Re: A little challenge for relativists.

Tom Roberts:
>Bilge wrote:
>> Tom Roberts:
>> >Bilge wrote:
>> >> List the theoretical foundations.
>> >1. There is an ether which permeates all of space and everywhere
>> > defines a unique intertial frame.
>> >2. Clocks and rulers in motion wrt the ether frame behave as
>> > described by a Lorentz transform from the ether frame.
>>
>> #1 is false, as the coordinates I've given show.
>
>Not true. Funky coordiantes have no power over a physical assumption
>like this.

You can't imagine how odd it seems to be trying to convince you that
physics isn't coordinate dependent and to dispell a notion that there is
some physical significance to the labels on a coordinate.

>Just because you can display a set of coordinates does not mean that
>they correspond to any physical system, and yours don't.

Quite frankly, that is crap. I can only wonder if you actually tried to
picture the physics, since the light front coordinates correspond
_exactly_ to the synchronization procedure outlined by einstein. Explain
to me how observers along a time slice t = 0 synchronize their clocks or
determine their rulers are at rest, then talk to me about which
coordinates correspond to a ``physical system.'' I'm curious to know
how an observer whose definition of t = 0 consists of a point at the
apex of his past and future light cones does all this stuff.

>> They cannot be reached by a lorentz transform.
>
>But your coordinates do not represent any inertial frame

Oh, of course not - the whole thing about the lorentz transforms
doesn't work anywhere except outside the light cone on spacelike
intervals - What was I thinking...

>(there is no time coordinate,

You can look this up. I'm not going to argue over terminology
that is common just because it's not congruent to that which
is common in general relativity (if that is even the case).

>and it is not possible to lay rulers down AT REST along one of the
>axes).

This is almost funny, since no observer can actually observe such
a ruler. Every point along your ruler at rest is outside the light
cone of of every other point for any constant time slice. If you
want berate coordinates for being ``funky'' or not corresponding to
reality, you ought to start with coordinates which require information
no observer can obtain.

Here's the most obvious counter example. Look at your clock.
Now look at it again 1 second later. ds^2 = 1 sec. You just
measured a time interval using one of those funky coordinates
while at rest.

>See below for the futility in attempting to refute LET via strange
>coordinates.

I'm not refuting LET using strange coordinates. On the contrary,
I'm refuting LET on the basis that lorentz freely moves between
regions inside and outside the light cone and he equivocates the
time coordinates across the light cone in order to assert the
existence of some absolute frame. The entire point of the exercise
is that the coordinates I gave are the canonical coordinates for
three regions which cannot be connected by a lorentz transform.

>> #2 is meaningless as stated.
>> Lorentz relies on a great deal more than that.
>
>Hmmm. This is enough to establish LET for correspondence with SR.

Last time I checked, the group of transformations that defined
relativity was the poincare group, not the lorentz group.

>Yes, Lorentz used all of Maxwell's equations....

But that isnt all. He also used the fact that div A = 0
in the coulomb gauge to insure the transversality of light.

>> The coordinates I gave define an inertial frame
>
>No, they don't. See above and below.

If it's too much trouble to look this up, I'll find a url for you.

[...]
>> I have another set of coordinates [...]
>
>Attempting to find other coordinates has no power to refute a physical
>theory like LET.

Then I assume you think there's no hamiltonian that can be defined
for observers who are causally connected, since the coordinates
you snipped are the ones for which such a hamiltonian (i.e.,
total energy) is defined.

>When one says "inertial frame" and one says they are related by Lorentz
>transforms, that implicitly means Cartesian coordinates for space

If you don't think you can perform lorentz transforms between observers
in those coordinates, you should try performing one before telling
me it cant be done.

>implemented with rulers at rest in the frame, and a time coordinate
>implemented by standard nutually-synchronized clocks at rest in the
>frame. THAT'S WHAT WE MEAN BY "INERTIAL FRAME". <shrug>

Oh really? Then I take it that you know how to synchronize clocks
between observers located on a constant time slice? Please explain
how one does this without first making the measurement in a funky
coordinate system and inferring the position of a particle at
different time than the one to which the observers synchronize
their watches. Last time I checked, einstein's synchronization
procedure defined synchronized using light signals, which don't
propagate instantaneously.

[...]

>> >That is, the semi-Riemannian geometry needed to justify them seems
>> >more in the spirit of GR than SR.
>>
>> Only because you probably look at general relativity more than
>> at quantum theory.
>
>Quantum theory has nothing whatsoever to do with this.

I didn't suggest that it did. I suggested a reason that you think
this requires the machinery of general relativity to justify. Since
only you know why you think these coordinates aren't justified, I
should have simply said, ``No it doesn't,'' rather than speculate
as to why you think that.

>Neither SR nor LET deal with quantum phenomena.

I hope this isn't going to be a digression on an irrelevant tangent
based on misconstruing my suggestion to mean that quantum mechanics
is somehow an essential part of the argument rather than just a possible
reason _you_ think general relativity is involved.

[...]

>But as you said, g+00 = g_11 = 0. THAT MAKES THEM NULL COORDINATES. <shrug>
>
>For instance, a light pulse along the +x axis will have x^0=constant;
>one along the -x axis will have x^1=constant.

I'm not going to argue about what you want to call them, since the name
is irrelevant and it's rather pointless to trade references for the
purpose of <shrugging> back and forth, since I can find any number of
references that agree with what I said - I made sure that what I posted
was consistent with terminology in widespread usage at the present time.
I'm not going to be a slave to terminology to the extent that it impairs
my ability to read the articles I want to read, just because the
terminology differs in different areas of physics.

>> > In GR such null basis vectors always come in pairs, as
>> > the signature of the metric is -2 and cannot be modified
>> > by a mere change of coordinates.
>> I haven't changed the signature. The signature is the sum of the
>> _eigenvalues_. The eigenvalues of that metric are, +/-1/sqrt(2), -1,-1.
>> That gives 1/sqrt(2) + (-1/sqrt(2)) + (-1) + (-1) = -2.
>
>Yes.

Then why did you suggest I changed the signature of the metric?
It wasn't difficult to check.

>> Right. The point being that everybody can't use it. I've just
>> given examples of 2 coordinate systems which cannot be reached via
>> lorentz transforms.
>
>But in neither of them can a timelike observer be at rest and be
>surrounded by a rigid framework of clocks and rulers as meant by the
>phrase "inertial frame". So they are NOT coordinates of any inertial
>FRAME. <shrug>

I assume your shrug means I'm mistaken about the possibility of
defining a hamiltonian for any observers other than those who aren't
causally connected. That's odd, since I figured that the most fictional
coordinates would be the ones requiring information no real observer
could obtain, i.e., the ones along constant slices of time.


.

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