[ExI] Problems with Special Relativity

[scerir]

Good points Lee.
Time is short now, but I try to answer something here,
and maybe something later.

[Lee]
But an analogous *pedagogical* situation would be to say
to a student trying to master Newtonian Mechanics,
"of course, there are discrepancies, and so you perhaps
should not spend a whole lot of time trying to understand
things like the formulas for centripetal acceleration,
Newton's proof that a sphere of material behaves as though
its mass were concentrated at one point, and so on."
It seems to me very important to try to understand what
a theory is *saying* before focusing very much attention
on not-well-understood subtleties. For example, I believe
that were I to just shut out all these questions and
conceptual difficulties you're bringing up *while* I am
thinking of the various well-known paradoxes, I should try
to remain completely inside the SR theory, and endeavor
to understand it on its own terms.

------

How to teach SR and how to learn SR are interesting subjects
indeed.
John Bell writes [1]:
"The approach of Einstein differs from that of Lorentz in two
major ways. There is a difference of philosophy, and a difference
of style.
  The difference of philosophy is this. Since it is experimentally
impossible to say which of two uniformly moving systems is *really*
at rest, Einstein declares the notions "really resting" and "really
moving" as meaningless. For him only the *relative* motion of two
or more uniformly moving objects is real. Lorentz, on the other
hand, preferred the view that there is indeed a state of *real*
rest, defined by the "aether", even though the laws of physics
conspire to prevent us identifying it experimentally. The facts
of physics do not oblige us to accept one philosophy rather than
the other.  And we need not accept Lorentz's philosophy to accept
Lorentzian pedagogy. Its special merit is to drive home the lesson
that the laws of physics in any *one* reference frame account for
all physical phenomena, including the observations of moving
observers. And it is often simpler to work in a single frame,
rather than to hurry after each moving object in turn.
  The difference of style is that instead of inferring the
experience of moving observers from known and conjectured laws of
physics, Eintein starts from the *hypothesis* that the laws will
look the same to all observers in uniform motion. This permits
a very concise and elegant formulation of the theory, as often
happens when one big assumption can be made to cover several
less big ones. There is no intention here to make any reservation
whatever about the power and the precision of Einstein's approach.
But in my opinion there is also something to be said for taking
students along the road made by Fitzgerald, Larmor, Lorentz and
Poincaré. The longer road sometimes gives more familiarity with
the country."

In my opinion what Bell is saying is more than reasonable.
SR does not seem to me to explain things in the proper,
physical ways. It seems to me there is too much conventional
stuff.

I suggest this example, which is - not by chance - an
elaboration of Bell's spaceships paradox.

Two twins, Alice and Bob, plan a journey that involves
accelerating from their home inertial frame S into a new
inertial frame S', moving at speed v.
They use identical spaceships, each containing exactly
the same amount of fuel, and parked on the x axis of their
home reference frame S, separated by a distance L.
They synchronize the clocks in their spaceships with a clock
which remains in home reference frame S.
They start their engines, at the same time (this is easy and
possible) and both accelerate off to the right along the x axis.
After using all their fuel in the same amount of time, both
spaceships have reached the speed v, and are travelling inertially
in the new reference frame S'.
Alice and Bob know that their accelerations (I would say:
their dynamics) were identical.

There are, at this point, these possibilities.

1) Alice and Bob, knowing that their dynamics were
IDENTICAL, think and believe that the clocks inside their
spaceships registered the same time (since the start),
and that they have the same age. What they think seems,
from a logical point of view, and perhaps from a natural
(nature's choice) point of view, completely reasonable
and true.

2) Alice and Bob this time unfortunately know SR.
Their thinking is then counterintuitive. Despite of
the fact that they experienced the SAME dynamics they
know that their pre-synchronized clocks went out of
synchrony during their travel. Quantitatively this
de-synchronization turns out to be (from Lorentz Transf.)
  dt = - gamma v L / c^2 (in reference frame S')
  where gamma = (1 - v^2/c^2)^-1/2
  L = the initial distance between the spaceships
  c = light velocity
  v = (inertial) velocity of reference frame S' over S.
Obviously the above de-synchronization corresponds
to a differential aging of the twins. (It is perhaps
uncertain if they can read different times on
their pre-synchronized clocks or if they can read
different times on their clocks only when their clocks
are re-synchronized.)

[1] John Bell, 'How to Teach Special Relativity', in
'Progress in Scientific Culture', vol.1, n.2, Summer 1978.