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

[cianfa72]

Another try. Let us assume I have a vacuum. I synchronize my clocks using Einstein synchronisation. Now I replace the vacuum by a material. I don't touch the clocks anymore after this substitution. Is it possible that I measure now a different speed in one direction in comparison to the reverse direction?

Your experiment involves two legs: a light beam sent from clock A to clock B (outbound leg) reflected back to A (return leg).

Assume that the measurement of two-way speed of light when the vacuum is replaced by a material doesn't change (note that a such measurement involves a clock alone hence the synchronization convention is irrelevant). Then we can ask if the one-way speed of light in both directions is the same or not when the vacuum is replaced by a material (provided that clock A and B were Einstein's synchronizated in the vacuum case that is the same as the one-way speed of light in both directions was the same by very definition of Einstein's synchronization convention).

 

[Nugatory]

Does it have an actual physical content about a property of the light or is it just a re-statement of the Einstein's synchronization procedure/convention?

Why not both? Einstein clock synchronization assumes that light has the useful property of moving at the invariant speed, so measurements using Einstein-synchronized clocks must yield that speed.

 

[PeroK]

Another try. Let us assume I have a vacuum. I synchronize my clocks using Einstein synchronisation. Now I replace the vacuum by a material. I don't touch the clocks anymore after this substitution. Is it possible that I measure now a different speed in one direction in comparison to the reverse direction?

It's not clear what you aim to achieve by this. You could, for example, emit a pulse of light in one direction, have it reflect off a mirror and then pass through an inserted medium on its way back. In that way, you would get a "different speed" on the return leg. But, that's not what this is about. This is about the fact that the Einstein synchronisation convention is just that: a convention. Once you have adopted this convention there's no particular theoretical issue with devising an experiment where the measured speed is different in each direction - assuming speed is defined in accordance with your chosen convention.

The whole issue of the one way speed is light is really a slightly unintuitive consequence of the relativity of simultaneity. It's not that you cannot define remote simultaneity if you want to, it's that this definition is not unique. Likewise any measurement of a one-way speed of light is not the only possible measurement. If you change your synchronisation convention, you change your measured one way speed.

 

[Ibix]

I'm thinking red-shift should indicate a different distance if light speed is different.

Cosmological redshift? If you pick a non-isotropic light speed then you've changed your definition of "now", so the distances to distant galaxies "now" are indeed different. It doesn't affect the measured redshift, though, because that's independent of your choice of coordinates. You've changed distance and travel time and chosen to work in non-orthogonal coordinates, but inevitably done so in a way that the effects of the changes cancel out whenever you try to measure anything.

 

[cianfa72]

Why not both? Einstein clock synchronization assumes that light has the useful property of moving at the invariant speed, so measurements using Einstein-synchronized clocks must yield that speed.

Sorry, if we define the one-way speed of light to be $c$ by means of Einstein's synchronization procedure/convention applied to spatially separated clocks at rest in an inertial frame, then by definition the measurement of such one-way speed must return that constant/invariant value $c$.

However if we repeat the experiment again using a light source moving at a given velocity $v$ w.r.t our inertial frame then we can ask: do the two spatially separated clocks remain synchronized as well ?

If the answer is positive then I believe we can attach an actual physical content to the Einstein's statement in #36, namely "light is always propagated in empty space with a definite velocity which is independent of the state of motion of the emitting body."

 

[Dale]

Does it have an actual physical content about a property of the light or is it just a re-statement of the Einstein's synchronization procedure/convention?

Yes, it has physical content. The physical content is that the two-way speed of light is c.

It is also a convention. There are many possible one-way speed of light combinations with the same physical content. Einstein’s statement chooses the simplest of those.

 

[cianfa72]

Yes, it has physical content. The physical content is that the two-way speed of light is c.

ok, that makes sense.

It is also a convention. There are many possible one-way speed of light combinations with the same physical content. Einstein’s statement chooses the simplest of those.

So it is a convention just from the one-way speed of light point of view. In particular assuming Einstein's synchronization convention means the one-way speed of light results as isotropic.

 

[cianfa72]

As in my post #41 I believe there is also another physical content. It is that given an inertial frame if we do a measurement of two-way speed of light the result is always the same regardless of the state of motion of the light source employed w.r.t the given inertial frame.

 

[HansH]

as far as I understand it could be that the 1 way speed of light can vary between c/2 and infinite. Does anyone know if ever work has been done to find out if this really can be the case or that the only conclusion can be that the one way speed is c in all directions? At this moment I think I have proof that it can only be c but I want to first give our Dutch forum the chance to discuss my input and see if it can be dismantled and come back here later, but at least good to know if any analyses was ever done.

 

[Ibix]

Does anyone know if ever work has been done to find out if this really can be the case or that the only conclusion can be that the one way speed is c in all directions?

Einstein synchronise your clocks. Pick one clock and a direction to call $\hat{\vec{x}}$, and set every other clock fast or slow by an amount $x/v$ where $x$ is the x coordinate of the clock and $v$ is a constant of your choosing with dimensions of velocity, the only restriction being that $|v|>c$. Congratulations, you have changed the one way speed of light.

At this moment I think I have proof that it can only be c

If you think you have this then you have unknowingly introduced that assumption somewhere. The choice of one-way speed is just the choice of an angle between your $t$ and $x$ axis (which may be implemented by the process I described above). There is no measurable consequence to such a choice.

 

[Dale]

Does anyone know if ever work has been done to find out if this really can be the case or that the only conclusion can be that the one way speed is c in all directions?

Yes, there has been almost 100 years of work in this topic already. The original work was by Reichenbach in 1924

https://books.google.com/books?id=O...tization of the Theory of Relativity"&f=false

Here is a good review article on the topic, which is probably a better place to start than Reichenbach’s original work, particularly if one believes that they have made a major breakthrough in this field without actually knowing any of the prior art.

https://arxiv.org/abs/gr-qc/0409105

Finally, this is my favorite reference on the topic. When I do my own calculations on this topic I use Anderson’s approach since the math is easier than Reichenbach’s.

https://www.sciencedirect.com/science/article/abs/pii/S0370157397000513

I think I have proof that it can only be c

As I have already mentioned above, this is wrong. It is not a matter of clever experiments. As has been well understood for 98 years, there is simply no possible experiment which can distinguish Einstein’s synchronization convention from Reichenbach’s or Anderson’s

 

[HansH]

Yes, there has been almost 100 years of work in this topic already. The original work was by Reichenbach in 1924

As I have already mentioned above, this is wrong. It is not a matter of clever experiments. As has been well understood for 98 years, there is simply no possible experiment which can distinguish Einstein’s synchronization convention from Reichenbach’s or Anderson’s

thaks a lot for these references I will check. (hopefully not too complicated as I am not a prefessional physicist) regarding your remark about clever expriments of course I agree that there is no experiment possible as you cannot see the difference in the one directional speed in any measured result. But do you also think that it is not possible to proove that there can be a additional limitation on the range between c/2 and infinite? because I think I have that proof now. (but of course I could have made a mistake)

 

[Ibix]

At this moment I think I have proof that it can only be c

I took a quick glance at your pdf and didn't see a metric tensor anywhere. That means that most likely you haven't realized that the metric is no longer diagonal in non-orthogonal coordinates (and likely that your basis vectors are no longer normalised). If you are implicitly assuming a diagonal metric, this is equivalent to assuming an isotropic speed of light.

 

[Dale]

But do you also think that it is not possible to proove that there can be a additional limitation on the range between c/2 and infinite? because I think I have that proof now. (but of course I could have made a mistake)

You have definitely made a mistake. There is no additional limitation. Are you familiar with the math of GR? If so, the proof is nearly trivial.

 

[HansH]

I took a quick glance at your pdf and didn't see a metric tensor anywhere. That means that most likely you haven't realized that the metric is no longer diagonal in non-orthogonal coordinates (and likely that your basis vectors are no longer normalised). If you are implicitly assuming a diagonal metric, this is equivalent to assuming an isotropic speed of light.

of course tat could be my limitation as i am not that familiar with general relavitity. But assuming flat space without mass nearby and no moving persons etc, do we than still need a metirc tensor making things different?

 

[Ibix]

But assuming flat space without mass nearby and no moving persons etc, do we than still need a metirc tensor making things different?

Yes.

Let's say I am at the origin, you are at (1,1). How far apart are we? If you say $\sqrt 2$ you are assuming that the coordinates are orthonormal. I could be measuring distance in the x direction in different units from in the y direction - so we could be 1m apart in one direction and 1km apart in the other. I might not have defined my x and y directions as perpendicular, in which case we could be almost 2 units apart or almost zero (assuming I'm using the same distance units this time) depending on whether my axis directions are almost parallel or almost anti-parallel. The metric tensor is what deals with all of this and makes the answers consistent.

If you are using non-orthogonal and possibly unnormalised coordinates (which you are if you are considering a non-isotropic speed of light), you need to account for that in your maths. You don't appear to be doing this, so you are implicitly using orthonormal coordinates, which means that you are implicitly assuming an isotropic speed of light. That's why your answer is that the speed of light must be isotropic - because you assumed it.

 

[HansH]

Yes.
so If I understand you right you say that at using the normal coordinates we are used to in daily life that then the one way speed of light is always c?

 

[Ibix]

Choosing to use orthonormal coordinates on spacetime (not just space) is the same as choosing that the one way speed of light is isotropic, yes.

If you want to consider non-isotropic speeds of light you have chosen to consider non-orthonormal coordinates, and you need to factor the implications of that into your maths.

 

[HansH]

ok thanks, but that means that what I wanted to proof is already a given fact. My assumption was that the one way speed of light could have different values depending on the synchronisation of your clocks. That was at least my understanding from this movie:

 

[Dale]

But assuming flat space without mass nearby and no moving persons etc, do we than still need a metirc tensor making things different?

This doesn't have anything to do with curved spacetime and gravitation. It is just that the math that is used in GR makes this issue very clear, almost trivial. In GR, the math is designed so that one can write the laws of physics in a form where it is clear that the laws of physics are independent of the choice of coordinates. For example, in this form we can write Maxwell's equations as $\partial^2 A^\sigma=\mu_0 J^\sigma$ where $A$ is the four-potential in the Lorenz gauge and $J$ is the four-current density. This form of Maxwell's equations holds in Cartesian coordinates, in polar coordinates, in accelerating reference frames, and in any set of coordinates whatsoever.

Importantly, when expressing the laws of physics in this manner, called "manifestly covariant", the outcome of any physical measurement is also manifestly covariant. Meaning that the outcome of any experiment is independent of the coordinates.

So, if we start with standard Einstein-synchronized coordinates $(t,x,y,z)$ we know that the one-way speed of light is $c$. We can then make the following coordinate transformation without changing the result of any physical measurement since they are manifestly covariant: $$t \rightarrow T + \kappa X$$ $$x \rightarrow X$$ $$y \rightarrow Y$$ $$z \rightarrow Z$$
Now, this coordinate transformation changes the one-way speed of light and makes it anisotropic. But, since our laws of physics and our experimental results are all manifestly covariant, it does not change any experimental result. Meaning that any result predicted by the isotropic one way speed of light is also predicted by the non-isotropic one-way speed of light.

 

[Ibix]

ok thanks, but that means that what I wanted to proof is already a given fact. My assumption was that the one way speed of light could have different values depending on the synchronisation of your clocks.

So... you already know it's impossible to measure the one way speed of light, so you know your device gives the same output whatever you assume about the one way speed of light. So what was the point of this thread?

 

[HansH]

The point was that I thought I had a method to determine the 1 way speed of light as I discribed, but it turned out there was a bug in my reasoning because the 2 almost parallel lines that I proposed are not exacly parallel and therefore still cancel out the effect I wanted to measure. but now there are some residual related items left where the discussion is about.

 

[PeroK]

The point was that I thought I had a method to determine the 1 way speed of light as I discribed, but it turned out there was a bug in my reasoning because the 2 almost parallel lines that I proposed are not exacly parallel and therefore still cancel out the effect I wanted to measure. but now there are some residual related items left where the discussion is about.

You can perhaps learn something from this line of enquiry, but if you understand relativistc spacetime then you must realize that any scheme to measure a definitive one-way speed must have a flaw in it. You might like to try to prove that are finitely many prime numbers but you must know from the outset that any such proof must have a hidden flaw.

 

[HansH]

This doesn't have anything to do with curved spacetime and gravitation.

So, if we start with standard Einstein-synchronized coordinates $(t,x,y,z)$ we know that the one-way speed of light is $c$.

Standard Einstein-synchronized means that you assume c back and forth to syncronize your clock as I understood.
so then am I right that the one way speed of light as presented in this movie can still be anything between c/2 and infinite ? but that then seems to be in contradiction with the remark of Ibix in #54 ?
'Choosing to use orthonormal coordinates on spacetime (not just space) is the same as choosing that the one way speed of light is isotropic, yes.'

 

[Ibix]

but that then seems to be in contradiction with the remark of Ibix in #54 ?
'Choosing to use orthonormal coordinates on spacetime (not just space) is the same as choosing that the one way speed of light is isotropic, yes.'

That's not a contradiction. It's exactly what I said. Using Einstein synchronised clocks is using orthonormal coordinates and you have an isotropic speed of light. If you don't Einstein synchronise your clocks you aren't using orthonormal coordinates and you don't have an isotropic speed of light.

 

[HansH]

That's not a contradiction. It's exactly what I said. Using Einstein synchronised clocks is using orthonormal coordinates and you have an isotropic speed of light. If you don't Einstein synchronise your clocks you aren't using orthonormal coordinates and you don't have an isotropic speed of light.

so to get things clear: do you then say that in that movie the one way speed of light is always c (that is what I thought isotropic speed of light means). in the move I don't see they don't talk specifically about ways to choose coordinates so I think they use standard orthonormal coordinates everyone uses in daily life.

 

[Ibix]

I haven't watched the movie so I've no idea what their argument is. As I have already said, if they are considering anisotropic one way speeds of light then they are considering non-orthonormal coordinate systems - whether they choose to say so explicitly or not.

 

[Dale]

am I right that the one way speed of light as presented in this movie can still be anything between c/2 and infinite ?

Yes. I may have understood your position incorrectly. I thought that your position was that the one way speed must be c.

but that then seems to be in contradiction with the remark of Ibix in #54 ?
'Choosing to use orthonormal coordinates on spacetime (not just space) is the same as choosing that the one way speed of light is isotropic, yes.'

That is not in conflict. @Ibix is correct

in the move I don't see they don't talk specifically about ways to choose coordinates so I think they use standard orthonormal coordinates everyone uses in daily life

Since the standard coordinates have the isotropic one way speed of light, and since they are discussing coordinates with non-isotropic one way speeds of light, it is clear that they are using non-standard coordinates. Even if they don’t talk about it explicitly.

By the way, this is why even correct videos are not as effective as a good textbook.

 

[cianfa72]

Using Einstein synchronised clocks is using orthonormal coordinates and you have an isotropic speed of light. If you don't Einstein synchronise your clocks you aren't using orthonormal coordinates and you don't have an isotropic speed of light.

In this discussion we have been assuming a flat spacetime so we are really talking about SR and not the general case of GR.

 

[HansH]

Yes. I may have understood your position incorrectly. I thought that your position was that the one way speed must be c.

no so far I saw no reason why it cannot be an arbitrary value between c/2 and infinite. However writing down the equations and generating the graphs as I posted here: https://www.physicsforums.com/threa...by-combined-measurements.1014053/post-6620171

, I realized that the requirements that resulted in these graphs are in my opinion not compatible with the other requirement that the 2 way speed of light must be c in every directon. (because that is a given fact) it could of course be that I made a mistake somewhere but otherwise my conclusion is that due to this compatibility issue the only option left is that the one way speed of light is also c in every direction. as said I will first give some room to our dutch forum to find a potential problem in my reasoning. but later I will post this probably as a new topic (if not clear yet then) as it is not directly related to the proposal that this topic is about.

 

[Ibix]

In this discussion we have been assuming a flat spacetime so we are really talking about SR and not the general case of GR.

I don't think I've said otherwise.

no so far I saw no reason why it cannot be an arbitrary value between c/2 and infinite.

It can be.

 

[HansH]

There is no one-way speed of light. Sorry to disappoint.

maybe you have 99 equations in 100 uniknowns. Same problem.

At this moment it is the other way around. describing the idea of 1 way lightspeed in a 2d situation I have more equations than variables and therefore a contradicton. so based on that I con only draw the conclusion that light cannot have a 1 way speed depending on direction for a 2 or 3 dimensional world, so if that is not what the physics world derived, then something should be wrong in my assumptions.

 

[Frabjous]

Such a material could be used to build a perpetual motion machine. So no.

Would you explain how? I am not familiar with this one.

 

[Ibix]

then something should be wrong in my assumptions.

...as we have been telling you for some time now.

Let's do this properly. See the diagram in post #1. In the usual Einstein coordinates we describe light leaving S, traveling to A or B, and being reflected to R.

The light leaves S at $x=0$, $y=0$, $t=0$.
It arrives at A/B at $x=\pm X$, $y=0$, $t=X/c$.
It arrives at R at $x=0$, $y=Y$, $t=X/c+(X/\cos\alpha)/c=\frac Xc(1+\sec\alpha)$.

Now let's work in a frame where the speed of light is not isotropic. To do this, we simply apply the coordinate transform $x'=x$, $y'=y$, $t'=t+\kappa x$, where $\kappa$ is a constant with dimensions of inverse velocity and $|\kappa|<\frac 1c$ so that our spatial planes remain spacelike.

The light leaves S at $x'=0$, $y'=0$, $t'=0$.
It arrives at A/B at $x'=\pm X$, $y'=0$, $t'=X/c\pm\kappa X$.
It arrives at R at $x'=0$, $y'=Y$, $t'=\frac Xc(1+\sec\alpha)$.

Note that the only actual difference from the Einstein case is the arrival time of the light at A and B.

From this we can deduce the speed of light along AR and BR. The distance traveled is $X\sec\alpha$ and the time taken is $\frac Xc(1+\sec\alpha)-(X/c\pm\kappa X)$ (i.e., the arrival time at R minus the arrival time at A/B), so the speed is $$c_\pm=\frac{c}{1\mp \kappa c\cos\alpha}$$There are a few interesting cases. First, if $\kappa=0$ this clearly reduces to the isotropic case. Second, if $\alpha=0$ then AR and BR are antiparallel and we have a 1d problem in which we get $c_\pm=c/(1\mp\kappa c)$. It's easy to see that the average speed, $c_{av}$, satisfies $\frac{2X}{c_{av}}=\frac{X}{c_+}+\frac{X}{c_-}$, and hence that $c_{av}=c$ for all $\kappa$ - i.e. that the two-way speed of light is preserved.

If you get different equations from these you are doing something wrong.

 

[PeroK]

then something should be wrong in my assumptions.

And if that's still the case after 70 posts, then perhaps you need to rethink your approach to learning physics?