Arindam Banerjee
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> Asking very politely, have you pointed out Einstein's errors
> to the scientific world through a paper, or in a technical
> colloquium?
Yes. Back in 2005 I published the errors involved in the analysis of
the MMI experiment. On and off, I have mentioned it. It is present
in Usenet. I am reproducing the article below. If you are interested
you can follow all the links in google groups with keywords such as
Michelson Morley Arindam Banerjee Einstein.
I hold that Usenet discussions on science are at least as valid as
held in any other fora. For anyone can take part in it. It is the
most public way to analyse any matter, since any one can take part.
There is no compulsion, no holding back save for those who have
something to hide, such as their real identities.
****
The Michelson-Morley interferometer experiment, with its famously
unexpected null results, is the sole source and also remains the core
hard undeniable scientific evidence for the theories of relativity.
One of the outstanding features about this experiment is that it is
simple in concept, and has been done with painstaking efforts by many
scientists.
In this article, I will quote exhaustively from a textbook (details
below) about the nature and philosophical background behind this
experiment and will pinpoint the great blunder that was made in the
analysis of the null results. I will show as clearly as can be, the
nature of this blunder. I hope and believe that the intelligent
reader
will understand the subtlety underlying this very fine error, and
grasp
the enormous and highly positive consequences - with the
re-invigoration of physics from the most fundamental level.
Arindam Banerjee
Melbourne, July 2005.
Reference:
Textbook Details:
"Physics of the Atom", by M. Russell Wehr and James A. Richards,
Jr. of the Department of Physics, Drexel Institute of Technology.
Addison-Wesley Publishing Company, Inc.
First Printed in 1964.
______________________________¬_________________________
"This book is neither a treatise nor a survey. It is a textbook
which bridges the gap between classical physics and the present
frontiers of physical investigation." - extract from the Preface, by
the writers. Philadelphia, Pa., July 1959.
Chapter 5 - Relativity (excerpts)
Pg111 ->
5-1 Consider the interpretations of physical events that might be
made
by a person of high IQ born and brought up on a merry-go-round. He
would experience a force somewhat like the force of gravity. It
would
be down at the centre of rotation, and, because of the centrifugal
component, it would be directed down and out at points away from the
centre.
If our merry-go-round observer were to have the genius to devise a
whole system of mechanics, the mechanics he would devise would not be
the mechanics of Newton.
For Newton's laws to be valid precisely, we must observe events from
what is called an inertial frame of a Galilean-Newtonian co-ordinate
system. Such a system is one which has no acceleration. The whole
structure of classical physics, then, is based on the assumption that
we interpret all events as they would be interpreted by an observer
whose viewpoint is an inertial reference frame.
The genius of Newton is, in part, that although he never could step
off
the earth physically, he did step off it mentally. He interpreted
events as though he had no acceleration. Because of this shift in
his
viewpoint, he was able to write his laws of mechanics in the
particularly simple form that he did.
But Newton never really knew where he projected himself to, and this
worried him. He excluded the earth as a vantage point because the
earth not only rotates but revolves around the sun. The sun offered
possibilities, but even the sun moves and is probably accelerated
through space. The stellar constellations were named by the ancients
and the stability of their arrangement led to their being called the
"fixed" stars. Yet it would be the strangest of co-incidences if
the "fixed" stars really were fixed.
It would seem that, however, that if we locate a frame of reference
so
that it is fixed relative to the stars, this vantage point will be
sufficiently steady for Newton's laws to serve well for every
practical purpose. Such a vantage point is good enough for the
practical men who want to fly aircraft, etc. But for a philosopher or
physicist whose primary concern is the understanding of the nature of
things and whose goal is the discovery of truth, uncertainty about
the
frame of reference represented a serious flaw in the logical
structure
of classical physics.
5-2 The search for something more fixed than the stars went
something
like this. James Clerk Maxwell demonstrated that electricity and
light
are related phenomena. Starting with known properties of electricity
and magnetism, Maxwell derived equations which are identical in form
to
the equations which describe many wave phenomena. He could
demonstrate, furthermore, that the velocity of the waves he
discovered
was the same as the velocity of light. He could derive many other
properties of light, and it was soon accepted that he had put the
wave
theory of light on a firm foundation. In this theory, light is an
electromagnetic wave motion.
Every wave motion has something that "waves". Surely, it was
argued, light waves must involve the waving of something even in free
space. No one knew what it was, but it was given the name
"luminiferous ether".
Light passes through many kinds of materials. It passes through
relatively heavy materials like glass, and it passes through the
nearly
perfect vacuum that must lie between the stars and the earth. Thus
ether must permeate all of space.
However fanciful it may seem to us, physicists felt that this ether
might be just the thing to which to attach a Newtonian co-ordinate
system. It was conceived that Newton's laws would hold exactly for
an observer moving without acceleration relative to the ether.
If the ether is assumed to be at rest, then the interesting question
is: How fast are we moving through the ether? Since all speculations
about the ether stem from its properties as a medium for carrying
light, an optical experiment is indicated. It is not hard to compute
how sensitive the apparatus must be to measure the ether drift.
Assuming, for the sake of argument, that the sun has no ether drift,
the velocity of the earth through the ether must be its orbital
velocity. If the sun has an ether drift, then the drift of the earth
will be even greater than its orbital velocity at some seasons.
Knowing that the earth's orbit is about 93 million miles, we can find
the orbital velocity to be about 18.5 miles per second. By
performing
the experiment at the best season of the year, we know that we should
be able to find an ether drift of at least 18.5 mi/sec. The velocity
of light is 186,000 mi/sec. Great as our orbital velocity is, it is
only .0001 times the velocity of light; so it is evident that a very
sensitive instrument is required.
5-3 A device of sufficient sensitivity was made and used in the
United
States by Michelson and Morley in 1887. The principle of their
apparatus is brought out by the following analogy.
Suppose two equally fast swimmers undertake a race in a river between
floats anchored to the river bed.
(Arindam's note: please note the expression - "floats anchored to
the river bed" meaning that they are stuck to the ground, or the
inertial frame of reference. Also let us mutter here, with Galileo,
that the earth, it moves!)
_____________________River Bank______________________
C
Speed of river -> v
Same distance L lies between A and C, and A and D.
Speed of swimmer with respect to the water is c.
A D
______________________River Bank_______________________
Two equal courses, each having a total length 2L, are laid out from
the
starting point, float A. One course is AD, parallel to the flow of
the
river relative to the earth, and the other AC, perpendicular to it.
How will the times compare if each of the swimmers goes out and back
on
his course? Let the speed of each swimmer relative to the water be
c,
and let the water drift or velocity with respect to the earth be v.
When the swimmer on the parallel course goes downstream, his velocity
will add to that of the water, giving him a resultant velocity of (c
+v)
with respect to the earth. The time required for him to swim the
distance L from A to D is L/(c+v). On his return, he must overcome
the
water drift. His net velocity then is (c-v), and his return time is
L/(c-v). His total time is the sum of these two times. This is given
by
Time_parallel = L/(c+v) + L/(c-v) = 2Lc/(cc - vv).
The other swimmer, going perpendicular to the water drift, spends the
same time on each half of his trip, but he must head upstream if he
is
not to be carried away by the current. The component of his velocity
that carries him toward his goal is the square root of (cc - vv) with
respect to the earth. The total time for his trip also depends on
the
water drift, and is
Time perpendicular = 2L/(square root of (cc - vv)).
To see how these two times compare, we divide the parallel course
time,
by the perpendicular course time, to get
Time parallel/Time perpendicular = 1/(square root of (1 - vv/cc))
In still water v=0, the ratio of the times is unity, and the race is
a
tie, as we would expect. In slowly moving water, the ratio is
greater
than unity and the swimmer on the perpendicular course wins; or put
differently, if the swimmers are stroking in phase when they leave
float A, they will be out of phase when they return to it. If the
velocity of the river increases to nearly that of the swimmer, then
the
ratio tends towards infinity. If the river velocity exceeds the
swimmer velocity, the entire analysis breaks down. The ratio becomes
imaginary and both swimmers are swept off the course by the current.
The point is that, by observing the race, the velocity of the water
relative to the system of anchored floats can be measured.
The optical equivalent of the above situation is to have a race
between
two light rays over identical courses, one parallel and one
perpendicular to the ether drift. The instrument used, is called a
Michelson interferometer, is shown schematically below.
_C_ .
_B_
Light entry
_________A //_______________D
____observer (eye, telescope)
Light enters the apparatus from the source at the left. At A it
strikes a glass mirror (angled at 45 deg) which has a half-silvered
surface. Half the light is reflected up toward B and C, while the
other half refracts at both surfaces of A and emerges parallel to the
original beam and goes on to D. Both C and D are full-silvered,
front-surface mirrors which turn their beams back towards A. The
beam
from C is partly reflected at A, but part of that beam refracts
through
A and goes to the observer. The beam from D partially refracts
through
A and is lost, but part of the beam is also reflected toward the
observer. The plate of glass at B has the same thickness and
inclination as that at A, so that the two light paths from source to
observer pass through the same number of glass thicknesses. If the
light from the slit did not diverge and remained very narrow in going
through the apparatus, the observer would see a line of light. The
brightness of this line would depend on the difference in the optical
length* of the two light paths. (*Footnote: Two paths have the same
optical length if light traverses both in the same time.
The optical lengths of the interferometer paths can be changed by
changing their physical length, by changing the index of refraction
of
the region through which the light passes, or, if the swimming
analogy
applies, by moving the apparatus relative to the light-carrying
medium.) If these (optical lengths) differed by any whole number of
wavelengths of the light (including zero) the line would be bright.
If
the path differed by an odd number of half-wavelengths, then the line
would be dark. Between these extremes every brightness gradation
would
be observed. In practice, light does diverge in the apparatus, and
there are a great many slightly different paths being traversed
simultaneously. Consequently the observer does not see but a
multiplicity of lines. The loci of points where the paths differ by
whole wavelengths are bright, and where the paths differ by an odd
number of half-wavelengths there is darkness. Thus, as one path
length
is varied, the observer sees fringes, like the teeth of a comb, move
across the field, rather than a single line becoming lighter and
darker. It is fortunate that the optical system works as it does,
since it is easier for the eye to detect differences in position than
differences in intensity.
The precision of this device is remarkable. If yellow light from
Sodium
is used, the wavelength is 5.893*10**-7 m. Moving the mirror C away
from A one-half this distance will increase one path length by a
whole
wavelength and cause the pattern to move an amount equal to the
separation of two adjacent dark lines. If we can estimate to
hundredths of fringes, then the smallest detectable motion is only
2.9*10**-9m.
The similarity between the Michelson interferometer and the swimming
race should be evident. Light corresponds to the swimmers and has
the
free-space velocity, c, with respect to the ether medium. The ether
drift corresponds to the water current drift and has the velocity v
with respect to the earth. Just as we could learn about the river
flow
by seeing the outcome of the swimmers' race, so we wish to measure
the ether drift by conducting a "light race" over equal paths
parallel and perpendicular to the ether drift.
Suppose that instead of taking the ratio of the times for the two
paths
of the river race we now take their difference; then
t = time difference = 2Lc/(cc-vv) - 2L/square root of(cc-vv) =
Lvv/ccc after using the first two terms of the binomial expansion, to
a
good approximation if v<<c.
In the interferometer, the time difference should appear as a fringe
shift from the position the fringes would have if there were NO ether
drift. The distance light moves in a time t is d=ct and if this
distance represents n waves of wavelength W, then d=nW. Therefore
the
fringe shift would be n=Lvv/(Wcc)
Thus if the light race is carried out with speed of light c and
wavelength W in an interferometer whose arms are of length L, one of
which is parallel to the ether drift of velocity v, then the equation
n=Lvv/(Wcc) gives the number of fringes that should be displaced
because of the motion of the earthe through the ether compared with
their positions if the earth were AT REST in the ether.
5-4 The Michelson-Morley Experiment. The apparatus used was large
and
had its effective arm length increased to about 10 m by using
additional mirrors to fold up the path. The entire apparatus was
floated on mercury so that it could be rotated at constant speed
without introducing strains that would deform the apparatus.
ROTATION
WAS NECESSARY in order to make the fringes shift, and by rotating
through 90deg, first one arm and then the other could be made
parallel
to the drift, thereby doubling the fringe displacement given in the
earlier equation. We can now estimate whether this instrument should
be sensitive enough to detect the ether drift. Recall that at some
time of the year the ether drift v was expected to be at least the
orbital velocity of the earth, which is about .0001c. Thus we expect
vv/cc to be at least 10**-8. Using light of wavelength 5*10**-7 m,
the
computed shift is n=0.4 fringe. Michelson and Morley estimated that
they could detect a shift of 0.01 fringe. Sensitivity to spare!
Measurements were made over an extended period of time at all seasons
of the year, but no significant fringe shift was observed. Thinking
that the earth might drag a little either along with it just as a
boat
carries a thin layer of water when it glides, Michelson and Morley
took
the entire apparatus to a mountain laboratory in search of a site
which
would project into the drifting ether. Again a diligent search
failed
to measure an ether drift. The experiment "failed".
Few experimental failures have been more stimulating than this. The
negative result of the Michelson-Morley experiment presented a
challenge to explain its failure. Fitzgerald and Lorentz presented
an
ad hoc explanation. They pointed out that there might be an
interaction between the ether and objects moving relative to it, such
that the object became shorter in all its dimensions parallel to the
relative velocity. Recall that in the flowing water analogy the
ratio
of the times of the swimmers was
1/square-root of (1-vv/cc).
If the route parallel to the flow had been shorter by this factor,
then
the ratio of the times would have been one and the race would have
been
a tie. A similar shortening of the parallel interferometer arm would
account for the tie race Michelson and Morley always observed. The
shortening could never be measured because any rule used to measure
it
would also be moving relative to the ether and would shorten also.
Whether you accept the Fitzgerald-Lorentz contraction hypothesis or
not, the Michelson-Morley experiment indicates that all observers who
measure the velocity of light will get the same result regardless of
their own velocity through space.
5-5 The constant velocity of light. Michelson and Morley found that
the speed of the earth through space made no difference in the speed
of
light relative to them. The inference is clear: either that the
earth
moves in some way through ether space more slowly than it moves about
the sun, or that ALL OBSERVERS MUST FIND THAT THEIR MOTION THROUGH
SPACE MAKES NO DIFFERENCE IN THE SPEED OF LIGHT RELATIVE TO THEM.
The above inference was clear, at least to Einstein, who took the
second alternative and made it a cornerstone of his special theory of
relativity.
Recall that the Michelson-Morley experiment was carried out to
measure
the speed of the earth relative to the ether in order to establish a
frame of reference relative to which Newton's laws would hold. The
failure of that experiment meant that the search for the fixed
reference system must be made by another technique or abandoned
altogether. Einstein explored the alternative of abandonment. He
asked himself where he would stand (both literally and figuratively)
if
there were no "Newtonian" frame of reference. In this case there
could be no absolute velocities, for every velocity would have to be
measured relative to an origin that might and probably would be
moving.
Since there can be no preferred frame of reference, any frame must
be
as good as any other. To be universal, the laws of physics must be
the
same for all observers regardless of any motion they may have.
Contrary to the first paragraphs of this chapter, one's viewpoint
MUST MAKE NO DIFFERENCE in one's interpretation of events observed.
If he is to be correct, the man born and brought up on a merry-go-
round
must deduce the same laws of physics as anyone else.
**** End of exhaustive quotations from the textbook "Physics of the
Atom", from 5-1 to 5-5. The following sections, in brief, are about:
5-6 General and Special theories of relativity.
5-7 Classical Relativity
5-8 Einsteinian Relativity. Quote: p123 The Michelson-Morley
experiment was based on the assumption that since the classical
velocity transformation is not invariant, it should be possible to
measure the velocity of light in the ether relative to the earth.
The
experiment demonstrated that at least one velocity is invariant - the
velocity of light. Einstein accepted this as a second fundamental
assumption of this special theory of relativity. He postulated that:
(2) ALL OBSERVERS MUST FIND THE SAME VALUE OF THE FREE-SPACE VELOCITY
OF LIGHT REGARDLESS OF ANY MOTION THEY MAY HAVE.
5-9 Relativistic space-time transformation equations.
5-10 The relativistic velocity transformation
5-11 Relativistic mass transformation
5-12 Relativistic mass-energy equivalence
5-13 The upper limit of velocity
5-14 Examples of relativistic calculations
5-15 Pair production
5-16 Summary. We have seen how Einstein's attention to a flaw in
logic in Newtonian mechanics led him to consider the importance of an
observer's viewpoint. We have seen how the "failure" of the
Michelson-Morley experiment led Einstein to assign special
significance
to the velocity of light in free space. We have seen how these
considerations led to new concepts of space, time, mass, energy, and
matter. When we realize that this was but one of Einstein's
achievements, we begin to sense the magnitude of his contribution to
human thought.
(End of quotes from the book "Physics of the Atom".)
****
Before I tackle the most fundamental issues relating to the
Michelson-Morley interferometer experiment - and yet again expose the
bungle there, this time as clearly as possible - let me first, with
sadness, reflect upon the horrendous consequences of this most
pernicious theory of relativity.
The deepest theories of physics are by no means complete in
themselves,
with some relevance to engineering; they have an intimate connection
with individual and social life, by providing the practical basis for
individual and group thought structures. By outing the need for any
absolute frame of reference, Einstein's relativity implicitly gave
the license to all forms of individual and social thinking as equally
valid. Thus, the thinking of the child molester or serial killer is
as
valid - from the extension of Einstein's relativity to real life - as
the thinking of the law enforcer or saint. There is no basis for
differentiation between virtue and vice, between appearance and
reality. All are equally valid in the same relativist currency.
What
is truth, or what is lie, becomes merely a matter of opinion
announced
and imposed by the loudest and the strongest of the time.
Thus I see the stupidities, indecencies, and the extraordinary
bloody-mindedness of the 20th century (a century of world wars, mass
murders, extreme human inequalities; now leading to another dominated
by selfishness, fear and greed) as an indirect yet inescapable
consequence of Einstein's theories, to some extent. Men can turn
into self-important brats more easily, as their subconscious can now
find good excuse, from the supposedly undeniable basics of physics,
to
disregard absolute checks upon behaviour. Einstein himself showed
this, when he felt no constraints about writing a letter to the
President of the USA urging the development of the atomic bomb;
knowing
fully well that its development would cause immense evil.
For in a relativistic mental set-up, there can be no high and defined
end to aspire unto; there can be no striving for the realization of
absolute truths as fixed goals. There is, thus, only the scope of
degeneration of whatever remaining values that were handed down by
the
non-relativists of earlier generations. This is painfully evident
from
the moral atrophy and social degeneration in modern societies; as
also
from those failed communist regimes where the whims of dictators
became
the highest values for all.
______________________________¬_______________________
It is evident from the above (extracts from the paras 5.1 to 5.5 of
the
textbook "Physics of the atom) that the entire basis of Einstein's
theory of relativity depends upon the null result of the Michelson
-Morley interferometer experiment. This single fact is of vital
importance. Equally important is that analogy given earlier,
relating
to the swimmer; swimming parallel to, and perpendicular to, the
flowing
river. For based upon this analogy, and this analogy alone, was the
logic and also the mathematics for the analysis of the Michelson-
Morley
interferometer experiment developed.
Let us see how far this analogy relates to the dynamics of light on
this our moving earth. The diagram is redrawn below:
_____________________River Bank______________________
C
Speed of river -> v
Same distance L lies between A and C, and between A and D.
Speed of swimmer with respect to the water is c.
River Bank ____ A_____________________D
We must note here, once again, that in this analogy A, C and D are
fixed floats on the river bed. So, while the swimmer himself is
affected by the flow of water, which gives him a higher or lower
speed
depending upon his direction, the floats are not affected at all.
They
are stuck to the river bed, and thus, have the same fixedness as the
river bank.
If this analogy (with respect to the motion of earth in ether) is
correct, then the subsequent mathematics (that gives us the famous
Lorentz transformation) is correct. But is this analogy correct?
For the analogy to hold, the river is the Earth moving with speed v
and
the river bank is the ether or absolute frame of reference. Any
object
floating on the river, then, has to have the same speed of the river.
When an object is stuck to the river bed (not allowed to drift) it is
implicitly given a velocity of -v, so that its net velocity with
respect to the river bank frame of reference is v-v=0.
This implicit, totally arbitrary giving of a negative velocity to the
float, equal to the velocity of the river flow, making it thus fixed
with respect to the river bank, was completely missed by all the
physicists, past and present. However, it is an absolute and
undeniable fact that all the stationary objects on Earth have the
same
velocity v around the Sun, since the Earth is moving with that
tangential speed around the Sun, according to Galileo and all later
non-Aristotelian astronomers. There is no way it is possible to give
any object on earth a negative velocity through some external ether
hook-up process! All objects on Earth move at the same speed v. So
we
do not see objects from Earth being left behind, as it were, as we
orbit the Sun! There is no way we can go to and from goal posts
fixed
in the ether reference! Nor can light travel to and from goal posts
fixed in the ether reference!
However, by fixing the floats on the river bed (which is the same
reference as the river bank) all the physicists have implicitly
assumed
all the above. They have kept the floats fixed in the ether
reference,
while implicitly holding they are in the Earthly reference. This
implies that the Earth is not moving at all! For if the Earth is
moving, there could be no question of keeping the floats fixed to the
river bed, for any valid analogy. They would have to drift with the
velocity v with respect to the river bank.
So the terrible mistake in this analogy was to keep the floats fixed
to
the river bed/ether, as opposed to letting it drift with the flow.
The
importance of this point simply cannot be overstated. When extended
to
the Michelson-Morley experimental set-up, this means - absolutely! -
that all the mirrors stay fixed in etheric space while the earth
moves
away from them with velocity v! Ridiculous! But this is exactly
what
must happen when we extend the analogy of the swimmers, with the
floats
drifting but fixed to the river bed, to the apparatus in the so-vital
Michelson-Morley interferometry experiment.
Bodies, and light, can, have to, and do travel to and from "goal
posts" fixed in the moving Earthly reference! There is simply no way
in which the mirrors used in the Michelson-Morley experiment can be
assumed to remain fixed in etheric space, while the Earth moves away
from the set-up! If we admit this, then we must allow that the
swimming analogy was flawed. The correct analogy would be to cut the
floats loose, and let them drift with the velocity v.
Now let us see the consequences of this change.
_____________________River Bank______________________
C C'
Speed of river -> v
Same distance L lies between A and C, and between A and D.
Speed of swimmer with respect to the water is c.
A A' D D'
______________________River Bank_______________________
The figure above shows the change of position of the float with time.
As earlier there are two equal lengths L, marked out by the
perpendicular course AC and the parallel course AD. (L=AC=AD). But
now the floats are *not* fixed to the river bed, so they drift with
velocity v. After time t, which is L/c, they move to the points A',
C' and D'.
t=L/c is the time the swimmer would have swum the lengths L in the
absence of flow, that is, with v=0.
So AA', DD' and CC' are all of length vt or vL/c.
Let us take the swimmer taking the route AD, parallel to the river
bank. He starts from A, towards D. He has the speed (c+v) as he is
swimming with the flow. Since the target float D is moving, the
swimmer now has to travel a further distance DD' to catch up. So, he
has actually swum the distance AD' instead of the earlier AD. AD'
= AD+DD'.
So he has swum the length L+vL/c, with the speed c+v. The time it
would take him to do that will be (L+vL/c)/(c+v).
Now (L+vL/c)/(c+v) = L(1+v/c)/(c+v) =L(1+v/c)/(c(1+v/c)) = L/c = t.
Which means, no matter what the speed of the river, the swimmer would
reach his goal float in the same time, provided the float was *not*
tethered, freely drifting instead.
Now let us consider the route AC, that is the one perpendicular to
the
river bank. The swimmer swims with velocity c in the perpendicular
direction, but is pushed sideways as a result of the flow. He has an
additional component of velocity thus, which pushes him sideways to
the
float which also has moved by the distance CC' in the time t. The
magnitude of the velocity of the swimmer, on his way to C' has to be
square root of (cc+vv).
The distance he covers is square root of (L*L + vt*vt) or square root
of (L*L + v*v*L*L/(c*c)) or (L/c)*square root of (cc+vv). So the
time
taken to cover this distance will be distance/speed or L/c*square
root
of (cc+vv)/square root of (cc+vv) which is L/c which again is t.
So no matter whether the swimmer is swimming with the current or
perpendicular to the current - if the floats are drifting, he will
always cover the distances involved in exactly the same time as if
there was no flow in the water.
For the sake of completion, we now consider the return journeys in
both
the parallel and perpendicular directions.
_____________________River Bank______________________
C C' C''
Speed of river -> v
Same distance L lies between A and C, and between A and D.
Speed of swimmer with respect to the water is c.
A A' A'' D D' D''
______________________River Bank_______________________
Over the time 2t, the floats will have moved the distances AA'',
DD'' and CC''. The swimmer on the parallel path, having
reached the float at D, turns back towards the float and will meet it
at the point A''. The distance he now covers is D'A" which is
A'D'-A'A" or L-vt or L-vL/c or L(1-v/c). The speed of the
swimmer is (c-v) as he is going against the flow. So the time taken
by
the swimmer to reach the float on the return journey is L(1-v/c)/(c-
v)
or L(1-v/c)/(c(1-v/c)) = L/c = t.
In the perpendicular path, the swimmer covers the distance C'A''.
Using the earlier analysis, we can once again find that the time it
would take him to cover this distance would be t. (His speed would
be
the same as that going from A to C'; and the distance C'A'' is
also the same as AC'.)
We thus see that no matter what angle the direction of travel, the
time
for travel for a source between two points in a medium which has no
matter what velocity with respect to some fixed reference, is always
the same. This goes totally against all modern physics, which is
relativistic, and based upon the Lorentz transformation dealt with
earlier.
We now see what really happened in the Michelson-Morley
interferometer
experiment. The diagram is given again below, with some changes
following our earlier discussion.
C__C'
____ B
Light entry A A' A''
___________ // |D D'
______ observer (telescope, film)
Light going through A will be reflected by the mirror not at position
D
but at a further distance, at D'. The light will thus travel the
path AD' with the speed (c+v) which is the path AD+DD'; DD' being
the extra distance it will have to move, because the Earth is moving,
and the mirror along with everything else is fixed on the Earth.
Since
the Earth is moving, the mirror D moves the extra distance DD' by the
time the light starting from A reaches it. Since the Earth is
moving,
the partially silvered mirror at A moves the distance AA' when the
light originating from A reaches D'. On the return path, the light
will travel backwards from D', towards the partially silvered mirror,
with the speed (c-v) and will meet the partially silvered mirror at
A''. The partially silvered mirror will move the further distance
A'A" by the time it takes the returning beam of light to meet it.
Thus the formulation is exactly the same as it was in our case for
the
swimmer doing the parallel course. Both going and coming times will
be
exactly the same, that is t=L/c. Totally independent of the velocity
of the source of light!
In the perpendicular direction, the speed will be square root of
(cc+vv). Because of its initial speed v, the light will have to move
in on the moving mirror initially at C at an angle and with a higher
magnitude of velocity - just as any stone thrown out parallel to and
from a moving train, with respect to the ground. It will reach it at
the position C'. This light will also have to travel the extra
distance (square root of (L*L + v*v*L*L/(c*c)) - L). As we have
seen, the time to cover this will be L/c=t. Again, this time is
totally independent of the velocity of the source of the light.
>From the above, it is clear that the return times are exactly the same
no matter what the direction of the light source. Thus, the rotation
of the whole apparatus - as was done - should not lead to any
change in results at all, relating to the interferometer pattern.
The
null result is entirely to be expected. A wrong analogy had led to a
wrong expectation. But with the correct analogy, the right results
(the null results) were obtained.
The consequences are drastic. The existence of ether as the medium
of
propagation of all electromagnetic waves (including light waves) is
upheld. It had been wrongly demolished. We also find that the speed
of light does change with the speed of the light emitting source. If
the speed of the light source is v, with respect to ether, then the
speed of light with respect to ether, when directed in the direction
of
v, is c+v. The null results of the Michelson-Morley interferometer
experiment confirm both of the above. The speed of light cannot be
constant, irrespective of the speed of the source.
To confirm this, let us now do the above analysis again. This time,
following Einstein's Postulate (given below, and quoted from the text
book), we take c to be always c and never anything more or less.
Thus
on the parallel path, the time taken to cover the distance AD' will
be (L+vL/c)/c and D'A" will take (L-vL/c)/c which is 2L/c or 2t.
However, in the perpendicular path, the times will be square root of
(L*L + v*v*L*L/(c*c))/c. That is, t*square root of (1+vv/cc) for the
going path and the same for the return path, giving 2*t*square root
of
(1 + vv/cc). This is different from the parallel path, which is 2t.
So, if the speed c of light is always constant, and independent of
the
speed of the light-emitting source, as per the current thinking, then
the Michelson-Morley interferometer experiment would have shown the
fringes, with our corrected analysis! How ironic!
All the Einsteinian constructions resulting from the Michelson-Morley
interferometer experiments are thus reduced to glaring nonsense. For
Einstein's first postulate, the basis behind all his theories of
relativity, namely,
ALL OBSERVERS MUST FIND THE SAME VALUE OF THE FREE-SPACE VELOCITY OF
LIGHT REGARDLESS OF ANY MOTION THEY MAY HAVE
as simply wrong. Wrong. Proved wrong, logically and mathematically,
using the results of painstakingly done experiments.
To make my point, further, with mathematics, for the general case of
light proceeding at any angle (and not just the two angles, zero
degrees and ninety degrees) let us consider the light source going at
an angle (theta) with respect to the parallel path. We use the same
notations (L,v,t,c) as used earlier.
Then, the velocity of light will be in that direction:
Square root of ((c*cos(theta)+v)^2 + (c*sin(theta)^2), by breaking up
the speed c along two the x-y components, and adding the flow speed v
to the parallel component. Note: the ^2 means squaring the bracketed
expression ahead of it. After expansion, the above expression
becomes
square root of (c*c + v*v + 2v*c*cos(theta)).
Within time t, the float/mirror will have moved the distance vt = vL/
c
along the parallel path. The distance the swimmer/light will have to
move is thus:
Square root of ((L*cos(theta)+v*L/c)^2 + (L*sin(theta)^2). Which
after
expansion becomes (L/c)*square root of (c*c + v*v +2v*c*cos(theta)).
Dividing the distance traveled by the speed of travel, we get the
time
as L/c for the general case of light proceeding at any angle from the
source as being t=L/c, completely independent of the velocity of v.
So what is really happening? What are the so-called relativistic
effects of Einstein, really? Really, what is happening (and this is
a
completely original thought, given right now) is that between any two
points on a body like Earth moving with a speed higher than zero with
respect to a fixed frame of reference; the actual distance traveled
by
a ray of light, from one point to the other, is usually different
from
the actual measured distance. So, if we mark out two points on
Earth,
and measure the distance between them carefully, then, the ray of
light
will always move a distance more or less than the marked distance,
except for just one particular angle. This angle can be found easily
from the above formula for the actual length traveled, thus by
putting
the expression
v*v + 2v*c*cos(theta) = 0;
or theta = inverse of cos(-v/(2*c)).
Arindam Banerjee.
Melbourne, August 2005.
Author's Note: This article can be freely distributed for discussion
strictly for non-commercial purposes only. Comments are welcome.
The
author is solely responsible for this article. All rights are
reserved.
> If you have, and if it is simple enough to
> understand, I would love to read it.
See above. I hope the diagrams come out okay.
> Do you suggest any modifications, or you think the
> entire theory is worth nothing and should be junked.
Yes, along with quantum theory of light emission (do away with the
photon concept, for it is waves and only waves) plus the concept of
entropy as the law of conservation of energy becomes a special case
with my yet to be proven through experiment e=0.5mVVN(N-k). It can
be
easily proven by blowing up the bows of a small boat with an rail
machine gun. If the boat accelerates with that, then the equation is
proven if it is also agreed that there is no reaction from the firing
of a rail gun.
Cheers,
Arindam Banerjee