One-Way Speed of Light: Is it Possible?

[Dale]

the delay or anticipation of the apparent eclipse is not being effected by the particular direction the signal takes across the solar system

This is precisely the assumption that the one way speed of light is isotropic. Romer’s measurements cannot be converted to a speed without this assumption.

And stop with the shouting in all caps. It is obnoxious

 

[Ibix]

What am I missing?

If you work out the maths, the version of time dilation you get in an anisotropic speed of light case is not negligible (and not isotropic) in a light speed measurement even with the clocks moving at fairly low speed. Rømer assumed that all the variation in signal timing was due to variation in distance, reasonably enough because he predated Einstein by more than two centuries. But that means he neglected time dilation in the moon/clock as Jupiter moved, and that is where an assumption of an isotropic one way speed of light entered his experiment.

You can re-analyse this type of experiment using an anisotropic speed of light and show that the timing results are the same independent of the choice of anisotropy.

 

[Eclipse Chaser]

how do your arguments make measuring the one-way speed of light any more difficult than measuring the two-way speed of light given the clocks move in either case?

 

[Ibix]

how do your arguments make measuring the one-way speed of light any more difficult than measuring the two-way speed of light given the clocks move in either case?

A two-way speed of light measure only requires one clock and it is free to regard itself as at rest, so time dilation can always be neglected. You can re-analyse the experiment with the clock moving if you want; if you assume an anisotropic speed of light the extra/reduced clock drift will cancel out with the extra distance travelled by light on one leg of its journey.

One-way light speed measures aren't dfficult. However, the analysis always contains an assumption of the ratio of one way speeds somewhere that guarantees the result will match the assumption, give or take experimental error.

 

[PeroK]

how do your arguments make measuring the one-way speed of light any more difficult than measuring the two-way speed of light given the clocks move in either case?

It's not difficult to measure the one-way speed of light. The answer you get depends on your simultaneity convention (which is implied by your choice of coordinate system). The default coordinate system seems so natural that you don't even realise you are making any assumptions.

 

[PeroK]

PS Romer's work was done using classical space and time (it was even pre-Newton). He would have used an absolute time coordinate. But, he probably didn't realise there was any alternative. Time was assumed to be self-evidently absolute.

That assumption in itself had to be dropped in adopting the theory or relativity.

Likewise, the speed of light would not have been invariant in his calculations.

The adoption of relativistic ideas, such as the relativity of simultaneity, are not intuitively obvious.

 

[PeroK]

PPS assuming classical physics, you can of course measure the one-way speed of light. But, those measurements would contradict the assumptions. In the sense that you would expect the speed of light to depend on the motion of the source, but find through experiment that it does not.

 

[Dale]

how do your arguments make measuring the one-way speed of light any more difficult than measuring the two-way speed of light given the clocks move in either case?

The issue isn’t difficulty. It is assumptions. The one way speed of light depends on the simultaneity/isotropy assumption. The two way speed does not.

 

[Vanadium 50]

Maybe it would be clearer without so many words. Why don't you write an equation "c =" using only distances and times?

 

[Eclipse Chaser]

I agree that the one-way speed of light can not be measured with 100% accuracy but we're debating whether or not, when measuring the round-trip speed, the light travels a different speed in on the going leg direction of the journey than it does on the return leg direction of the journey. Roemer's methodology only has one leg and he's not measuring the speed of the signal, he's measuring the change of phase angle between two fixed frequencies at two different distances. If the measurement is imprecise for the arguments you've presented, isn't the round-trip measurement imprecise, even if less so, for the same reasons?

And to Vanadium 50: I took my last math course (calculus) 45 years ago so I'm a little rusty and maybe you can help but my best shot would be: C = (φ2 – φ1) x ΔD where φ2 & φ1 are the phase angles between the two signals (1. arrival of the eclipse signal and 2. click of the metronome) at two different distances D1 and D2. ΔD is just D2 - D1, i.e.. the diameter of Earth's orbit.

 

[Ibix]

If the measurement is imprecise for the arguments you've presented

You are misunderstanding us. The measurement of a one-way speed is no more or less precise than the measurement of a two way speed. The difference is that the analysis of the one way speed experiment includes an assumption about the ratio of one-way light speeds in the opposite directions.

Rømer assumed isotropy and found isotropy. If you reanalyse the experiment assuming a specific anisotropy you will get that specific anisotropy from the results.

Again: this is nothing to do with experimental precision. It is entirely to do with an unavoidable assumption in the analysis.

 

[Eclipse Chaser]

I applaud your patience and was about to give up under the weight of your logic but I have one last (?) question. Doesn't the fact that Roemer got repeatable results over dozens of tests that including dozens of different directional parameters argue against your claim that his experiment includes an assumption..."

 

[Ibix]

Doesn't the fact that Roemer got repeatable results over dozens of tests that including dozens of different directional parameters argue against your claim that his experiment includes an assumption..."

No, just that he always used the same assumption.

The results he gets, as you point out, are merely arrival times of light. From that and an analysis of how far away the clocks were he can calculate a speed of light. The assumption (that clock drift due to time dilation is negligible) is in the calculation, not in the results. You can take the exact same results Rømer got, work out the clock drift due to some chosen isotropy, and the modified calculations will give you that chosen isotropy.

The whole problem is that the assumption about isotropy doesn't affect the results. If it did then we could detect it.

 

[PeroK]

I applaud your patience and was about to give up under the weight of your logic but I have one last (?) question. Doesn't the fact that Roemer got repeatable results over dozens of tests that including dozens of different directional parameters argue against your claim that his experiment includes an assumption..."

Until 1905 no one realised they were making assumptions about space and time and no-one realised that simultaneity was relative.

Once you realise that simultaneity is relative, the next question is whether the Einstein synchronization convention is the only possibility. It's not. Any measurement that involves measuring times at two different locations is inherently ambiguous

If you insist that there is no ambiguity, then you run into problems studying GR. There are lots of threads on here where we have the same argument about never falling into a black hole. It's the same issue in a new context.

 

[Dale]

I agree that the one-way speed of light can not be measured with 100% accuracy

This has nothing to do with 100% accuracy. As you have been told many times it is about the assumptions that were made in the analysis. Specifically, the assumption that the speed of light is isotropic.

Roemer's methodology only has one leg and he's not measuring the speed of the signal, he's measuring the change of phase angle between two fixed frequencies at two different distances. If the measurement is imprecise for the arguments you've presented, isn't the round-trip measurement imprecise, even if less so, for the same reasons?

It has nothing to do with accuracy or precision. Those are completely separate concerns. It has to do with the assumption of isotropy. Any one way measurement has to make some assumption about the amount of anisotropy. The one way speed depends on that assumption, and the two way speed is independent of that assumption.

 

[PeterDonis]

we're debating whether or not, when measuring the round-trip speed, the light travels a different speed in on the going leg direction of the journey than it does on the return leg direction of the journey

No, we're not. For a round-trip speed measurement, you do not have to assume anything about the one-way speed of light.

We are not "debating" anything here. We are continuing to tell you that for a one-way measurement, doing it the way you are describing (the way Roemer did it), you do have to assume something about the one-way speed of light--that it is isotropic.

 

[PeterDonis]

Doesn't the fact that Roemer got repeatable results over dozens of tests that including dozens of different directional parameters argue against your claim that his experiment includes an assumption..."

Not at all. It just shows that he used the same assumption every time.

 

[PeterDonis]

Thread closed for moderation.

 

[Dale]

After discussion among the mentors, we will leave this thread closed. In closing, I wanted to briefly summarize a small part of the existing literature on this topic for @Eclipse Chaser

Using Anderson's convention, the metric in 1+1D flat spacetime is $$ds^2=-c^2 \ dt^2 + dx^2 - 2c\kappa \ dx dt - \kappa^2 \ dx^2$$ Here, $\kappa$ is a factor that describes the assumed asymmetry in the one-way speed of light. The speed of light in the $+x$ direction is $c/(1-\kappa)$ and the speed of light in the $-x$ direction is $c/(1+\kappa)$. Isotropic one-way speed is $\kappa=0$.

This gives a time dilation factor of $$\lambda = \left( 1- \frac{v^2}{c^2} +2 \kappa \frac{v}{c} + \kappa \frac{v^2}{c^2} \right)^{-1/2}$$ a series expansion to second order for small $v$ gives $$\lambda \approx 1 - \kappa \frac{v}{c} + \left( \frac{1}{2} + \kappa^2 \right)\frac{v^2}{c^2} $$ Notice that relativistic time dilation is a first order effect for $\kappa \ne 0$. Meaning that the assumption that

Earth's orbital speed is about 67,000 MPH = 0.0001C, hardly sufficient for relativistic effects to slow down a timer.

already implicitly assumes $\kappa=0$.

A measurement that would attempt to measure the one way speed of light cannot assume $\kappa$. The measurement itself must be sensitive to $\kappa$. No such measurement exists, for reasons described in detail in Anderson's paper above.

Romer did not know anything about time dilation, so he unknowingly assumed that there was no time dilation and thereby assumed $\kappa=0$. So his measurements were a measurement of $c$, not $c/(1\pm \kappa)$.