Measuring the one-way speed of light with a black hole?

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!

• Nov 2, 2020 at 6:59
• This question is based on the incorrect premise that the guy in the video knows what he's talking about. Maybe some of his other videos are good, but this one is just crankery. I've written a few answers about this; here's one and here's another. In short, nothing can measure the "real" speed of light as he's defined it because it's just a physically meaningless change of coordinates. Nov 2, 2020 at 7:35
• @benrg Thanks for the response with links. I read through your answers, and they make complete sense and are helpful. Still, if we proceed—even with this false premise—would my method work? At this point it's just a thought experiment for me. Also, would you have any possible ways of getting the data to escape the event horizon? I saw something online about how information between entangled particles travel at >c. Let me know what you think. Thanks.
– user276997
Nov 2, 2020 at 8:38
• 'Put a clock on the event horizon of a black hole (and somehow prevent it from falling in)'. This is not possible. Any experiment predicated on impossible things is also not possible.
– user107153
Nov 2, 2020 at 10:44
• This is not one way speed of light.
– MBN
Nov 2, 2020 at 10:45

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.

• Can you explain (simply, please--I have a shallow understanding of GR) why saying that the light travels in one direction in spacetime is like proposing a different theory? I thought that was GR.
– user276997
Nov 2, 2020 at 16:09
• Light travels in all directions in space. In the absence of gravitating bodies, space is homogeneous and isotropic, and this means that all the significant properties, including the causal connectivity (i.e. which intervals are spacelike, which timelike), are isotropic and homogeneous. This implies that the maximum speed for signals does not depend on the direction in space that the signals are travelling in. Nov 2, 2020 at 18:11
• So does that mean that the whole premise of the Veritasium video is incorrect? He says that (as far as we know) there is no way of measuring the one-way speed, so we wouldn't know if the speed for signals depends on the direction in space.
– user276997
Nov 2, 2020 at 18:34
• Yes the premise is incorrect. Physics address questions like this by introducing a wide-ranging and deep model such as General Relativity. It is not simply a measurement here, a measurement there. It is a whole set of phenomena all linked together in a coherent, logical, elegant whole. Nov 2, 2020 at 19:57
• Interesting. Veritasium made it sound as if there were many physicists trying to figure out the answer to this problem (which implies that it is not incorrect).
– user276997
Nov 2, 2020 at 21:01

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

• No, this situation is nothing like the fiber optic cable. In this case, the light travels in a straight line in spacetime due to the black hole.
– user276997
Nov 2, 2020 at 16:10
• @NotSoPedantic The Moon rotates around the Earth also along a straight line in spacetime, but not along a straight line in space. Geodesic are not trajectories. Nov 2, 2020 at 17:21
• So does the one-way speed mean in one direction in space or one direction in spacetime?
– user276997
Nov 2, 2020 at 18:32
• @NotSoPedantic In space. Nothing can move back in time. Nov 4, 2020 at 20:23

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 $$2\pi r$$, 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.

• Ah, yes. You are correct: the photon sphere. Honestly, I don't know anything about black holes, so I thought it was the event horizon, but you are right. Thank you!
– user276997
Nov 2, 2020 at 16:07

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 ..

• I don't think so. I don't know too much about GR, but I don't think light bends spacetime. Instead, I think light merely travels along the path of spacetime, which has been curved by, in this case, a black hole. As for the unification of the direction of the light, I think that is irrelevant in this case. Only the photons traveling completely tangent to the event horizon will complete a revolution around the black hole, so it doesn't matter if there are other photons that don't complete this. Maybe I'm wrong, so let me know.
– user276997
Nov 2, 2020 at 8:42
• @NotSoPedantic Mass bends spacetime, mass and energy have an equivalence, so energy also bends spacetime. Nov 2, 2020 at 10:42
• @AdrianHoward Oh. Does the mass have to be converted to energy before it can bend spacetime, or can it do that while it's still in energy form?
– user276997
Nov 2, 2020 at 16:11
• @NotSoPedantic Both mass and energy warp spacetime, you might read; en.wikipedia.org/wiki/Spacetime Nov 2, 2020 at 23:22
• @AdrianHoward Interesting; thanks for the link. So this wouldn't work because the light itself would also bend spacetime?
– user276997
Nov 3, 2020 at 0:11

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.