I Why is Rømer's light speed measurement not one-way?

[Warp]

Some years ago the popular youtuber Veritasium made a video about how it's (at least seemingly) impossible to measure the one-way speed of light, and how no matter what you are trying to do, you'll always be measuring the two-way speed, even if your contrived example is trying to masquerade it as being just the one-way speed measurement.

My initial thought was: Wasn't the very first accurate measurement of the speed of light (by Ole Rømer) using the moons of Jupiter a one-way measurement?

After all, Rømer did not send anything to the moons of Jupiter and measure the two-way speed. He measured only and solely the light arriving from those moons to Earth, without sending anything there from Earth.

I asked ChatGPT this (and some followup questions) and it gave a lengthy explanation, but I didn't quite fully understand it. Perhaps the only takeaway that I got was that since Rømer had to do two separate measurements, and the experiment cannot be done with one single measurement, that indirectly implies that it's actually a disguised two-way measurement. However, I didn't quite understand the reasoning behind this.

 

[PeterDonis]

Wasn't the very first accurate measurement of the speed of light (by Ole Rømer) using the moons of Jupiter a one-way measurement?

No. To calculate speed from Romer's data, you need to know, not just what distance the light traveled, but the time it took to travel. You know what time the light arrived at Earth; that gets read directly off Earth clocks. But you also need to know what time the light left Jupiter. That is not a direct measurement. It's a convention.

In relativity, there is no physical fact of the matter about "when" an event that's distant from you happened by your clock. That includes "when" the light left Jupiter that you're now observing on Earth. To assign an "Earth time" to that distant event, you need to adopt a convention about simultaneity--what events elsewhere than on Earth happen at the same time as particular events on Earth.

That basic fact is why the one-way speed of light is not a physical fact either; it depends on what simultaneity convention you adopt. Only the two-way speed of light, which can be measured by a single clock, is a physical fact independent of human conventions.

 

[PeterDonis]

I asked ChatGPT

Please be aware that this is not a reliable source, and is not permitted as a basis for a PF discussion.

 

[PeterDonis]

the only takeaway that I got was that since Rømer had to do two separate measurements, and the experiment cannot be done with one single measurement, that indirectly implies that it's actually a disguised two-way measurement. However, I didn't quite understand the reasoning behind this.

It's not valid reasoning. As I noted in my previous post just now, ChatGPT is not a reliable source.

 

[Warp]

Please be aware that this is not a reliable source, and is not permitted as a basis for a PF discussion.

I am not even allowed to briefly mention that I asked it the question and didn't fully understand its answer, which is why I'm asking here?

Is this some kind of weird "He Who Shall Not Be Named" thing?

 

[Warp]

No. To calculate speed from Romer's data, you need to know, not just what distance the light traveled, but the time it took to travel. You know what time the light arrived at Earth; that gets read directly off Earth clocks. But you also need to know what time the light left Jupiter. That is not a direct measurement. It's a convention.

I don't understand. The experiment doesn't rely on knowing what time the light left Jupiter. It relies on measuring how long Jupiter's moon traverses to the other side of the planet (as well as knowing the radius of Earth's orbit). It doesn't matter what the time is at Jupiter, what matters is how long it takes for its moon to orbit around it (as seen from here), or more precisely how this time changes depending on which direction the Earth is moving.

 

[Nugatory]

Is this some kind of weird "He Who Shall Not Be Named" thing?

No, it's more like if you show up at a convention of ichthyologists asking them to explain exactly where Dr Seuss's classic "One Fish, Two Fish, Red Fish, Blue Fish" fails to explain fish biology - the source is worse than useless. Of course no one would actually make that mistake, but ChatGPT produces more plausible bogus results - without the rule we would be overwhelmed by LLM-based misunderstandings.

 

[Ibix]

Rømer's experiment simply uses Jupiter's moons as clocks and attributes the apparent variation in rate solely to variation in light flight time due to the changing distance to Jupiter. So he neglected time dilation of those moving clocks - understandable given that he predates Einstein by centuries. However, if you derive the equivalent of time dilation with a free choice of one-way light speeds, you will find it is only negligible in this experiment if light speed is isotropic. So in a modern view of the experiment, by neglecting time dilation Rømer implicitly assumed isotropy.

Generally, you can do one-way measurements of light speed (as Rømer did). But you can't do it without assuming the ratio of the speeds in opposite directions somewhere in your analysis (as Rømer did).

 

[Dale]

If you read Roemer’s paper you will see that he assumed that the speed of light was the same in all directions. Different parts of the experiment involved light going in different directions at different times of the year. He assumed that the speed of light was the same in all cases regardless of the direction.

This assumption of the isotropy of the speed of light is the same as assuming the Einstein simultaneity convention which is the same as assuming that time dilation is negligible.

 

[PeterDonis]

I don't understand. The experiment doesn't rely on knowing what time the light left Jupiter. It relies on measuring how long Jupiter's moon traverses to the other side of the planet (as well as knowing the radius of Earth's orbit). It doesn't matter what the time is at Jupiter, what matters is how long it takes for its moon to orbit around it (as seen from here), or more precisely how this time changes depending on which direction the Earth is moving.

Sorry, I misstated it. The simultaneity convention comes in with the time it takes light to cross Earth's orbit; the simultaneity convention Romer implicitly used was equivalent to assuming that the speed of light is the same in all directions (or, to put it another way, that the time it takes light to cross Earth's orbit is the same at all times of the year). Others have stated the assumption in the latter form.

 

[Ibix]

There's a modern(ish - it's from 1970) analysis of Rømer in the Australian Journal of Physics available here:
http://adsabs.harvard.edu/full/1970AuJPh..23..243K

 

[Ibix]

If you read Roemer’s paper you will see that he assumed that the speed of light was the same in all directions.

That's interesting, actually, because in at least some models of light you would expect variation in light speed in this experiment. I guess he was aware of Galileo's attempts to measure light speed (too high to measure) and maybe guessed his precision wouldn't be good enough - or at least thought that an isotropic model was good enough for a first stab? I've only found his paper as a scanned image in French, which I can't read or autotranslate.

 

[Klystron]

Do not neglect that Ole Romer knew that Io's light originated from Sol (the Sun) and measured same. Describing light from Io or another moon, even in Jovian transit, as 'one-way' ignores the solar light source.

 

[Warp]

So I understand from the responses that his experiment assumes that the speed of light is the same in all directions, and the result of the experiment is calculated using that assumption, but the experiment all in itself doesn't prove that the speed of light actually is the same in all directions?

But I'm still not sure if that answers the question of whether that experiment actually measures the one-way speed of light or not.

(To me it very heavily looks like so. After all, there is literally nothing being sent from the measurer to Jupiter. Every single piece of information that's being measured is from Jupiter to Earth, to the measurer. If you put a filter between Earth and Jupiter that only allowed anything to move in the direction of Earth but not the other direction, the measurement would not be affected, which sounds to me like it's indeed measuring the speed of light in that one single direction and does not depend at all on measuring the speed in the opposite direction. In other words, it measures the one-way speed of light.)

 

[Warp]

Do not neglect that Ole Romer knew that Io's light originated from Sol (the Sun) and measured same. Describing light from Io or another moon, even in Jovian transit, as 'one-way' ignores the solar light source.

That doesn't matter. It doesn't matter where the light originates from, as that has zero effect on the measurement being made. Io could just as well be producing and emitting the light itself (eg. via some volcanic activity), and it would still give the exact same result.

 

[PeterDonis]

I'm still not sure if that answers the question of whether that experiment actually measures the one-way speed of light or not.

Your question has been answered: Romer's experiment does not show that the one-way speed of light is an invariant physical quantity. It can't, because the one-way speed of light is not an invariant physical quantity; it's a matter of convention.

Romer calculates the speed of light by taking the width of Earth's orbit and dividing it by the difference in travel times of the light coming from Jupiter's satellites. But, as has been stated, that calculation assumes that the speed of light is the same in all directions--or, to put it more concretely in terms of the circumstances of the observations, the speed of light across Earth's orbit is the same no matter what time of the year the observations are made. And as I stated, that is equivalent to assuming a simultaneity convention.

Every single piece of information that's being measured is from Jupiter to Earth

But to Earth at different times, using light traveling coming to Earth from different directions. The calculation assumes that none of that affects the speed of light: it combines information collected at different times, using light coming from different directions, into one calculation of one speed of light. That requires assuming that the speed of light is the same in all directions, which, as noted, is equivalent to assuming a simultaneity convention. (It also requires assuming that the speed of light doesn't change with time.)

it's indeed measuring the speed of light in that one single direction

No, it's not. The light coming from Jupiter to Earth is not always traveling in "one single direction". "From Jupiter towards Earth" is not "one single direction". It's different directions at different times.

 

[PeterDonis]

how it's (at least seemingly) impossible to measure the one-way speed of light, and how no matter what you are trying to do, you'll always be measuring the two-way speed,

I haven't seen the Veritaseum video you mention, but it should be made clear that this is a misstatement of the issue. The issue is not that you can't set up a process to measure something that can be reasonably called "the one-way speed of light". The issue is that any such measurement will involve adopting conventions that have no physical meaning but are just for human convenience, like conventions about the one-way speed of light being the same in all directions, or about simultaneity.

Measuring the two-way speed of light, by contrast, does not require adopting any such conventions. Physicists usually describe this by saying that the two-way speed of light is an invariant physical quantity, while the one-way speed of light is not, it's convention-dependent.

It can be hard to see this because the most common convention that is adopted, namely, that the one-way speed of light is the same in all directions, is also the one most people's intuitions adopt anyway, so it doesn't seem like there's any convention that needs to be adopted, it just seems like "the way things are". But it isn't; it's a convention.

 

[Ibix]

Describing light from Io or another moon, even in Jovian transit, as 'one-way' ignores the solar light source.

That isn't the relevant point. The terminology isn't great, but a one-way speed measure is one where the light (or whatever) path does not end in the same place it starts, whereas a for a two-way measure it does. Rømer's approach is a one-way measure.

Edit: in track and field events, the 100m sprint is usually a straight line while 400m is a lap of the field. The 100m is a so-called one-way measure of speed (and subject to $\pm 100\mathrm{m}/c$, about $\pm 0.3\mathrm{\mu s}$, of timing arbitrariness as a result), while the 400m is a so-called two-way speed measure.

Depending on your model of light you might predict that this experiment would show anisotropy due to the light coming from the Sun and reflecting off Io, but that is a separate issue.

 

[Ibix]

But I'm still not sure if that answers the question of whether that experiment actually measures the one-way speed of light or not.

It's impossible to measure the one-way speed of light in a relativistic universe without an assumption of the answer being built into the analysis somewhere. More precisely, if your one-way speed is $fc$ then you must assume $f$. Rømer assumes isotropy (i e. $f=1$), so he's effectively measuring the two-way speed of light.

 

[Ibix]

In other words, it measures the one-way speed of light.

To put it slightly differently from my last, he measures the one way speed of light on the assumption that it's isotropic. The assumption crept in because he assumed that moving clocks keep the same time as stationary clocks, and this assumption is equivalent to assuming isotropy.

If he had not assumed that, and had corrected the eclipse timings for the direction-dependent clock drift that comes with anisotropic light speed, he would have come up with the anistropy he chose by correcting the clock drift.

 

[PeterDonis]

The assumption crept in because he assumed that moving clocks keep the same time as stationary clocks, and this assumption is equivalent to assuming isotropy.

I don't think this is correct. Assuming that moving clocks keep the same time as stationary clocks is equivalent to ignoring relativistic effects, and is a reasonable approximation as long as all relative speeds are much smaller than the speed of light. In the solar system that works fine.

The assumption of isotropy of the one-way speed of light comes in because the light paths from Jupiter to Earth that come into play in Romer's calculation are in different directions. Note that this is true in both a solar system barycentric frame and in an Earth-centered frame. In the barycentric frame, the Earth-Jupiter line lies along different directions when Earth and Jupiter are at their closest and farthest separations. In the Earth-centered frame, Jupiter is in a different place in Earth's sky at those two points.

 

[Ibix]

I don't think this is correct. Assuming that moving clocks keep the same time as stationary clocks is equivalent to ignoring relativistic effects, and is a reasonable approximation as long as all relative speeds are much smaller than the speed of light. In the solar system that works fine.

Sure - but we're trying to measure the speed of light, which isn't slow.

Slow clock transport is equivalent to Einstein synchronisation. If you choose a different synchronisation you get a direction-dependent clock drift as you (or in this case, Jupiter) transport the clocks, because they remain synchronised with stationary Einstein synchronised clocks. The drift cannot exceed $\pm d/c$ as you transport them a distance $d$, since simultaneity planes must be achronal. That is negligible as long as you aren't trying to use them to measure the speed of something that takes time comparable to $d/c$ to cover the same distance - so the clock drift is important when measuring one way light speed.

 

[PeterDonis]

we're trying to measure the speed of light, which isn't slow.

The light isn't, but the clocks are. The speed of the clocks is what's relevant for the approximation I described.

Slow clock transport is equivalent to Einstein synchronisation.

A particular kind of slow clock transport is, yes. And Einstein synchronization is equivalent to an isotropic one-way speed of light, which is the assumption Romer was implicitly making.

But none of that has anything to do with the speed of the clocks after they are assumed to be synchronized and whether it's a valid approximation to ignore the relativistic effects due to that speed. That is the approximation involved when you assume that moving clocks keep the same time as stationary clocks. You can make that assumption even if you adopt a different simultaneity convention from Einstein synchronization, which results in an anisotropic one-way speed of light.

 

[Dale]

his experiment assumes that the speed of light is the same in all directions, … but the experiment all in itself doesn't prove that the speed of light actually is the same in all directions?

Correct. You cannot prove something that you assume.

In other words, it measures the one-way speed of light

You cannot measure something that you assume.

If you want to measure the one way speed of light you need to not assume that it is isotropic.

A non-isotropic assumption would be, for example, Anderson’s approach where the anisotropy in the speed of light is given by a parameter $\kappa$. In Anderson’s approach the one way speed of light is $\frac{c}{1\pm \kappa}$.

So an experiment to measure the one way speed of light would be an experiment to measure $\kappa$. But it can be shown that no such experiment exists.

 

[Ibix]

But none of that has anything to do with the speed of the clocks after they are assumed to be synchronized and whether it's a valid approximation to ignore the relativistic effects due to that speed. That is the approximation involved when you assume that moving clocks keep the same time as stationary clocks. You can make that assumption even if you adopt a different simultaneity convention from Einstein synchronization, which results in an anisotropic one-way speed of light.

Consider a simplified experiment with 1d inertial motion. Described in an Einstein frame where Earth is at rest, Jupiter approaches us, passes, and recedes with some very low speed $v$. It emits regular light pulses with some interval $\Delta t$ as measured by our Einstein frame. Rømer's direct measurements are the arrival time intervals, which will be $(1\pm\frac vc)\Delta t$.

With an anisotropic light speed the coordinate time between pulse emissions is different from the isotropic case. This is easy to see by drawing a Minkowski diagram in Einstein coordinates and adding an anisotropic coordinate grid. Slanted simultaneity planes with the same vertical spacing have different spacings on the diagonal of Jupiter's worldline, and this difference is crucial to Rømer's measurements being invariant - it's the changed coordinate time between ticks that compensates for the changed travel time of the light to yield the same time between consecutive pulse reception events in either coordinate frame. You can't neglect it or you could detect anisotropy. In fact if you neglect the change in the coordinate tick rate you have something like an ether model with an ether wind, which would be a detectable anisotropy if it were a correct theory.

Now note that Rømer has a 2d case, not a 1d one. In an anisotropic coordinate system the coordinate tick rate of Jupiter's clocks is time-varying since its direction of motion with respect to the anisotropy is changing. So if he isn't applying a time varying correction to the tick rate, he's assuming isotropy.

 

[PeterDonis]

If you want to measure the one way speed of light you need to not assume that it is isotropic.

Hm, that's a good point--if you assume the speed of light is isotropic, then as soon as you've measured the two-way speed, you've also measured the one-way speed.

 

[PeterDonis]

In an anisotropic coordinate system the coordinate tick rate of Jupiter's clocks is time-varying since its direction of motion with respect to the anisotropy is changing. So if he isn't applying a time varying correction to the tick rate, he's assuming isotropy.

The "coordinate tick rate of Jupiter's clocks" does not enter into the analysis anywhere. The "ticking" of the "Jupiter clock" is the observed orbital motion of Jupiter's satellites. Those observations are independent of any choice of coordinates.

 

[Warp]

Hm, that's a good point--if you assume the speed of light is isotropic, then as soon as you've measured the two-way speed, you've also measured the one-way speed.

Perhaps Rømer's experiment alone doesn't prove that the speed of light is the same in all directions, but if the result is the same as the two-way speed as measured in a different experiment, wouldn't this combination of two experiments prove it?

Or would it merely prove that the one-way speed of light just happens to coincide with the two-way speed in that one particular direction?

 

[Ibix]

but if the result is the same as the two-way speed as measured in a different experiment, wouldn't this combination of two experiments prove it?

No, because the result is only the same if you assume isotropy.

 

[Ibix]

The "coordinate tick rate of Jupiter's clocks" does not enter into the analysis anywhere.

Something coordinate dependent has to enter your analysis if you are hoping to derive a coordinate dependent quantity like the one-way speed of light from invariant quantities like Rømer's observations (or indeed, any observations).

 

[cianfa72]

It can be hard to see this because the most common convention that is adopted, namely, that the one-way speed of light is the same in all directions, is also the one most people's intuitions adopt anyway, so it doesn't seem like there's any convention that needs to be adopted, it just seems like "the way things are". But it isn't; it's a convention.

So, coming to the second postulate of Einstein's special relativity, it is basically two folded:

1. the two-way speed of light is the invariant $c$
2. the propagation of light is isotropic

The latter(2) is equivalent to pick as synchronization convention in any inertial frame the Einstein's synchronization convention.

 

[Ibix]

the second postulate of Einstein's special relativity, it is basically two folded:

No, Einstein separately and explicitly assumes isotropy in his 1905 paper. He just doesn't call it a postulate.

 

[cianfa72]

No, Einstein separately and explicitly assumes isotropy in his 1905 paper. He just doesn't call it a postulate.

Ah ok, so the SR's Einstein second postulate is just: the two-way speed of light (w.r.t. any inertial reference frame) is the invariant $c$.

 

[Ibix]

Ah ok, so the SR's Einstein second postulate is just: the two-way speed of light (w.r.t. any inertial reference frame) is the invariant $c$.

I think this boils down to details of where exactly you define what. Is an inertial frame necessarily orthogonal? Or does it merely require that inertial objects have constant coordinate velocity? If the former then you've already got isotropy; if the latter you need to specify it if you want to get it. Or arguably, Einstein not making a formal distinction between one- and two-way speeds means that he was assuming they were the same and hence assuming isotropy and didn't really need a separate assumption.

I don't think it really matters, and I very much doubt Einstein fully understood what he had done at the point he was writing his paper. So exactly what comes from what postulate is probably not particularly well-defined.

 

[Warp]

If the speed of light were different in different directions, couldn't this be observed in other ways, such as unexpected redshift/blueshift, or unexpected patterns in the cosmic microwave background radiation?

(I know this isn't really related to my original question anymore, but anyway...)

 

[jbriggs444]

If the speed of light were different in different directions, couldn't this be observed in other ways, such as unexpected redshift/blueshift, or unexpected patterns in the cosmic microwave background radiation?

No. All we would need to get the speed of light to be different in different directions would be to change our simultaneity convention. But simultaneity conventions have no physical effects.

 

[Ibix]

If the speed of light were different in different directions, couldn't this be observed in other ways, such as unexpected redshift/blueshift, or unexpected patterns in the cosmic microwave background radiation?

No. You get a different Doppler formula and a different emission frequency and the two cancel out.

It doesn't matter what question you ask. The difference between an isotropic one-way speed and an anisotropic one is how I personally choose to lay out my coordinate system. My personal choice cannot lead to any difference in measurements, only in how I describe how those measurements come to be.

 

[PeterDonis]

Something coordinate dependent has to enter your analysis if you are hoping to derive a coordinate dependent quantity like the one-way speed of light from invariant quantities like Rømer's observations (or indeed, any observations).

Yes, and the coordinate-dependent thing in Romer's analysis is the simultaneity convention, or, equivalently, the assumption that the one-way speed of light is isotropic. But that has nothing to do with the "coordinate tick rate of Jupiter clocks".

 

[Ibix]

Yes, and the coordinate-dependent thing in Romer's analysis is the simultaneity convention, or, equivalently, the assumption that the one-way speed of light is isotropic. But that has nothing to do with the "coordinate tick rate of Jupiter clocks".

The coordinate time between ticks depends on the simultaneity convention for moving objects.

 

[PeterDonis]

The coordinate time between ticks

Does not come into the analysis anywhere. The analysis uses the observed time between ticks (the "ticks", as I said before, being the observed orbits of Jupiter's satellites) as recorded by Earth clocks.

 

[Warp]

No. You get a different Doppler formula and a different emission frequency and the two cancel out.

It doesn't matter what question you ask. The difference between an isotropic one-way speed and an anisotropic one is how I personally choose to lay out my coordinate system. My personal choice cannot lead to any difference in measurements, only in how I describe how those measurements come to be.

Are you saying that if the speed of light is different in different directions, that's completely unobservable?

Surely if light moved in one direction at c and in another direction at 1m per year, there would be some observable effect?

 

[Ibix]

Are you saying that if the speed of light is different in different directions, that's completely unobservable?

That's exactly what I said, yes.

Surely if light moved in one direction at c and in another direction at 1m per year, there would be some observable effect?

That isn't consistent with relativity - you require the two-way speed to be $c$, so the average of the two one-way speeds must be $c$ (in the sense that $\frac 2c=\frac 1{c_\mathrm{fast}}+\frac 1{c_\mathrm{slow}}$). Note that electromagnetic theory depends on relativity, so you would need a completely different universe to describe your 1m/s vs c scenario.

Also note that if you adjust the one-way speed of light you adjust all others too - a thing going at half light speed in the isotropic case will be doing half the relevant light speed in the anisotropic case. This is because it's just a coordinate change.

 

[Dale]

Are you saying that if the speed of light is different in different directions, that's completely unobservable?

Yes. There is no experiment that depends on Anderson’s $\kappa$