On 10/7/21 8:52 AM, Nicolaas Vroom wrote:
> Op woensdag 1 september 2021 om 21:27:09 UTC+2 schreef J. J. Lodder:
>> The assertion was that you can at least in principle use laboratory
>> measurements of the speed of light to see if it varies.
>>
>> To see that you can't you need to have at least a vague idea of
>> how such measurements are done. A) you build a stable light
>> source.
Better, build TWO that have variable frequency & wavelength such that
you can lock their wavelengths to the optical resonator of (B). This
requires high coherence and narrow linewidth, so lasers are needed.
>> B) you set up a fixed resonator for it to create a standing wave.
Better, put both light sources of (A) into the same optical cavity. Lock
both lasers to the cavity, on adjacent fringes [Pound-Drever-Hall laser
locking].
Note that for stability, the cavity must be temperature controlled and
in vacuum.
>> C) using the tricks of the trade you determine how many wavelength
>> there are in it.
The best "tricks" don't care what the length of the cavity is, nor how
many wavelengths are in it. Because with TWO light sources locked to
adjacent fringes of the cavity you will measure its Free Spectral Range
frequency = c/(2L) (in vacuum).
>> D) idem, and far more difficult, you measure the frequency of your
>> light source, wrt to an atomic clock. (frequency dividing,
>> multiplexing, counting etc. very hard)
In actual practice this is the SIMPLEST aspect of this. Electronics up
to 10-20GHz is straightforward, while building highly stable, highly
performant optical cavities is not.
>> E) Knowing wavelength and frequency give you speed of light.
Better, measuring the FSR yields the speed of light. But you will know
the FSR frequency far more accurately than you will know the length of
the cavity, so it's better to look for variations in FSR frequency, and
thus variations in c, rather than attempt a direct measurement of c.
[We know the lengths of our optical cavities to at best
a few parts per thousand. We measure FSR frequencies a
billion times more accurately.]
> IMO item B seems to me very tricky. [...] The question is how do you
> exactly build this rectilinear oscillator.
It's called a Fabry-Perot interferometer, aka optical cavity, aka F-P
etalon. Building one is simple, making it exceptionally stable is not.
> [... naive discussion omitted] (I disagree with the remark of Tom
> Roberts 25/9/2021:
>> The precise value of L does not matter, as this is looking at
>> variations.
For the experiment I discussed, this is obvious -- you clearly do not
understand what I was describing.
In general, experiments looking for variations in some quantity can be
MUCH more sensitive than measuring the quantity. That is true here --
variations in FSR frequency can be accurate to a few parts in 10^12,
perhaps better; measurements of c are at best a few parts per billion
(using a pre-1983 definition of the meter, limited by the ability to
apply such a definition).
> I agree with his remark:
>> Don't use GPS, as they will steer its clocks to offset any
>> variation in c.)
The experiment I described is something we routinely do in our optical
lab. But we don't have any optical cavity that is nearly stable enough,
because our research does not require it. Obtaining funding to build an
exceptionally stable cavity is unlikely; nor are we particularly interested.
Tom Roberts