# When has the speed of light been measured, recently?

Yes, it is weird, absurd, but I can't stop thinking that the would-be superluminal neutrino speed has been computed by an arithmetic operation (space/time) and not by direct comparison with a simultaneous light ray running in "parallel".

So the "unspeakable", outrageous question: is the speed of light increasing in the last months? When it has been measured the last time? Also: is the speed of light measured in a one-way or two-ways (forward and back) method?

It is a "politically incorrect" question, but its logic is rock-solid, I think.

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Since the speed of light has now been fixed at 299,792,458 metres per second, this might be asking whether the metre is shrinking. – Henry Dec 11 '11 at 22:39
@Henry - Admittedly a late comment, but that redefinition happened three quarters of a century after Einstein's miracle year, over a century after the Michelson-Morley experiment. A very large number of ever improving measurements of the speed of light were made in the intervening century before the CGPM was willing to deem the speed of light as a fixed constant. – David Hammen Sep 23 '14 at 21:43
– Void Sep 23 '14 at 22:06

Humanity operates quite a number of spacecrafts in various places in the Solar System and communications with their on-board computers depends on the speed of light. This is because the frequency on which commands and data is sent and received varies with spacecraft and ground station's relative velocities by tens of kHz due to Doppler effect (the relative speed of a spacecraft is often in the range of many km/s and a lot of communication takes place on gigahertz frequencies, e.g. S-band).

Also, flight dynamics teams at different space agencies constantly monitor spacecraft positions and velocities by performing very precise measurements which also involve the speed of light. These measurements are correlated with flight dynamics predictions based on orbital mechanics. Any major disagreement would constitute an emergency.

Don't worry: XXI century Homo sapiens would very quickly notice if the speed of light attempted to play a trick on us.

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If the question were phrased in terms of dimensionless quantities, like the speed of light relative to atomic radii and frequencies, this would be a satisfying answer. Measuring the speed of light is meaningless without specifying the units. – Ron Maimon Dec 12 '11 at 10:51
Of course I am interested in the speed of light for comparison with the would-be superluminal neutrino at OPERA experiment. So, if it is true that the neutrino speed has been given in terms of m/s by the OPERA physicists, then I am interested in the speed of light measured in m/s. – user6090 Dec 13 '11 at 7:13
@RonMaimon I agree that explicit unit specification is missing from the question. The context suggest that the OP is interested in the speed of light relative to the distance from CERN to Gran Sasso and the time units used by the famous experiment. – Adam Zalcman Dec 13 '11 at 15:37
@user6090 Meter is defined as the distance travelled by light in vacuum in 1/299792458 of a second, so the speed of light is always 299792458 m/s by definition. Hence you can think of neutrinos' speed expressed in m/s as scaled ratio of their speed to c. – Adam Zalcman Dec 13 '11 at 15:37

The speed of light is being measured very accurately right now for this message to get to you. It's going down a fibre that uses DWDM to separate the channels which requires the speed of light to be very accurately what the engineers expect.

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Does DWDM fails or work incorreclty if the speed of light is some 2x10-5 different from usual? – user6090 Dec 11 '11 at 22:31
Channels are about 25GHz wide on 300THz so close to that – Martin Beckett Dec 12 '11 at 15:54

A $2 \times 10^{-5}$ shift in the speed of light would have shown up in a variety of ways. For instance, the laser ranging that is used to monitor the distance to the moon.

The reason no one has attempted to run side-by-side speed test is related to the difficulties of doing neutrino speed measurements. Between needing a high-intensity, moderately high energy accelerator at one end; a physically large detector at the other end; the need to shield the detector from cosmic rays; and wanting a long enough distance to between them to tolerate nano-second scale timing uncertainties and still get the necessary precision the line of flight for the neutrinos has to follow a chord though the Earth. Accordingly the only way to run a side by side trial would be to dig a multi-hundred kilometer tunnel that goes very deep and is straight enough for a uninterrupted line of sight. Good luck getting funding for that.

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It is the Gelmini tunnel. :-) – user6090 Dec 11 '11 at 22:29

There has been a lot of coverage of the faster-than-light neutrinos and therefore reasonable to think about the subject. There are some theories that suggest that the speed of light is not a constant, but that change would be over the lifetime of the Universe. In any case, there is no evidence for such changes in the speed of light. As for how often it is measured, well, all the time. GPS navigation makes use of Special Relativity all the time which has the speed of light built into it. It is good to question long standing theories in light of new evidence, but it is going to take a lot to dethrone Relativity; it has been tested far too rigorously for us to question it on the basis of single statistical result.

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It is not possible, even in principle, to unambiguously detect a change in the speed of light over time, and this was true even before the SI units were redefined so as to give $c$ a defined value. The trouble here is that $c$ has units, and if a fundamental unitful number seems to change over time, there is always an ambiguity in whether the number is changing or the standards used to define the unit are changing. It is only possible to unambiguously detect a change over time in a unitless constant. For example, it's quite conceivable that the unitless fine structure constant $\alpha=e^2/\hbar c$ has changed over time, and there have even been claims that this has been detected.[Webb 2001] This claim is probably wrong, since later attempts to reproduce the observations failed.[Chand 2004] Rosenband et al.[Rosenband 2008] have done laboratory measurements that rule out a linear decrease of alpha with time large enough to be consistent with Webb's results. Even if Webb's claims are correct, this is not evidence that $c$ is changing, as is sometimes stated in the popular press. If an experiment is to test whether a fundamental constant is really constant, the constant must be unitless.[Duff 2002] If the fine-structure constant does vary, there is no empirical way to assign blame to $c$ as opposed to $\hbar$ or $e$. John Baez has a nice web page discussing the unitless constants of nature.

J.K. Webb et al., 2000, "Further Evidence for Cosmological Evolution of the Fine Structure Constant," http://arxiv.org/abs/astro-ph/0012539v3

J.K. Webb et al., 2010, "Evidence for spatial variation of the fine structure constant," http://arxiv.org/abs/1008.3907 ; Phys. Rev. Lett. 107, 191101 (2011)

H. Chand et al., 2004, Astron. Astrophys. 417: 853, http://arxiv.org/abs/astro-ph/0401094 ; See also http://arxiv.org/abs/0711.1742 , http://arxiv.org/abs/0905.1516

Srianand et al., 2004, Phys.Rev.Lett.92:121302, http://arxiv.org/abs/astro-ph/0402177

Duff, 2002, "Comment on time-variation of fundamental constants," http://arxiv.org/abs/hep-th/0208093

Rosenband et al., 2008, 319 (5871): 1808-1812, http://www.sciencemag.org/content/319/5871/1808.abstract

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the would-be superluminal neutrino speed [...]

The relevant comparison is between

Obviously, by the very definition of "signal front", a neutrino detector at LNGS would necessarily have learned about a neutrino bunch having been released at CERN at the latest by the arrival/detection of neutrinos which had been released, or even earlier.

Any particular mode of signalling, such as through the transmission of neutrinos, cannot precede the corresponding signal front; it cannot be superluminal (in this specific sense) by definition.

And this argument is of course utterly independent of setup particularities, such as the possible presence or absence of "Earth's crust material between" signal source and receiver.

When has the speed of light been measured [...] ?

"Signal front speed", a.k.a. "speed of light in vacuum" is just an unambiguous non-zero symbol (often abbreviated as "$c_0$", or only "$c$") which is used for expressing distance values (characterizing pairs of "ends" which were at rest to each other) as "$\frac{c}{2} \text{ ping duration}$". Reasonably to be measured are instead duration ratios, especially.

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