Re: Time dilation and expanding space

On 5 Mar, 14:19, "Robert Karl Stonjek" <ston...@xxxxxxxxxxxxxx> wrote:
"George Dishman" <geo...@xxxxxxxxxxxxxxxxx> wrote in message news:1173101514.761789.325380@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
On 4 Mar, 20:44, "Robert Karl Stonjek" <ston...@xxxxxxxxxxxxxx> wrote:
....
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.

That is utter rubbish. 3D+Time copes with black holes etc

Nonsense, even the Schwarzschild metric doesn't
cope with a black hole fully but has a coordinate
singularity at the event horizon.

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.

See my more thorough treatment of this issue
in my note to David A. Smith.

I'll look at that later.

and not all
spatial expansion involves faster than c totals. The fact of the matter is
that there is no 3D+ time equivalent for ANY spatial expansion. Also, there
are conditions where c is exceeded in SR. Two photons emitted in opposite
directions from some point move away from each other at 2c such that at 1s
there is a 2*c distance between them.

The distance is 2c and both photons are moving at
speed c in that frame so c has not been exceeded.

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 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.

There is no cause for this spacetime expansion. In all other examples of
spacetime expansion or spacetime curvature, gravity or motion is involved.
But not with the expansion of spacetime.

Let me give you a clear analogy which you should be able to solve quite
easily if naked spacetime expansion is a valid concept:-
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?

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 gravtiationally bound object
such as a cluster of galaxies.

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 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.

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.

.. 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.

Sorry, no.

Opps, wrong.

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

"First of all, be very careful using the word "dust" in
cosmology, as it has two completely different meanings:
To astronomers, "dust" consists of micron sized grains
made of carbon and heavier elements (or their compounds)
which float around in space and absorb light passing by,
obscuring distant stars; dense clumps of dust. are
visible as "dark nebulae". .... To cosmologists, "dust"
means any form of matter which does not exert a pressure
which is comparable to its energy density, or in other
words any form of matter which is cool enough that its
particles are not moving at relativistic speeds. Most
cosmologists think of entire galaxies as constituting
the "grains" of this dust!"

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.

A manifold by definition can be mapped onto three dimensions+time.

No it cannot. For example it can be shown that it's
not possible to map the surface of a sphere onto a
flat *** hence the concept of "coordinate patches".
Some 4D manifolds have the same problem. Perhaps you
should get a GR textbook rather than relying on a
book intended for public consumption.

Such a the famous GR book 'Gravitation', by MTW. MTW stands for Misner,
Thorne and Wheeler. The 'Thorne' is 'Kip Thorne', which book I refer to. I
do have the book Gravitation. One of its other authros says this:-

"In general relativity, for instance, it is sometimes easier to talk of the
three dimensional geometry of space evolving through time, and sometimes
easier to talk of the four-dimensional geometry of spacetime that just "is".
It is not a question of one description being right and the other wrong, or
even of one being better than the other. They are simply two ways to
describe the same physics."

Note "easier to talk of" does not mean "mathematically equivalent",
just
as it is easier to talk of galaxies moving away with some speed when
they
are at z < 1 but it becomes more difficult at high z.

That's from John Wheeler in 'Geons, Black Holes
& Quantum Foam', P.270 (paperback). Wheeler, after Einstein, *is* General
Relativity.

Perhaps you might like to give me a reference refuting Wheeler's and
Thorne's position?? (I have 'Gravitation', so a page number for that book
will do).

I don't disagree with their position that discussing the subject is
often easier in 3D. That's far from saying that any curved space
can be mapped into 3D + time.

Note that even if one approach is simpler or yields better or more accurate
result, the other approach can still be utilised ...

.... sometimes. As I say, it is limited.

.... It just means that less
applicable approach yields poorer results, is more convoluted, more
complicated or whatever.

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.

RKS Previously:
[Three space plus time is not a simple approximation. As Thorne says - the
two are equivalent. You are confusing Newtonian approximation with two
different accounts of the same thing and with the same precision ie one can
use the standard GR model of clocks and rods to explain ANY GR phenomena,
except for the expansion of spacetime.

A manifold by definition can be mapped onto three dimensions+time. It
should be possible to do this with expanding spacetime (even if precision is
lost ie an approximation), after all, space is not changing in dimension -
space is not expanding.]

And that is _wrong_. Not what Thorne said, what you said. If you
haven't already seen it, I strongly recommend this tutorial from
Ned Wright:

http://www.astro.ucla.edu/~wright/cosmo_01.htm

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.

They are not accumulating inertial motion relative to us (observers here on
Earth).

Actually they would be losing kinetic energy and momentum
as the expanson slowed but of course that ignores the
apparent acceleration.

You have attempted a not-very-clever stab at the Hubble constant.
Since 2006 the figure has been 77 (km/s)/Mpc with a certainty of 15%.

My value was from the 1 year WMAP results, perhaps your is
from the 3 year revision.

Now, why not have a stab at answering the question?

AFAICS I have, I have explained the effect of the mapping
and further discussed what Thorne means by equivalence of
the views in that context.

Curved spacetime can always be mapped onto three dimensions+time. All valid
forms, anyway.

Sorry, that is simply not true.

Thorne, Wheeler and other GR experts await your wise council on this issue.

I think you will find what I said in MTW. Although I don't have
the book, I'm sure if you look up "coordinate patches" it will
tell you why they are a necessity rather than just a convenience.

Let's start with the basics - can space expand or contract? The answer is
no.

Of course it can, why shouldn't it.

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

What is the agent of spacetime expansion?

"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.

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

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.

Saying that it is all too hard just doesn't wash.

And GR can not model time except where motion is involved. The closest you
get is a light cone that expands, but it is still a temporal snapshot.

What on earth are you talking about, a light cone by
definition is a 4D structure. It describes a 3D sphere
which expands as a function of time such that the
radius is c*t. The 4D view is a "snapshot" but not in
the usual sense of 3D at some instant, the time axis
is extended in the 4D picture.

You
can not model a simple experiment where a clock is left on a massive body
for one hour as measured by that clock and show why that clock is losing
ever more time to a space based clock.

Of course you can, how do you think gravitational
slowing is predicted?

Consider three identical clocks A, B and C. Let all three clocks be in
space well away from any massive body. Let the clocks be synchronised. Let
two of the clocks B and C be conveyed to the massive body. Let one of the
clocks, B, be immediately conveyed back to clock A and the difference in
their measured time be compared. B will show that less time has passed than
A. GR has no problem modelling this.

Now, after some interval, let C be conveyed back to A and B (the conveyance
being identical for each trip to and from the massive body). C will have
measured less time than A OR B. GR can not model this because it involves
an interval that does not include any motion.

Utter nonsense, of course it copes with it without
the slightest problem.

Kip Thorne mentions the
'snapshot' nature of GR in his book, so I don't think I need to rigorously
prove this point.

I haven't read that particular book but you are obviously
misreading it in some way. GR has no problem at all with
any of the examples you have given. I think perhaps he may
have been describing the equaivalence between the static
4D view and the time-variable 3D view but that's quite
different from what you are describing.

See my note to David - no point in repeating book quotes etc.


OK, I may come back to this if you don't cover it and I have
time later.

George

.

Quantcast