# Why isn't the Roemer type experiment a one way measure of c?

• I
I can't read the tons of posts and replies about one-way light speed in this forum. I was criticised once for sustaining light speed should be equal in both outward and return trips and Einstein's method of syncing clocks as the only reasonable one. Then I studied some scientific articles gently suggested by somebody here and I became persuaded that nobody succeeded yet in measuring the one-way light speed. After that, someone else argued against the need of measuring the space and time in the round-trip of light that I claimed in a different thread.
Finally, I went through the details of Roemer experiment. And I learned that in Roemer measure we deduce light speed from time increment that light from Jupiter satellite Io takes to travel the diameter of Earth orbit to reach observer's telescope. Thus, this appears to be a one-way or inward trip speed measure obtained from distance and retardation time.
What I expect now is an ultimate and expert explanation of why Roemer's measure can't be viewed as a one way measure of light speed.

## Answers and Replies

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Ibix
Roemer is essentially using Io as a clock and assuming that the variation in its apparent tick rate is entirely due to varying distance. If you assume that light speed is anisotropic you'll find that there is a clock rate correction due to motion which Roemer does not include (because he predates Einstein by a way), which means he's assuming the Einstein synchronisation convention. If you assume an anisotropic speed of light and include the clock rate correction you'll get the same apparent clock rate variation that Roemer did whatever the one-way speed of light.

I haven't actually done the maths. I did something similar for another "one-way speed of light" experiment which hinged on length contraction which could probably be adapted. Search for posts by me containing the name kkris1.

vanhees71
I don't understand what actually this sentence implies:
If you assume that light speed is anisotropic you'll find that there is a clock rate correction due to motion
1. anisotropic respect to the Jupiter--> Earth and Earth --> Jupiter directions? This is totally arbitrary to me given that absolute space doesn't exist. Any anisotropy could be used to establish preferential landmarks or directions.
2. "due to motion" means "due to the motion of the observer getting farther"? We can easily imagine the same experiment observing Io's light from a rocket close to Earth perfectly still in Io's frame and observing, in the same way, Io's light after six months from the same frame in a different position. If I observe the two events not from my own clock (which underwent movement), but from the synchronized clocks I find in the two places of Io's frame from which I observe the two hiding events, I am sure I'd obtain the same result of Roemer type experiment from moving Earth, with only minor (milliseconds) corrections.

But I'm not interested in corrections. The point is asking what is the meaning of an arrival time difference Δt of the same light signal as received at two different synced clocks in-built in the same frame of the light source at a known distance Δd. What is Δd/Δt if not the one-way & one-direction-measure of c? If we cannot think of syncing time within the same inertial frame univocally, because of problems in slowly transporting clocks which have been previously synchronized in the same place, then I must think of similar problems in transporting one-meter steel bars from factory to other places. That would mean that we cannot ever speak of a reference frame, if not as a mirage or mythological unattainable thing, neither in the framework of special relativity.

Secondly. If I repeat a modern version of Romer experiment, I'll find the same c value of another experiment in which light "travels"on the two-way trip. Then, for me, that would be enough to authorize us to tell c is the same for any trip.

Ibix
I don't understand what actually this sentence implies:
Jupiter is moving relative to Earth. If you assume an anisotropic speed of light, it turns out that you cannot neglect time dilation even at low speeds. And the effect of the time dilation will cancel with the added/reduced travel time (due to the non-c speed of light) to give you the exact same observations on Earth whatever the one-way speed of light.
This is totally arbitrary to me given that absolute space doesn't exist.
Of course it's arbitrary. Coordinate choices always are.
Any anisotropy could be used to establish preferential landmarks or directions.
No it couldn't - see my first paragraph.

pervect
Staff Emeritus
I can't read the tons of posts and replies about one-way light speed in this forum. I was criticised once for sustaining light speed should be equal in both outward and return trips and Einstein's method of syncing clocks as the only reasonable one. Then I studied some scientific articles gently suggested by somebody here and I became persuaded that nobody succeeded yet in measuring the one-way light speed. After that, someone else argued against the need of measuring the space and time in the round-trip of light that I claimed in a different thread.
Finally, I went through the details of Roemer experiment. And I learned that in Roemer measure we deduce light speed from time increment that light from Jupiter satellite Io takes to travel the diameter of Earth orbit to reach observer's telescope. Thus, this appears to be a one-way or inward trip speed measure obtained from distance and retardation time.
What I expect now is an ultimate and expert explanation of why Roemer's measure can't be viewed as a one way measure of light speed.
I'm not sure what you've read and haven't read. We don't need to dig into the details of Roemer's experiment to understand the issues with measuring one-way speeds in general.

The two key points I see them are this:

1) If you change your clock synchronization, you get different one-way speeds. For instance, if you measure the speed of a plane going from Chicago to Los Angeles, it takes about 4 hours as measured on the plane. For the time being we'll ignore air resistance and prevailing winds, which makes the speed (very slightly) different in each direction in real experiments.

With ta 2 hour timezone difference between Chicago and Los Angeles (representing a different clock synchronization convention, one that is in actual use though generally not used for physics), it appears that it takes roughly 2 hours for the plane to fly in one direction and roughly six hours in the other.

So far we don't have any inconsistencies, but when we try to do more experiments, we start to find some issues with the picture of using arbitrary clock synchronizations (which in this problem are the standard timezones) to calculate physical quantities. For instance, we might imagine that we collide very rugged planes flying in opposite directions, to see if they have the same momentum, or different momentum. If they have the same momentum in opposite directions, we expect the rugged planes to stop in midair and fall straight down, while if they have different momenta, then we expect the fall to be in some direction other than straight.

It may or may not be necessary to point out that in our simplified version of the problem, we expect the rugged planes to fall straight down, and in a more realistic problem we might see small effects due to air resistance and winds, but certainly nothing that would be consistent with one plane having three times the momentum of the other plane.

2) Different inertial frames require different clock synchronization conventions according to special relativity. I would tend to guess that in spite of your reading, you're not familiar with this fact.

So at a rough guess, in spite of your reading, you are not really analyzing the problem according to special relativity, most likely due to some key parts being omitted from your reading. You are apparently analyzing the problem in some other paradigm.. Unfortunately, the rest of us are analyzing the problem according to the framework of special relativity, so we're getting different answers because we are using different theories.

Discussing the details of Roemer's experiment simply isn't going to be productive if we're analyzing them in different frameworks. And it's not a particularly easy way to learn the framework of special relativity, which would be my guess as to what the underlying issue is.

The key point here is point 2, which is called the "relativity of simultaneity" and discussed in experiments like Einstien's train. And it's a logical consequence of the assumptions of special relativity, as discussed by Einstein himself, and in a lot of standard texts. It's also noteworthy as being quite counter intuitive.

ComplexVar89, vanhees71, Ibix and 1 other person
Mister T
Gold Member
I can't read the tons of posts and replies about one-way light speed in this forum.
Do you understand that measuring a one-way speed of anything involves synchronizing two clocks that are separated along the line of motion?

vanhees71, Ibix and BvU
Staff Emeritus
2019 Award
I can't read the tons of posts and replies about one-way light speed in this forum.
Pity, because the answer to your questions are probably there.

BvU
What I expect now is an ultimate and expert explanation of why Roemer's measure can't be viewed as a one way measure of light speed.
L. Karlov, “Does Roemer's method yield a unidirectional speed of light?” Australian Journal of Physics 23, 243-258 (1970)

L Karlov “Fact and Illusion in the speed of light determination of the Roemer type” American Journal of Physics, 49, 64-66 (1981)

vanhees71 and Ibix
Ibix
L. Karlov, “Does Roemer's method yield a unidirectional speed of light?” Australian Journal of Physics 23, 243-258 (1970)

@Alfredo Tifi - I notice that Bartolomeo has posted this before in one of your threads (this one). I recommend you read it. Section VII is the formal mathematics underlying my first paragraph in #4.

I think it's much easier (almost trivial) to understand by drawing a Minkowski diagram and adding the axes for the synchronisation convention appropriate for a non-isotropic light speed (which, of course, does not change the events depicted at all - so QED). But the maths is perhaps more reassuring.

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vanhees71
I would use this experiment to measure the one-way speed of light in both directions:

1. Find a place in empty space far away from gravitating bodies.

2. Synchronize two identical clocks at point O.

3. Send them for a long trip at same speed v << c in opposite directions. They must lie on the same line.

4. When one clock reaches a point A say, then you know the other clock reaches a point B such that OA=OB because of equality of respective velocities.

5. Get them both to emit a light signal back to point O, at a time 12.00 by their respective readings.

If both light signals reach point O simultaneously, then you know that the one-way speed of light is the same in both directions. QED

Ibix
If both light signals reach point O simultaneously, then you know that the one-way speed of light is the same in both directions. QED
No - see post #4, the maths for which is in Karlov's paper linked by Bartolomeo in #8. In short, if you assume an anisotropic speed of light then the clock travelling in the "slow light" direction accumulates extra time compared to the other, and this difference is exactly compensated by the different light travel times on the return leg.

PAllen
2019 Award
I would use this experiment to measure the one-way speed of light in both directions:

1. Find a place in empty space far away from gravitating bodies.

2. Synchronize two identical clocks at point O.

3. Send them for a long trip at same speed v << c in opposite directions. They must lie on the same line.

4. When one clock reaches a point A say, then you know the other clock reaches a point B such that OA=OB because of equality of respective velocities.

5. Get them both to emit a light signal back to point O, at a time 12.00 by their respective readings.

If both light signals reach point O simultaneously, then you know that the one-way speed of light is the same in both directions. QED
You assume isotropy of time dilation. To consistently allow for anisotropic light speed, other anisotropies must also be admitted. You can dispense with any measurement strategy if you assume isotropy of all physical laws. For then, invariance of two way speed plus isotropy, immediately implies invariance of one way speed.

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ComplexVar89, PeterDonis and Ibix
You assume isotropy of time dilation. To consistently allow for anisotropic light speed, other anisotropies must also be admitted. You can dispense with any measurement strategy if you assume isotropy of all physical laws. For then, invariance of two way speed plus isotropy, immediately implies invariance of one way speed.
I think I am just assumming Galilean Relativity here but please correct me if I am wrong. In the frame of point O both velocities are identical.

Of course if point O is moving relative to another observer, the velocities of the clocks are not the same and they are nor synchronized anymore but the experiment is still valid in Special Relativity terms.

I chose v << c, because it's easily verifiable. Any speed would do.

Ibix
In the frame of point O both velocities are identical.
You are missing @PAllen's point. The standard time dilation formula assumes the one-way speed of light is the same as the two-way speed. If you don't want to assume your answer then you need to derive a time dilation formula without that assumption. Then you find that time dilation is different in opposite directions in general, and the difference in time accumulated by the moving clocks is exactly enough to compensate for the difference in travel times of the returning light pulses.

Read Karlov's paper for the maths.

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ComplexVar89, PeterDonis and Bartolomeo
PeterDonis
Mentor
2019 Award
I think I am just assumming Galilean Relativity here
I'm not sure what you mean by "Galilean Relativity" (and bear in mind that in this subforum "relativity" specifically means SR and GR), but you are making an additional assumption in your #4 and #5:

4. When one clock reaches a point A say, then you know the other clock reaches a point B such that OA=OB because of equality of respective velocities.
But you don't know that both clocks read the same at the events when they reach these respective points, unless you assume that their time dilation factors are the same. That requires isotropy of time dilation, i.e., the time dilation for a speed ##v## is the same regardless of which direction the motion is in.

5. Get them both to emit a light signal back to point O, at a time 12.00 by their respective readings.

If both light signals reach point O simultaneously, then you know that the one-way speed of light is the same in both directions.
Only if you know that the emissions of light from points A and B at the same time by the clock readings, were in fact simultaneous in the frame you are using (the rest frame of points O, A, and B). But you only know that if, as above, you assume isotropy of time dilation.

Only if you know that the emissions of light from points A and B at the same time by the clock readings, were in fact simultaneous in the frame you are using (the rest frame of points O, A, and B). But you only know that if, as above, you assume isotropy of time dilation.
Ah, ok, I see what you mean, and now suppose there was a way to prove isotropy of time dilation in all directions, then for the case of argument one could say that I was assuming isotropy of space in all directions ( a rod lengthens or shortens according to which direction it's pointed at .)

I can see it's pointless to try to prove this, I am satisfied with your answers and I rest my case.

Mister T
Gold Member
Send them for a long trip at same speed v << c in opposite directions.
There is no way to know that the speeds are the same without first assuming that which you are trying to establish.

Paul Colby
Gold Member
While I agree direct experimental checks are a good thing it seems to me that almost any experimental check on electrodynamics is also an indirect check on the normal notion of light speed. To posit that light speed is anisotropic requires that you provide an updated electrodynamics that is consistent with all known EM phenomena that have been checked by experiment. That's a big list.

PAllen
2019 Award
While I agree direct experimental checks are a good thing it seems to me that almost any experimental check on electrodynamics is also an indirect check on the normal notion of light speed. To posit that light speed is anisotropic requires that you provide an updated electrodynamics that is consistent with all known EM phenomena that have been checked by experiment. That's a big list.
No, it is sort of trivial. You do a coordinate transform from Minkowski coorinates to a so called Edwards frame. The form of Maxwell’s equations become more complex as judged by most humans, but there are, in principle, no changes in predicted observations.

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Paul Colby
Gold Member
No, it is sort of trivial. You do a coordinate transform from Minkowski coorinates to a so called Edwards frame. The form of Maxwell’s equations become more complex as judged by most humans, but there are, in principle, no changes in predicted observations.
So, the earth is spinning and revolving around the sun and the galactic center and we're magically in an Edwards frame to the precision needed to replicate EM observations to current standards? sweet.

Paul Colby
Gold Member
Maxwell’s equations become more complex as judged by most humans, but there are, in principle, no changes in predicted observations
yes, I question this statement.

Ibix
It's really just a case of doing a coordinate substitution. You use ##x'=x## and ##t'=t+x(c-c_+)/cc_+##, where ##c_+## is one of the one-way speeds of light, to eliminate x and t and their derivatives from all equations, as far as I understand. That doesn't change any physics, it just makes the maths horrible and makes interpretation in terms of x' and t' highly counter-intuitive.

Paul Colby
Gold Member
So, the speed of light which is ##1/\sqrt{\epsilon_o\mu_o}## becomes an anisotropic expression in a non-Edward's frame I presume. This implies that the voltage on a charged capacitor will depend on it's orientation (direction of E-field). This is not observed.

Ibix
So, the speed of light which is ##1/\sqrt{\epsilon_o\mu_o}## becomes an anisotropic expression in a non-Edward's frame I presume. This implies that the voltage on a charged capacitor will depend on it's orientation (direction of E-field). This is not observed.
Did you remember to work out what a device that works as an electric field meter when analysed in a Minkowski frame does when it's analysed in an Edwards frame? I bet what it does depends on its orientation so that its predicted output is invariant as the capacitor is rotated.

All PAllen and I are saying is that physics is invariant under coordinate transforms. Only the interpretation changes. And the one-way speed of light is a coordinate dependent phenomenon. The round trip can't be because it would mess up proper time measurements.

jbriggs444
Paul Colby
Gold Member
Did you remember to work out what a device that works as an electric field meter when analysed in a Minkowski frame does when it's analysed in an Edwards frame? I bet what it does depends on its orientation so that its predicted output is invariant as the capacitor is rotated.
Well, I use an electrometer, which is also a capacitor. It (or any other voltage meter for that matter) need not change orientation with the capacitor under test. So yes I have analyzed the electric field meter. The effect remains and to the limits of my knowledge is unobserved.

As a general concern all expressions, such as the transition frequencies of atoms and such, which depend on ##\epsilon_o## become anisotropic. As I say, the list is large and contains some really high precision measurements. I think my skepticism is warranted.