| Author |
 Topic  |
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Eugene Shubert
Radio Wave
5 Posts |
 Posted - 02/25/2003 :
00:11:53      
What is an absolute frame of
reference? Does an absolute frame of reference exist for
(S^3)xR? What about SxR?
See http://www.everythingimportant.org/relativity/simultaneity.htm
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Integral
PF Mentor
USA
2657 Posts |
 Posted - 02/25/2003 :
00:27:38
An absolute frame of reference is one which is
stationary with respect to all movement. On the earth we use
the ground as an absolute frame of reference. All velocities
are measured with respect to the earth, which is considerd to
be stationary.
No such reference frame exists for the universe in
general.
__________________________
"A Physicist is an atom's
way of learning about atoms"
G. Wald
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alis
Radio Wave
USA
79 Posts |
Posted - 02/25/2003 :
03:31:54
As I understand it, an absolute frame of reference
would be a "preferred" frame of reference that all observers
can agree on. Ever since Galileo, we've generally assumed that
no such absolute frame for the universe exists -- eg all
frames are equally valid.
You can define a particular absolute frame on (S^3)xR if
you want, though there's no natural way to do so. This is
equivalent to picking a preferred parameterization (or atlas
if you're into diffgeom). In general we try and avoid this,
since we assume the particular paramaterization we pick is
arbitrary and wish to study the underlying
space/manifold/thingy.
---
The good Christian should beware of mathematicians
and all those who make empty prophecies. The danger already
exists that mathematicians have made a covenant with the devil
to darken the spirit and confine man in the bonds of Hell. -St
Augustine
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Eugene Shubert
Radio Wave
5 Posts |
Posted - 02/25/2003 :
04:04:00 
alis,
If I made no error, it seems to me that there’s an absolute
frame of reference for SxR. If an absolute frame exists for
SxR, how could it not exist for (S^3)xR? Where is my
mistake?
http://www.everythingimportant.org/relativity/simultaneity.htm
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alis
Radio Wave
USA
79 Posts |
 Posted - 02/25/2003 :
08:06:58
Gaaah. I spent an hour or two playing around with this
before convincing myself you're right. Learned a lot, though.
Some thoughts:
- We seem to get the preferred reference frame by breaking
the symmetry of spacetime in making the identification RxS.
This separates out the time coordinate, and because of the
different topologies, we can't globally mix them back
together like we could in RxRn. I'm not sure what exactly the
conditions on the second half of this direct product would be
in order to get SR frame-equivalence back. From what I
remember of my Riemannian geometry, I would guess we would
need it to be simply-connected and noncompact.
- If we were willing to allow bizarre time dimension
topologies, we could get frame-invariance back... this might
be applicable to some of the crazy QG stuff going on.
- I'm not sure how much of this weirdness is due to
connectedness, which would affect S3, since it's
simply-connected unlike S1. Since we can trivially embed S1 in
S3, I suppose there are probably still preferred frames, but
my gut feeling is that there's going to be big
differences.
- You could make a far simpler case for preferred frames by
invoking the twin paradox: in our S1 universe, the twin's
points of view are totally symmetric, so which one is older
when they meet? That forces us to pick one of their
frames.
- I think we will still keep rotational and translational
symmetry in these odd cases, even though we must define a
preffered rest frame. I think... hmm...
All this topology is making my brain hurt. What do you
think? Any ideas?
BTW, I think perhaps you should repost this under a
different title... toss around "topologies" or "global
symmetry breaking" or something. :) Most people I think will
assume you've just got some juvenile crackpot objection to SR
and skip it, and this is one of the most interesting posts
I've seen in a long while....
-Ali
---
The good Christian should beware of mathematicians
and all those who make empty prophecies. The danger already
exists that mathematicians have made a covenant with the devil
to darken the spirit and confine man in the bonds of Hell. -St
Augustine
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Hurkyl
Visible Light Wave
USA
697 Posts |
Posted - 02/25/2003 :
17:33:53
RxS has no global frames of reference.
When we step away from the usual RxRn into the
world of differentiable manifolds, we (generally) lose the
notion of a global coordinate system. Reference frames, thus,
only exist locally. In particular, no coordinate chart
can cover all of RxS.
quote:
- You could make a far simpler case for preferred frames by
invoking the twin paradox: in our S1 universe, the twin's
points of view are totally symmetric, so which one is older
when they meet? That forces us to pick one of their frames.
The asymmetry is provided by differences in the, if you
allow me to borrow terminology, branch cuts for each twin
(assuming they cover maximally). As each observer watches his
twin, he will necessarily be forced to chart that twin as
having jumped across a discontinuity in the reference frame,
and the effects of this discontinuity will generally be
asymmetric (in particular, it will depend on the angle the
reference frame is oriented WRT the cylinder).
Hurkyl
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Edited by - Hurkyl on 02/25/2003 17:45:23
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alis
Radio Wave
USA
79 Posts |
Posted - 02/26/2003 :
00:02:41
quote:
RxS has no global frames of reference.
Sure it does... we just need to define an
atlas. But the preferred inertial frames we are talking about
here can be considered just locally.
I think branch cuts are the wrong way to think about this
(and they bring up nasty memories of AMa grunge.) There's no
reason to make one of our charts maximal, and we can happily
define compatible ones covering the whole cylinder. If we pick
the correct ones, everything will even work out fine. But
Lorentz symmetry is no longer global, as the direct product
RxS defines a particular time axis and hence also particular
surfaces of simultaneity.
---
The good Christian should beware of mathematicians
and all those who make empty prophecies. The danger already
exists that mathematicians have made a covenant with the devil
to darken the spirit and confine man in the bonds of Hell. -St
Augustine
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Hurkyl
Visible Light Wave
USA
697 Posts |
Posted - 02/26/2003 :
06:04:16
I thought that reference frames were merely individual
coordinate charts, not entire subatlases?
If you define a reference frame as simply being a
mapping from R2 onto RxS, the aligned one still
isn't the unique flat frame... it is unique in the fact that
the inverse map is periodic in space but 1-1 in time, but
non-aligned reference frames still work, and generate a map
that is periodic in a direction oblique to the time and space
axes; i.e. going forward in time x seconds is equivalent to
going east in space y meters.
I *think* that the oblique reference frames are torii but I
can't prove it yet because I gotta go. I'll have more to say
when I get back!
Hurkyl
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Hurkyl
Visible Light Wave
USA
697 Posts |
Posted - 02/26/2003 :
16:37:32
Bleh, they're not torii I dunno what I was thinking
there!
Hurkyl
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alis
Radio Wave
USA
79 Posts |
Posted - 02/27/2003 :
01:18:44
I was curious how you were planning on fitting a torus
on the surface of a cylinder. :)
Incidentally, I just learned that the standard global GR
solutions -- Friedmann-Lemaitre-Robertson-Walker (choose any
two) spacetimes -- also have a set of preffered frames,
because of the imposition of isotropy and homogeneity.
Neat....
---
The good Christian should beware of mathematicians
and all those who make empty prophecies. The danger already
exists that mathematicians have made a covenant with the devil
to darken the spirit and confine man in the bonds of Hell. -St
Augustine
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Eugene Shubert
Radio Wave
5 Posts |
Posted - 02/27/2003 :
02:00:57
Ali,
What are the physical implications of preferred frames in
the universe? Suppose a physically distinguished time
parameter is imposed on the universe by physical law. Could
you identify one equation of physics that would need to be
revised? In SR it’s meaningful to say that there are events E1
and E2 in spacetime such that for observer1, event1 comes
before event2 but for observer2 event1 comes after event2.
(E1=event1, E2=event2). In RxS, RxS^2 and RxS^3, this
disagreement about “time order” is clearly seen to be just a
poor choice in the manner we synchronize clocks. Have you
thought about the impact of an absolute “time order” in a FRW
universe containing black holes?
http://www.everythingimportant.org/relativity/simultaneity.htm
Sincerely,
Eugene Shubert
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Edited by - Eugene Shubert on 02/27/2003
03:00:49 |
russ_watters
Radio Wave
USA
24 Posts |
Posted - 02/27/2003 :
08:40:17
quote:
What are the physical implications of preferred frames in
the universe? Suppose a physically distinguished time
parameter is imposed on the universe by physical law. Could
you identify one equation of physics that would need to be
revised?
Thats a big supposition. The lack of a
universal frame of reference is the first part of Relativity.
And its implicaiton is that the laws of the universe are the
same for everyone regardless of your frame of reference.
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Eugene Shubert
Radio Wave
5 Posts |
 Posted - 02/27/2003 :
09:09:30
Russ,
A preferred frame of reference is an elementary consequence
of topology. Presupposing a closed and bounded universe and my
postulate about light speed yields the principle of relativity
locally. http://www.everythingimportant.org/relativity/simultaneity.htm
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alis
Radio Wave
USA
79 Posts |
Posted - 02/27/2003 :
09:56:42
Eugene-- I've only got a vague grasp on GR at this
point, so I have no idea what black holes would do. But
wouldn't a preferred set of frames:
1) suggest that we
should use comoving coordinates in doing cosmological
calculations
2) be the set of frames in which the CBR has
no dipole anisotropy
Assumptions of global homogeneity/isotropy of the universe
seem far trivial...
---
The good Christian should beware of mathematicians
and all those who make empty prophecies. The danger already
exists that mathematicians have made a covenant with the devil
to darken the spirit and confine man in the bonds of Hell. -St
Augustine
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