# “We don’t really know the speed of light”

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Eh?  How have I not heard of this before?  I came across this today in the article linked below.

“The speed of light is an assumption, not a certainty. It’s an assumption in that we have never experimentally measured the one-way speed of light. The best we have been able to do, even with our most sophisticated modern technology, is measure the roundtrip speed of light and assume that the speed is the same in both directions.”

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I follow the argument regarding how we have measured c but I don't understand what supports the premise that the speed of light may/could be anisotropic.  The speed of light being a property arising from  the nature of the particle (photon, massless) and the two constants which describe the permittivity of free space (the electric constant) and the permeability (the magnetic constant).  So what I don't understand is that are we saying the values of these two constants change for a particular part of the return trip?  Or have I missed something, quite possible, and usually often

from Maxwell's equation's   C = 1/ (ϵoµo)1/2

Jim

Edited by saac
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Within special relativity it is impossible to measure the one way of light. The reason is that you need to synchronise the clocks at the two ends and depending on the protocol  you use you can either get whatever answer you like or you have to assume the one way speed of light is the average of the two way speed.

There is a long discussion here One way speed of light.

Obviously,  as @saac points out Maxwell's equations provide an indirect method of measuring c.

Regards Andrew

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1 hour ago, saac said:

I follow the argument regarding how we have measured c but I don't understand what supports the premise that the speed of light may/could be anisotropic.  The speed of light being a property arising from  the nature of the particle (photon, massless) and the two constants which describe the permittivity of free space (the electric constant) and the permeability (the magnetic constant).  So what I don't understand is that are we saying the values of these two constants change for a particular part of the return trip?  Or have I missed something, quite possible, and usually often

from Maxwell's equation's   C = 1/ (ϵoµo)1/2

And my students do just this. I teach a second-year e&m lab course that performs one experiment per week. In consecutive weeks, the students measure ϵo and µo using

https://media.vwr.com/interactive/p...h_2014/files/assets/basic-html/index.html#289

and then compare to the speed of light. For µo , we send up to 20 amps through the metal rods.

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I may not be undertanding correctly but doesn't a ring-laser gyro depend on 'c' being isotropic? If it were anisotropic you couldn't null the gyro when it's non-rotating. Since it sends lasers both ways around a fixed path it surely demonstates the isotropic nature. Or have I overlooked something?

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7 hours ago, wulfrun said:

I may not be undertanding correctly but doesn't a ring-laser gyro depend on 'c' being isotropic? If it were anisotropic you couldn't null the gyro when it's non-rotating. Since it sends lasers both ways around a fixed path it surely demonstates the isotropic nature. Or have I overlooked something?

I think it would be ok as long as the round trip average were c. However, there is no evidence for any anisotropy that I  am aware of.

Regards Andrew

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What are the implications for wavelength and frequency if light speed is anisotropic?  Would these necessarily be anisotropic too?  What about photon energy? Would photons have more (or less) energy depending which way they were going? You’d have thought we might have noticed.  Or maybe I don’t understand the problem.

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Didn't  the Michelson-Morley experiment show the speed of light in both directions was the same? This suggests (but doesn't prove) isotropy of c.

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6 minutes ago, michael.h.f.wilkinson said:

Didn't  the Michelson-Morley experiment show the speed of light in both directions was the same? This suggests (but doesn't prove) isotropy of c.

No, only the average average speed was the same. The light goes back and forth in both legs of the interferometer.

Regards Andrew

Edited by andrew s
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14 minutes ago, Ouroboros said:

What are the implications for wavelength and frequency if light speed is anisotropic?  Would these necessarily be anisotropic too?  What about photon energy? Would photons have more (or less) energy depending which way they were going? You’d have thought we might have noticed.  Or maybe I don’t understand the problem.

Photon energy is not a constant but frame dependent as in blue and red shift s seen in stellar spectra. It's difficult to say what the impact would be if c were anisotropic as our best theories are based on it being isotropic.

The fact SR, GR and QED do so well experimentally rather supports the view that c is isotropic.

Regards Andrew

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3 hours ago, andrew s said:

No, only the average average speed was the same. The light goes back and forth in both legs of the interferometer.

Regards Andrew

Indeed. I imagine those raising this question are considering whether the speed of light going away from the observer is different from the speed of light approaching the observer.  Or have I misunderstood what they’re saying?

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59 minutes ago, Ouroboros said:

Indeed. I imagine those raising this question are considering whether the speed of light going away from the observer is different from the speed of light approaching the observer.  Or have I misunderstood what they’re saying?

Yes that is how I understand it.  Regards Andrew

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Part of me thinks even if it did would it make any material difference?  It might be easy to conclude not. On the other hand, as that article suggests, string theory may predict that light speed is anisotropic. So, confirmation  one way or the other would provide  some experimental evidence which I understand is lacking for string theory.

Edited by Ouroboros
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47 minutes ago, Ouroboros said:

Part of me thinks even if it did would it make any material difference?  It might be easy to conclude not. On the other hand, as that article suggests, string theory may predict that light speed is anisotropic. So, confirmation  one way or the other would provide  some experimental evidence which I understand is lacking for string theory.

If it does it will need to provide a new theory of relativity as well so that it can be measured. Given its track record on providing testable predictions I wouldn't hold my breath. ☠

Regards Andrew

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13 minutes ago, andrew s said:

If it does it will need to provide a new theory of relativity as well so that it can be measured. Given its track record on providing testable predictions I wouldn't hold my breath. ☠

Regards Andrew

The theory of relativity will still work as well as it does now in the areas that it works well now even if it turns out that the speed of light is anisotropic. New or modified theories always have to be back compatible as it were with older theories in areas where those work well.  It's just that the newer theory explains something additional better that the older theory fails to explain as well

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4 hours ago, Ouroboros said:

The theory of relativity will still work as well as it does now in the areas that it works well now even if it turns out that the speed of light is anisotropic. New or modified theories always have to be back compatible as it were with older theories in areas where those work well.  It's just that the newer theory explains something additional better that the older theory fails to explain as well

Unfortunately, you can't measure the one way speed of light within SR as you need to synchronise clocks using something like the Einstein synchronisation protocol. It is in this sense you would need a new theory that legitimise a one way measurement.  Yes I agree in the limit it would need to reduce to SR.

Regards Andrew

Edited by andrew s
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Since the speed of light connects frequency and wavelength and diffraction depends on wavelength shouldn't anisotropic c  move the position of the spectral lines from my spectrograph calibration lamp when pointing in different directions?

Robin

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Doesn't an experiment like the LHC critically depend on knowing the speed of light? I thought this was figured out already.

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6 minutes ago, Sunshine said:

Doesn't an experiment like the LHC critically depend on knowing the speed of light? I thought this was figured out already.

We new the speed of light very accurately but now it is a defined value and time is defined in terms of it rather than c = d/t

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1 hour ago, robin_astro said:

Since the speed of light connects frequency and wavelength and diffraction depends on wavelength shouldn't anisotropic c  move the position of the spectral lines from my spectrograph calibration lamp when pointing in different directions?

Robin

I think there would be issues of getting the required accuracy  but I need to think about if its possible in principle or not. It's not unlike using Maxwell's equations and its constants being measured in different directions.

Regards Andrew

PS On reflection (pun intended) you would need to known the there was no relative motion between the lamp and the receiver to the required accuracy.  I can't see how you could do this without using a light interferometer which brings you back to a two way light beam.

Edited by andrew s
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3 hours ago, andrew s said:

PS On reflection (pun intended) you would need to known the there was no relative motion between the lamp and the receiver to the required accuracy.  I can't see how you could do this without using a light interferometer which brings you back to a two way light beam.

It depends on the size of the effect of course but in principle as a thought experiment you could use a rigid stick so the two are guaranteed to be comoving. Perhaps though in a universe where the speed of light is anisotropic  the length of the stick depends on the orientation 😉

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3 hours ago, andrew s said:

It's not unlike using Maxwell's equations

I would say the relationships between wavelength, frequency and velocity and  between the wavelength and the diffraction pattern are more universal  as it is independent of the physical nature of the wave. (It is effectively just geometry)

Edited by robin_astro
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7 hours ago, robin_astro said:

I would say the relationships between wavelength, frequency and velocity and  between the wavelength and the diffraction pattern are more universal  as it is independent of the physical nature of the wave. (It is effectively just geometry)

I think you would need to specify exactly how you would make the measurement for me to comment on if it's doable or not. The devil is in how you do the measurement. The "one way"  speed derived from the timing of the Jovian moon eclipses  (used as a clock) can give different results depending on how you analyse it. I'll look out the reference.  In your proposal the lamp acts as a clock so it may be analogous.

As I have said before there is no evidence for any anisotropy,  if there were Maxwell's equations would need to change and you would still need the two speed to be c.

Yes, the wavelength,  frequency  and velocity are geometry no argument there but that is exactly what GR and SR are geometry.  Also your wave is governed by Maxwell's equations so to my mind they are on a similar footing.

Regards Andrew

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3 hours ago, andrew s said:

I think you would need to specify exactly how you would make the measurement for me to comment on if it's doable or not.

Actually I have already done it when testing the stability of my ALPY spectrograph. (To a precision of better than 1 in 10^4)

The spectrograph consists of a lamp filled with excited neon atoms, a transmission diffraction grating and a camera recording the spectrum, all mounted rigidly in a line. I pointed it in a number of different directions including east and west for example. There was no detectable movement in the position of the centroid of spectral lines on the camera sensor as measured from the counts in in each pixel. ie the measured wavelength was constant .   For this to be true in an anisotropic c universe either the dimensions of the instrument must  depend on the orientation in a complex way (the camera sensor is orthogonal to the light beam) or the mean frequency of the photons (the clock)  changed depending on the  orientation of the instrument which seems unlikely given the random orientation of the atoms in space.

Cheers

Robin

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@robin_astro I found the link to the re-analysis of Romer's velocity measurement.  Unfortunately,  it's a book but I managed to read some of it on line. It seems you can have a isotropic speed of light that make sense but they predict the same outcomes as the normal Einstein synchronisation protocols. It did not address your proposal.

Giving it more thought, let's assume you measured a shift. The issue is then how to interpret it.  It could be due, to an anisotropic change in c or in distance. For example we assume the Hubble red shift is due to expansion rather than  changes in c or t.

As far as I can tell it is a convention to adopt Einstein's synchronisation protocol and indeed this is now fixed in our system of units where the value of c is fixed.

Regards Andrew

1 in 10^4 is good but not conclusive in the esoteric realm of the measurement of fundamental constants 😀 No Nobel prize just yet but it's nice to have an upper bound.😏

Edited by andrew s

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