Prev: Evidence of the medium of space
Next: The participants in these newsgroups are arithmetic morons
From: mathematician on 30 Jul 2010 04:56
Newsgroups: sci.physics.relativity
From: mathematician <hapor...(a)luukku.com>
Date: Fri, 23 Jul 2010 01:55:34 -0700 (PDT)
Local: Fri, Jul 23 2010 11:55 am
Subject: Re: Preferred Frame Theory indistinguishable from SR

Message-ID: <829e903d-1810-4feb-842c-
b071551fb6a3(a)u26g2000yqu.googlegroups.com>
References: <i02a4f01747(a)drn.newsguy.com> <VZ-
dnVDuYY2WGLjR4p2dnAA(a)giganews.com>

On Jun 26, 7:41 am, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote:
> Daryl McCullough wrote:
> > There is a preferred frame, F, and there is an associated
> > coordinate system such that

> > 1. Light travels in straight lines at speed c, as measured in F's
> > coordinate system.

> > 2. An ideal clocks in motion relative to F has an elapsed time
> > given by dT/dt = square-root(1-(v/c)^2), where t is the time
> > coordinate of F's coordinate system, and v is the velocity of
> > the clock, as measured in F's coordinate system, and T is the
> > elapsed time on the clock.

> > 3. An ideal meterstick in motion, with the stick aligned in the
> > direction of its motion, will have a length given by
> > L = square-root(1-(v/c)^2).

> > I would think that anybody could see that rules 1-3 are consistent.
> > You cannot deduce a contradiction from these rules. Note that the
> > contradiction that so many anti-relativists think that they have
> > found in SR, namely, mutual time dilation, is not present in these
> > rules, because these rules only mention time dilation with respect
> > to a specific, preferred frame. So there is no possibility of deriving
> > a "twin paradox" that is a logical contradiction. Right?

> > Well, all the weirdness of SR, including mutual time dilation and
> > the relativity of simultaneity *follows* logically from principles
> > 1-3! You can prove that if 1-3 are true in the preferred coordinate
> > system, then they are *also* true as measured in any coordinate system
> > that is related to the preferred coordinate system through the
> > Lorentz transforms.

> Yes. This is just one of the theories that are equivalent to SR (i.e. they are
> experimentally indistinguishable from SR). This is one way of deriving the
> equations of LET (Lorentz Ether Theory). Lorentz used a completely different
> method in his 1904 paper.

> There is a much larger class of theories equivalent to SR, consisting of all
> theories in which these two criteria apply:

> a) the round-trip speed of light is isotropically c in any inertial
> frame
> and
> b) the one-way speed of light is isotropically c in one frame

> Note that (a) is solidly established experimentally, and (b) is basically what
> it means to have an aether frame, or any sort of "preferred" frame.

> If you work out the details, you find that all of these theories
> have transforms between inertial frames that differ from the
> Lorentz transform only in the way coordinate clocks are
> synchronized in inertial frames. Note that except for SR and
> LET, the synchronization method is ad hoc and artificial.

> In all of these theories except SR and LET, slow clock transport relative to a
> moving inertial frame CANNOT be used to synchronize the coordinate clocks of the
> frame. And the difference is PRECISELY what it takes to make experiments and
> observations be identical to those of SR and LET.

> In all of these theories other than SR (which is the only member of this class
> without a preferred frame), there is no possible experiment that can determine
> which frame is the preferred frame. That is, no matter which frame you
> arbitrarily select to be the "ether frame", the predictions for any experiments
> or observations are unchanged. IOW: (b) can be applied to any inertial frame.
> Only in SR does (b) apply to all inertial frames simultaneously.

> NOTE: the modern interpretation of this is that it is all
> irrelevant. That's because these different "theories" merely
> apply different coordinates to the underlying space-time
> manifold, and use different transforms among them. Yes, except
> for SR and LET those coordinates are pretty unusual.... The
> uniqueness of SR is precisely that (b) applies to all frames.
> SR is also the only theory that includes the PoR.

> I posted a much longer series of three articles on this 'way back in 1999
--http://groups.google.com/group/sci.physics.relativity/msg/
15ceaad17be...

> Tom Roberts

You said above that there is no possible experiment that can
determine
which frame is the preferred frame.

Could you Tom answer the following question:

Q1. If we use finite long pseudosphere as 2+1 dim. model of
the Universe (one space dimension is shrunken away from
the full 3+1 dim. model, picture of this pseudosphere is
in my profile page). Time dimension is the symmetry axis
of the pseudosphere and it starts from the bottom of the
finite long pseudosphere("bottom of the bag").
Would this structure form the preferred frame
which is unobservable?

Hannu
From: Tom Roberts on 30 Jul 2010 12:13
mathematician wrote:
> On Jun 26, 7:41 am, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote:
>> Daryl McCullough wrote:
> >> [...]
>> Yes. This is just one of the theories that are equivalent to SR (i.e. they are
>> experimentally indistinguishable from SR). This is one way of deriving the
>> equations of LET (Lorentz Ether Theory). Lorentz used a completely different
>> method in his 1904 paper.
>
>> There is a much larger class of theories equivalent to SR, consisting of all
>> theories in which these two criteria apply:
>
>> a) the round-trip speed of light is isotropically c in any inertial
>> frame
>> and
>> b) the one-way speed of light is isotropically c in one frame
>
>> Note that (a) is solidly established experimentally, and (b) is basically what
>> it means to have an aether frame, or any sort of "preferred" frame.
>
>> If you work out the details, you find that all of these theories
>> have transforms between inertial frames that differ from the
>> Lorentz transform only in the way coordinate clocks are
>> synchronized in inertial frames. Note that except for SR and
>> LET, the synchronization method is ad hoc and artificial.
>
>> In all of these theories except SR and LET, slow clock transport relative to a
>> moving inertial frame CANNOT be used to synchronize the coordinate clocks of the
>> frame. And the difference is PRECISELY what it takes to make experiments and
>> observations be identical to those of SR and LET.
>
>> In all of these theories other than SR (which is the only member of this class
>> without a preferred frame), there is no possible experiment that can determine
>> which frame is the preferred frame. That is, no matter which frame you
>> arbitrarily select to be the "ether frame", the predictions for any experiments
>> or observations are unchanged. IOW: (b) can be applied to any inertial frame.
>> Only in SR does (b) apply to all inertial frames simultaneously.
>
>> NOTE: the modern interpretation of this is that it is all
>> irrelevant. That's because these different "theories" merely
>> apply different coordinates to the underlying space-time
>> manifold, and use different transforms among them. Yes, except
>> for SR and LET those coordinates are pretty unusual.... The
>> uniqueness of SR is precisely that (b) applies to all frames.
>> SR is also the only theory that includes the PoR.
>
>> I posted a much longer series of three articles on this 'way back in 1999
>
> You said above that there is no possible experiment that can
> determine
> which frame is the preferred frame.
>
> Could you Tom answer the following question:
>
> Q1. If we use finite long pseudosphere as 2+1 dim. model of
> the Universe (one space dimension is shrunken away from
> the full 3+1 dim. model, picture of this pseudosphere is
> in my profile page). Time dimension is the symmetry axis
> of the pseudosphere and it starts from the bottom of the
> finite long pseudosphere("bottom of the bag").
> Would this structure form the preferred frame
> which is unobservable?

The context of my discussion is SR and the set of theories equivalent to SR.
They all share the same space, which is infinite 3-d Euclidean space; they all
add a time coordinate to it, but the manner of doing that depends on the theory.

Your "pseudosphere" does not apply to any of these theories.

Note that in GR, which is not restricted in its geometry like that, many/most
manifolds have a "preferred frame" in the sense that the math is easiest in
coordinates related to some symmetry of the manifold. For instance, in the FRW
manifolds that are the basis of big-bang cosmology, there is an obvious and
observable local "preferred frame" -- that in which the local dust particles
(galaxies) are at rest. But this is a VERY DIFFERENT theoretical context than SR....

And also, that "preferred frame" does not participate in the
dynamics of the theory. It is "preferred" by humans merely because
the math is simplest when using it. The math is simplest because
there is an underlying symmetry of the geometry that makes it so.

Your "pseudosphere" surely has such a "preferred frame". But I have no idea if
it is a solution to the equations of GR (seems doubtful).


Tom Roberts
 | 
Pages: 1
Prev: Evidence of the medium of space
Next: The participants in these newsgroups are arithmetic morons