Physics Asked on June 22, 2021
After watching a video by Veritasium about measuring (or, more accurately, not measuring) the one-way speed of light, I believe I have come up with a way to measure it. I’m guessing somebody else has thought about this setup before, so there is probably something I am missing that explains why it (most likely) isn’t the answer to the problem.
Here it is:
Put a clock on the event horizon of a black hole (and somehow prevent it from falling in). Send a light pulse tangent to the event horizon. Since the light would travel around the event horizon, it would return to the clock, at which point you could measure the time difference. The distance the light travels on the event horizon is just the circumference, so you could use $v=Delta x /Delta t$ to find the one-way speed of light. I haven’t studied GR (I’ve only watched a few videos and read a little bit about it), but I’ve heard that spacetime is warped by mass (this is why there is gravity, which also causes black holes). Since spacetime around a black hole warps, I belive the light would just travel in a straight line in spacetime, which would mean that we are finding the one-way speed of light.
I’m guessing something is wrong with this setup (other than its obvious impracticality), so what is it? Is it my lack of knowledge of GR or something else?
Also, I don’t know how to extract the data from the event horizon, so if you have any ideas for that, please let me know. Thanks in advance!
You do not want to be at the event horizon at $r_s=2GM/c^2$ but at the photon sphere $r_p=3GM/c^2$: at this radius a photon will orbit the black hole, so you can shine a light in one direction and then measure the time until you see the flash in the other direction.
What is the spatial distance travelled here? It turns out that the radial coordinate is defined so that circles of radius $r$ around the black hole have circumference $2pi r$, so this is fairly unproblematic.
It might look a bit worrysome that $c$ shows up in the formulas above if you are trying to measure it, but note that you can find $r_p$ empirically by just shining light from your spacecraft.
Correct answer by Anders Sandberg on June 22, 2021
Although spacetime is expanding or deforming, it also works when the light travels, so the light in spacetime does not travel in straight lines, but rather bends spacetime. Do not forget that one of the properties of the speed of light is propagation, so you will not be able to unify the direction of the speed of light in a specific direction, no matter how it is traveling in a strong gravitational object, because this will increase the spread of the light and slow it down and not unify the it's direction .
About how can we extract the data from the event horizon in a Black Hole with a gravitational pull that absorbs anything in the universe, from waves, rays, and even light, the ultimate speed in the universe This is done by photographing the material that falls on it (on the black hole) and this material emits radiation from the gamma radio .. And this radiation also goes out and reaches us because this material did not reach the edge of the event horizon .. And if it reached the event horizon, nothing came out. No radiation and nothing else ..
Answered by Arslan Ahmed on June 22, 2021
If the aim is to measure one way speed of light, then there are plenty of methods much more practical than anything involving a black hole. But more significantly, the whole notion of a non-isotropic speed of light in flat space makes no sense at all in general relativity. It amounts to proposing a different theory of spacetime. Similarly, if the black hole is spherically symmetric then it is spherically symmetric. So light will travel at the same speed in two opposed directions. If you are considering a rotating black hole (Kerr black hole) then you have to account for the effect of that rotation on the spacetime.
There are interferometers that measure the effect called Sagnac effect. This is the effect that the time taken by light to travel around a loop differs in the two directions around the loop, if the loop is fixed in a rotating reference frame. By such methods one can measure the difference very accurately. THis is not quite the same as what you are asking about but perhaps it will be useful.
Answered by Andrew Steane on June 22, 2021
In this same video it talks about a firbe obtic cable in a circle, this is analagous to your setup. if the speed of light is different depending on direction then the speed of light orbiting the black hole would vary as you go around the blackhole. meaning it would not work as it will all avg out and get the accepted value of C
Answered by jensen paull on June 22, 2021
The "one-way" speed of light, from a source to a detector, cannot be measured independently of a convention as to how to synchronize the clocks at the source and the detector. What can however be experimentally measured is the round-trip speed (or "two-way" speed of light) from the source to the detector and back again. Albert Einstein chose a synchronization convention (see Einstein synchronization) that made the one-way speed equal to the two-way speed. The constancy of the one-way speed in any given inertial frame is a postulate, and the basis of his special theory of relativity, although all experimentally verifiable predictions of this theory do not depend on that convention.
Answered by john john on June 22, 2021
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