Inertia Itself

Albro Swift wrote:
 The equivalence of mass and energy is not a logically necessary
 consequence of the simple principles of special relativity.  It
 is, however, strongly suggested by those principles - one of the
 first (of many) examples of the remarkable heuristic power of
 Einstein's theory.

Ilja Schmelzer wrote:
 Lorentz ether theory suggests them too. At least as far as I remember,
 the interesting kinematical formulas have been in Poicare's paper too.

It is true that hints of mass-energy equivalence can be found in 
various places in classical physics, such as Maxwell's equations, and 
even moreso in the equations of Lorentz's theory.  In fact, Lorentz 
even stated (pre 1905) that the "electrical mass of a particle 
appears to increase with its velocity", and other people made similar 
observations.  Nevertheless, the discovery of mass-energy equivalence 
remains an excellent (perhaps the best) illustration of the superior 
heuristic power of relativity.  

It is sometimes said that the scientific content of Lorentz's theory 
(as corrected by Poincare) is more or less equivalent to the content 
of special relativity, and that the differences are only matters of 
interpretation...and therefore unimportant.  For example, some 
people consider it irrelevant whether we regard Lorentz's  t'  
parameter for a moving electron as a pseudo-time or "true" time.  
However, Lorentz himself came to understand the crucial significance
of this interpretive distinction, most particularly with regard to 
the consideration of issues such as the equivalence of mass and 
energy.  The thought that t' has exactly the same ontological status 
as any other t, and that therefore the planes of simultaneity for 
different reference frames all represent equally valid loci of "the 
world now" is a huge conceptual step, with new and profound HEURISTIC 
content.  

For example, this view makes possible the conception that INERTIA 
ITSELF is a manifestation of energy.  Notice that we're not speaking 
here of an object being progressively harder to accelerate as it 
pushes against the drag of the ether, nor are we talking about
the electric "handles" on a particle becoming weaker at higher
velocities, thereby making it harder to accelerate.  These were 
the kinds of notions Lorentz and others had in mind with regard 
to his "electrical mass", and these notions surely would never (and 
historically did not) lead to the thought that INERTIA ITSELF is 
actually a frame-dependent quality.  Without the "kinematic"
interpretation of relativity we could not seriously contemplate 
the actual equivalence of mass and energy.

Thus it is precisely the non-empirical interpretative content of 
relativity, according to which all inertial frames are truly
equivalent, that powerfully compells the mind to reconcile the 
equivalence and transmutability of entities and properties that 
were formerly seen as fundamentally unlike (e.g., time and 
space, E and B fields, mass and energy, etc.).  The old notion 
of absolute time, distinct from space, simply could not (and 
certainly did not) lead to such reconciliations, so it can hardly 
be disputed that relativity was the key to these advances in 
our understanding.



Albro Swift wrote:
 ...this view [relativity] makes possible the conception
 that inertia itself is a manifestation of energy.

Ilja Schmelzer wrote
 This view is always possible.

Mass-energy equivalence is conceptually coherent only if space
and time are actually frame-dependent and transmutable.  On this
basis it's clear that the actual inertia of a body increases
with its velocity, i.e., as our time axis diverges from the
proper time axis of the body.  However, if we believe in a unique
"true" time axis, then the body always has a "true" mass and
energy-momentum (projected along the "true" time and space
axes, respectively), so any changes we see in the tendancy to
accelerate cannot (by definition) be manifestations of inertia.
In other words, acceptance of those effects as inertia would
be tantamount to accepting the relativistic interpretation of
frame-dependence of space and time.

Remember that we're speaking here of interpretations and
heuristic, and in this context the perceptions/presumptions of
actuality versus appearance are crucial.  For example, as you
push an object faster through the air, it becomes harder to
accelerate, but we do not infer from this that the actual
inertia of the object is increasing.  We adhere to our belief
that the inertia of the object is fixed, and we understand
the increasing resistance to acceleration is due to the drag
of the ether (air).  The point is that we would be very
unlikely to proceed from this experience to some notion that
mass and energy are equivalent.  We can see that it's harder
to accelerate things as they go faster, but we don't consider
that to be a change in inertia itself.  It takes a very
profound and fundamental shift in our view of space and time
to regard an apparent change in inertia as "real" inertia,
thereby enabling us to identify it with the inertia of the
same object at rest, and infer that perhaps inertia and
energy are actually two manifestations of the same thing.


Ilja Schmelzer wrote
 indeed, without Einstein, based on Poincare, scientists would
 have searched for Lorentz-invariant formulas almost everywhere.

There's no need to phrase this in the conjectural tense.  
Einstein WAS a scientist who, based on Poincare, searched for 
Lorentz-invariance...and found it everywhere.  You would prefer 
that he had only found it ALMOST everywhere, but even if he had 
missed the obvious, it wouldn't have been long before someone 
else noticed it.  As Einstein said, the theory of special 
relativity was ripe for discovery in 1905.


Ilja Schmelzer  wrote
 The main part of relativity was done without this key by
 Poincare.  After Poincare, every part of physics would have 
 been reconsidered from point of view of this symmetry group, 
 with or without Einstein's theory.

After Poincare, every part of physics WAS reconsidered from 
the point of view of this symmetry group, and the result IS 
Einstein's theory.


Albro Swift wrote:
 Mass-energy equivalence is conceptually coherent only if space
 and time are actually frame-dependent and transmutable.  ... if 
 we believe in a unique "true" time axis, then ...any changes we 
 see in the tendancy to accelerate cannot (by definition) be 
 manifestations of inertia...  Acceptance of those effects as 
 inertia would be tantamount to accepting the relativistic 
 interpretation of frame-dependence of space and time.

Ilja Schmelzer wrote:
 Sorry, I don't bother if you like to "accept those effects as
 inertia".  If you feel better accepting this, fine for you.

Thanks.  I was actually a bit more ambitious, hoping not only to 
gain from you a dispensation for my views, but also to suggest
a lack of coherence in your views.  Let me try to condense the 
message still further:

  Complete mass-energy equivalence is logically incompatible 
  with the concept of absolute time.

This is the reason any "ether" theory can only incorporate
mass-energy equivalence in an entirely ad hoc and logically
incongruous way.  You can only achieve *complete* mass-energy
equivalence if the world is *completely* Lorentz-covariant,
and this completeness rules out any possibility of physical 
significance for the notion of absolute time.



Albro Swift wrote:
 ...as you push an object faster through the air, it becomes 
 harder to accelerate, but we do not infer from this that the 
 actual inertia of the object is increasing.  ...we understand
 the increasing resistance to acceleration is due to the drag
 of the ether (air).  The point is that we would be very
 unlikely to proceed from this experience to some notion that
 mass and energy are equivalent.

Ilja Schmelzer wrote:
 Because we have not observed the Lorentz symmetry in air 
 resistance.

The question at hand is how the resistance to acceleration of 
an object at rest is ontologically, not descriptively, related 
to the resistance to acceleration of an object in motion.  Your 
thesis is that they are ontologically utterly different, but 
that they just happen to be descriptively identical - or at 
least indistinguishable by any known method - and that this damn 
silly Einstein thoughtlessly jumped to the nitwit conclusion 
that they were ontologically the same, which immediately 
suggests complete mass-energy equivalence.  Then, to make matters 
worse, this unjustified prediction of complete equivalence was 
subsequently born out by observations, thus (seemingly) confirming 
Einstein's idiotic approach as one of the most spectacularly 
successfull theories in the history of human thought!


Albro Swift wrote:
 There's no need to phrase this in the conjectural tense.
 Einstein WAS a scientist who, based on Poincare, searched for
 Lorentz-invariance...and found it everywhere.

Ilja Schmelzer wrote:
 No, he has rejected parts of physics which are not Lorentz-
 invariant as not being part of physics.  This was a metaphysical 
 decision, based on positivism.  This was a popular methodology 
 1905, but since 1934 we have a better one, Popper's.

You're misinformed.  There are no (known) physical phenomena
that demonstrate a violation of Lorentz covariance.  (I know you
believe that EPR experiments demonstrate such a violation, but
your belief is founded on a highly questionable interpretation
that is neither necessary nor even very compelling.)  Also, 
as you can read about in almost any book on the philosophy of 
science written SINCE 1934, realtivity is NOT a positivist theory.
(Einstein tried positivism once in his youth, but he didn't 
inhale.)  


Albro Swift wrote:
 After Poincare, every part of physics WAS reconsidered from
 the point of view of this symmetry group, and the result IS
 Einstein's theory.

Ilja Schmelzer wrote:
 It could have been my ether theory as well.

Indeed it could, or any of a number of other equally unsatisfactory 
theories, which makes us appreciate relativity all the more.