Re: E = 3/4 mc? or E = mc?? The forgotten Hassenohrl 1905 work.

Paul B. Andersen <relativity@paulba.no> wrote:

Den 08.12.2024 12:30, skrev J. J. Lodder:

Paul B. Andersen <relativity@paulba.no> wrote:
 

Den 07.12.2024 22:19, skrev Paul B. Andersen:

>
But it isn't impossible, if you had extremely precise instruments,
that you would measure a value slightly different from 299792458 m/s,
e.g. 299792458.000001 m/s.

>
This is indeed "completely, absolutely, and totally wrong".
>
I somehow thought that the "real speed" of light in vacuum
measured before 1985 was different from 299792458 m/s.

 
Of course it was. The adopted value was a compromise
between the results of different teams.
BTW, you are also falling into the 'das ding an sich' trap.
 

(Which it probably was, but the difference hidden in the error bar)
And since the definition of metre only contain the defined constant c,
i thought "the real speed" of light could be different from c.

 
Yes, that is where you go wrong.
 

But this is utter nonsense!

 
Beginning to see the light?
 

Now I can't understand how I could think so.
My brain seems to be slower than it used to be. :-(
>
The real speed of light in vacuum is exactly c = 299792458 m/s,
and 1 metre = (1 second/299792458)c, is derived from c,
which means that the measured speed of light in vacuum will
always be c.

 
Correct.
Perhaps I can explain the practicalities behind it in another way.
If you measure the speed of light accurately
you must of course do an error analysis.
The result of this that almost all of the error results from
the ecessary realisation of the meter standard. (in your laboratory)
So the paradoxal result is that you cannot measure the speed of light
even when there is a meter standard of some kind.
 
You may call whatever it is that you are doing
'a speed of light measurement',
but if you are a competent experimentalist you will understand
that what you are really doing is a meter calibraton experiment.
Hence the speed of light must be given a defined value,
for practical experimental reasons. [1]
 
Jan

 
This is my way of thinking which made me realise that I was wrong:
How do we measure the speed of light?
We measure the time it takes for the light to travel a known distance.
So we bounce the light off a mirror and measure the round trip time.
How do we calibrate the distance to the mirror?
We measure the time it takes for the light to go back and forth
to the mirror.
L = (c/299792458)?t/2 where t is round trip time in seconds
AHA!!!
 

 
[1] Which have not changed.
(and will not change in the forseeable future)
Meter standards are orders of magnitude less accurate
than time standards. (see why this must be?)
 

 
No, I don't understand.
The definition of metre only depends on the two constants
??_Cs and c and both have an exact value.
Is it because the time standard only depend on one constant?
 
I can however understand that practical calibration of the meter
is less precise than the calibration of a frequency standard.
 
------------------
 
I would like your reaction to the following;
 
In:
https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9.pdf
I read:
https://www.bipm.org/en/cipm-mra
 
"The CIPM has adopted various secondary representations of
  the second, based on a selected number of spectral lines of atoms,
  ions or molecules. The unperturbed frequencies of these lines can
  be determined with a relative uncertainty not lower than that of
  the realization of the second based on the 133Cs hyperfine transition
  frequency, but some can be reproduced with superior stability."
 
This is how I interpret this:
The second is still defined by "the unperturbed ground state
hyperfine transition frequency of the caesium 133 atom"
   ??_Cs = 9192631770 Hz by definition.
 
But practical realisations of this frequency standard,
that is an atomic frequency standard based on Cs133 is
not immune to perturbation, a magnetic field may affect it.
 
So there exist more stable frequency standards than Cs,
and some  are extremely more stable.
But the frequencies of these standards are still defined
by ??_Cs. 1 hz = ??_Cs/9192631770
This is "Calibration of a frequency standard".
 
The "secondary representations of second"
don't change the duration of a second
and the "secondary representations of metre"
don't change the length of a metre.

Instead of replying point by point I'll sum up the whole situation.
(as I understand it, and perhaps repeating what I wrote earlier)

For understanding all this you must realise
that there are two kinds of frequency standards:
microwave ones, typically in the (perhaps many) GHz range,
and
optical ones, typically in the hundreds of THz range.
The GHz ones may serve as absolute frequency standards and as clocks.
The optical ones (like the standard stabilised HeNe laser)
may also serve as (secondary) meter standards.
Standards labs supply lists of 'recommended' optical frequencies.
The optical frequency sources are of course also 'floating' frequency
standards on their own.

The GHz ones can be calibrated against each other by direct counting.
So their accuracy may equal that of the Cs standard. (by the definition)
The stability of frequency standards can in general be established
by comparing ensembles of them against each other. (so indepently of Cs)
Which kind of standard to use depends on what you need:
relative or absolute accuracy.

AFAIK about those matters, the idea among metrologists at present
is to leave things as they are,
until a really big step forward can be made.
(hopefully already at the next CGPM)

Some of the optical frequency standards are far more stable indeed.
(nowadays pushing 10^18, last time I looked)
But their frequencies (in terms of the Cs standard!)
are known to a much lesser accuracy.
(pushing 10^12, again last time I looked)
The use of frequency combs caused a revolution here. (see 2005 Nobel)

Summary: optical frequency standards can be far more stable,
but their frequencies are (relatively speaking!) poorly known.

Once you have a calibrated optical frequency standard, [1]
for which you know the frequency in terms of the Cs standard,
you know its wavelength, by the definition of  c,
so you can start measuring distances and sizes
in terms of its wavelength, hence in meters.
It has become a secondary meter standard.

So measuring distances/lengths is inherently much less accurate
than measuring time/frequency.
And, circle closed, this was precisely the reason
for giving  c  a defined value.
So c really cannot be measured anymore,
not because some crazed guru-followers decreed so,
but because of hard experimental realities and necessities.

Hope this clears up the questions you had,

Jan

[1] This is the ongoing, never-ending, program I mentioned earlier:
finding optical frequency standards, aka secondary meter standards,
to ever greater accuracy and reproducibiliy.
The original <1983 series of measurements, then called 'measuring c',
was just good enough to base the definined value of c on.
Those decades of added precision had to go into better frequency/meter
standards, not into a 'better' value of c.

PS There are first indications that it may be possible
to harness a gamma ray line from a nuclear transition
in the not to far future, for again greatly increased stability.
Very low frequency, as gammas go, but still in the very far UV.
Challenges, challenges.