
A proof of the constancy of the velocity of light (1913) - panic
https://en.wikisource.org/wiki/A_proof_of_the_constancy_of_the_velocity_of_light
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alok-g
Can someone please explain the argument in easier terms?

I am stuck here itself:

>> Then from the law of motion of the star we can derive an equation: >>
u=f(t-t0)

The function 'f' is not specified. What is it and how is it derived from the
laws of motion?

Also, what really is tau-0? It is the time at which light from a stationary
star at the same distance would have reached the observer, or alternatively is
the time under Lorentz/Einstein's theory. However, what meaning is that
holding in the said argument.

~~~
mannykannot
I will take a shot at it, starting with the intuition behind it, which is
easiest to explain if we assume one large star and one small one, so that the
former seems to be almost fixed, with the smaller one orbiting it.

Unless the star's orbit is perpendicular to our line of sight, the small star
will alternately move away from us and towards us as it performs each orbit.
If Ritz is correct, then as it moves towards us, the light from the star would
be sped up by the star's velocity in our direction, and as it recedes, the
light would equivalently be slowed down.

Over the time it takes for the light to reach us, the faster light from that
part of the orbit when the star is approaching us would tend to catch up with
the slower light from the previous part of the orbit when it is receding from
us. The longer the light is in transit, the more catching up it does, to the
point where it might even pass the earlier light.

This would change the relative timing of the arrival of the light on Earth
from different parts of the orbit, reducing some intervals and stretching
others.

On the other hand, if the light travels at constant speed, the timing is
undistorted as seen from Earth (other than the small change due to the
differing distance, not speed, over an orbit, which is small and does not
increase with the time of flight of the light.)

This means that if we attempt to reconstruct the orbit of the star, we get
different results depending on which assumption about the speed of light that
we choose. For example, if it is a circular orbit and the speed of light is
variable, the half-orbit when it is receding would seem longer to us than the
half-orbit when it is approaching us. If, when observed from Earth, both half-
orbits are the same duration, we can deduce that the speed of light is
constant, as a correction for variable c would give an orbit that is not
consistent with Kepler's laws of orbital motion (we can identify the start and
end of the half-orbits from the rate of change of the doppler shift, which
would be zero at the furthest and closest distance, independently of the speed
issue.) (Note that this is a simplified example, as I imagine we would like to
be able to make a determination with less than one full orbit's data, and with
elliptical orbits in arbitrary orientations, and for a wide range of stellar
mass ratios.)

As for the equations, 1 is just saying that the radial speed is some function
of time. The specific function depends on the relative masses of the stars,
the orbit's size and eccentricity, and the orientation of its plane and axes
relative to Earth, but De Sitter does not need to specify what it is, as later
on he merely has to show that, as observed from Earth, the motion would be
measurably different depending on which assumption is made about c.

Tau is the time of arrival of light emitted at t, in the form of t + the time
of flight at c + an adjustment for the radial speed of the star. That
adjustment is zero if the speed of light is constant, and, to a first
approximation, (u * distance) / (c*c) if c is variable.

Equations 2 give the deduction of the radial velocity from the observations
made on Earth, as a function of time of observation rather than time of
emission, and the key point is that they differ according to which assumption
about c you use. It is significant, I think, that the correction term au, in
the variable c case, varies with time, as u, the radial velocity, itself does
so. This shows that the reconstructions cannot both be consistent with
Kepler's laws, and the assumption that gives a consistent reconstruction is
correct.

The rest of the paper establishes that this is a large enough effect to be
measurable in many cases, and reports that those measurements show c to be
constant.

~~~
alok-g
Makes sense. I understand now. Thanks a lot!

I guess the aspect of variability of speed of light with respect to the
observer (as opposed to the source) may still remain. In other words, if we
were to talk about impact of the revolution of the earth instead of the the
star, the difference between the two may not be large enough anymore.

~~~
mannykannot
Thanks - I am glad I could help.

I posted a reply to your question about 20 minutes ago, but I think it was
mostly wrong. Meanwhile, here is something about Ritz's theory:

[https://en.wikipedia.org/wiki/Emission_theory](https://en.wikipedia.org/wiki/Emission_theory)

(This has a good simulation of the effect at
[https://en.wikipedia.org/wiki/Emission_theory#Refutations_of...](https://en.wikipedia.org/wiki/Emission_theory#Refutations_of_emission_theory)
)

[https://en.wikipedia.org/wiki/Ritz_ballistic_theory](https://en.wikipedia.org/wiki/Ritz_ballistic_theory)

My corrected reply is that what would make this effect measurable (if Ritz's
theory were correct) is the catching up of the fast light to the slow light
over the long journey to Earth. What matters for that effect is only the range
of speeds imparted to the light by the star's motion. We are measuring the
timing of observed orbital events, not the speed of the light, and the only
significant effect of Earth's orbit on those measurements comes from its
_position_ in its orbit, nearer to or further from the binary, which makes at
most a 1000 second difference (the time of light to cross our orbit) and is
easily taken into account.

In other words, I agree with you.

The emission theory article notes that this theory is consistent with the
Michelson-Morley experiment, so De Sitter's argument appears to be very
significant in establishing the correctness of relativity.

By the time of this paper, Ritz had already succumbed to tuberculosis at the
age of 31.

~~~
alok-g
Makes sense. Thanks again! :-)

------
g82918
So this is interesting. But it doesn't deal well with the idea that the speed
of light may be variable across time. Not a particularly mainstream theory but
the idea that the speed of light depends on time is kind of fun at least to
consider.

~~~
eesmith
[https://iopscience.iop.org/article/10.3847/1538-4357/aae5f7/...](https://iopscience.iop.org/article/10.3847/1538-4357/aae5f7/pdf)
says:

> On the other hand,during the past 2 decades great attention has been paid to
> the theories with varying speed of light (VSL), in which the speed of light
> might be dynamical and could have been varying in the past. ...

> The measurement of c in the distant universe is an almost completely
> uncharted territory. Recently, with the angular diameter distances measured
> for intermediate-luminosity quasars extending to high redshifts, Cao et
> al.(2017a) performed the first measurement of the speed of light referring
> to the redshift baseline z = 1.70. The result was in very good agreement
> with the value of c obtained on Earth(i.e.,at z = 0).

~~~
fergbrain
> “It is worth recalling that Ellis & Uzan (2005) gave a sobering review of
> serious conceptual problems one faces while trying to change the status of c
> in physics. In particular, they stressed that it is usually not consistent
> to allow a constant to vary in an equation that has been derived from a
> variational principle under the hypothesis of this quantity being constant.
> Therefore, one needs to go back to the Lagrangian and derive new equations
> after having replaced the constant by a dynamical field.”

The math is a bit out of my depth...did they go back to the Lagrangian and
derive new equations after having replaced the constant by a dynamical field?

~~~
g82918
People have at least once though the citation escapes me, it was 2006ish. And
it could be found in agreement with observation. Not that I believe in it.

~~~
eesmith
I missed this the first time -
[https://en.wikipedia.org/wiki/Variable_speed_of_light](https://en.wikipedia.org/wiki/Variable_speed_of_light)
(I used Google Scholar to find that first reference).

There are about a dozen references in the 2006ish timeframe.

------
bcwarner
It's interesting how succinct this is. How come this didn't appear before
being postulated in Einstein's theory of special relativity, given that there
was a 16 year gap between this and the Michelson-Morley experiment?

~~~
g82918
One idea is that there weren't many double stars so the evidence was weak.

