global reference that guarantees it is the same distance and same rate of time if measured in a different direction.
You’re relying on a round trip again. Of course they’ll be the same (up to measurement errors, and small discrepancies due to earth’s rotations, etc).
You are assuming there’s some globally preferred frame of reference in which you can measure these distances and clock rates. Not so. They’ll be the same but that’s because you’re measuring the two-way again. It’s not a true one-way measurement.
A lot of this hinges on the idea of some outside global arbiter who can measure things from an outside perspective. But in the real world, we’re inside. It’s a variant of the classic train window experience. If you are on a train traveling at constant speed, you can’t tell if you’re on a train that’s moving or if the rest of the world is moving while the train sits still. You can say “Oh, it just stands to reason the train is moving” but that’s bringing some kind of outside global knowledge into it. From the perspective of the physics and just what you can observe directly, both are equally valid ways of describing the observations and how things react.
I am by no means an expert on quantum but my understanding is that quantum entanglement still does not allow information, such as clock synchronization states, to be passed faster than the speed of light.
Though if it could, that would be something. You could transmit data to the past, even.
You have two experimenters (X and Y) and a pulsar. Imagine they are arraigned in triangle shape in space. The bottom two points of the triangle would be the experimenters, say 1000 miles apart, and the pulsar is the top point. The pulsar is 1 light year away and equidistant from both experimenters.
Now, a third experimenter (Z) has a giant opaque shield covering the pulsar from the view of both the first two experimenters. The pulsar is average and pulses about 1 pulse per second. Z removes the shield and at the moment the 10th pulse reaches X and Y, the experiment begins. X fires a light beam the moment the 10th pulse reaches him. When the 10th pulse reaches Y he starts his timer and stops it when the light beam arrives at his measuring device.
Then repeat the experiment, but this time Y fires the light and Z does the measuring (this would rule out any anisotropic deflection of light coming from the pulsar.
Now clearly this is impractical, but as a thought experiment could it work?
Or maybe, along the same lines, instead of a pulsar have a device that fires simultaneous lasers at the experimenters.
One is the assumption of instantaneous knowledge - sharing knowledge has a lightspeed delay. You’re assuming that each of these observers can tell exactly what is happening elsewhere instantaneously with 0 delay. In reality, that can’t happen - the information itself is transmitted at the speed of light at maximum.
Another is - how are you establishing that X and Y are equidistant from the pulsar in the first place? If each of X and Y tells Z they are 1 light year from the pulsar, that’s already a two-way measurement of the speed of light by itself. If Z is measuring they are equidistant from the pulsar, that’s also a two-way measurement of the speed of light.
Note this last issue is the same one in the OP - that such a measurement can be established, i.e. that absolute knowledge of ‘distance’ can exist without making any assumption about the speed of light.
No, light light from the pulsar arrives at each experimenter at the same time, independently, and their respective experiments start. It’s not important that they can share what they are doing instantaneously.
It’s a given of the thought experiment. Did anyone question Einstein about the propulsion methods of his elevator in space?
ETA: OK, instead of a pulsar, put a device on the moon that fires simultaneous lasers at two points on the earth 100 miles apart.
Am I correct in thinking that the fundamental problem is there is no such thing as simultaneity in SR/GR?
So, how would it be possible to arrange two things, separated by any amount of space, and say they are in sync?
It’s only when the beam comes back, that any sort of meaningful measurement can be made. A two-way circuit is intrinsic to any relativistic measurement.
It doesn’t really have to be pulsar, how are you establishing these distances in the first place?
The purpose of a thought experiment is have a situation where the laws of physics are not otherwise violated, even if the situation itself is ridiculous.
Setting up a situation where distances are absolutely known is equivalent to the very thing that you are trying to establish, i.e. why bother with the experiment if you are going to simply assume your conclusion is true before running the experiment.
If absolute distance can’t be determined, how do we know what the (assumed) speed of light is? It seem that measuring an out and back reflected speed would require knowing how far away the reflector is.
“The speed of light can be determined using a time of flight measurement. The time of flight method of measuring the speed of light is based on the fact that the speed of light is finite and constant. Therefore, light will take a finite amount of time to travel a distance. By measuring the time the light takes to travel a certain distance, one can determine the speed in which it travelled”.
It would rule it out because then the times would be different between the two experiments? Does that assume that light travels between the experimenters at the same speed both ways?
It more or less is null, at least for getting the absolute accuracy we need. That’s one of the more interesting things that’s come about over the last century.
We can use a ‘known’ distance to get a two-way measurement of the speed of light. Naturally, this measurement will come with error bars because our actual knowledge of distance has a limited precision, and at the very limits, depends on knowing the speed of light, i.e. what we are trying to measure (!?). It’s even in the lead paragraph. “Surprisingly, it is possible to get a reasonably accurate measurement without highly specialized instrumentation”.
So it can get us pretty close. Certainly close enough for most practical purposes. If you check further in your linked page, it even asks about sources of error and how to improve both precision and accuracy, i.e. the page assumes such an experiment gets close but will have limited precision/accuracy.
But for the kind of thing in the OP, which is more theoretical, ‘close enough’ doesn’t really exist like it does for an experiment meant for practical purpsoes.
Can a solid object of established physical dimensions confirm both the absolute distance between its two ends and that those two ends are at zero relative velocity to each other?