Mathew Orman wrote:

http://www.btinternet.com/~sapere.aude/

This is a fantastic site! Thanks for the link.

Here's a snippet for those who won't take the time to review it, namely
Dirk.

"In short, although one need not question the existence of a truly
dynamic (non-reciprocal!) effect involving
a quantity g = (1 - v2/c2)-1/2, the relativistic argument, when
corrected, would give us a g which equals 1."

Maybe Dirk will look up this section of the article for a more detailed
form of the argument that I've been trying to impress upon him:)

And Dirk has yet to conclude correctly, from his own arguments, that by
proving that t=t'=t''=0, that either gamma=1, or all observers are
permanently at rest in the same frame, which is exactly the same
conclusion as the former, since gamma=1 implies v'''=0. Thus by
beginning with the premises that

x=/=0, x'=/0, x'=/0 t=/=0, t'=/=0, and t''=/=0 we can, as Einstein does
in his little book "Relativity", prove by use of the lorentz transform,
that the relative ticking rates of the clocks in these frames is

dt = dt'gamma'
dt = dt''gamma''

Dirk, then applies the transform once more to these equations to
conclude that 'all' of the above parameters are equal to 0, in stark
contradiction to the premise that they are all not equal to zero. And
even having proved on his own that the lorentz transform is internally
inconsistent, he fails to grasp the reality of that conclusion.

Moreover, (And this is for Sam) the Michelson-Morley experiment only
proves one thing, that if we hold the speed of light to be constant wrt
some 'proper' frame, regardless of direction wrt the origin of the
proper frame coordinate system, then an object in motion wrt that frame
will be physically altered in dimensions wrt that frame according to the
equation:

L2/L1 = gamma

Which is the only solid conclusion that can be reached based upon the
premises given.

L1 is the length of the moving longitudinal arm (x oriented arm) wrt
proper frame, and L2 is the length of the moving lateral arm (y oriented
arm) wrt proper frame.

It does follow that if we hold the length of the lateral arm to be
constant in its physical translation between the two frames (yet another
pure assumption), then we find that L_o, the proper (or 'rest') length
of the lateral arm can be substituted into the equation, thus giving

L_o/L1 = gamma

From which follows that

L1 = L_o / gamma

Or IOW, the longitudinal arm L1 is shortened by the factor 1/gamma wrt
its rest length when it is set in motion wrt proper frame.

Thus if we apply the first equation of the Galilean transform to get
space intervals wrt the two frames respectively, then

x' = x - vt

But since our moving observers x-ruler is contracted by a factor
1/gamma, then x' in K-meters, translates to

x'/gamma K'-meters, or

As the K' frame observer perceives it

x' = (x - vt)gamma

Thus the first equation of the lorentz transform is just the first
equation of the Galilean transform with a scaling component factored in.

The fourth equation must be treated with much more rigor, since as it
turns out, the time ratios given one way propagation along the x axis
are unequal, depending upon the direction of propagation wrt the K
frame, while given two way propagation these ticking rates resolve to

t' = t gamma

which is just he ticking rate relationship derived by Einstein, as
mentioned above. Thus for any harmonic oscillation, one full cycle must
be considered in order to obtain consistency of time ratios.

This, in and of itself is reason enough to scrap the fourth equation of
the LT.

We can account perfectly for the results of the MM experiment using the
alternate transform

x' = (x- vt)gamma
t' = t gamma

Try it.

Now this, despite its correctness in the given context, is really
unimportant, since we have made a tacit assumption above that warrants
further investigation, namely, that the lateral arm length remains
constant through physical translation between frames. We could just have
easily assumed that the longitudinal arm remained constant in length, in
which case we would have derived

L2/L_o = gamma

and thus

L2 = L_o gamma

Or IOW, the lateral arm will have increased in length by a factor gamma.

Once again we find that the time intervals of the respective beams are
equal, thus equally satisfying the requirements of the empirical
outcome.

In fact, there is no basis for either assumption, as there are literally
an infinite number of variations to arm length that can be applied that
will also account for the equal time intervals.

For example

Let L2 = L_o sqrt gamma
Let L1 = L_o/sqrt gamma

Thus by substitution into the required

L2/L1 = gamma

we get

L_o sqrt gamma/(L_o/sqrt gamma) = gamma

Which is necessarily also true.

And thus we find by several such arbitrary manipulations to length, that
we can arbitrarily alter the length of either arm and still provide for
the MM results by simply making the necessary alteration to the other
arm's length.

In short for any values of L2 and L1, there are values of p and q that
render the following equation true,

L2 p/L1 q = gamma

From which follows that we can draw no valid conclusions from a
geometric analysis of the MM experiment based upon the premise of
constant light speed wrt proper frame. The experiment was quite
worthless.

In short, the MM proved absolutely nothing that was useful, period.

Richard Perry

http://www.cswnet.com/~rper
Electromagnetism: First Principles