I have a question about a thought experiment.

Suppose I have an inertial frame of reference, labelled A.  I'll
consider this my "stationary" perspective.

Passing by A is frame of reference called B, where B is travelling at
c.  Any observations made from A will see objects in B flattened.  My
understanding is that an entire universe could be in B.  Observations
from A would see B containing enourmous area, but with no thickness.

My question then relates to another frame of reference which I'll call
B'.  This frame of reference is also travelling at c, and in the same
direction as B.  However, B' is some distance behind B.  Both B and B'
can be seen from A, and they both appear flattened.  However, they
both contain an entire universe, and should be incapable of seeing
each other.

Flipping the perspective around... imagine that WE are in B.  Then
there is some frame of reference called A which is travelling at c,
and that frame of reference sees us as a flat universe.  That same
frame of reference can also see another flat universe, called B',
travelling along behind us, but completely inaccessible to us.  In
fact, when viewing the current universe from a passing frame of
reference at velocity c, there would be an infinite number of flat
universes, all parallel to this one.

It can be seen here that the frame A does not need any occupants for
this to hold.  It simply provides the perspective for identifying B
and B', and any other frames parallel to them.

Is this conjecture sound?  Where can I go to see a discussion on this please?

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Request for Question Clarification by hedgie-ga on 17 Jan 2006 16:06 PST

Most of the reasoning and terminology makes sense, but

 "entire universe could be in B" 

 sounds like B is a box. It is not a box and there is only one universe,
 per definition. Let's say you mean some big structure, like a galaxy.
 (They used to  call them 'island universes' in the olden times).

 So you have big object at center of B and another at center of B',
 and they  look like two pancakes to an observer at A. 

 Object B is at rest relative to B' and and I see no reason for saying 
 that  object at B is completely inaccessible to observers at B'.

 Objects B and B' look like pancake to observer at A, just as Milky Way and
 Andromeda look like two thin pancakes to a hypotetical observer living
 near to what we consider 'event horizon', in a galaxy moving with near speed 
 of the light relative to us.

Sp what is that conjecture again?

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Clarification of Question by quoll-ga on 18 Jan 2006 15:58 PST

You said that the two boxes look like two pancakes to an observer in
A.  But the boxes are boxes in space, and they are separated by space,
so there is a third larger box which contains those two boxes. 
Wouldn't this larger box also get compressed down to a pancake?  By
induction, that would mean an entire universe would compress down to a
pancake. (Unless the rules change in some way for intergalactic
distances?)

My point is that no matter how large a box you consider, it always
ends up in the one "pancake" to an observer in A (I call that pancake
"B").  But this observer would be capable of seeing another pancake
(B') that is separate from the first.  Since every part of space can
be compressed into B (as above), then the contents of B' must be
separated from the contents of B by something other than 3D space. 
(I'm guessing that the dimension is time, and I have reason to suggest
that, but Google asks that we keep the scope of individual questions
down).

Reading my earlier question, a conjecture wasn't defined, sorry.

The conjecture is that relativity can be used to show an infinite
number of parallel universes, with the separation between the
universes being a dimension other than space.  Is there a flaw in the
reasoning (and hence my understanding of relativity)?  Are there areas
on the net where this sort of thing is discussed.

(My area of expertise is quantum physics, not relativity, and I'd like
to learn more about GR)

quoll-ga

 Regarding  

 "Are there areas on the net where this sort of thing is discussed?"

These should be useful:

To discuss:
http://groups.google.com/group/sci.physics.research?lnk=li

 These are expert debates, so I suggest you do not use fuzzy concept like
 'parrallel universe' out of context of the Everett Interpretation of
QM,  without defining it first.

To learn more:
http://relativity.livingreviews.org/


Regarding: "Is there a flaw in

The conjecture is that relativity can be used to show an infinite
number of parallel universes, with the separation between the
universes being a dimension other than space"

 Yes. 1) Separation in Relativity is not 'in space' or 'time' but is
measured by Minkowski Metrics:
http://mathworld.wolfram.com/MinkowskiMetric.html
http://www.theory.caltech.edu/people/patricia/grela.html

      2) It is necessary to differentiated between 'B looks like a pancake' 
(to A but not to B) and 'is a pancake' . The 'is' is reserved for invariant
 concepts (such as Minkowski distance, see 1)

 In summary: There are events E1 E2.. which are 'out of the light cone' of other
events F1, F2, and so not acessible to them.
Reference to Light Coness:
" That is to say, "all observers will universally agree on the Light
Cones at each event..".
http://www.phy.syr.edu/courses/modules/LIGHTCONE/minkowski.html


 So, there are parts of our universe which we 'cannot see' or communicate with. 
 These are not  called 'parallel or separate universes' in GTR.

One can speculate on topology of this universe,
 (seen as a curved surface in n-dimensional space, connected or not) 
http://www.answers.com/topic/connected-space

and such speculation becomes interesting when connected to or related to some
experimental data.

 The possibility of 'complex topology' of universe

http://en.wikipedia.org/wiki/Topology_of_the_universe

is already present in GTR and Riemann Space
http://en.wikipedia.org/wiki/Differential_topology
http://mathworld.wolfram.com/RiemannSpace.html

Hedgie

This would be sound, were it not for the fact that if this "universe"
contained anything, it would have mass and thus could not be traveling
at the speed of light relative to frame A. Only objects with zero rest
mass (like the photon) can travel at the speed of light.

Note that I was careful not to mention the frame of reference for A
containing anything.  Since I suggest putting "us" into frame B, then
A necessarily can't contain anything.

However, I believe that it is still possible to look at B and B' from
a frame like A, which is travelling at c relative to them.  As I
suggested, frame A gives us a way of looking at both B and B', even
though there is no way for B and B' to see each other.

Maybe it's not possible to look at the "mass-filled" B from A, since
any energy calculations done from that frame of reference give
infinite values.  But I don't *think* it invalidates anything I've
mentioned, so my question still stands.

Quoll,

I don't see any flaws in your argument, it just seems more elaborate
than it needs to be. You are certainly free to postulate that another
universe follows ours infinitely removed in time, but completely
disconnected from us. You can do this with or without the theory of
relativity, although it might get more interesting if you through in
General Relativity. Keep thinking about it. Einstein's original
insights about relativity came from thinking about what it would look
like if you could travel with a light wave.

typeo: through -> throw

typo: typeo -> typo

(I'd better quit editing now)

Hi quoll,

It's an interesting situation to think about, but I think some aspects
of your conjecture are incorrect, or at least not well defined.

I think the main point of confusion is that you may have missed the
point that just because B and B' are both travelling at c with respect
to A doesn't mean we know anything about how B and B' appear to each
other. For example, B and B' could be stationary with respect to each
other, in which case they'd certainly appear to be the same to A but
would not be separated.

But a little contemplation of the relativistic velocity addition
formula should point out to you that exactly the same thing will be
true if B' is moving relative to B at any velocity short of c - it is
a well known result that if one component velocity is c and the other
is not -c, the result is c. So the mere condition that B and B' both
have velocity c with respect to A doesn't tell us anything about their
relative velocities.

In addition, I'm not really sure how valid it is to actually define a
pair of reference frames with relative velocity c. All the
transformation equations develop singularities if you do that, so I
don't think you can really say exactly what would happen - just
because at successively higher speeds the other object will look more
and more squashed does not imply that "at c" the object will look
infinitely squashed. In particular, I don't think you can consider one
frame to be inertial when looking from the other.

A final note - I don't think it's a good idea to think of this in
terms of separate universes. Instead, think of separate slices of our
own universe. This is more accurate. Remember that every photon that
hits your eyes is travelling at velocity c relative to you, and if you
look at two photons from the same source you will have a situation
much like what you proposed. How do the photons appear to each other?
I don't think you can answer that question, because neither can ever
see the other. Does that mean they are not in the same universe?
Certainly not as far as we're concerned.

Don't let me discourage you, though. It is an interesting scenario to
think about. It's just that I don't think we can say much sensibly
about it, because the theory basically doesn't say anything about what
happens when your target frame is moving at c with respect to your
source frame.