I One-Way Speed of Light: Is it Possible?

[kochanskij]

TL;DR Summary

If light travels at C+V in one direction and C-V in the other, could we detect that? How? If not, could this indicate something profound about light and spacetime?

From what I've read, it is not possible to measure the one way speed of light. We must reflect it off a mirror and then divide its travel time by 2, giving us its round trip average speed. Time dilation makes synchronizing two separated clocks impossible. We just assume light goes at C in all directions. (I'm not talking about the speed of its source or detector. Assume everything is in the same inertial frame) Please correct me if I'm wrong.

If it goes at C+V in one direction, it must go at C-V in the opposite direction. We always measure an average speed of C. But we can never know what V is. Could this lead to something profound about light and space and time? Maybe light has no definite one way speed. Maybe it is in a superposition of all speeds. V is every velocity 0 < V < C. Is this possible? Has any physicist explored this? Or is the one way speed of light just a trivial curiosity?

 

[Dale]

It is just an arbitrary convention that can be chosen as desired. There are many, many threads on this topic already here.

https://www.physicsforums.com/threads/the-one-way-speed-of-light.1016771/
https://www.physicsforums.com/threads/sr-and-one-way-speed-of-light-tests.4602/
https://www.physicsforums.com/threads/how-to-measure-the-one-way-speed-of-light.461274/
https://www.physicsforums.com/threads/one-way-speed-of-light-measurement-proposal.584743/
https://www.physicsforums.com/threads/measuring-one-way-speed-of-light.750191/

just to give a few threads..

 

[FactChecker]

TL;DR Summary: If light travels at C+V in one direction and C-V in the other, could we detect that? How? If not, could this indicate something profound about light and spacetime?

From what I've read, it is not possible to measure the one way speed of light. We must reflect it off a mirror and then divide its travel time by 2, giving us its round trip average speed. Time dilation makes synchronizing two separated clocks impossible. We just assume light goes at C in all directions. (I'm not talking about the speed of its source or detector. Assume everything is in the same inertial frame) Please correct me if I'm wrong.

If it goes at C+V in one direction, it must go at C-V in the opposite direction. We always measure an average speed of C. But we can never know what V is. Could this lead to something profound about light and space and time? Maybe light has no definite one way speed. Maybe it is in a superposition of all speeds. V is every velocity 0 < V < C. Is this possible? Has any physicist explored this? Or is the one way speed of light just a trivial curiosity?

The first thing to realize is that measuring the one-way speed of light requires that the clocks at both ends are perfectly and undeniably recording identical times. That opens a can of worms that is not possible to solve.
The next thing to realize is that Einstein's theory of Special Relativity solved some problems for the first time and made predictions (including atomic energy, physics happening slower for fast-moving objects, etc.) that have been convincingly confirmed. So, whatever he needed to assume for that theory is strongly supported.

 

[Herman Trivilino]

TL;DR Summary: If light travels at C+V in one direction and C-V in the other, could we detect that?

No.

If not, could this indicate something profound about light and spacetime?

It indicates that simultaneity is relative. I think that's pretty profound.

Time dilation makes synchronizing two separated clocks impossible.

That doesn't sound right to me. Do you have a reference for this claim?

Has any physicist explored this?

Of course. It's a well-understood phenomenon. For at least 100 years, I think.

 

[Ibix]

Or is the one way speed of light just a trivial curiosity?

I'd go with this option. You can choose to use coordinates in which the speed of light is anisotropic. In SR they just make all the maths messier so nobody does so, but you could. However, it's quite common to do in GR because it tends to be more convenient to pick coordinate systems adapted to the geometry of spacetime than worry about whether they're everywhere orthonormal.

 

[Sagittarius A-Star]

If it goes at C+V in one direction, it must go at C-V in the opposite direction.

No. The two-way-speed of light must be $c$.

If the distance is $L$ and the light moves with $c+v$ in one direction, because the 4D-reference coordinate-system was defined this way, then the time for both directions is
$t=\frac{L}{c+v}+\frac{L}{u}= \frac{2L}{c}$

Then light must go at
$u= \frac{c+v}{1+2v/c}$ in the opposite direction.

Calculation:
https://www.wolframalpha.com/input?i2d=true&i=Divide[L,\(40)c+V\(41)]+Divide[L,u]=2Divide[L,c]

 

[kochanskij]

No. The two-way-speed of light must be $c$.

If the distance is $L$ and the light moves with $c+v$ in one direction, because the 4D-reference coordinate-system was defined this way, then the time for both directions is
$t=\frac{L}{c+v}+\frac{L}{u}= \frac{2L}{c}$

Then light must go at
$u= \frac{c+v}{1+2v/c}$ in the opposite direction.

Calculation:
https://www.wolframalpha.com/input?i2d=true&i=Divide[L,\(40)c+V\(41)]+Divide[L,u]=2Divide[L,c]

Thank you for your correction. I feel silly that I forgot that you don't find an average velocity by adding the two velocities and dividing by 2. A very basic error on my part.

 

[cianfa72]

Sorry to resume this thread. Many times in PF has been discussed that the invariance w.r.t. inertial frames of one-way speed of light is just a matter of simultaneity convention employed to define it. In particular in SR inertial frames are defined in a such way that the one-way speed of light is actually the invariant $c$ (based on the Einstein synchronization convention).

However the two-way speed of light is actually measurable and experimentally it is the invariant $c$ as well.

A problem I see is that it is implicitely assumed that Einstein's synchronization convention can be always applied consistently.

What do you think about ?

 

[PeterDonis]

it is implicitely assumed that Einstein's synchronization convention can be always applied consistently.

No. In flat spacetime it is known that you can always apply Einstein synchronization between clocks at rest relative to each other.

In curved spacetime it is known that you can't always do that, and nobody assumes that you can.

 

[cianfa72]

No. In flat spacetime it is known that you can always apply Einstein synchronization between clocks at rest relative to each other.

Is it actually an experimental result ?

 

[PeterDonis]

Is it actually an experimental result ?

Where would you go to find a flat spacetime to experiment in?

It's a mathematical result using the known geometric properties of flat spacetime and inertial worldlines.

 

[cianfa72]

It's a mathematical result using the known geometric properties of flat spacetime and inertial worldlines.

Ok, so using for instance families of mutually "at rest" inertial worldlines in flat spacetime we can check that Einstein's synchronization convention holds consistently.

 

[PeterDonis]

Ok, so using for instance families of mutually "at rest" inertial worldlines in flat spacetime we can check that Einstein's synchronization convention holds consistently.

Yes.

 

[ESponge2000]

TL;DR Summary: If light travels at C+V in one direction and C-V in the other, could we detect that? How? If not, could this indicate something profound about light and spacetime?

From what I've read, it is not possible to measure the one way speed of light. We must reflect it off a mirror and then divide its travel time by 2, giving us its round trip average speed. Time dilation makes synchronizing two separated clocks impossible. We just assume light goes at C in all directions. (I'm not talking about the speed of its source or detector. Assume everything is in the same inertial frame) Please correct me if I'm wrong.

If it goes at C+V in one direction, it must go at C-V in the opposite direction. We always measure an average speed of C. But we can never know what V is. Could this lead to something profound about light and space and time? Maybe light has no definite one way speed. Maybe it is in a superposition of all speeds. V is every velocity 0 < V < C. Is this possible? Has any physicist explored this? Or is the one way speed of light just a trivial curiosity?

But when we have 2 orbiting points of reference (say earth and mars or earth and the moon) and we can assert changes in positions of recognizable objects or chemical elements we see on their surfaces , and with reasonable accuracy we know the earth AU distances to these objects, but that the directions are not fixed due to orbits around the sun, how does this not allow us a means to test the equality of c in multiple directions , given what we see from the other surface is a one-way transmission of light ?

If as a null hypothesis we assume the bizarre that in a certain direction c travels at infinity and the reverse at half of 299K meters / sec , I would think we would have to observe some very strange motions upon other planets in our definition of distance and time from a point on earth , because any orbit or lack of staying still would impact the speed of real events in our observations , unless c is not altered by changing directions and it would imply it being possible to observe motion in reverse for rotating objects around you , no?

 

[PeroK]

it would imply it being possible to observe motion in reverse for rotating objects around you , no?

No, because observable phenomena do not depend on a simultaneity convention.

 

[Ibix]

given what we see from the other surface is a one-way transmission of light ?

What do you think would change in the observations you make if you changed your definition of the one way speed of light?

 

[PeterDonis]

what we see from the other surface is a one-way transmission of light ?

How do you know what time according to your clock the light was emitted from the other surface? Answer: there is no direct observable that tells you that. It's a convention--a simultaneity convention.

 

[ESponge2000]

How do you know what time according to your clock the light was emitted from the other surface? Answer: there is no direct observable that tells you that. It's a convention--a simultaneity convention.

You don’t know what time according to your clock the light was emitted from the other surface, but you can calculate the acceleration of falling objects onto the surface of another planet with approximation like we know what we should see is how long something takes that’s falling on planet mars

We can then compare for us how long an object falls from our time A to time B to time C , While knowing we are rotating with respect to mars during within time A time B time C … We can compare the Time A to Time b interval with the Time B to Time C interval to see if positions on things we know the gravity should measure , comply and match between A and B the rates for B to C .

 

[Vanadium 50]

This sounds incredibly confused. Why not write down an equation: the one way speed of light = some function of clock and ruler readings.

 

[PeterDonis]

you can calculate the acceleration of falling objects onto the surface of another planet with approximation like we know what we should see is how long something takes that’s falling on planet mars

We can calculate how long it would take by the object's own clock for it to fall to the surface of a planet from a given altitude. That is an invariant, yes. But that's not what you are looking for. You are looking for the time it takes by a distant observer's clock. That requires adopting a simultaneity convention.

 

[Ibix]

you can calculate the acceleration of falling objects onto the surface of another planet with approximation like we know what we should see is how long something takes that’s falling on planet mars

This syntax is a mess. I think what you are saying is that you look up Mars surface gravity and calculate how long it takes for a rock to fall 5m or something. Say that's 1s, just for convenience. Then you watch it through a telescope.

The light from the "rock starts to fall" event leaves 1s before the light from the "rock lands" event. So the light from the "rock starts to fall" event arrives 1s before the light from the "rock lands" event, independent of light speed.

If you are considering that Mars might have changed distance to Earth significantly in the time the rock was falling then you are proposing an impractical version of Rømer's measurement of light speed. The answer to that depends on how you account for time dilation and you get the (possibly non-isotropic) one-way speed you assumed in your time dilation calculation. If you assume time dilation is negligible (as Rømer did implicitly, since he predated Einstein by more than two centuries) then you get isotropic light speed.

 

[cianfa72]

This syntax is a mess. I think what you are saying is that you look up Mars surface gravity and calculate how long it takes for a rock to fall 5m or something. Say that's 1s, just for convenience. Then you watch it through a telescope.

The light from the "rock starts to fall" event leaves 1s before the light from the "rock lands" event. So the light from the "rock starts to fall" event arrives 1s before the light from the "rock lands" event, independent of light speed.

What you watch through a telescope say on the Earth is the difference in proper time elapsed on a clock attached to the rock between the event "the rock start to fall" and "the rock lands" on Mars surface.

Note that this "elapsed time" is invariant since it is measured by a clock that follows the rock's spacetime path.

 

[Eclipse Chaser]

TL;DR Summary: If light travels at C+V in one direction and C-V in the other, could we detect that? How? If not, could this indicate something profound about light and spacetime?

From what I've read, it is not possible to measure the one way speed of light. We must reflect it off a mirror and then divide its travel time by 2, giving us its round trip average speed. Time dilation makes synchronizing two separated clocks impossible. We just assume light goes at C in all directions. (I'm not talking about the speed of its source or detector. Assume everything is in the same inertial frame) Please correct me if I'm wrong.

If it goes at C+V in one direction, it must go at C-V in the opposite direction. We always measure an average speed of C. But we can never know what V is. Could this lead to something profound about light and space and time? Maybe light has no definite one way speed. Maybe it is in a superposition of all speeds. V is every velocity 0 < V < C. Is this possible? Has any physicist explored this? Or is the one way speed of light just a trivial curiosity?

Roemer measure the one-way speed of light 350 years ago by timing the eclipses of Jupiter's moon Io from different distances as the Earth orbited the Sun. The measurement has been repeated often with increasing accuracy. No clocks needed.

The first thing to realize is that measuring the one-way speed of light requires that the clocks at both ends are perfectly and undeniably recording identical times. That opens a can of worms that is not possible to solve.
The next thing to realize is that Einstein's theory of Special Relativity solved some problems for the first time and made predictions (including atomic energy, physics happening slower for fast-moving objects, etc.) that have been convincingly confirmed. So, whatever he needed to assume for that theory is strongly supported.

Rømer calculated the ONE-WAY speed of light in 1676 by observing that the eclipses of Jupiter's moon Io occurred 22 minutes later when Earth was on the opposite side of the Sun from Jupiter than when it was on the same side. He realized that light took 22 minutes for light to travel the diameter of Earth's orbit. By dividing the diameter of Earth's orbit by 22 minutes he calculated the speed of light to be 131,000 miles per second. The same method can be used today to more accurately measure the ONE-WAY speed of light.

What am I missing?

 

[Dale]

No clocks needed.

Jupiter and its moons is a clock. The motion of astronomical objects was the first clock

Romer assumed a synchronization convention where the one way speed was the same in every direction

What am I missing?

see post 2 for a very incomplete list. There has been a lot written on this topic. Besides what is on this forum see especially Reichenbach and Anderson in the peer reviewed literature.

 

[FactChecker]

Roemer measure the one-way speed of light 350 years ago by timing the eclipses of Jupiter's moon Io from different distances as the Earth orbited the Sun. The measurement has been repeated often with increasing accuracy. No clocks needed.

How do you measure "timing" without clocks?

Rømer calculated the ONE-WAY speed of light in 1676 by observing that the eclipses of Jupiter's moon Io occurred 22 minutes later when Earth was on the opposite side of the Sun from Jupiter than when it was on the same side. He realized that light took 22 minutes for light to travel the diameter of Earth's orbit. By dividing the diameter of Earth's orbit by 22 minutes he calculated the speed of light to be 131,000 miles per second. The same method can be used today to more accurately measure the ONE-WAY speed of light.

What am I missing?

That is comparing the time it takes when the Earth was near Jupiter in its orbit with the time it takes takes on the other side, farthest from Jupiter. How do you know that time is the same on two "synchronized" clocks at those two locations? The differences may be tiny at the velocities of the Earth, so it may give a fairly good answer for that era, but it turns out that there is no way to know the one-way speed of light with complete accuracy.

 

[Eclipse Chaser]

How do you measure "timing" without clocks?

That is comparing the time it takes when the Earth was near Jupiter in its orbit with the time it takes takes on the other side, farthest from Jupiter. How do you know that time is the same on two "synchronized" clocks at those two locations?

What's different in Roemer's methodology is that you don't need a light-speed communication back TO the source to confirm the arrival of a light-speed communication FROM the source. ONE continuously running timer is not functionally the same as "two clocks" that require synchronization. And scale matters. Earth's orbital speed is about 67,000 MPH = 0.0001C, hardly sufficient for relativistic effects to slow down a timer. All imperial measurements have a degree of error, but Roemer's is NOT direction dependent.

 

[PeterDonis]

What's different in Roemer's methodology is that you don't need a light-speed communication back TO the source to confirm the arrival of a light-speed communication FROM the source.

You never need that anyway. When you receive a light signal, you don't have to send another light signal back to the source for you to know that you received the signal.

ONE continuously running timer is not functionally the same as "two clocks" that require synchronization.

But ONE continuously running timer, by itself, does not tell you the one-way speed of light. You need to assume a synchronization for that. In Roemer's case, he had to assume, as @Dale said, a synchronization that makes the one-way speed of light the same in all directions (more precisely, that does that for someone at rest relative to the barycenter of the solar system). He didn't state this assumption explicitly, but it is implicit in his calculations.

 

[Dale]

ONE continuously running timer is not functionally the same as "two clocks" that require synchronization.

Romer had local clocks here on Earth. And Jupiter’s moon is another clock. So his experiment indeed has two clocks. That is a hallmark of one way speed of light measurements.

In order to convert his observations of these two clocks into a speed, he had to make some assumptions. If you look into the math, one of those assumptions is that the speed of light is the same in all directions. That assumption is a synchronization convention.

 

[Eclipse Chaser]

It's late, but I can not follow your reasoning when you say "ONE continuously running timer, by itself, does not tell you the one-way speed of light."

Think of it as a single metronome that clicks every time Io disappears behind Jupiter (roughly every 42.5 hours). When earth is far away, the eclipses occur 11 minutes AFTER the click, when earth is near, the eclipses appear 11 minutes BEFORE the click, year after year after year, REGARDLESS OF DIRECTION. Maybe a good night sleep will help me understand exactly what needs to be "synchronized." (Thanks for engaging.)

 

[FactChecker]

What's different in Roemer's methodology is that you don't need a light-speed communication back TO the source to confirm the arrival of a light-speed communication FROM the source. ONE continuously running timer is not functionally the same as "two clocks" that require synchronization.

It requires that one clock, traveling great distances and speed remained exactly synchronized with its original time. IMO, that is a greater assumption that assuming two synchronized clocks. And if everything on Earth that depended on time underwent the same time dilation as the clock did, how would that be detected?

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

It is a good point that the effect would be very small. But it is still there, even at walking speed. And the effects at speeds approaching c are much greater. So yes, we know the one-direction speed of light to a reasonable accuracy for most applications, but not all.

 

[PeterDonis]

I can not follow your reasoning

Because you are ignoring the key thing that I and others have told you, that a synchronization convention is involved. We have even described that convention specifically to you.

REGARDLESS OF DIRECTION

Yes, REGARDLESS OF DIRECTION. Which means that, in order to convert this time difference into a one-way speed, you are (although you apparently haven't realized it--and as I said, neither did Roemer) adopting a synchronization convention (or simultaneity convention) that makes the one-way speed of light the same in all directions. Without that assumption you cannot convert the time difference into a speed.

 

[PeterDonis]

the effect would be very small. But it is still there, even at walking speed. And the effects at speeds approaching c are much greater. So yes, we know the one-direction speed of light to a reasonable accuracy for most applications, but not all.

The fact that a simultaneity convention must be adopted to calculate the one-way speed of light has nothing to do with relativistic effects being large or small. It has to do with the inherent nature of a one-way speed. The only relativity-specific thing involved is the fact that simultaneity is a convention--in Newtonian mechanics it isn't because Newtonian mechanics assumes that there is an absolute simultaneity.

 

[Vanadium 50]

How does this measurement work?

You have a clock far away. (Jupiters moons). You read the clock, you wait and move and then you read it again. Let's label the events - A is when light left Jupiter and B when it was received on Earth, and C is when it left Jupiter at the later time, and finally D is when it was received on Earth then. In a time t_D - t_B, the Earth has moved x_D - x_B. (x is a vector)

Right?

So, there are not one but two light paths here. One along the line AB and the other along CD. Which one did Roemer measure?

If you answer, "it's the same thing!" there's your convention - that sthe speed of light is the same in two different directions.

 

[Eclipse Chaser]

"Regardless of direction" refers to the fact that in measurements taken year after year after year, the delay or anticipation of the apparent eclipse is not being effected by the particular direction the signal takes across the solar system. It's repeatable

The metronome on Earth is timing the ONE-WAY light-speed eclipse signal from Jupiter, multiple times over multiple years, in multiple directions, but it's a ONE-WAY signal. We don't need to know when it happens, we just need to know it appears latter when we're farther away.

How does this measurement work?

You have a clock far away. (Jupiters moons). You read the clock, you wait and move and then you read it again. Let's label the events - A is when light left Jupiter and B when it was received on Earth, and C is when it left Jupiter at the later time, and finally D is when it was received on Earth then. In a time t_D - t_B, the Earth has moved x_D - x_B. (x is a vector)

Right?

So, there are not one by two light paths here. One along the line AB and the other along CD. Which one did Roemer measure?

If you answer, "it's the same thing!" there's your convention - that sthe speed of light is the same in two different directions.

"So, ... Which one did Roemer measure?"
He didn't "measure" either. He compared the ARRIVAL FREQUENCY of their signals to the clicking of a local metronome.
They are not two clocks that need to be synchronized.
The only assumptions are that the eclipses and the clicks, individually occur at at a constant frequency.
The positions of Earth and Saturn clearly don't alter the frequency of a local metronome. nor of the the eclipses.

I'll let you take the last shot if you care to, but I think I need a good night sleep. Again, thanks for the engagement.

 

[PeterDonis]

He compared the ARRIVAL FREQUENCY of their signals to the clicking of a local metronome.

You can call his raw observation of the light signals that if you want (though I'm not sure that's how most people would describe it), but his raw observation of the light signals alone did not tell him the one-way speed of light. He had to calculate the one-way speed of light, and that calculation required assuming a simultaneity convention. We have repeatedly explained why.

 

[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.