# Tutorial #1, why you can't measure 'changes in the speed of light'

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### J. J. Lodder

Sep 1, 2021, 3:27:09 PM9/1/21
to
The original discussion on the question has become muddled by side
paths, so I'll start again.
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.
B) you set up a fixed resonator for it to create a standing wave.
C) using the tricks of the trade you determine
how many wavelength there are in it.
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)
E) Knowing wavelength and frequency give you speed of light.

All this is the end point of a long evolution.
With a very broad brush:
Starting in the 19th century,
physicists were completely ignorant of the structure of matter,
so units such as platinum bars with scratches
were accepted without further thought.
The speed of light was something you measured with rulers and clocks.

By the end of the 19th people like Rowland
started optical precision measurements,
using interferometry and spectral lines with calibrated wavelengths.
Ultimately all modern precision manufacture came to depend on it.

This soon raised a problem:
the precision of wavelength calibrations inceased to the point
where it came to be limited by the precision to which meter rods
could be reproduced at the site where the wavelength measurements
were done.

So the next step was obvious and inevitable:
the meter was redefined in terms of a suitable stable wavelength,
and the metal bars and blocks became secondary standards.

Next came the precision speed of light measurements, see above.
Again, the same problem arose:
the precision of the light speed measurement was limited
by the accuracy to which that standard wavelength could be reproduced.

So, again, the meter was redefined
now in terms of the frequency of the light source
and a defined value for the speed of light.

This eliminated the meter completely as a fundamental unit,
and all measurements of distance and size
were reduced to measurements of time intervals.
What used to be a measurement of the speed of light
now became a calibration of a standard wavelength,
so of a secondary meter standard.

So the speed of light has dropped out of the story.
If it were to change,
all -measured- lengths of all objects would change in the same way,
and by Alice, this would be unobservable.

Next comes the very good question:
in how far does this capture physical reality?
After all, we can invent other length units.
Would they all vary in the same way? Can we test this?

Going back in history,
the only other length unit that is reproducible enough
for comparison is the metal bar meter.
Supposing some fundemental things are time dependent,
would the platinum meter change in the same way
as the optically defined meter?
(or as I joked several times already,
since precision manufacturing uses optical standards,
would yesterdays pistons fit tomorrows engines)

More practical, in the lab,
would a standing wave that fits an optical resonator
set on a metal frame or granite block go on fitting it forever?

If not, we have a new effect, but what is it,
and how would we interpreted it?
I'll explain in a #2 that the problem could not lie
with the frequency, hence with the clocks,
so we must look at the length units.

Fortuantely, a hundred years of progress
has given us an understanding of the structure of matter,
so we understand our units, at least in principle.

For optical wavelengths the scale is set by the Rydberg unit
(energy, inverse wavelength, frequency)
In crap-free units the Rydberg wavelength is 1/ \alpha^2 m_{electron}
(with a whole slew of higher order corrections)

For dimensions of material objects otoh
the scale is the Bohr radius,
which is (again crap-free) 1/\alpha m_{electron}.
(again with a whole slew of higher order corrections)
So they differ to lowest order by a factor of \alpha.

Now, after all these preliminaries, we can deal with Helbig's question.
The meaningless question: can the measured speed of light vary?
becomes a meaningful question if we rephrase it as:
if things in the universe are variable,
would all possible length units vary in the same way?

(note that this transforms a meaningless question
about dimensioned things into a meaninful question
about dimensionless ratios between units)

From the arguments above the answer is yes,
and we could in principle observe such an effect in the lab.
OTOH there is no way that we would interpret such an observation
as a variable speed of light, supposing we would know what that means.
The prime suspect will be \alpha. (but it might be something higher up)

And for Philip: I hope that this provides the explanation you asked for,

Jan

(about time in #2)

### J. J. Lodder

Sep 5, 2021, 6:45:50 AM9/5/21
to
J. J. Lodder <nos...@de-ster.demon.nl> wrote:

[Followup to myself, continued with more personal,
and perhaps more controversial ideas]

Let us suppose for the sake of argument
that 'Helbig's nightmare' becomes true,
and that all kinds 'fundamental' things
turn out to be variable.

In particular, let us assume that we have an experimental basis for it,
in that we have several independent length and time units,
all reproducible to adequate precision,
and drifting with respect to each other.
Hence we will have many variable 'speeds of light',
wich we can all measure by hand-picking units.

Will this force us to give up the relativity postulate,
and the idea of a universal absolute speed,
and hence the idea of relativistic space-time?

I think that the answer will be no.
Instead we will say that one should use 'fitting'
pairs of units, with matching space and time units
related by a factor c_{universal}

So in summary: we'll keep the spacetime, (and c=1)
and describe all that variable mess
in terms of new laws of physics in space-time.

Bottom line: we'll give up that space-time
only if all else fails,

Jan

### Eric Flesch

Sep 22, 2021, 4:57:16 AM9/22/21
to
On 01 Sep 2021, nos...@de-ster.demon.nl (J. J. Lodder) wrote:
>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. ...

I just wanted to thank the OP for his excellent precis. It has
bothered me for a long time that with defining our length scale in
reference to c-dependent physical outputs, that we've given up an
absolute length scale as a basis of measurement. That is, we've
assumed c to be ever unchanging WRT a physical rod. If that
assumption is wrong, we've disabled our ability to find out. We have
put blinkers on ourselves. It can't be right to do that.

In all the sciences, only astronomy looks directly backwards into
time. We assume that there is no overhead in doing so. And yet there
is the redshift which we interpret as physical recession. But who can
say what exactly separates the present from the past? The redshift
may be a symptom of something else as yet unmodelled.

Normally if we set up an apparatus or a software system and switch it
on, then if its particles/data are seen to be expanding and
accelerating all around, we adjudge that the system is mis-calibrated.
So we look for how to calibrate it. Our "accelerating expansion"
universe may simply be uncalibrated, and a new parameter needed to
calibrate it. I greatly hope that we haven't already blinkered
ourselves in such a way as to make that calibration impossible.

### Phillip Helbig (undress to reply)

Sep 22, 2021, 9:52:50 AM9/22/21
to
In article <614a76af....@news.aioe.org>, er...@flesch.org (Eric
Flesch) writes:

> On 01 Sep 2021, nos...@de-ster.demon.nl (J. J. Lodder) wrote:
> >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. ...
>
> I just wanted to thank the OP for his excellent precis. It has
> bothered me for a long time that with defining our length scale in
> reference to c-dependent physical outputs, that we've given up an
> absolute length scale as a basis of measurement. That is, we've
> assumed c to be ever unchanging WRT a physical rod. If that
> assumption is wrong, we've disabled our ability to find out. We have
> put blinkers on ourselves. It can't be right to do that.

What is to prevent you from measuring the speed of light in the same way
it was measured before the redefinition of the metre? If you actually
find it to vary, no reasonable person will say that that is wrong since
the speed of light is defined to be a constant. Nature doesn't care how
we define our units.

> In all the sciences, only astronomy looks directly backwards into
> time. We assume that there is no overhead in doing so. And yet there
> is the redshift which we interpret as physical recession. But who can
> say what exactly separates the present from the past? The redshift
> may be a symptom of something else as yet unmodelled.

There is no shortage of alternative theories. There is no shortage of
criticism of them. If you have a good idea, publish it, and let it be
debated.

ANYTHING may be a symptom of something else as yet unmodelled. But
there seems to be no reason to doubt the cosmological redshift.

> Normally if we set up an apparatus or a software system and switch it
> on, then if its particles/data are seen to be expanding and
> accelerating all around, we adjudge that the system is mis-calibrated.

For a normal system in the lab, yes. For the Universe, no. It follows
from GR that it can be static only if infinitely fine-tuned. We have no
reason to doubt the validity of GR on large scales.

> So we look for how to calibrate it. Our "accelerating expansion"
> universe may simply be uncalibrated, and a new parameter needed to
> calibrate it.

Again, publish a hypothesis and let it be debated.

> I greatly hope that we haven't already blinkered
> ourselves in such a way as to make that calibration impossible.

I don't think so, but in any case it doesn't have anything to do with
the definition of the metre or the constancy of the speed of light, at
least not at this level. (Note that some people have investigated
cosmological models with a varying speed of light.)

### J. J. Lodder

Sep 25, 2021, 3:12:20 AM9/25/21
to
Eric Flesch <er...@flesch.org> wrote:

> On 01 Sep 2021, nos...@de-ster.demon.nl (J. J. Lodder) wrote:
> >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. ...
>
> I just wanted to thank the OP for his excellent precis. It has
> bothered me for a long time that with defining our length scale in
> reference to c-dependent physical outputs, that we've given up an
> absolute length scale as a basis of measurement. That is, we've
> assumed c to be ever unchanging WRT a physical rod. If that
> assumption is wrong, we've disabled our ability to find out. We have
> put blinkers on ourselves. It can't be right to do that.

It is not just that we have given up on having an absolute lenght unit,
we have understood that we never had one to begin with,
if we look at things to sufficient accuracy.

We have not assumed c to be ever unchanging wrt to a physical rod,
we have defined distances (to much greater accuracy and reproducibility)
by giving the speed of light a defined value.
This has not diminished our ability to measure things in any way,
it only means that we have agreed
to incorporate observed changes somewhere else.
(if there are any)

The effect of this is to replace the physically meaningless question
of whether the -dimensioned- quantity c can vary
with the physically observable and meaningful question
of whether the dimensionless ratios of differently defined length units
are changing wrt to each other.

Jan

### J. J. Lodder

Sep 25, 2021, 3:12:21 AM9/25/21
to
Phillip Helbig (undress to reply) <hel...@asclothestro.multivax.de>
wrote:

> In article <614a76af....@news.aioe.org>, er...@flesch.org (Eric
> Flesch) writes:
>
> > On 01 Sep 2021, nos...@de-ster.demon.nl (J. J. Lodder) wrote:
> > >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. ...
> >
> > I just wanted to thank the OP for his excellent precis. It has
> > bothered me for a long time that with defining our length scale in
> > reference to c-dependent physical outputs, that we've given up an
> > absolute length scale as a basis of measurement. That is, we've
> > assumed c to be ever unchanging WRT a physical rod. If that
> > assumption is wrong, we've disabled our ability to find out. We have
> > put blinkers on ourselves. It can't be right to do that.
>
> What is to prevent you from measuring the speed of light in the same way
> it was measured before the redefinition of the metre?

Nothing. As a matter of fact these measurement -are- done routinely
in standards laboratories.
Nowadays they serve to calibrate secondary meter standards.

> If you actually find it to vary, no reasonable person will say that that
> is wrong since the speed of light is defined to be a constant.

That is precisely what reasonable people will say.
They will ask: varies -with respect to what-?
All that might be observed experimentally
is that the meter, as defined by clock and c,
varies wrt to the meter defined in some other way.
(platinum bar? seconds pendulum? some optical wavelength?)

Instead of people saying that the speed of light
has been observed to be variable
they will ask what the 'right' length unit is.

Jan

### Tom Roberts

Sep 25, 2021, 3:16:40 AM9/25/21
to
On 9/1/21 2:27 PM, J. J. Lodder wrote:
> [...]

Here's a description of a laboratory experiment to measure any variation
in the vacuum speed of light during a year, at the part per billion
level. Please explain why you think that it could not detect such
variations.

The basic idea is to construct a very stable vacuum optical cavity of
length L, and measure any variations in the frequency of its free
spectral range (= c/(2L)). The precise value of L does not matter,
as this is looking at variations.

Construct a temperature-controlled cell a meter or so on a side (c.f.
Kennedy-Thorndike), and inside it construct a vacuum optical cavity
whose length is ~ 0.5 meters, determined by material with essentially
zero coefficient of thermal expansion (e.g. invar). The free spectral
range of such a cavity is c/(~1 meter), which is ~ 300 MHz. Use
Pound-Drever-Hall laser locking to lock two high-quality lasers to
adjacent fringes and count their heterodyne frequency, using at least
four Cs-133 atomic clocks to generate the timebase [#]. By counting for
1000.000000000000 seconds and averaging multiple counts this should
easily have a resolution of ~0.1 Hz (out of ~300 MHz). Make measurements
repeatedly over at least a year.

[#] Don't use GPS, as they will steer its clocks to offset
any variation in c.

This should detect variations in c over one year, at the part per
billion level. In principle it could do better....

Tom Roberts

### J. J. Lodder

Sep 25, 2021, 5:03:58 AM9/25/21
to
Tom Roberts <tjrobe...@sbcglobal.net> wrote:

> On 9/1/21 2:27 PM, J. J. Lodder wrote:
> > [...]
>
> Here's a description of a laboratory experiment to measure any variation
> in the vacuum speed of light during a year, at the part per billion
> level. Please explain why you think that it could not detect such
> variations.

Thank you for this perfect illustration of my point.
Supposing there would be an effect, what would we conclude? [1]

Your naive assumption is that blocks of metal must have a constant
length. They feel real solid, don't they?
However, if we assume that fundamental constants
(such as alpha for example) might be variable
there is no reason to believe in constancy of the length of
metal rods.

Given what we know about spacetime, and about the physics of metals,
my guess is that the second interpretation will be the preferred one,

Jan

[1] I ignore the practical point that the limited accuracy
of your setup (a mere 10^-9) will not yield a meaningful result anyway.
We already know that things are far more stable than that.
So the practical conclusion will be some kind of experimental error.

### Phillip Helbig (undress to reply)

Sep 25, 2021, 1:15:45 PM9/25/21
to
In article <1pfxkcn.125esf5v7jrgeN%nos...@de-ster.demon.nl>,
nos...@de-ster.demon.nl (J. J. Lodder) writes:

> > If you actually find it to vary, no reasonable person will say that t=
hat
> > is wrong since the speed of light is defined to be a constant.
>
> That is precisely what reasonable people will say.
> They will ask: varies -with respect to what-?
> All that might be observed experimentally
> is that the meter, as defined by clock and c,
> varies wrt to the meter defined in some other way.
> (platinum bar? seconds pendulum? some optical wavelength?)
>
> Instead of people saying that the speed of light
> has been observed to be variable
> they will ask what the 'right' length unit is.

Except that (as in varying-speed-of-light cosmological models) it might
vary with respect to ALL possible standards, in which case it wouldn't
make sense to define any sort of length with respect to that speed, just
as one doesn't define any length with respect to the speed of someone
riding a bike, say.

### J. J. Lodder

Sep 26, 2021, 3:47:12 AM9/26/21
to
Phillip Helbig (undress to reply) <hel...@asclothestro.multivax.de>
wrote:

I'm sorry to say, but you are moving goalposts.
Paper is cheap, and people can write all kinds of ds^2 = ...
It is then up to those authors to explain what their models
mean in terms of observation and measurement.

We were discussing the measurability of the speed of light,
and perhaps of changes in it.
(or equivalently, calibration of length standards)
By the very nature of these experiments they can only be done
with any accuracy in the rest frame of standards laboratories.
By the relativity postulate the results must be the same
for all inertial observers.
So we can tell those LGM what our length and time units are.

Astronomically speaking, hence cosmologically
you are completely powerless to begin with,
for all astronomical distances can be known only
in terms of (light)seconds.
They are all based on the AU, which can only be measured accurately
in terms of (light)seconds.
To such an extent even that it became necessary
to give the AU a defined value in terms of meters, hence seconds.

So, if you leave the context of precision laboratory measurement
it is completely unclear to me what you are trying to argue,

Jan

### Jos Bergervoet

Sep 27, 2021, 1:39:54 PM9/27/21
to
On 21/09/26 9:47 AM, J. J. Lodder wrote:
> Phillip Helbig (undress to reply) <hel...@asclothestro.multivax.de>
> wrote:
>
>> In article <1pfxkcn.125esf5v7jrgeN%nos...@de-ster.demon.nl>,
>> nos...@de-ster.demon.nl (J. J. Lodder) writes:
>>
>>>> If you actually find it to vary, no reasonable person will say that t=
>> hat
>>>> is wrong since the speed of light is defined to be a constant.
>>>
>>> That is precisely what reasonable people will say.
>>> They will ask: varies -with respect to what-?
>>> All that might be observed experimentally
>>> is that the meter, as defined by clock and c,
>>> varies wrt to the meter defined in some other way.
>>> (platinum bar? seconds pendulum? some optical wavelength?)
>>>
>>> Instead of people saying that the speed of light
>>> has been observed to be variable
>>> they will ask what the 'right' length unit is.
>>
>> Except that (as in varying-speed-of-light cosmological models) it might
>> vary with respect to ALL possible standards, in which case it wouldn't
>> make sense to define any sort of length with respect to that speed, just
>> as one doesn't define any length with respect to the speed of someone
>> riding a bike, say.
>
> I'm sorry to say, but you are moving goalposts.

And you are more and more reverting to rhetoric instead of physics..

> Paper is cheap, and people can write all kinds of ds^2 = ...
> It is then up to those authors to explain what their models
> mean in terms of observation and measurement.
>
> We were discussing the measurability of the speed of light,
> and perhaps of changes in it.
> (or equivalently, calibration of length standards)
> By the very nature of these experiments they can only be done
> with any accuracy in the rest frame of standards laboratories.

A completely baseless claim. The first speed of light measurement
(RĂ¸mer) was actually done on an astronomical scale. Also, planned
experiments like LISA will be space-based and they certainly rely
very strongly on knowing the exact speed of light, even more so
then equivalent earth-based setups. Some of your arguments against
the measurability of c may be sound, but this singling out of some
rest frame isn't!

> By the relativity postulate the results must be the same
> for all inertial observers.

So then why would the lab-frame on Earth be the best?

> So we can tell those LGM what our length and time units are.
>
> Astronomically speaking, hence cosmologically
> you are completely powerless to begin with,

Only if we believe that previous, baseless claim!

--
Jos

[[Mod. note -- LISA does not rely on knowing the exact speed of light.
Instead, it relies on (among other things) knowing the inter-satellite
distances in *light-seconds*. See section 7 of
https://www.livingreviews.org/lrr-2014-6
for details.
-- jt]]

### Nicolaas Vroom

Oct 7, 2021, 9:52:29 AM10/7/21
to
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.
> B) you set up a fixed resonator for it to create a standing wave.
> C) using the tricks of the trade you determine
> how many wavelength there are in it.
> 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)
> E) Knowing wavelength and frequency give you speed of light.

IMO item B seems to me very tricky.
To get an idea about how a resonator works follow this link:
https://en.wikipedia.org/wiki/Resonator#Explanation

The condition for resonance in a resonator is that the round trip distance,
2 d, is equal to an integer number of wavelengths lambda of the wave:
2 d = N * lambda , N { 1,2,3, ... }
If the velocity of a wave is c the frequency is f = c / lambda,
so the resonant frequencies are:
f = N * c / 2d with N { 1,2,3, ... }
The question is how do you exactly build this rectilinear oscillator.

The problem: what you want to calculate is c = f *2d / N
Suppose you know f and you want to try N=10.
What should now be d, the distance between the sides?
You can start with d = 0.5m as Tom Roberts suggests 25/9/2021
But most probably that value is wrong.
That means you should not try 500mm but for example 501mm
Also that value I expect is wrong.
I have no idea what a correct value is, such that you get a stable resonator.
I also have no idea how "stable" your stable resonator is.
i.e. 1 hour? 1 day? 1 month?
The whole point is how accurate is this experiment i.e. calculation of c?
You can also rephrase this sentence:
How valid is your claim that when you resonator is not stable
that the cause is a variable speed of light?

(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.
But ofcourse there can be a misunderstanding from my side.
I agree with his remark:
> Don't use GPS, as they will steer its clocks to offset any variation in c.)

Nicolaas Vroom

### Tom Roberts

Oct 13, 2021, 3:48:10 AM10/13/21
to
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

### J. J. Lodder

Oct 15, 2021, 3:47:29 PM10/15/21
to
Nicolaas Vroom <nicolaa...@pandora.be> wrote:
[repost of another vanished posting, some minor edits]
> 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.
> > B) you set up a fixed resonator for it to create a standing wave.
> > C) using the tricks of the trade you determine
> > how many wavelength there are in it.
> > 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)
> > E) Knowing wavelength and frequency give you speed of light.
>
> IMO item B seems to me very tricky.
> To get an idea about how a resonator works follow this link:
> https://en.wikipedia.org/wiki/Resonator#Explanation

Yes, it is a poor way to go about it.

> The condition for resonance in a resonator is that the round trip distance,
> 2 d, is equal to an integer number of wavelengths lambda of the wave:
> 2 d = N * lambda , N { 1,2,3, ... }
> If the velocity of a wave is c the frequency is f = c / lambda,
> so the resonant frequencies are:
> f = N * c / 2d with N { 1,2,3, ... }
> The question is how do you exactly build this rectilinear oscillator.

Move mirrors on an optical bench, and count fringes. (in principle)

> The problem: what you want to calculate is c = f *2d / N
> Suppose you know f and you want to try N=10.
> What should now be d, the distance between the sides?
> You can start with d = 0.5m as Tom Roberts suggests 25/9/2021
> But most probably that value is wrong.
> That means you should not try 500mm but for example 501mm
> Also that value I expect is wrong.
> I have no idea what a correct value is, such that you get a stable resonator.
> I also have no idea how "stable" your stable resonator is.

The best you can do at present is 2 x 10^-11,
which is the accurracy to which the secondary meter standard
can be defined. (stabilised He-Ne laser at 632.99121258 nm)

> i.e. 1 hour? 1 day? 1 month?
> The whole point is how accurate is this experiment i.e. calculation of c?
> You can also rephrase this sentence:
> How valid is your claim that when you resonator is not stable
> that the cause is a variable speed of light?

See above.
What such an experiment would be really testing
is variability of \alpha.
As such PhH's proposal is completely useless.
He has been beaten beforehand
by the astronomers with their huge telescopes,
(such as the Keck)
They have fixed the variability of \alpha
to be less than 10^-5 over ten billion years, so 10^-15/year,
assuming linearity.
May be better by now, I haven't kept up with the latest numbers.

This is far out of reach of anything you can hope to do
in a laboratory in a few years.

Jan

### Jos Bergervoet

Oct 19, 2021, 1:59:46 AM10/19/21
to
On 21/10/15 9:47 PM, J. J. Lodder wrote:
> Nicolaas Vroom <nicolaa...@pandora.be> wrote:
> [repost of another vanished posting, some minor edits]
>> 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.
>>> B) you set up a fixed resonator for it to create a standing wave.
>>> C) using the tricks of the trade you determine
>>> how many wavelength there are in it.
>>> 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)
>>> E) Knowing wavelength and frequency give you speed of light.
>>
>> IMO item B seems to me very tricky.
>> To get an idea about how a resonator works follow this link:
>> https://en.wikipedia.org/wiki/Resonator#Explanation
>
> Yes, it is a poor way to go about it.

And anyhow, the above says that D) is in fact far more difficult.
What would actually be the first divider? Are there injection-locked

--
Jos

### J. J. Lodder

Oct 22, 2021, 3:07:41 PM10/22/21
to
Nowadays the easiest way of doing it is with optical frequency combs.
No point in me repeating Google on this,

Jan

### J. J. Lodder

Oct 23, 2021, 5:03:08 PM10/23/21
to
[missingin action, presumed lost, repost]
Tom Roberts <tjrobe...@sbcglobal.net> wrote:
> 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.

[snipped a mess of garbled attributions without further comment.
Some of the > >> stuff is by me, some of it is by others]

> 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.

As I implied in previous postings,
the revolutionary step in the redefinitions of the meter
was to replace material standard meter
(lines on a metal bar) with an optical standard meter.
(the wavelengty of a krypton line, later a laser)
There is no good a-priory reason to assume that the two must be,
and will forever remain the same thing.

That experiment that 'we are not particularly interested in'
could in principle test the question.
(but there are good reasons to believe
that it could not possibly yield a useful result)

The speed of light in all this is merely a red herring.
All there is to it is that experimentally
one can maintain an optical frequency standard
to much greater precision than a wavelength standard.
(by several orders of magnitude)

If we wouldn't care about best reproducibility
we could in principle go back to a wavelength standard
to make c measurable again, but to no better than
the reproducibility of the wavelength standard.

Jan

### Jos Bergervoet

Oct 24, 2021, 5:12:09 PM10/24/21
to
How do you feed in the high frequency signal and how do you get
out the signal with the frequency divided by N?

> No point in me repeating Google on this,

If repeating published material is of no use, then our moderators
should only allow 'original research' to be posted here. I doubt
whether that would be a useful strategy.. Especially in a "tutorial"
it would be quite unnatural!

--
Jos

[[Mod. note -- Yes, tutorial material is (may be) ok for the newsgroup.

For this topic,
https://en.wikipedia.org/wiki/Optical_frequency_comb
might be a starting point. The link (#3 of 5 in the "External Links" section)
"Optical frequency comb for dimensional metrology, atomic and molecular
spectroscopy, and precise time keeping" looks quite relevant, but the
linked-to archive.org copy is "temporarily offline" right now. :(
-- jt]]

### J. J. Lodder

Oct 25, 2021, 10:49:25 AM10/25/21
to
The other way round, from microwave to optical.

> > No point in me repeating Google on this,
>
> If repeating published material is of no use, then our moderators
> should only allow 'original research' to be posted here. I doubt
> whether that would be a useful strategy.. Especially in a "tutorial"
> it would be quite unnatural!

The basic idea is that you generate a 'Dirac comb'
of equally spaced lines in the frequency domain.
This can be done in several way,
using ultra-short laser pulses for example.
High precision is achieved by counting the 'low' frequency difference
between the elements of the comb.
Such a frequency comb functions as a ruler
from which you can read off an unknown optical frequency.

The point for the defined light speed discussion is that you can measure
light frequencies with far greater precision
than you can define a lengthh standard,

Jan

For example:
<https://www.nist.gov/topics/physics/optical-frequency-combs>