Re: ABSOLUTE TRUTH ABOUT ABSOLUTE SPACETIME

From: J.J. (nospam_at_nospam.com)
Date: 06/26/04 

Date: Sat, 26 Jun 2004 17:34:34 GMT

"Perfectly Innocent" <perfectlyInnocent@as-if.com> wrote in message
news:c45b45b3.0406260712.7e39082c@posting.google.com...
> Correction:
>
> "J.J." <nospam@nospam.com> wrote in message
news:<bmECc.110733$0y.63662@attbi_s03>...
> > "Perfectly Innocent" <perfectlyInnocent@as-if.com> wrote in message
> > news:c45b45b3.0406232153.2e353f45@posting.google.com...
> >
> > The way we choose to synchronize clocks has no effect on physical
phenomena.
> > It does, however, affect the form of the equations that we use to
describe
> > phenomena. As I see it, your synchronization scheme would lead to
> > frame-dependent, complicated equations for expressing the laws of
physics.
> > Take the one-dimensional wave equation
> >
> > (D_tt - D_xx) u(x,t) = 0.
> >
> > Let's assume that this expresses the propagation of a longitudinal pulse
on
> > a slinky in the preferred frame of the SxR spacetime. Now consider a
slinky
> > in another inertial frame. What would the wave equation look like in
this
> > frame if one adopted your synchronization scheme?
>
> I'm trying to prove an existence and uniqueness theorem. Are you
> trying to turn my theorem into a debate about arbitrary conventions,
> like the metric system verses British pounds, inches and acres?
>

I'm just pointing out the important fact that if all inertial frames define
time according to your global synchronization scheme, then the mathematical
expression of very simple laws of nature will look unduly complicated in all
but the preferred frame. I think this is important. SR is more than just a
theory about adopting some clock synchronization. It's about dynamics -
mass, momentum, energy, electrodynamics, etc. E-synching clocks allows the
dynamical laws to be expressed in the simplest form - a form which is the
same for all inertial observers.

> > > There is only one physically distinguished, globally applicable
> > > definition of simultaneity for SxR.
> >
> > But, I don't see much use for this definition of simultaneity.
>
> Do you see any logic that prohibits me from connecting simultaneity
> with "cosmic time" and choosing the only physically distinguished,
> globally applicable definition of simultaneity, to prove theorems
> about simultaneity?
>

As I see it, you could do the same thing in R^3 x R by arbitrarily choosing
one inertial frame as 'preferred' and forcing all other frames to
synchronize their clocks using your scheme. All inertial frames would then
agree as to whether or not two events were simultaneous. Logic doesn't
prevent this nor would it prevent proving some mathematical theorems based
on this synchronization. But I don't see this as having much value other
than as a mathematical exercise.

> > > Ah, but the problem is that the occupants of any other frame can't
> > > E-synchronize all their clocks so that all the clocks of that frame
> > > are synchronized. They must resort to S-synchronization to achieve
> > > total global synchronization.
> >
> > That's true. But why should so much importance be given to global
> > synchronization? What is the physical significance of whether or
> > not two events are simultaneous according to global synchronization.
>
> Perhaps we need to backtrack a bit and take a careful look at your
> questions in the context of an ordinary Newtonian universe, governed
> by Galilean spacetime. How do you answer your own questions in that
> familiar context?
>

In Galilean spacetime, it is assumed that there is only one 'time' (up to an
arbitrary choice of zero time and arbitrary choice of scale factor).
Synchronized clocks were assumed to display this absolute time. All
observers agree as to whether or not two events are simultaneous. The
physical significance is that if two events are not simultaneous according
to synchronized clocks, then in principle the events could be causally
connected (as it was assumed that there is no upper speed limit for
signals).

In SR there is no way to synchronize clocks so that simultaneity (or lack of
simultaneity) has this significance. This includes SxR.

Now I repeat my question (for you to answer, please). What is the physical
significance of whether or not two events are simultaneous according to your
global synchronization scheme in SxR?

> > Why would any
> > inertial frame choose global synchronization if it leads to unduly
> > complicated mathematical equations for simple phenomena?
> > Personally, I would much prefer locally E-synched clocks.
>
> Global questions require global definitions. Why do you believe that
> personal preferences and ease of computation is a determining factor
> that somehow obliterates cosmic time?
>

Please give a specific example of a global question that *requires* a
'global definition' to answer. Show me the significance of your 'cosmic
time' that would make me want to give up ease of computation and to give up
the ability to express dynamical laws in the same simple form for all
inertial frames.

> > > Also, you still misunderstand the PofR.
> > >
> > Please elaborate.
>
> I interpret the PofR as a law of physics. That requires a minor
> adjustment in semantics from the way it's usually described. If you
> think about it, the statement that "the laws of nature require the
> same mathematical form in all local inertial frames" literally implies
> that "the laws of physics demand that clocks be synchronized." I have
> an amusing thread on that idea in the google archives for
> sci.physics.relativity titled, oddly enough, "Do the Laws of Physics
> Demand that Clocks be Synchronized?" :-)
>
> See http://www.everythingimportant.org/viewtopic.php?t=221 for the
> highlights.
>

As an inhabitant of an inertial reference frame, I can set my clocks anyway
I want. Suppose I choose a 'crazy' way to do this. Now, in principle I
can express any law of physics in terms of my crazy time. The mathematical
form of the law will surely be messy. However, if all other inertial frames
choose the same crazy method for setting their clocks, then they will find
that the same law will have the same (messy) mathematical form. In my
opinion, this is the physical content of the PoR. The laws of physics have
the same mathematical form in all inertial frames (as long as they set their
clocks in the same way.) If you choose the Einstein synchronization, then
the laws will assume their simplest form.

Your global synchronization scheme forces each inertial frame to adopt a
different prescription for synchronizing clocks. So, of course, the
mathematical expressions of the laws of nature will no longer have the same
form in each frame. (Did you express the slinky wave equation in an
arbitrary frame using your global time?) This is certainly a heavy price to
pay. I keep coming back to the same question. What's the payoff? What do
all these inertial frames gain by setting their clocks your way that would
more than offset the confusion and inconvenience that results from giving up
the mathematical invariance of the physical laws?

> > > > The poor student trying to learn SR is likely to find the SxR
spacetime
> > > > more confusing than enlightening. If introducing an absolute time
in
> > > > the SxR spacetime were really useful, then why don't people
introduce
> > > > an absolute time in the usually assumed topology R^3 x R?
> > >
> > > People do. They've done it.
> >
> > That's interesting. Can you give me a specific reference?
>
> http://arxiv.org/PS_cache/hep-th/pdf/0207/0207042.pdf
>
> Please see the Ives-Tangherlini formulae on the bottom of page 2.
>

I'm not able to understand the significance of this paper (my fault,
conceded) nor it's relevance to the question of the pedagogical value of
discussing global synchronization in SxR for teaching SR to beginning
students. Note that the author of the paper states in the abstract that

    'In the framework of brane models the postulates of
     special relativity theory is revised. It is assumed
     that there exists preferred frame and relativity
     principle is violated on the brane.'

If clarification of SR for beginning students can be achieved by having them
consider such models in which the postulates of SR are revised and the
principle of relativity is violated, then that would be great. In my
opinion, beginning students are more likely to find confusion rather than
enlightenment in this approach. I would like to be proved wrong.

> > Is this done in
> > any introductory text as a pedagogical aid to understanding SR?
>
> It's only a matter of time.
>
> > > I believe it brings clarity. The way to think of it is that the PofR
> > > would apply locally to one class of physical law but other laws could
> > > be allowed that operate differently but consistently.
> >
> > I guess we will just have to disagree as to what brings clarity. I
can't
> > see the clarity that arises from splitting the physical laws into
classes
> > this way. Could you elaborate on what you mean by laws that operate
> > differently but consistently? A specific example would be helpful.
>
> "It is popularly believed that there is some strange disparity between
> quantum physics and physics generally, that whereas ordinary physical
> interaction takes time to travel, at speeds up to the finite limit c,
> quantum interaction (action-at-a-distance) is instantaneous,
> regardless of distance." The clarity that SxR brings to this backwater
> debate on quantum mechanics is that it's easily conceivable that
> light-speed EM forces and unknown instantaneous action-at-a-distance
> forces coexist simultaneously in the same universe. Physicists who
> reject David Bohm's theory on the basis of SR causality need to
> discard their invalid arguments and learn SxR.
>
> There really isn't any instantaneous quantum interaction propagating
> anywhere, at least I don't believe there is, but google whips up 633
> hits for +instantaneous +"action at a distance" +Bohm. Is there
> anything improper about me pointing out that physicists are using
> faulty arguments in their debates?
>

Many students taking their first course in SR haven't even learned standard
QM yet, and they're certainly not familiar with 'backwater debates' and
speculations regarding coexistence of light-speed EM forces and
instantaneous action-at-a-distance forces.

> Identical experiments can be performed in different "inertial frames
> of reference," each yielding dissimilar outcomes. I can't imagine
> what's so difficult about the example I've already published:
> http://www.everythingimportant.org/viewtopic.php?p=1949#1949
> We may call the structure and results of this kind of phenomena a
> category II law of physics. I've explained the structure of this law
> in great detail.
>

I don't need 'cosmic time' to tell me that light takes a different time
interval to circumnavigate SxR in one direction compared to the other (in an
arbitrary frame). I just need one clock and a light source. I don't need
globally synchronized clocks.

> We may also take it as an axiom whether or not superluminal signaling
> exists in SxR. We can build any consistent FTL theory we prefer. It's
> like the Axiom of Choice. Assuming that the Axiom of Choice is true
> doesn't contradict ZF set theory, provided that ZF set theory is
> consistent without the Axiom of Choice. Likewise, assuming that the
> Axiom of Choice is false leads to no contradictions in ZF set theory.
> The Axiom of Choice, then, is independent of all the other axioms of
> ZF set theory. The only concern for a mathematician is mathematical
> consistency, and the logical implications of reasonable axioms.
>

Sorry, I fail to see how all this helps students learn SR.

> > Some students might enjoy thinking about these things quite early on.
But,
> > my feelings are that the average beginning student is not going to
profit
> > from it and is likely to find it confusing. It would be interesting to
see
> > an outline of a set of lectures that incorporates SxR that you would
present
> > to students who are learning SR for the first time.
>
> First I'd begin with my derivation of the Lorentz transformation from
> a Galilean synchronization:
>
> x'=x-uT
> T'=T
>
> http://www.everythingimportant.org/relativity
>
> Then I'd go through my second derivation of the Lorentz
> transformation, which completely bypasses the use of Einstein's
> bungled relativity principle and the notion of groups. It needs,
> primarily, the SxR topology and the Galilean transformation:
> http://www.everythingimportant.org/relativity/simultaneity.htm
>

Can you concisely pinpoint where Einstein 'bungles' the relativity
principle? In your opinion, is there a 'relativity principle'? If so, can
you state it in one or two clear sentences?

> At this point I would assign an extraordinary exercise:
>
> Without cheating by resetting clocks to make the computations trivial,
> use the transformation equations for SxR:
>
> x'=Y(v)(x-vt)
> t'=t/Y(v)
>
> Y(v)=1/sqrt(1-v^2/c^2)
>
> Compute the outcome to the following experiment in an arbitrary moving
> frame. (This to me is a delightful curiosity). Suppose you have two
> synchronized clocks side-by-side and slowly transport one of them to
> any convenient distance D and then measure the speed of light, i.e.,
> D/(t2-t1). Prove that the measured value will be c. (t1 is the time on
> the stationary clock when the light pulse is sent. t2 is the time when
> the light arrives as measured by the slowly transported clock. Take
> the limit of ultraslow transport for a perfect answer of c).
>
> Try this problem. It's amazingly enjoyable!
>

I don't see this as a curiosity. It's widely known that if you very slowly
move clocks from a common point in an inertial frame, then the clocks will
end up Esynched. Therefore, the speed of light will be c as measured by
these clocks. You don't need your global 'cosmic time' nor your particular
transformation equations in order to deduce this (even in SxR).

> Also, let me know if you can do the exercises and construct a full
> proof of the claims made on this page:
>
> http://www.everythingimportant.org/relativity/generalized.htm
>
> Two-dimensional gravity (everything you need to know about the metric
>
> ds^2 = f(x)dt^2 -dx^2
>

I'm more interested in staying on topic. My original post was to question
the pedagogical value of SxR in teaching SR. I'm trying to stay with that.
I want to know the pedagogical value of using SxR to teach SR to beginning
students. I want to know the physical significance of your 'cosmic time'.
I want to know why inertial frames would prefer to give up locally Esynched
clocks (that make dynamical laws have a simple mathematical form) in favor
of 'cosmic time'. I want to know how 'cosmic time' is going to clarify SR
for beginners - especially, how is 'cosmic time' going to be helpful in
expressing the dynamical laws of physics in an arbitrarily chosen inertial
frame?

J.J.

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