[ExI] Problems with Special Relativity

[Lee Corbin]

Serafino writes (From: "scerir" <scerir at libero.it> Sent: Saturday, August 09, 2008 9:45 AM)

> After 100 years there are still uncertainties, conceptual
> uncertainties in SR.

Perhaps. 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.

Then *later*, with another part of my mind, in a different mood
perhaps, attend to:

>  (The solution of these conceptual difficulties may also
> solve, at least partially, the conceptual divergence between
> SR and QT?)

I understood, of course, that there is an enormous clash
between General Relativity and QT, but about SR and QT?
I thought Dirac successfully extended SR to quantum theory.

> The first question might be: Is there too much relativism
> in SR [1]? The second might be: Is it correct to say that,
> according to SR, one-way velocities are devoid of physical
> interest [2][3]?

For [2] you give as reference "A.Einstein, "Relativity, The Special,
The General Theory", Methuen, London, 1920, see page 18.
A similar statement also by H.Poincarè."

Well, I read that Einstein passage, entitled "VII  The Apparent
Incompatibility of the Law of Propagation of Light with the Principle
of Relativity", and he shows there that the *Galilean* relativity is indeed
incompatible, and he goes on to say that in reality, however, a new
theory, that he is going to introduce in chapter VIII called "Special
Relativity", is "a logically rigid theory [that] can be arrived at".

Place the phrase "Prominent theoretical physicists were therefore"
in Google search, and it takes one to pages in "The Tests of Time"
that has most of section VII, including the page 18 you refer to.
Page 18 has the simple equation w = c - v, for reference. Einstein
at this point is merely introducing the whole thing to a beginning reader.

> The third might be: Given that SR define a "relative" simultaneity
> is it possible to define an "absolute" simultaneity [4]?

It seems to me that perhaps, yes, this is the case, for one
case I know of.  Let's stipulate that all velocities are to be
brought to zero relative to the CMB, then why not? Say
you are somewhere between the galaxies and so am I,
a mere what? 1 light year?  I don't know the physics, but
there has to be some minimal separation between us so
that we may both be at rest wrt the CMB, and yet be---
not "moving" exactly, relative to each other--- but merely
noticing that over small intervals of time there is becoming
more space between us because of the expansion of
the universe.

In such a circumstance, it should be possible for us to
calibrate our clocks based upon signals from someone
exactly half way between us who is also at rest with
respect to the CMB. Is this what you could be getting
at? Otherwise, I have no idea of what anyone could
be thinking of, in terms of establishing "absolute"
simultaneity. It's no longer a concept easily graspable
by me.

> One-way velocities are rather natural properties of physical
> objects - like photons going from a point to another point.
> It seems strange, or maybe paradoxical, that one-way velocities
> are not reflected in the conceptual basis of a theory. Even in
> the conceptual basis of an operational theory like SR.

I have no idea what you mean by "one-way velocities",
though you do say in your footnote

> [3] One could also say that one-way velocity of light
>    has never been measured, since SR assumes one clock
>    and a mirror and ... a two-way velocity of light.
>    (To measure a one-way velocity it is usually said one
>    would need two clocks, and they have to be synchronised,
>    and again synchronisation is a tricky concept and a
>    conventional choice in SR. I do not think this is correct
>    anymore.)

>From my understanding of what I read in Taylor and Wheeler's very fine
book "Spacetime Physics"
http://www.amazon.com/Spacetime-Physics-Edwin-F-Taylor/dp/0716723271
there is no conceptual problem at all in setting up synchronization. I think that
all elementary SR books go into that. Furthermore, in the book "Gravitation and Intertia"
http://www.indiaplaza.in/books/science/0691033234/all/gravitation-and-inertia.htm
sadly out of print in the West (!), Wheeler and Ciufolini even manage to do in it
General Relativity.

> But there are different, or more general approaches [5].
> According to which the usual SR is just an important, special
> case of a broader class of theories. These theories are also
> consistent with the existent experimental results. The usual
> Lorentz Transformations are just an important but special case
> of a broader class of transformations, sometimes called Equivalent
> Transformations (and among them the Inertial Transformations).
> The Equivalent Transformations contain a free parameter reflecting
> the well-known clock synchronisation conceptual arbitrariness.

Do explain. As I described above for the special case of no motion
with respect to CMB, whenever there is no relative motion just inside
the Special Theory of Relativity, you and someone else get your
clock signals from someone halfway between you who is also
not moving relative to you.  (Actually, just the two of you can do
it with a slightly more complicated protocol, as of course you
know, if you send several signals back and forth). Why is this
problematic?

> Lorentz Transformations are recovered for a particular value
> of that parameter. Actually all performed SR experiments
> (Michelson, aberration, etc.) seem to be insensitive to the
> choice of that parameter.
>
> Two points somehow relevant here (since we are discussing the
> Bell's spaceships paradox).
> - The length of a moving rod can only be obtained by marking
> the simultaneous position of its both end points. Therefore it
> depends on the definition of simultaneity of (distant) events.

Which I thought was easily explained in elementary texts.
(Thanks to your reminder, I retract any wrong impressions
I've given people about simultaneity being entirely a useless
concept;  it's merely entirely useless and meaningless---
according to traditional SR---only if there is relative
velocity between observers.)  The length is measured
by using rods and clocks at rest with respect to each other,
as, again, of course you know.

> A theory which defines the "absolute" (and not the relative)
> simultaneity of distant events would help a lot!

And then SR would be flat wrong. We really have evidence
of that?

I'll reply to the remainder of your post in another thread.

Best regards,
Lee

> - Imagine Bell's spaceships, and their dynamics exactly as in
> that paradox. Imagine each spaceship has its own clock,
> synchronised with a clock on Earth. We can say that, since
> spaceship A and B have at every instant of time exactly the
> same velocity, their clocks accumulate exactly the same delay
> with respect to the clock on Earth. So two events simultaneous
> on Earth - taking place at points near which spaceships A & B
> are passing - must be simultaneous also for the travellers of
> A & B. We are facing here an "absolute" simultaneity which cannot
> be explained by Lorentz Transformations (but can be explained
> via Equivalent Transformations).
>
> Paradoxical aspects of SR sometimes may have something to do
> with the conceptual uncertainties of the theory.
>
> [1] The best source is this one (maybe). F. Selleri (ed.),
>    "Open Questions in Relativistic Physics", Apeiron,
>    Montreal, 1998.
> [2] A.Einstein, "Relativity, The Special, The General
>    Theory", Methuen, London, 1920, see page 18. A similar
>    statement also by H.Poincarè.
> [3] One could also say that one-way velocity of light
>    has never been measured, since SR assumes one clock
>    and a mirror and ... a two-way velocity of light.
>    (To measure a one-way velocity it is usually said one
>    would need two clocks, and they have to be synchronised,
>    and again synchronisation is a tricky concept and a
>    conventional choice in SR. I do not think this is correct
>    anymore.)
> [4] "Absolute simultaneity" does not mean "absolute time"!
> [5] Only to mention here papers by Reichenbach, Jammer,
>    Mansouri & Sexl (1977), Croca, Selleri, etc.