Re: Experimental verification of the relativity theory

[Ken Caviness <caviness@SOUTHERN.EDU>]

Pentcho Valev wrote:

> John Mallinckrodt wrote:
>
> > Pentcho offers a valuable parable from the history of thermodynamics
> > which, in essence, is a nice illustration that one cannot use the
> > true statement, A => B, to reach any conclusion about the truth of
> > its converse, B => A.
> >
> > That is precisely why I was so careful to say that the spectacular
> > agreement of the predictions of special relativity with every
> > experiment that has been
> > performed "give us such enormous confidence in" (rather than "prove")
> > the primary postulate.
> >
> > There is a critically  important aesthetic aspect of science at work
> > here.  We NEVER "prove" ANYTHING about WHY the real world does what
> > it does in an experimental science like physics.  Instead, we seek
> > "simple" models of reality that have "wide ranges of applicability"
> > and that make new, hopefully counterintuitive or previously
> > unsuspected predictions.   Thus, the attractiveness of a premise is
> > in some direct proportion to 1) its simplicity, 2) the range of
> > physical phenomena it "explains", and 3) the degree to which its
> > validated predictions run counter to our previous intuitions.
> >
> > Judged by these criteria, the primary premise of special relativity
> > looks like a very serious winner!
>
> Let me disagree. We have in fact two initial premises (axioms) and the
> alleged corollary, Lorentz equations. In which cases the corollary is NOT
> really a corollary and if it is not, what are the implications? An
> obvious case is one in which there is another (third) initial premise
> which has remained hidden for some reason.
...
> since some time ago we found a third premise in the relativity
> theory (Ken called it "wild"), Lorentz equations are NOT a corollary of
> Einstein's two initial premises.

As mentioned, I did not remember previously seeing the 3rd premise you
quoted.  The phrasing still seems very odd to me.  But the supposition
of local linearity, added to Einstein's 2 premises, does allow us to
derive the Lorentz transformation.  You seem to be avoiding that point.

> The implication is that experimental
> verification of Lorentz equations can tell us nothing about the two
> axioms.

No.  Now your logic is faulty.  You have pointed out that whatever
additional assumptions are needed in deriving the Lorentz transformation
from Einstein's postulates, the converse can be done (B->A).  In fact,
it's simple algebra to show that if the Lorentz equations are used, any
speed measured as c in one inertial frame will also be measured as c in
all other inertial frames.  As John Mallinckrodt writes, experimental
verification of the predictions of the Lorentz equations gives us a high
degree of confidence in them, and then by your own admission we must
accept Einstein's "postulate" of the constancy of the speed of light.
In this view it's a result of the experimental model, but reliable none
the less.  And in physics, if something is invariant, it usually has
some fundamental importance, which may only be brought into view when
the theory is restructured.  It is this that Einstein did in 1905, not
coming up with any new equations (Lorentz derived them earlier) but
revolutionizing science by starting with the constancy of the speed of
light (actually an extension of the principle of inertia so productively
used by Gallileo and Newton, that uniform motion and rest are
indistinguishable).

> Lorentz equations are not a corollary of the two axioms not only because
> there is a third axiom - there are other logical flaws.

No.  At least no flaw has been pointed out so far in this thread.  ;-)
But as with all scientific models, relativity is only an approximation
with a range of applicability.  It fails at the level where quantum
effects become significant, for example.

But that's not the point now.  Your thought experiment seemed
paradoxical, but closer examination showed that relativity correctly
applied passes with flying colors (again).  Note:  the number of
apparent paradoxes which turn out to be explained by relativity is
another indication that it is reliable, or at least the future theories
will likely inherit many of the features of relativity.

> I would like to
> call the attention to the fact that, in a deductive theory, experimental
> verification has only minor importance. 95% of the importance should be
> attributed to the validity of the arguments, and here the situation is
> deplorable. Apart from the problem you raise at the beginning of your
> text above, there are countless others. Nobody seems to know the
> relations between the statements "if...then....",  "if and only if...
> then....",  "A if a sufficient (but not necessary) condition for B",  "A
> is a necessary (but not sufficient) condition for B" etc. etc. And these
> are only the elementary aplications of logic in physical sciences - in a
> deductive theory, the logical complexity is much greater.
>
> Pentcho

In _science_, agreement with experimental results is far more important
than the "beauty" of the original premises used in constructing a
model.  But I certainly agree that, given a set of premises one must
very carefully indicate what results logically follow.  Having taken a
lot of graduate mathematics and having taught almost as much math as
physics, I'm perhaps more sensitive to this than some, but I strongly
doubt your statement that "nobody seems to" understand basic logical
implications.  That's pretty basic fodder for physicists.

I must close, tests to grade, miles to go before I sleep.  But I suggest
before you consign relativity to the trash-heap you consider the
experimental results, such as:  time-dilation/distance-contraction for
cosmic-ray generated muons in the upper atmosphere, time dilation
effects in GPS, relativistic mass increase of high speed particles in
accelerators, measurement of relativistic doppler shift, etc.  Then
there are verifications of general relativity: precession of the
perihelion of Mercury's orbit, aberration of starlight passing by the
sun during a solar eclipse, gravitational redshift, etc.  (Note that
special relativity can be derived from the equations of GR as a
first-order approximation in the absence of large masses, so
confirmation of GR validates the usefulness of SR, too.)

I applaud your effort to precisely pin down a set of necessary and
sufficient premises to derive the Lorentz transformation.  But don't
fall in love with a model that disagrees with relativity.  Odds are that
any such model has already been experimentally disproven.

Ken Caviness