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

[PeroK]

If you define you 4D-coordinate system based on an Einstein clock synchronization, then you have an isotropic one-way speed of light (because you have stipulated it this way).

If you define you 4D-coordinate system based on a non-Einstein clock synchronization, then you have an anisotropic one-way speed of light (because you have stipulated it this way).

I think the OP's assumption is that these must represent two different physical realities. He's assuming that they can't both be valid, so it must be one or the other. And, is trying to devise an experiment to reveal which one is correct.

The OP does not see how both these conventions can be possible in the same universe.

Perhaps (not certainly) the issue is that you don’t fully recognize the anisotropic one-way speed of light as a simple coordinate transform. You appear to have some proficiency with mathcad. Perhaps you should implement the coordinate transform posted previously and play around with it to convince yourself that it does indeed change the one way speed of light but not the two way speed of light.

And, the OP's assumption is that such a "coordinate transformation" changes the physics (as it changes the one-way speed of light).

And, since it changes the physics, there must be an experiment that proves that this coordinate transformation is not physically valid.

Finally, I was thinking of an analogy. We know that classical projectile motion problems can be done with the acceleration of gravity being $g = \pm 9.81 \ m/s^2$. I.e. we can set up a problem with "up" being positive and $g = -9.81 \ m/s^2$. Or, we can do a coordinate transformation so that "up" is negative and $g = 9.81 \ m/s^2$.

The OP's assumption would be that "up" is either positive or negative and there must be an experiment to determine which is correct.

 

[HansH]

at this moment I am mainly digesting the info I get from you, but perhaps it makes sense for the proper understanding to verify if next fragment of this movie is correct:

because of they say that you receive the light from one direction istantly and from the other direction at c/2 you see the complete universe as is it now in one direction and a it was far in the past in the opposite direction. so is this a coordinate transformation or real speed of light using same physical coordinates (as he looks on both directions using coordinates as we measure on Earth so suppose they are the same)

edit: because if it is only based on a coordinate transformation, I could use another transformation and this would mean for the movie that what I saw in one direction first seeing Mars instantly then changes into seeing Mars 20 minutes ago, so that would means I invented a time machine so could not be true.

 

[Dale]

so is this a coordinate transformation

Yes, despite the wonderment in his voice as he talks about this topic, it is nothing more than a coordinate transformation. There is no physics involved.

This is one of his worst videos ever. Not that what he says is wrong, but he leaves out the most important fact (that it is just a coordinate transform) and speaks in a way that makes the audience think he is talking about some mysterious unknown physics instead of some completely understood and mostly useless math.

if it is only based on a coordinate transformation, I could use another transformation and this would mean for the movie that what I saw in one direction first seeing Mars instantly then changes into seeing Mars 20 minutes ago, so that would means I invented a time machine so could not be true.

Well, one of the mathematical requirements of a coordinate system is that it must be a one-to-one mapping from spacetime to R4. So while you could change from seeing Mars instantly to seeing it 20 min ago, you would have to do so gradually in a way that avoids mapping the same event to two different coordinates. Thus you would not get a “time machine”

 

[Ibix]

you see the complete universe as is it now in one direction and a it was far in the past in the opposite direction.

This is because he has applied a coordinate transform such that "stuff hapenning now" is defined to be exactly what he sees in that one direction (and stuff he hasn't seen yet in others).

He hasn't changed what he sees, he's chosen to change how he interprets what he sees.

 

[Ibix]

I should add that I think the $c_+=\infty$, $c_-=c/2$ case is on rather dubious ground because one of your "spatial" coordinates is lightlike. There's nothing wrong with it mathematically, but it has even fewer of the properties of a frame (depending on your definition of "frame", of course) than the $c<c_+<\infty$ cases have.

 

[PeroK]

At about 15:45 in this video he asks: "If it makes no difference to physics, then what is the point of talking about it?". Good question!

 

[Vanadium 50]

You had the stamina to sit through the video? My hats off to you.

 

[PeroK]

You had the stamina to sit through the video? My hats off to you.

No. The link started at 15 minutes!

 

[HansH]

This is one of his worst videos ever. Not that what he says is wrong, but he leaves out the most important fact (that it is just a coordinate transform) and speaks in a way that makes the audience think he is talking about some mysterious unknown physics instead of some completely understood and mostly useless math.

Thus you would not get a “time machine”

I think this explains a lot and could be the reason why this topic gets so long. Because this movie triggered me to find out what is going on. it sounded very strange to me and even worse, put me completely on the wrong leg by this 'looking into the past or not' explanation. so simple coordinate transformation, nothing special and no actual speed of light being different than in the way most people think of the speed of light.

 

[PeroK]

I think this explains a lot and could be the reason why this topic gets so long. Because this movie triggered me to find out what is going on. it sounded very strange to me and even worse, put me completely on the wrong leg by this 'looking into the past or not' explanation. so simple coordinate transformation, nothing special and no actual speed of light being different than in the way most people think of the speed of light.

There is a similar issue with the expanding universe. In comoving coordinates we have galaxies essentially stationary and space expanding. The galaxies have only a subluminal peculiar velocity relative to expanding space.

But, change to different coordinates and we have the galaxies moving faster-than-light (as a coordinate speed). The assumption in GR is the locally-measured (two-way!) speed of light is always $c$. And, we do not have expanding space in these coordinates.

We can't read too much into this, because these are coordinate-dependent statements. The invariant statement is that universe overall has a certain spacetime curvature, which may manifest itself as expanding space, coordinate speeds greater than $c$ or whatever else - depending on the choice of coordinates.

 

[HansH]

There is a similar issue with the expanding universe.

these are coordinate-dependent statements. The invariant statement is that universe overall has a certain spacetime curvature, which may manifest itself as expanding space, coordinate speeds greater than $c$ or whatever else - depending on the choice of coordinates.

I think you mean the statemanent that the whole universe once was a big as an orange? but you cannot talk about the size of an orange because the size itself to measure with was also reduced with the same factor? same way to put people on the wrong leg I assume. I think I get it.

 

[Ibix]

I think you mean the statemanent that the whole universe once was a big as an orange?

No - this is a common but totally incorrect statement. The observable universe was once the size of an orange (if classical gravity is valid that early, anyway), but the whole universe was always infinite as far as we are aware.

I think the point @PeroK is making is that you can make galaxy velocities vary wildly by a simple coordinate change. This is not solely a light phenomenon.

 

[cianfa72]

The assumption in GR is the locally-measured (two-way!) speed of light is always $c$.

So, regardless of the coordinate chart employed to cover locally a limited region of spacetime, the outcome of experiments designed to measure locally the two-way speed of light is always the same: it is isotropic with fixed speed $c$.

 

[Ibix]

So, regardless of the coordinate chart employed to cover locally a limited region of spacetime, the outcome of experiments designed to measure locally the two-way speed of light is always the same: it is isotropic with fixed speed $c$.

Yes. Locally, all GR spacetimes look like Minkowski spacetime for the same reason your kitchen floor looks Euclidean even though it's part of the curved surface of the Earth.

 

[HansH]

Yes, despite the wonderment in his voice as he talks about this topic, it is nothing more than a coordinate transformation. There is no physics involved.

Just one question about this movie as a check for me. at a certain moment they compare both situations left and right where left is the standard with normal Einstein synchronisation I suppose. but the question is what they are doing in the right picture: is this the coordinate transformation you talked about several times or are they showing here something else. What I would think is that they make a space time diagram with positive light speed c/2 and negative light speed infinite, but with the original horizontal end vertical coordinates (horizonta; is the distance between Earth and Mars), vertical is the time between sending a signal and receiving back the signal from Mars. but I am not sure. 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?

 

[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).