Re: Time dilation and expanding space


I'm not claiming that it can be done to completion, only that it can be
done, at least approximately.

No, you have been claiming that the two were perfectly
equivalent. Outside the event horizon you can select a
time axis and map to 3D plus time, but the time for in
infalling object to reach the horizon is infinite in
that mapping while it is finite in the proper time of
the object, and in fact it takes a finite time to reach
the physical singularity at the centre.


In 3D plus time one has to calculate the amount of time dilation at each
height above the surface (or singularity) and will eventually arrive at the
same result. Although the resolution of the resulting calculation will
depend on the number of calculations done, one will arrive at the same
result in principle.

Neither has it been exceeded in expanding spacetime, which is the point
I
was making ie if we consider only the speed of the objects (eg galaxies)
through space then none are exceeding the speed of light.

Again that just highlights the difference. Over short
distances galaxies recede with distances increasing by
less than c m/s and you can say the galaxy is moving
away at that speed, or you can say space is expanding
at the Hubble rate and there is an additional proper
motion relative to the local flow, the descriptions
are pretty much equivalent. However for high red shifts
that gets problematic and eventually for large enough
distances the rate of increase exceeds c. Bear in mind
the current models suggest the universe is probably
infinite so Hubble speeds go to infinity. Your simple
mapping doesn't cater for that.


I think you mean that *spacetime* is expanding.
In the simple mapping, space is not expanding (only space-time). The
simpler mapping needs to refer to the cause of the spacetime expansion eg
around a gravitating body it is the gravitational potential that causes
spacetime it expand. The only problem with Hubble expansion is that the
cause is aesthetic rather than scientific.

I was making the
point that greater than light speed can be noted (as with my example and
with the apparent speed of objects carried along with expanding
space-time)
without the speed of light actually being exceeded (as you most
correctly
noted above).

Indeed, but expansion of spcae _does_ result in recession
velocities in excess of c when you try to map to a 3D plus
time view.


Not necessarily. Objects are not moving inertially ie that are not moving
with respect to the space around them. One can measure this inertial speed
in principle by comparing the motion of the object to the motion of comoving
space debres, as there are always other objects in space. If the object
under observation ios moving with respect to all other objects then we can
say that it motion is inertial, but if all objects in the area are moving in
the same direction with approximately the same speed then we would conclude
that the motion is not inertial. If it is not inertial then the motion is
not apparant in a 3d space model. The redshift will have the same cause as
that which cause the spacetime expansion in the first place. For the
redshift of an object in the vacinity of a gravitasting body it is the
gravitational 'force' that causes the redshift in 3D+T.

In other words, in 3D+T, distant galaxies are not moving away from the
obsever. This was, however, the assumption in the early days (that galaxies
had inertial motion).

All you are doing in your trivial solution is to lower the density of
matter
in the volume.

That's right, just as cosmological expansion is reducing the
meamn density of matter in the universe as clusters of galaxies
move apart.


This density theory requires a reference - or is this your own conclusion?

It is my understanding that earlier theory predicted that the density would
fall with distance and so there should be fewer galaxies with larger spatial
gaps between them as we peer deeper and deeper into space. The voids were
thought to be a sign of just this. But Hubble was pointed into the voids
for a deep space probe and found that no only were they teeming with
objects, but the density of objects was no different to what it is locally.

Note that the only matter visible at ever greater distances is stars,
galaxies and then blusterers of galaxies. The density of these objects
should decrease along with the spatial expansion. There is no evidence that
this actually happens.

In fact one would expect spacetime to be more compact at greater distances.
But it isn't - there is more of it.

... This is
not expanding space-time by any measure that I am aware of.

It is expanding space as a function of time which is the model.


I'll need at least one reference to this 'expanding space', and not from a
newspaper article - an academic reference to expanding space as distinct
from expanding spacetime.

Consider this question - will light passing through your trivial example
be
redshifted due to the lower density of the gas ..

Yes, a photon emitted by a particle of dust on one side of the
box will appear redshifted when received by a particle on the
other side because they are moving apart. Bear in mind each
dust particle is the analog of a cluster of galaxies.


That is redshift due to scattering, which does not require expanding
spacetime. Remember that the GR account describes light being stretched as
it passes over expanding space time, not as it is scattered by intervening
dust particles.

.. and will a clock signal
projected across the volume show time dilation (due to the transit
across
your expanding space)??

Yes, since each particle is moving relative to the other, the
norma gamma function applies.


Explain.

Expansion is not a function of dust particles in space.
Redshift is not caused by scattering (specifically, interaction with the
dust particles). Indeed, if that were the case then we would see
greater
redshift where the density of matter is greater, not less as in expanded
spacetime.

Your solution smacks of a personal conjecture rather than a reference to
generally agreed cosmological principles or cosmological models. If I
am
wrong in this, please supply some form of reference so that I can study
your
position in greater detail eg book or paper, online resource etc.

Treating the largest gravitationally bound structures as 'dust' is
the basic approach in cosmological models. I did a web search and
at the top here's a reference from a FAQ on dark matter:

http://www.jb.man.ac.uk/~jpl/cosmo/bad.html#CDM


That does not make your conjecture correct. I asked you how you would expand
space in principle - you suggested that if you expanded space that gas
particles would move apart. That is hardly an answer. Further, we would
expect to see a much lower density of galaxies locally (where spacetime has
been expanding for the last 15 billion years) than distally (where spacetime
has had less time in which to expand). But these observations have not been
forthcoming.


But in general if you look up how the acceleration parameter
is found for any model, the contribution of the non-zero mean
matter density is described as a dust model. Have a look in
MTW, I don't have a copy but I'm sure the term will be covered.


I'm not disputing the definition of dust. I was challenging you to expand
space in the laboratory *in principle* and you referred to gas molecules and
dust. Are you suggesting that you can fit galaxies into the lab? It is
reasonable to refer to particles in my reply. Further, your explanation
with gas particles was flat out wrong, or you missed out the essential part
of the explanation.

You said:
"Trivial, move the boundaries of the volume outwards and the mean distance
between the gas molecules increases. Cosmology at large scales treats
matter as 'dust' where each 'grain' represents a gravitationally bound
object such as a cluster of galaxies."

in response to:
"consider a volume evacuated to replicate the density of space (a near
vacuum by Earthly standards). Now, given whatever tools you need, including
those that exist only 'in principle', how would you go about expanding or
contracting the spacetime in this volume?"

All you have managed to provide is a lame explanation of the condition of
your volume after the expansion occurs and then to go on to carefully
explain a well known definition of the word 'dust'.

And don't try to bring in the Friedman equation - stochastic local expansion
found in the equation does not explain the orderly expansion of the entire
universe.

The mapping is the Hubble flow, distant galaxies are
'moving' away from us at a speed of 71km/s for every
MPc they are distant. That is trivial.

You have not answered the question. Distant galaxies are not moving
'through space'.

In GR's 4D expanding view that is true. The mapping onto
3D that you are attempting maps the increasing distances
onto a non-expanding space therefore they _are_ moving
'through space'. That is what Thorne is saying, the view
of space expanding and objects not moving through it (or
more accurately just having small proper motions) is
equivalent to the view of space not expanding an objects
moving. I am pointing out the limitation, it is valid
for small distances but you reach a point where GR has
no problem with space expanding such that the distance
grows faster than c as long as the object's proper motion
remains small.


Space does not expand in any formulation of GR that I am aware of. Feel
free to refute my position with a reference, and not to one of those
books
for 'general consumption'.

Well this is intended for the public but is entirely valid. I don't
have any text books here (I'm at work on lunch break) but I can
probably dig something out of D'Inverno or Peebles later if you
insist.

http://www.astro.ucla.edu/~wright/cosmo_03.htm#MSTD


The author quoted changes from describing curved space to describing curved
space-time as if the two are equivalent. I assume that he meant curved
space-time further up the web page.

Indeed, the expansion of space is a more plausible concept than the
curvature of space suggested on that page.

"agent"? Do you mean the metric? Or perhaps the answer
should be residual momentum from the big bang.

Momentum of what?

Yes, of the galaxies as they move apart.


Galaxies are not accumulating momentum - they are commoving with the
expanding spacetime. That is why their motion is described as non-inertial.

The matter that bubbled up from quantum fluctions
(current inflation model as I understand it) ?

Inflation was a bit later AIUI. All the sources I have seen suggest
it started after the GUT era, around 10^-35 s or 10^-34 s and lasted
until 10^-32s.

http://en.wikipedia.org/wiki/Timeline_of_the_Big_Bang


Inflation models assume multiple universes etc. What Guth did was to bring
together quantum physics, particularly GUT models and cosmology together.
Actual inflation was just one feature of the new cosmology.

How would you replicate the expansion of spacetime *in principle*??

Move things apart or.

Spacetime is not 'things'.

You should consider what Einstein said on that matter.

Expanding a gas uniformly in a balloon does not
effect spacetime within that balloon.

It increase the volume as a function of time.


But that does not effect spacetime. Spacetime hosts the balloon, so to
speak. The expansion of spacetime is something quite different.


--
Kind Regards
Robert Karl Stonjek


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