Experiment shows speed of light is not constant
David Seppala
\ B
C |
O
E
D |
\ A
S
A better diagram can be viewed by going to the to the physics link on the bottom of the page at http://www.flash.net/~dseppala
Light from a source at S falls on a lightly silvered mirror A, acting as a beam splitter. The reflected pencil goes to a revolving mirror D, thence to the concave mirror E, to the second mirror C revolving about the same axis O, where it proceeds to the plane mirror B and is reflected back to A. The transmitted pencil pursues the same path in the opposite direction, returning via DA to the starting point, where it meets the first pencil, producing interference fringes which are observed in an interferometer.
Actually, this experiment was performed by Michelson in 1913. Michelson concluded from this experiment that the speed of light is not affected by reflection off a moving mirror. However, the equations used by Michelson to reach that conclusion contained errors. When the errors are eliminated, Michelson's experiment and data reveal that the speed of light varies with the velocity of the source (which is also the simplest explanation of his famous earlier experiment).
Michelson states:
The time occupied by the pencil DEC is
T1 = 2 (D + d) / V1
(A1)
while that taken by pencil CED is
T2 = 2 (D + d) / V2
(A2)
where D is the distance OE, d = distance the revolving mirror moves
while light passes over DEC, and V1 is the resultant velocity of the first
pencil, V2 that of the second.
Michelson's equations A1 and A2 contain two errors. First, if d = distance the revolving mirror moves while light passes over DEC, the equation for each path should be 2D + d, not 2D+2d. The next error depends on whether the speed of light is constant or not. If the speed of light varies after reflecting off the moving mirrors, the "d"s along the two paths are not equal, d1 does not equal d2.
The corrected equations for the two paths are:
T1 = (2D + d1) / V1
(A3)
and
T2 = (2D + d2) / V2
(A4)
Now Michelson used the ratio:
d / (2D) = v / V
(A5)
where
v is the velocity of the
revolving mirrors and V is the speed of light
to eliminate the unknown d from the equations.
When Michelson solved for
(T1-T2) * V/ lambda (A6)
which is what the experiment measures (lambda being the wavelength of the light), Michelson found using the erroneous equations A1,A2 and A5 that for a constant speed of light, the displacement of the interference fringes should be approximately
(8D*v) / (V * lambda). (A7)
and his measurements agreed with the prediction of equation A7. So he concluded erroneously that the speed of light remains constant . However, when we use 2D + d, as the correct expression as stated earlier, the displacement is only half the value expressed by A7, so the experimental data conflicts with the hypothesis that the speed of light remains constant.
However, if light reflecting off mirrors behaves like every other object in an ideal inelastic collision, then
V1 = c +2v
(A8)
and
V2 = c - 2v
(A9)
and the ratios replacing A5 become
d1 / (2D) = v
/ ( c + 2v)
(A10)
and
d2 / (2D) =
v / (c - 2v)
(A11)
Using the corrected equations (A3, A4,A10 and A11) we again arrive at an expression approximately equal to A7, and this equation agrees with Michelson's experimental data. The conclusion from this experiment is that the speed of light does not remain constant after reflecting off a moving mirror.
Michelson's results were published in a paper titled, "EFFECT OF REFLECTION FROM A MOVING MIRROR ON THE VELOCITY OF LIGHT". Unfortunately, I don't have the name of the publication. For those who want to examine the data and parameters of this experiment, and who can't find the paper, a scanned version will be put on my website after June 20, 1998. Follow the physics link at the bottom of the page http://www.flash.net/~dseppala
David Seppala
David Seppala
The Michelson paper referred to in this posting can be viewed, by
following
the Physics Link at the bottom of the page at
http://www.flash.net/~dseppala
Jim Carr
David Seppala <dsep...@flash.net> writes:
>
>An experiment was conducted to determine if the speed of light remains
>constant after reflecting of a moving mirror. The experiment uses the
>following setup:
Which I have slightly modified to add the "*" locations which are
a distance d from the C (or D) positions. (I also corrected the
typo you mention in another article.)
>
> * C \ B
> | |
>
>
> O E
>
>
> | |
> D * \ A
>
> S
>
>A better diagram can be viewed by going to the to the physics link on
>the bottom of the page at http://www.flash.net/~dseppala
Except you did not draw the location of the mirrors in the
rotated position and make a mistake as a result.
>Light from a source at S falls on a lightly silvered mirror A, acting as
>a beam splitter. The reflected pencil goes to a revolving mirror D,
>thence to the concave mirror E, to the second mirror C revolving about
>the same axis O, where it proceeds to the plane mirror B and is
>reflected back to A. The transmitted pencil pursues the same path in
>the opposite direction, returning via DA to the starting point, where it
>meets the first pencil, producing interference fringes which are
>observed in an interferometer.
>Actually, this experiment was performed by Michelson in 1913. Michelson
>concluded from this experiment that the speed of light is not affected
>by reflection off a moving mirror. However, the equations used by
>Michelson to reach that conclusion contained errors.
The important one is correct, the others result from the approximation
he states in a footnote -- where he neglects effects in second order.
>Michelson states:
> The time occupied by the pencil DEC is
> T1 = 2 (D + d) / V1 (A1)
> while that taken by pencil CED is
> T2 = 2 (D - d) / V2 (A2)
>where D is the distance OE, d = distance the revolving mirror moves
>while light passes over DEC, and V1 is the resultant velocity of the
>first pencil, V2 that of the second.
This is correct.
>Michelson's equations A1 and A2 contain two errors. First, if d =
>distance the revolving mirror moves while light passes over DEC, the
>equation for each path should be 2D + d, not 2D+2d.
No. Look at the picture up above. On the top path it has to travel
an extra distance d to get to the mirror, then that same distance d
to get back to there the other beam started out. Conversely, the
other beam travels 2d less than the first one did to get to the
bottom mirror.
>The next error
>depends on whether the speed of light is constant or not. If the speed
>of light varies after reflecting off the moving mirrors, the "d"s along
>the two paths are not equal, d1 does not equal d2.
This is a second order effect since v << V.
>Now Michelson used the ratio:
>
> d / (2D) = v / V (A5)
>where v is the velocity of the revolving mirrors and V is the speed
>of light to eliminate the unknown d from the equations.
Using 2D rather than 2D+2d is consistent with the neglect of larger
effects that scale as the distance l between the mirrors (which is
larger than d). It is true that d/(2D+2d) is approximately equal
to d/2D to the order of approximation being used since d <<< D.
<... HTML duplicate snipped ...>
Nothing wrong with that paper on the order of a factor of 2.
Besides, why not look at data where v was approximately equal to V
and huge effects would be predicted by "emission" theories?
--
James A. Carr <j...@scri.fsu.edu> | Commercial e-mail is _NOT_
http://www.scri.fsu.edu/~jac/ | desired to this or any address
Supercomputer Computations Res. Inst. | that resolves to my account
Florida State, Tallahassee FL 32306 | for any reason at any time.