Re: Time dilation and expanding space


"Robert Karl Stonjek" <stonjek@xxxxxxxxxxxxxx> wrote in message
news:v1AGh.7092$8U4.4486@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx

The two are largely equivalent. There are a number of
ways to look at the situation. One is that light from
a distant source has its wavelength 'stretched' while
in transit so it is something that "happens to the light
after transmission". When thinking of supernovae, the
overall light curve gets stretched so a curve that would
last 20 days if nearby might seem to last say 25 days at
some large distance. That is because the light at the
end of that period was emitted from 5 light days farther
away. You can think of that as the source moving away by
5 light days in 20 days or a speed of 0.25c, or you can
think of the space between expanding by 5 light days in
the time. None of those views treats the effect as being
at the source.

There is one very important difference. Space time is a manifold -
basically, one can think of three spatial dimensions and one time
dimension
OR to consider just three (flat) spatial dimensions and time separately. -
the results are the same. Kip Thorne in 'Black Holes & Time Warps' goes
into some detail to explain this and gives examples with illustrations to
make the point.

Within limitations, that is correct of course. What you
get then is pseudoforces such as gravity and other
coordinate effects. However, you need to keep in mind
that it is a simplification with limitations.

Thinking of gravitational time dilation, for instance, we can think of
light
as being stretched as it climbs out of the gravity well or we can think of
the clock on the surface of the massive object as running slower relative
to
the clock of the observer (somewhere away from the gravitating object).

Yes, what you are doing is selecting an arbitrary orientation
for the time axis at the distant clock, typically taking the
tangent to that clock's worldline or using it's rest frame as
your 'universal' coordinate frame.

The two are equivalent except that GR does not model the conditions
whereby
no light is emitted ie the clock simply sits on the planet for a couple of
years.

I don't see what you mean there, light isn't involved and
GR models the slowed rate of the planetary clock perfectly.

GR is light temporal snapshots of spacetime - the time that is
modelled does not account for today and tomorrow, for instance.

That appears to be nonsense. GR deals with spacetime as a
4D manifold and 'tomorrow', or more simply the future is
the region in advance of the observer's surface of
simultaneity.

Thus a clock on, say, the Earth will lag ever more behind a space clock.
The amount of time dilation is the same as the equation for gravitational
redshift ie
gamma=(1-2GM/c^2r)^.5

Note that space is NEVER curved, stretched or 'expanded', it is
spacetime -
space does not change. It is the time dimension that changes.

Bear in mind that even in SR, there is no 'absolute' demarcation
between space and time. What is bent in GR is spacetime and you
then choose a direction within that to call the time axis and
set up the spatial axes orthogonal to that. One man's space is
another man's time so it makes no sense to say only time can be
bent.

For example the old story is that when Einstein first predicted
the bending of light by the Sun he forgot the time part and got
the same result as Newton, however Eddington's first attempt was
unsucessful and Einstein corrected the prediction before the
actual measurement was made to double that of Newton. Half the
bending was spatial while half is temporal.

In the case of expanding space there is no way of expressing the manifold
in
three flat spatial dimensions plus time (separately) as it is for
gravitational or relative motional time dilation.

Thus the expanding space model is one gaping hole in it.

No, that's just a limitation of trying to use the classical view.
You could as well say that our modern view of the Earth as being
roughly spherical is wrong because it is impossible to draw a
map on a flat *** of paper.

There is a further problem with it. As we approach the speed of light,
the
distance between emitter and absorber falls to zero and the interval of
ANY
transit also falls to zero. Thus light can not change in frequency during
a
zero interval transit across a zero distance space.

From the "photon's point of view", time does not exist so the
concept of frequency is meaningless. What we call frequency
is a measure of the energy transferred in the interactions.

This is not a problem in all other relativistic redshift as one can
explain
the phenomena using three spatial dimension and time (not together as
spacetime). Eg gravitational time redshift is explained by the
gravitational time dilation at the emitter (the frequency of light is
actually lower at the point of emission). This was measured by Pound and
co
in the 60s.

One can not explain expanding space redshift in this way ..

As I explained you can, and in fact GR works even beyond the
horizon where the apparent recession speed reaches c and your
3D+time model fails. All you are showing is that the traditional
view cannot cope.

nor account for how
light can change its frequency in transit. In the spacetime model we can
point to light being stretched as it passes over expanding spacetime. But
the accompanying explanation from a frame closer to the speed of light or
from space and time separately is not forthcoming - simply put - there
isn't
one.

Here are three quotes from P403 of the above mentioned book:-
-) As an example, in the curved spacetime paradigm, the verbal picture of
Einstein's field equation is the statement that "mass generates the
curvature of spacetime." When translated into the language of the flat
spacetime paradigm, this field equation is described by the verbal picture
"mass generates the gravitational field that governs the shrinkage of
rulers
and the dilation of ticking clocks." Although the two versions of
Einstein'
s field equations are equivalent, their verbal pictures differ profoundly.

-) Some problems are solved most easily and quickly using curved spacetime
paradigm; others, using flat spacetime.

-) This freedom carries power. That is why physicists were not content
with
Einstein's curved spacetime paradigm, and have developed the flat
spacetime
paradigm as a supplement to it.

Sure, and for most physics problems even Newtonian gravity
is adequate. Physics is a practical science. Constant g on
the surface of the Earth is adequate for building design,
inverse square law does for most satellites, that plus
gravitational redshift and SR effects is good for GPS and
they use full blown GR when it comes to cosmology where
the simpler approximations run out of steam.

What is the flat space equivalent of expanding space - the version using
rods and clocks? Only the concept of expanding spacetime fails this
simple
test of consistency.

No, it's not the model that fails, it is the attempt to map
the curved spacetime onto a flat surface that doesn't work
in such extreme situations.

George


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