I Can we determine the one way speed of light by combined measurements?

[Ibix]

The right hand diagram should just be a sheared version of the left. If you move the 12.00 marker on the Mars line half way up the diagram then it would be correct, although the clocks are still Einstein synchronised and therefore not synchronised in this diagram. Alternatively you can move the 12.10 marker on the Mars line down to the middle to have them synchronised in this coordinate system (but this would be inconsistent with the left hand diagram).

Note that different scales at different places is fine, but is simply pointless extra complexity. Getting different scales that preserve particular light rays as straight is even harder.

 

[Dale]

So it this correct what happens here?

Yes, the diagram appears accurate.

 

[Sagittarius A-Star]

Also the time scale for the right picture is different for the left vertical line (20 minutes) and right vertical line (10 minutes). So it this correct what happens here?

The diagram on the right-hand side is wrong. The "12:00" on the bottom right-hand side should be 11:50. Reason: In the audio track of the video it says: "Their clocks are out-of-sync by 10 minutes".

 

[HansH]

it is so far clear that it is imossible to measure the one way speed of light. But there is one situation that I would appreciate to have an opinion of specialists:
when close enough to a black hole it is possible for light to make a complete circle. so being at that position it is said that the a lightbeam that you send can hit yu at the back of your head making one round around the black hole. but as I understood light always goes in a straight line, so one specific direction, but it is spacetime that is curved causing the light to pass the same position twice. But why is that not a possibility to measure the one way speed of light?

 

[Ibix]

But why is that not a possibility to measure the one way speed of light?

Because it's a two way measure, with the black hole's gravitational field in place of a mirror.

It's also GR where the speed of anything that isn't at your current location isn't necessarily well defined, and things like the constancy of the speed of light turn out to be flat spacetime specialisations of more geometrical concepts about light cones.

 

[Dale]

But why is that not a possibility to measure the one way speed of light?

A two way measurement is characterized by a single clock and a closed light path, which as, @Ibix says, is what you describe. But a one way measurement has light go on a geodesic, which also is what you describe. I am not sure that a strict categorization is possible in curved spacetime.

In order to get a speed you need both a time and also a distance. The arrangement of your experiment makes the time independent of synchronization, but the distance is not.

Suppose that we have a rope around the black hole and that the rope is laid out so that the light pulse follows its length the whole way around. Now, general relativity is a four-dimensional geometric theory, so in 4D spacetime that rope forms a cylinder. We can put marks at regular points along the rope, and those marks form lines going along the length of the cylinder, and we can put one mark next to the clock as the reference mark.

Then, the pulse of light forms a helix which winds around the cylinder, starting and ending at the reference mark. The intersection of the helix with the reference mark forms a pair of events, but the only frame-invariant measurements are the spacetime intervals along the reference line and the helix between those two events. The reference line interval gives us a time, but the helix interval is null so it does not give us a distance.

To get a distance we have to draw a set of spacelike lines circumferentially around the cylinder, and then measure the interval around the cylinder along those lines. The issue is that many different sets of lines are valid. We can have some that cut straight across the cylinder and others that slice it at an angle, and even other sets that are more exotic. The interval around the cylinder depends on which set of lines we choose. Each set of lines represents a different valid simultaneity convention. That convention will determine both the overall global length as well as the local one-way speed of light at each point.

Now, you may claim that there is only one natural set of lines to use, specifically the one cutting straight across the cylinder which would be the proper length of the rope. That is true, but the whole discussion about the one-way speed of light is not about naturalness. Indeed, it is clear that it is unnatural to assume an anisotropic one-way speed of light given the isotropic two-way speed of light. So naturalness is not at issue, the question is whether other unnatural conventions are nevertheless consistent with the observable data as predicted by the natural convention. In this case, they are.

So, although this approach does have some similarities with a flat-spacetime one-way measurement, it does not avoid the key problem inherent to all one-way measurements: the result depends on your chosen synchronization convention.

 

[Grinkle]

@Ibix @Dale

I have a tangential question if you would indulge me - is such an experiment achievable in principle? Would the measurement device be able to transmit its signal to an observer outside the EH? If light is orbiting, that is already closed spacetime and no signal can get out in any case, is my intuition and why I am asking that.

 

[Ibix]

If light is orbiting, that is already closed spacetime and no signal can get out in any case, is my intuition and why I am asking that.

There's an unstable circular orbit for light at 1.5 times the Schwarzschild radius, which is what we're talking about. There's no problem communicating to and from there.

There are no orbits at the horizon. Light can "hover" at the event horizon if it has no tangential component to its motion, but any tangential motion and it'll fall in.

 

[HansH]

@Dale:
Sorry, but I cannot follow your reasoning probably due to my limited knowledge of spacetime curvature. but if a circular orbit for light at 1.5 times the Schwarzschild radius is possible as mentioned, and there's no problem communicating to and from there, then why can't you measure the time between sending and receiving that light pulse send around 1 time and compare that with the same situation with the light pulse send in the opposite direction? Then you can compare both and conclude if c is the same in both directions. Or is there something going on with the distance of the path? Or do you mean something else that I missed?

Reference: https://www.physicsforums.com/threa...ined-measurements.1014053/page-4#post-6621913

 

[HansH]

the result depends on your chosen synchronization convention.

I don't thin I can follow you here. we are talking about 1 observer that sendt a light pulse and receives is also after one round around the black hole. Iassume synchronization is only needed if you have 2 observers at a distance from each other? Or do you mean that the observer can not have information how to remain at the same place during the experiment?

 

[Ibix]

why can't you measure the time between sending and receiving that light pulse send around 1 time and compare that with the same situation with the light pulse send in the opposite direction?

You can, and the times will be the same.

Or is there something going on with the distance of the path?

Yes. The distance depends on your choice of definition of "space".

 

[Dale]

Iassume synchronization is only needed if you have 2 observers at a distance from each other? Or do you mean that the observer can not have information how to remain at the same place during the experiment?

A synchronization convention is part of the definition of a coordinate system, regardless of the number of observers. Even a single observer needs a synchronization convention if they are going to assign times and positions to events.

then why can't you measure the time between sending and receiving that light pulse send around 1 time and compare that with the same situation with the light pulse send in the opposite direction? Then you can compare both and conclude if c is the same in both directions.

Because that does not exclude the possibility that the speed of light is not constant along the path. There is a wide range of anisotropic synchronization conventions that lead to a varying speed of light during the trip and are nonetheless compatible with a total trip duration that is fixed in both directions.

 

[HansH]

You can, and the times will be the same.

are you measuring the one way speed of light then? because the light follows a straight line in curved spacetime as it hits the back of your head.

 

[HansH]

A synchronization convention is part of the definition of a coordinate system, regardless of the number of observers. Even a single observer needs a synchronization convention if they are going to assign times and positions to events.

but what do you then synchronize compared to what? I think I still cannot follow as we talk about differences in time between sending and receiving the same lightbeam. I would think that when you synchronize the time that this gives the same adaption for both moments, so therefore I do not understand what an absolute synchronisation brings here.

 

[Dale]

but what do you then synchronize compared to what? I think I still cannot follow as we talk about differences in time between sending and receiving the same lightbeam. I would think that when you synchronize the time that this gives the same adaption for both moments, so therefore I do not understand what an absolute synchronisation brings here.

I think you have a misunderstanding of what a synchronization convention is. A synchronization convention is the convention by which you take any two events and decide whether or not they happen at the same time.

Einstein’s synchronization convention is based on the assumption that the one way speed of light is isotropic. A different assumption leads to a different one way speed of light.

 

[HansH]

I think you have a misunderstanding of what a synchronization convention is. A synchronization convention is the convention by which you take any two events and decide whether or not they happen at the same time.

Einstein’s synchronization convention is based on the assumption that the one way speed of light is isotropic. A different assumption leads to a different one way speed of light.

I think I know as that was the topic. But as I understood this is because you can only measure the 2 way speed of light so you can do an assumption about both one ways speeds of light for example light going to the moon and back via a mirror. assuming both speeds are the same it takes 1 second means that how you see the moon now is as it was 1 second ago. and if you assume the speed to the moon is 1/2c and back is infinite you assume you see the moon instantly. But here we have a different situation. you send 1 light beam that goes in a straigt line through a curved spacetime so I assume this is the one way speed of light. and because it hits you making 1 round I do not see why it makes sense to make a synchronization convention. Probably I still mis your point.

Reference: https://www.physicsforums.com/threa...ined-measurements.1014053/page-4#post-6806772

 

[Nugatory]

But here we have a different situation. you send 1 light beam that goes in a straigt line through a curved spacetime so I assume this is the one way speed of light.

That’s a two-way measurement. The essential difference between a one-way and a two-way measurement is that a two-way measurement uses two readings from the same clock, while a one way measurement uses two clocks.

A two-way measurement requires that the light signal make a round trip (to leave the clock and eventually get back again) and requires no clock synchronization (because there’s only one clock). The one way measurement doesn’t require a round trip (light leaves one clock, arrives at the other) but requires that the two clocks be synchronized (because only then will the difference between the start time at one and the arrival time at the other be the time of flight).

 

[HansH]

That’s a two-way measurement. The essential difference between a one-way and a two-way measurement is that a two-way measurement uses two readings from the same clock, while a one way measurement uses two clocks.

A two-way measurement requires that the light signal make a round trip (to leave the clock and eventually get back again) and requires no clock synchronization (because there’s only one clock). The one way measurement doesn’t require a round trip (light leaves one clock, arrives at the other) but requires that the two clocks be synchronized (because only then will the difference between the start time at one and the arrival time at the other be the time of flight).

I know, but Iassumed that light that goes around a black hole and hits the obeserver at the back of its head also only needs one clock to measure, as it passes the same point twice. So there is no second clock needed that needs to be synchronized because 2 measurements can be done with the same clock at the same place. and also no mirrors needed that force the light in the opposite direction (would cause 2 directions) but the straight line that the light follows is in fact a loop in a curves spacetime, therefore still is one same direction. Or do I mis something here?

 

[Dale]

because it hits you making 1 round I do not see why it makes sense to make a synchronization convention

Hopefully this graphic helps. Here we have two of the many possibilities, both of which are consistent with this measurement. Here the areal radius of the photon sphere is 1 light-second and the time is given at that radius rather than at infinity and I use units where c=1.

The measured result is just the time that the light pulse leaves and returns, so the vertical coordinate at the top and bottom of the graph. That is all that is measured. The rest is inferred from the synchronization convention.

The blue line represents the standard Einstein synchronization convention where the speed of light is 1 everywhere. The red line is the same physical scenario using Anderson's synchronization convention where the speed of light varies between 0.625 at $\theta=\pi$ and 2.5 at $\theta=0$ ($\kappa = 0.6$).

The measured time is the same for both so this measurement does not distinguish between the two conventions. To get a measurement of the one way speed of light you need to find a measurement whose outcome depends on Anderson’s $\kappa$, but no such measurement exists.

 

[Nugatory]

therefore still is one same direction. Or do I mis something here?

The “one direction” thing is a red herring - what matters is that there is one clock, and that makes it a two-way measurement. You are using gravity to direct the light on a closed path instead of bouncing it off mirrors, but it is still a closed path and the difference between the two readings of the same clock give you an invariant coordinate-independent travel time.

(As an aside, “direction” is a slippery concept in spacetime - you may be giving it more weight that it deserves).

 

[Ibix]

are you measuring the one way speed of light then?

No, I'd say it's a two way measure. You can run the light either way round it, which might be misleading you, but you could do the same with a triangular trip (still a two way measure) in flat spacetime. All the flexibility here is in how you define space, which is usually glossed over in SR because you can always choose a flat plane.

 

[HansH]

No, I'd say it's a two way measure. You can run the light either way round it, which might be misleading you, but you could do the same with a triangular trip (still a two way measure) in flat spacetime. All the flexibility here is in how you define space, which is usually glossed over in SR because you can always choose a flat plane.

I would assume the difference between the 2 is that with the triangular trip in flat space you change the direction of the light 3 times therefore using more directions in space. But in the other case you do not change the direction of the light by some mechanical means. so if you say it is the same, then I am again lost.

 

[HansH]

As an aside, “direction” is a slippery concept in spacetime - you may be giving it more weight that it deserves.

talking about one way speed of light it first requires to understand what 'direction' actually means. so at that point I am already lost. I would assume direction means what a light beam does always keeping the same direction (in vacuum) following a geodesic. so I think this reqires an explanation 1 level deeper about what direction actually is.

 

[HansH]

Hopefully this graphic helps.

actually I do not understand what you plot there. do you send lightbeams in a different direction? but how does that fit into the circular ring of light at 1.5 times the Schwarzschild radius? or do you do something else?

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[Dale]

but how does that fit into the circular ring of light at 1.5 times the Schwarzschild radius?

$\theta$ is the angular position around the ring. It is a spacetime diagram around the ring. The two plots show the same loop of light under two different synchronization conventions. Both are compatible with the same observation but they disagree about the one way speed of light.

 

[Nugatory]

talking about one way speed of light it first requires to understand what 'direction' actually means.

We’re doing a one-way measurement of the speed of light if we’re looking at the time it takes for light to travel along a path from the starting point to a different endpoint.
We’re doing a two-way measurement if we’re looking at the time it takes for light to travel a path that takes the light on a round trip back to the starting point.

Stated this way, we don’t need to understand what ‘direction’ actually means.

 

[Ibix]

I would assume the difference between the 2 is that with the triangular trip in flat space you change the direction of the light 3 times therefore using more directions in space. But in the other case you do not change the direction of the light by some mechanical means. so if you say it is the same, then I am again lost.

I would say that if this is confusing you, don't worry about it. By introducing curved spacetime you are adding a lot of complications that aren't really relevant to your original problem.

Fundamentally, the problem with the one way speed of light in flat spacetime boils down to the fact that you cannot synchronise clocks that are not in the same place without assuming a speed of light. If you have a method that only uses one clock then it's a two-way measure, however you construct the details. The same is true in curved spacetime, except there are added complications around what you mean by distance that mean that you won't necessarily find your speed of light to be constant over a long path (google Shapiro delay - one interpretation is in terms of a variable speed of light) although all local two way measurements along the path will show it to be $c$.

Ultimately, this kind of thing is why physicists don't care about the one way speed of light. It's just a consequence of the relativity of simultaneity, and understanding that is a help in curved spacetime. The only lesson to take from the one-way speed of light is that Newtonian physics isn't the same as relativity.

talking about one way speed of light it first requires to understand what 'direction' actually means

The problem is that "direction in spacetime" is well-defined but "direction in space" (and hence "velocity through space") depends on your definition of "space". You (whether you know it or not) want One True Division of spacetime into space and time, as there is in Newtonian physics. That is why one-way speeds are measurable in Newtonian physics. But relativity does not work that way - dividing spacetime into space and time can be done in many ways and one way speeds (of everything, not just light) depend on that choice.