Re: GR ?


"Significant Zero" <paulpsremove@xxxxxxxxxx> wrote in message
news:1121880144.7874.0@xxxxxxxxxxxxxxxxxxxx
>
> "Tom Roberts" <tjroberts@xxxxxxxxxx> wrote in message
> news:lOYCe.673$lX2.670@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> | Significant Zero wrote:
> | > Due you concur
> | > with the experimental facts that time and length are variant ?
> |
> | Your question does not make sense. I'm going to guess that you mean that
> | the spatial interval between a given pair of events, and the time
> | interval between them, can be different for two different coordinate
> | systems. If that's what you mean by "variant", then: yes.
> |
> |
> | > If so do you
> | > agree that to maintain the measured constancy of c locally their is a
> need
> | > for time and length to be changed in a proportionate manner so this
> apparent
> | > fact is maintained ?
> |
> | No. A simple counterexample is the Lorentz tranforms of SR in which the
> | changes are not "proportionate" -- the different synchronization of
> | clocks in different inertial frames is an essential aspect of SR.
> |
> | Yes, dx'/dx| = dt'/dt| = \gamma (d = partial), but in
> | |t |x
> | general one has NEITHER constant x NOR constant t.
> |
> | And it's not really appropriate to use the word "changed" here -- this
> | is merely a geometric projection of an invariant interval onto different
> | coordinate axes which are rotated wrt each other, so of course the
> | projections are DIFFERENT, but not really "changed".
> |
> | On a piece of paper draw a 2-cm line L; draw Cartesian axes
> | x-y, and x'-y' rotated wrt x-y. The projection of L onto the
> | x axis is different from its projection onto the x' axis,
> | but nothing has "changed" -- they were this way from the
> | instant you drew L and defined the coordinate axes.
> |
> | This is a subtle but important point: nothing is "changing", various
> | measurements are different; that's all. And at base the measurements are
> | different because they are measuring different things (e.g. a length
> | measurement in the unprimed frame measures at constant t, but one in the
> | primed frame measures at constant t').
>
> This seems to be saying that length contraction and time dilation are just
> observational distortions in the same way that railway lines get apparenly
> nearer as they extend to the horizon. Is this the way you explain to
> yourself the experimental variation in muon decay and contraction in the
> direction of motion ?

That is not what it is saying at all. Perspective is an illusion - length
contraction and time dilation is real - its explanation being different
observers project different aspects of invariant space-time intervals onto
their coordinate systems just like the rotating rod and the x coordinate.

>
> |
> |
> | > i.e A cubic meter of the vacuum state between galaxies
> | > has different characteristics to a cubic meter just outside an event
> horizon
> | > but in each place sol will be locally measured as constant but may not
> be
> | > the same relatively ?
> |
> | If by "characteristics" you mean some physical quantity like the metric
> | or curvature tensors, or perhaps gas density, ... -- certainly they can
> | be different in different locations. And yes, in GR any LOCALLY-INERTIAL
> | measurement of the speed of light will yield the answer c. But your
> | phrase "may not be the same relatively" does not make sense to me.
> |
>
> This may be difficult to explain but perhaps you will agree that a clock
in
> the in the two vacuum cases above will tick at different rates, so time
> according to the clocks is moving at a different rate ?

For a stationary inertial observer right next to the clocks they tick at
exactly the same rate (the so called proper time) so one can not say the
clocks tick at different rates. It is different observers in regions that
have different space-time curvature and/or are in different states of motion
that measure it differently. The reason it is measured differently is not
because the clocks behave differently - it is because of space-time
geometry - the proper time is always the same - but different coordinate
systems 'project' it differently.

> If so then if c is
> measured locally constant in these two environments but the clocks are
> running at different rates then actual length must have changed to
> accommodate the actual but locally unobservable change in c ?

C is only measured constant in inertial frames. Unless you are in free fall
an observer at the event horizon of a black hole is not inertial - and even
if they were in free fall only extremely small objects would not experience
tidal forces.

>
> |
> | > Maybe not in your terms but Lagrangians seem to be describing the
> actions of
> | > particles in systems not explaining what energy is,
> |
> | Certainly the Lagrangian of a system does not, in general, by itself
> | define energy. But if it is invariant over time translations then it
> | does (via Noether's theorem). And if it is not so invariant, energy is
> | not so useful....
>
> That makes no sense to me as energy is a dynamic and the only relatively
> static and invariant over time, form of energy that I can think of at the
> moment is a partical. Which implies that Lagrangian are not applicable to
> energy of fields.

Defining energy as the conserved Noether charge related to tine symmetry
does not mean it is static. You have been given the link that explains how
for classical particles it arrives at kinetic angry as 1/2 mV^2 which is not
static - it changes with particle velocity.


>
> |
> |
> | > are you letting the metric follow the geometry or are you using a
> | > flat Euclidean geometry and metric and referring GR's geometry to this
?
> |
> | The metric _IS_ the geometry.
>
> I tend to think as the metric as being the scalars that might apply to a
> given metric space and the ratios and relationships as being the geometry
> and both being an attempt at a notational system to describe physical
> reality.

Knowing the metric at every point of a Riemannian space allows us to
completely define the geometry.

>
>
> | And in general it is not possible to
> | "refer" a curved Lorentzian manifold to a "flat Euclidean geometry".
>
> I don't see the difficulty in overlaying one metric space with another and
> translating between them other than the complexity. In fact curvature is a
> Euclidean statement based on the relationship of a line to straight so GR
is
> already referenced to Euclidean space by that statement.

The curvature tensor is a coordinate independent object defined from the
metric that allows us to determine curvature without reference to Euclidian
space.

>
> | Except for my (counter)example of SR above, I have been discussing GR
> | and its general Lorentzian manifolds.
>
> As I understand it GR uses both and R............(cant remember the name
at
> the moment). space

I have no idea what you are trying to say. It is family obvious your
problem is that you do not seem to want to study the math - if you did many
of the questions you ask would be trivial.

Bill

> |
> |
> | Tom Roberts tjroberts@xxxxxxxxxx
>
>
>


.

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