Copyright (C) V.Skorobogatov, 2006,2012
About the result of the Michelson-Morly experiment
Starting from the explanation of the results of the Michelson-Morly
experiment given on the base of the 4D medium model [1], one may estimate
the time delay for the signal send in the longitudinal direction
with respect to the transversal one. The lightpathes to the mirrors and
backward are equal respectively
|
l1 = 2l0 /cos3α
l2 = 2l0 /cosα
| (1) |
Here l0 is the arm length at the rest state and α is the
angle of the deviation of the transversal ray with respect to the ray at
the rest state(see [1] for details). From here the time delay after the
reflections of the signals can be wrote as
|
Δt = 2l0 tg²α/c cos α.
| (2) |
It is the transcendental equation with respect to angle α, which
one can simplify if to substitude the velocity V of the interferometer
with respect to medium with help of the expression given in [1]
It results in the cubic equation with respect to the square of V. For
the not very big velocities in comparison with the light speed c we have
Let us estimate it for the velocity of the Earth revolving round the Sun,
i.e. for the V is about 30 km per sec. The delay is equal to 10-16
sec for the arm length l0 = 10 m. This value is beyond the
sensibility threshold of the photo detectors which is about
10-12 sec now. It means that even with using the impulse
laser as a light source it is need to use the arms' length up to hundred
kilometers to fix the time delay caused by Earth movement through the
medium.
The frequency shift Δω is connected with the time delay
by the expression
where n is a number of periods of the wave in the lightpath, or
After substituting (4) and (6) in eq.(5) the relative frequency shift
will put down as follows
and can be estimated for Earth velocity on the orbit around the Sun as
equal to about 10-8. This value is too low to be fixed by
interferometer.
In the conclusion we can say that the time delay and the frequency shift
as the effects of the second order with respect to V/c is too small for
using the Michelson-Morly interferometer as the velocity detector in the
case of the Earth movement velocity around the Sun.
Addendum
On the other day after publication author found in the Internet
the paper [2] wrote by Steven Bryant. His analysis obviously shows that
the sensibility of the Michelson-Morly interferometer is though
sufficient to detect the Earth velocity. It seems don't contradict the
estimations made here.
Addendum 2
It was said [1] that there is the distinction in values s1
and s2 which is hard to explain. But these values are differed
from each other as 2l0 tan³α, or as third power of
v/c at not very big velocity. Therefore that discrepancy may be
neglected.
Addendum 3
From the previous addendum it is clear that the whole effect in the Mickeson-Morley
experiment is of third order.
The fact that the longitudinal and transversal waves comes to the center of the
interferometer after all reflections with delay (4) means that the fringe shift of the
bands is equal to
s1 - s2 = 2l0 tan³α.
Thus even for the velocity of the ether wind equals 600 km/s, the velocity of the
local group of galaxies including the Milky Way in respect to the cosmic microwave
background radiation, as it is proposed in some theories, the fringe shift is equal
only 0.16 mkm for the interferometer arm of 10 m. Of cause, it is too small
value for the sensibility of such device as interferometer. Therefore the MMX gives
the "null result".
[1] V. Skorobogatov. The Light in the 4D model of Aether.
http://vps137.narod.ru/article2a.html. 2006.
[2]
Steven Bryant. Revisiting the Michelson and Morly experiment to reveal
an Earth orbital velocity of 30 kilometers per second.
http://www.relativitychallenge.com/papers/Bryant.CICS.MMX.Analysis.06302006.pdf. 2006.
