One-way speed of light

[FranzS]

Hi PF,
as far as my modest knowledge goes, measuring the one-way speed of light is impossible / non-sensical (?).
Thus I'm not here to actually propose a possible method for that purpose, but I just would like the savvy among you to point out the fallacy in my reasoning.

That said, I was thinking about an ideal situation where one could find himself right on the event horizon of a (non-spinning, non-charged?) black hole and could emit light tangentially to the event horizon surface. Ideally, wouldn't light travel around the black hole following a geodesic on the event horizon surface and eventually come back to where it started? In case it would, can this be considered as a one-way path?

Sorry in advance if I'm posing a stupid question, I'm here to learn. Thanks!

 

[PeterDonis]

measuring the one-way speed of light is impossible / non-sensical (?).

No, it's not impossible/non-sensical. It's just frame-dependent; in other words, what you're measuring isn't actually a property of light, it's a property of whatever reference frame you have chosen.

one could find himself right on the event horizon of a (non-spinning, non-charged?) black hole

You can, but only for an instant; you can't stay there. You must fall inward. Why? Because to stay at the horizon, you would have to move radially outward at the speed of light. And you can't.

and could emit light tangentially to the event horizon surface.

"Tangentially" is ambiguous here. If you think of the horizon (or more precisely the cross section of it that you are "at" at the instant when you, falling inward, are just crossing the horizon) as a 2-sphere, "tangentially" could mean emitting light tangentially to that 2-sphere. But such light would not stay at the horizon; it would fall inward (but not as fast as you do).

Or "tangentially" could mean emitting light tangentially to the horizon in a spacetime sense--but this "tangentially" is radially outward in a spatial sense, i.e., not tangential to the 2-sphere in the sense given above. Light emitted in this way will stay at the horizon, but (a) not in the way you are thinking (see below), and (b) you won't stay at the horizon, so you will never see that light again in any case.

wouldn't light travel around the black hole following a geodesic on the event horizon surface and eventually come back to where it started?

No. The horizon is a surface in spacetime; light emitted radially outward at the horizon travels in a null direction that works like traveling into the future, the way light emitted radially outward from an ordinary 2-sphere does. The difference is that, due to the curvature of spacetime, this radially outgoing light stays at the same radius, i.e., if you imagine the entire 2-sphere cross section of the horizon at an instant, and imagine a 2-sphere of light emitted radially outward from all around that 2-sphere, the 2-sphere of light will maintain a constant radius (more precisely a constant surface area, from which we compute a "radius"), even though it is moving radially outward. But no light ray ever returns to a point in spacetime that it was at before, and no light ray goes around the 2-sphere; each light ray stays at the same point on the 2-sphere that it was emitted from.

 

[Dale]

Ideally, wouldn't light travel around the black hole following a geodesic on the event horizon surface and eventually come back to where it started?

What you want is the photon sphere, not the event horizon.

This is a so called two-way measurement, the same as if you had placed a bunch of mirrors or a fiber optic cable to route the light in a circle.

 

[FactChecker]

Replace "one-way speed of light" with "one-direction speed of light" and you will see that your proposal is not what they wanted.

 

[PeterDonis]

Replace "one-way speed of light" with "one-direction speed of light" and you will see that your proposal is not what they wanted.

The OP specifically described light going around in a circle. So the photon sphere scenario @Dale described is what the OP said they wanted. (The OP just didn't realize that it needs to be done at the photon sphere, not the horizon, and that it does not qualify as a one-way speed of light measurement.)

Also, light that goes around a photon sphere does go in one direction only. So the scenario described meets your implied criterion for a "one-direction speed of light" measurement. It just doesn't qualify as a "one-way" measurement as that term is used in the literature. (We have had a number of previous threads on this topic in which references to that literature have been given, quite a few of them by @Dale.)

 

[FactChecker]

The OP specifically described light going around in a circle. So the photon sphere scenario @Dale described is what the OP said they wanted.

Is that what people really want when they say "one-way speed of light"?

 

[PeterDonis]

Is that what people really want when they say "one-way speed of light"?

"What people really want" when they ask questions without fully realizing the actual implications according to GR (or indeed any physical theory) often does not exist. The best we can do is to describe what the actual implications are and wait for the OP to ask follow up questions.

 

[Dale]

Replace "one-way speed of light" with "one-direction speed of light" and you will see that your proposal is not what they wanted.

The terminology isn’t great, but at this point we are pretty much stuck with it. “One way” is a path with a distinct beginning and end and “two way” is a closed loop path. What they are describing is a closed loop.