Time dilation and expanding space

For instance in the frame of a neutrino emitted at
a speed of almost c just after the big bang and
absorbed by a detector here on earth interval of
emission to absorption will be a few seconds and
the distance that the neutrino travelled will be just
a few millimetres.

That is all fine and good. However, I can emit a particle with
near zero speed near the event horizon, and it will be travelling
nowhere near c when it crosses the EH. Only for objects "falling
from infinity", or directed towards the EH with significant speed
is the phrase "approaching the speed of light" correct.


Even from near infinity, objects do not approach the speed of light in such
a way that a photon emitted from that object in the direction of travel is
even 1kph less than c (as measured from the high velocity traveller's
frame).

Let's not forget that a high speed observer, one near the speed of light by
our relatively stationary (with respect to the surface of the Earth) and
count themselves as stationary ie they may conclude that you and I are near
the speed of light. This is a perfectly valid conclusion to make in Special
Relativity theory.

Remember, you said *as we approach the speed of light*, and
talked about what we see.


We can talk about what we see at the quantum scale, shortly after the Big
Bang, inside a star during supernova etc - not being able to physically
attend the events does not invalidate a thought experiment, particularly is
mathematical accounts concur with presumed observations. The calculation of
gamma at close to c applies to the relatively stationary observers
observation of high velocity objects and of the high velocity observer's
observation of the relatively stationary observer ie
gamma=1/(1-u^2/c^2)^.5 ('u' being the speed of the object)

The calculation does not provide for a speed of c ie 1-c^2/c^2=0 though an
infinite gamma is rapidly approach as the speed approaches c. Electrons and
neutrinos can be emitted at very high speeds. Indeed, they are not exactly
collecting dust inside some of these bigger accelerators

Then what did you mean by:

Each of these explanations fail to take into account
that as we approach the speed of light the distance
the photon travels falls to zero and the interval of
transit also falls to zero - photons can not be held
in suspended animation.


I mean as "u approaches c" ie
gamma=1/(1-u^2/c^2)^.5

We have held photons in suspended animation (BE condensate). We
have trapped photons in quantum wells (we can even "measure" them
there without absorbing them). You seem to be saying that we
will measure c to decrease, if we are infallers. What did you
mean to say?


Let's see a reference to these photons held in 'suspended animation'.
Let's see a reference to photons trapped in quantum wells.

Light does not randomly lose a little energy in passing.
That is how we recognize ancient objects... because
their spectra are unaltered (absorption notwithstanding).
Light very much is in suspended animation, when you
consider it never loses energy, and were you to be able
to travel alongside it, would appear as a stationary E
and M field... a 'standing wave' as it were.

You can not travel alongside a photon, even in principle.
The reason is that the universe is far too small. For the
interval at c as a photon travels from one side of the
universe to the other is zero and the distance that the
photon travels at c is zero ie the point of emission and
absorption are touching in the c frame.

c has no frame. You cannot apply / infer the LT and say
something about what a photon sees, however much poetry you see
there. The derivation of the LT *forbids* v = c. And it is
clear that photons respond to that which they pass, so they are
"aware" of the space they are passing through.


One can assume a frame of v=c-1/infinity.

The path that photons take is the shortest one between the point of emission
and absorption - if spacetime is curved then the path will be likewise
curved. That does not mean that decisions are made 'in flight'. Indeed,
the very idea is an illusion. As u approaches c the length of the path
taken by high velocity object approaches zero and the interval of
transmission approaches zero.

In essence, the speed of a photon in the light
frame is zero, because it travels no distance in no
time.

No.


The path that photons take is the shortest one between the point of emission
and absorption - if spacetime is curved then the path will be likewise
curved. That does not mean that decisions are made 'in flight'. Indeed,
the very idea is an illusion. As u approaches c the length of the path
taken by a high velocity object approaches zero and the interval of
transmission approaches zero.

In any other calculus we would extrapolate to the infinite point by drawing
a graph and noting where the line passes through zero.


Here are some SR basics - the speed of light is
always c regardless of the frame of the observer
(assuming the beam of light is travelling through a
vacuum or the speed of single photons is being
observed). Thus if you managed to get yourself to
c-1/infinity speed and shone a torch, the light
would leave that torch at the speed of light *relative
to you and your torch*.

Thank you. Consider that a photon clustered near a "maxima of an
EM wave" will always be in that position. The wave is static to
the photon.


It is either wave *or* particle - you can't mix the metaphors.

Only large scale general relativity is not currently
modeled in QM

No. No part of spacetime is modelled in QM.

from 'Q is for Quantum: Particle Physics from A to Z':
"Relativistic Quantum Mechanics: The version of quantum mechanics that also
takes account of the requirements of the special theory of relativity (see
relativity theory). As yet, there is no satisfactory theory that includes
quantum mechanics and the \ general theory of relativity (see theory of
everything), but this does not matter when dealing with practical problems
such as the way atomic spectra are produced, because quantum gravity is
likely to be important only at the Planck scale.

But the requirements of the special theory are extremely important in
practical applications such as spectroscopy. This is most easily understood
by thinking of the electrons in an atom as tiny particles moving very fast
in their orbits; any system in which high speeds are involved (that is,
speeds that are a sizeable fraction of the speed of light) has to be
described in terms of the special theory if we want to predict its behaviour
accurately.

The first person to achieve this marriage of quantum theory and the special
theory was Paul Dirac, in 1928. Among other things, his development of
relativistic quantum mechanics led to the prediction of the existance of
antimatter."

Minkowski's 'SpaceTime' is a special relativistic concept.

Note that photon's are quantum particles and the path of photons does follow
curved spacetime eg in the vacinity of a massive object such as a star.

The history of space-time in QM is not new - here the abstract of paper by
Feynman from 1948:-

Space-Time Approach to Non-Relativistic Quantum Mechanics
R.P. Feynman Cornell University, Ithaca, New York
Reprinted in "Quantum Electrodynamics", edited by Julian Schwinger

Abstract Non-relativistic quantum mechanics is formulated here in a
different way. It is, however, mathematically equivalent to the familiar
formulation. In quantum mechanics the probability of an event which can
happen in several different ways is the absolute square of a sum of complex
contributions, one from each alternative way. The probability that a
particle will be found to have a path x(t) lying somewhere within a region
of space time is the square of a sum of contributions, one from each path in
the region. The contribution from a single path is postulated to be an
exponential whose (imaginary) phase is the classical action (in units of ~)
for the path in question. The total contribution from all paths reaching x,
t from the past is the wave function (x, t). This is shown to satisfy
Schroedinger's equation. The relation to matrix and operator algebra is
discussed. Applications are indicated, in particular to eliminate the
coordinates of the field oscillators from the equations of quantum
electrodynamics. "
http://dbserv.ihep.su/~elan/src/feynman48c/eng.pdf

Here is a short extract from 'The History of Quantum Mechanics':
"Heisenberg's work used matrix methods made possible by the work of Cayley
on matrices 50 years earlier. In fact 'rival' matrix mechanics deriving from
Heisenberg's work and wave mechanics resulting from Schrödinger's work now
entered the arena. These were not properly shown to be equivalent until the
necessary mathematics was developed by Riesz about 25 years later.
Also in 1927 Bohr stated that space-time coordinates and causality are
complementary. Pauli realised that spin, one of the states proposed by Bose,
corresponded to a new kind of tensor, one not covered by the Ricci and
Levi-Civita work of 1901. However the mathematics of this had been
anticipated by Eli Cartan who introduced a 'spinor' as part of a much more
general investigation in 1913.

Dirac, in 1928, gave the first solution of the problem of expressing quantum
theory in a form which was invariant under the Lorentz group of
transformations of special relativity. He expressed d'Alembert's wave
equation in terms of operator algebra.

The uncertainty principle was not accepted by everyone. Its most outspoken
opponent was Einstein. He devised a challenge to Niels Bohr which he made at
a conference which they both attended in 1930. Einstein suggested a box
filled with radiation with a clock fitted in one side. The clock is designed
to open a shutter and allow one photon to escape. Weigh the box again some
time later and the photon energy and its time of escape can both be measured
with arbitrary accuracy. Of course this is not meant to be an actual
experiment, only a 'thought experiment'.

Niels Bohr is reported to have spent an unhappy evening, and Einstein a
happy one, after this challenge by Einstein to the uncertainty principle.
However Niels Bohr had the final triumph, for the next day he had the
solution. The mass is measured by hanging a compensation weight under the
box. This is turn imparts a momentum to the box and there is an error in
measuring the position. Time, according to relativity, is not absolute and
the error in the position of the box translates into an error in measuring
the time.

Although Einstein was never happy with the uncertainty principle, he was
forced, rather grudgingly, to accept it after Bohr's explanation."

"Is space-time quantized?
In general relativity, space-time is assumed to be smooth and continuous-
and not just in the mathematical sense. In the theory of quantum mechanics,
there is an inherent discreteness present in physics. In attempting to
reconcile these two theories, it is sometimes postulated that spacetime
should be quantized at the very smallest scales. Current theory is focused
on the nature of space-time at the Planck scale. Loop quantum gravity,
string theory, and black hole thermodynamics all predict a quantized
space-time with agreement on the order of magnitude. Loop quantum gravity
even makes precise predictions about the geometry of spacetime at the Planck
scale."
(Wikipedia)

Well, I've shown you (some of) mine, now you show me yours - references
stating that Space-time is not modelled in quantum mechanics. It is true
that, for the most part, space and time are treated separately and
differently in QM - spatial co-ordinates are operators whereas time is a
parameter.

The standard around here really drops when you
stop quoting from text book learning and try to
think for yourself.

http://ptonline.aip.org/journals/doc...s_3/16_1.shtml
Since you start spouting more non-sequitur, here is curvature
here on Earth.

Thanks - agrees with everything I've said so far (as far as I can tell).


--
Kind Regards
Robert Karl Stonjek

Dear Robert Karl Stonjek:

"Robert Karl Stonjek" wrote in message
...

"N:dlzc D:aol T:com (dlzc)" wrote in message
...

.... snip
I have read the about the quantum mechanical processes
that force the electon into the proton to form neurtons.

Wrong. What provided the force that kept the proton and electron
closer than the 1s orbital? Wasn't it being slammed by lots of
local matter, made local by gravitation? Once the QM
relationship is formed to generate a neutron and (I think) an
anti-electron neutrino, then you are on solid ground. I offered
a compromise, that both quantum and classical effects were
required, but apparently hit one of your "hot buttons".

There are process with names like 'confinement principle'
(I don't recall exactly) and there are several steps,
described by quantum mechanics. Wheeler, a virtuouso
General Relativity scientist, blieves that Quantum
mechanics is needed to describe the singularity and I
concur with his view. Of course there is currently no
such description beyond the neutron star stage (I think).

I agree, but then I don't concern myself with the singularity.

David A. Smith

On 5 Mar, 14:19, "Robert Karl Stonjek" wrote:
"George Dishman" wrote in message oups.com...
On 4 Mar, 20:44, "Robert Karl Stonjek" 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 sheet 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

Dear Robert Karl Stonjek:

"Robert Karl Stonjek" wrote in message
...
For instance in the frame of a neutrino emitted at
a speed of almost c just after the big bang and
absorbed by a detector here on earth interval of
emission to absorption will be a few seconds and
the distance that the neutrino travelled will be just
a few millimetres.

That is all fine and good. However, I can emit a
particle with near zero speed near the event horizon,
and it will be travelling nowhere near c when it
crosses the EH. Only for objects "falling from
infinity", or directed towards the EH with significant
speed is the phrase "approaching the speed of light"
correct.

Even from near infinity, objects do not approach the
speed of light in such a way that a photon emitted
from that object in the direction of travel is even 1kph
less than c (as measured from the high velocity
traveller's frame).

Let's not forget that a high speed observer, one near
the speed of light by our relatively stationary (with
respect to the surface of the Earth) and count
themselves as stationary ie they may conclude that
you and I are near the speed of light. This is a
perfectly valid conclusion to make in Special
Relativity theory.

We are talking about stuff falling into a BH. But rather than
belabor the point...

Remember, you said *as we approach the
speed of light*, and talked about what we see.


We can talk about what we see at the quantum scale,
shortly after the Big Bang, inside a star during
supernova etc - not being able to physically attend the
events does not invalidate a thought experiment,
particularly is mathematical accounts concur with
presumed observations. The calculation of gamma at
close to c applies to the relatively stationary observers
observation of high velocity objects and of the high
velocity observer's observation of the relatively
stationary observer ie gamma=1/(1-u^2/c^2)^.5 ('u'
being the speed of the object)

The calculation does not provide for a speed of c ie
1-c^2/c^2=0 though an infinite gamma is rapidly
approach as the speed approaches c. Electrons and
neutrinos can be emitted at very high speeds.
Indeed, they are not exactly collecting dust inside
some of these bigger accelerators

Then what did you mean by:

Each of these explanations fail to take into account
that as we approach the speed of light the distance
the photon travels falls to zero and the interval of
transit also falls to zero - photons can not be held
in suspended animation.

I mean as "u approaches c" ie
gamma=1/(1-u^2/c^2)^.5

But you just said we always see light passing us at c. Not to
belabor the point...

We have held photons in suspended animation
(BE condensate). We have trapped photons in
quantum wells (we can even "measure" them
there without absorbing them). You seem to be
saying that we will measure c to decrease, if we
are infallers. What did you mean to say?

Let's see a reference to these photons held in
'suspended animation'.
Let's see a reference to photons trapped in quantum wells.

Slowed and/or stopped light
C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, Nature 409, 490
(2001).
C. H. van der Wal, M. D. Eisaman, A. Andr´e, R. L. Walsworth, D.
F. Phillips, A. S. Zibrov,
and M. D. Lukin, Science 301, 196 (2003).
D. F. Phillips, A. Fleischhauer, A. Mair, and R. L. Walsworth,
Phys. Rev. Lett. 86, 783
(2001).
L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature
397, 594 (1999).

Light trapped in a quantum well
http://adsabs.harvard.edu/abs/1998APS..MAR..M301W
http://ostc.physics.uiowa.edu/~prine...forslowing.htm
QUOTE
A unique aspect of the photonic bandstructure of [Bragg spaced
quantum well]s is the presence of a nonpropagating, intermediate
band, which can be used to slow and trap light.
END QUOTE

And of course you know that charge is (modelled as) virtual
photons, which are certainly trapped (at one end) on a charged
particle.

How about light faster than c?
http://www.vnunet.com/vnunet/news/21...increase-speed


Light does not randomly lose a little energy in passing.
That is how we recognize ancient objects... because
their spectra are unaltered (absorption notwithstanding).
Light very much is in suspended animation, when you
consider it never loses energy, and were you to be able
to travel alongside it, would appear as a stationary E
and M field... a 'standing wave' as it were.

You can not travel alongside a photon, even in principle.
The reason is that the universe is far too small. For the
interval at c as a photon travels from one side of the
universe to the other is zero and the distance that the
photon travels at c is zero ie the point of emission and
absorption are touching in the c frame.

c has no frame. You cannot apply / infer the LT and
say something about what a photon sees, however much
poetry you see there. The derivation of the LT *forbids*
v = c. And it is clear that photons respond to that which
they pass, so they are "aware" of the space they are
passing through.

One can assume a frame of v=c-1/infinity.

Applies only to massive particles.

The path that photons take is the shortest one between
the point of emission and absorption - if spacetime is
curved then the path will be likewise curved. That does
not mean that decisions are made 'in flight'. Indeed,
the very idea is an illusion.

Diffraction. 1/4 wave effects. Curvature isn't the only thing
light contends with.

Space and time are illusion. You have the cart before the horse.

As u approaches c the length of the path taken by
high velocity object approaches zero and the interval of
transmission approaches zero.

Only applies to massive particles.

In essence, the speed of a photon in the light
frame is zero, because it travels no distance in no
time.

No.

The path that photons take is the shortest one between
the point of emission and absorption - if spacetime is
curved then the path will be likewise curved. That does
not mean that decisions are made 'in flight'. Indeed,
the very idea is an illusion. As u approaches c the
length of the path taken by a high velocity object
approaches zero and the interval of transmission
approaches zero.

Repeating it does not make it more true.

In any other calculus we would extrapolate to the
infinite point by drawing a graph and noting where the
line passes through zero.

We cannot know what light perceives. But it "responds" to the
space and matter that it passes through / by / around. The LT do
not apply to light, however valid your extraction to faster and
faster massive particles might be. Light obtains finite results
at each end. The LT fails to yield a finite value.

Here are some SR basics - the speed of light is
always c regardless of the frame of the observer
(assuming the beam of light is travelling through a
vacuum or the speed of single photons is being
observed). Thus if you managed to get yourself to
c-1/infinity speed and shone a torch, the light
would leave that torch at the speed of light *relative
to you and your torch*.

Thank you. Consider that a photon clustered near a
"maxima of an EM wave" will always be in that
position. The wave is static to the photon.

It is either wave *or* particle - you can't mix the metaphors.

No, it is both a wave *and* a particle, and the test you describe
collapses the other behavior. You misunderstood.

Only large scale general relativity is not currently
modeled in QM

No. No part of spacetime is modelled in QM.

from 'Q is for Quantum: Particle Physics from A to Z':
"Relativistic Quantum Mechanics: The version of quantum
mechanics that also takes account of the requirements of
the special theory of relativity (see relativity theory).
....
But the requirements of the special theory are extremely
important in practical applications such as spectroscopy.
This is most easily understood by thinking of the
electrons in an atom as tiny particles moving very fast
in their orbits; any system in which high speeds are
involved (that is, speeds that are a sizeable fraction of the
speed of light) has to be described in terms of the special
theory if we want to predict its behaviour accurately.

The first person to achieve this marriage of quantum theory
and the special theory was Paul Dirac, in 1928. Among
other things, his development of relativistic quantum
mechanics led to the prediction of the existance of
antimatter."

Spacetime is "married" to QM. It is not part of it. Thank you
for providing the citation for me.

....
Well, I've shown you (some of) mine, now you show me
yours - references stating that Space-time is not
modelled in quantum mechanics. It is true that, for the
most part, space and time are treated separately and
differently in QM - spatial co-ordinates are operators
whereas time is a parameter.

No need. You have done it for me. Besides, the "separate space
and time" come about when trying to map *completed QM results* to
the macroscopic world. A "marriage" as you have provided a quote
to.

The standard around here really drops when you
stop quoting from text book learning and try to
think for yourself.

http://ptonline.aip.org/journals/doc...s_3/16_1.shtml
Since you start spouting more non-sequitur, here
is curvature here on Earth.

Thanks - agrees with everything I've said so far (as
far as I can tell).

I'm really not trying to disagree with you in principle. I don't
think we are that far apart on the facts. Just thought your "bag
of tricks" could hold another pertinent fact...

David A. Smith

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

We are talking about stuff falling into a BH. But rather than
belabor the point...

No, YOU were talking about objects infalling - I was considering an object
already there.

I mean as "u approaches c" ie
gamma=1/(1-u^2/c^2)^.5

But you just said we always see light passing us at c. Not to
belabor the point...


That's right - light as a speed of c relative to the observer.

We have held photons in suspended animation
(BE condensate). We have trapped photons in
quantum wells (we can even "measure" them
there without absorbing them). You seem to be
saying that we will measure c to decrease, if we
are infallers. What did you mean to say?

Let's see a reference to these photons held in
'suspended animation'.
Let's see a reference to photons trapped in quantum wells.

Slowed and/or stopped light
C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, Nature 409, 490
(2001).

Thanks for that. I'll look at each paper in turn.

"Observation of coherent optical information storage in an atomicmedium
using halted light pulses
CHIEN LIU, ZACHARY DUTTON, CYRUS H. BEHROOZI & LENE VESTERGAARD HAU

Electromagnetically induced transparency is a quantum interference effect
that permits the propagation of light through an otherwise opaque atomic
medium; a 'coupling' laser is used to create the interference necessary to
allow the transmission of resonant pulses from a 'probe' laser. This
technique has been used to slow and spatially compress light pulses by seven
orders of magnitude, resulting in their complete localization and
containment within an atomic cloud. Here we use electromagnetically induced
transparency to bring laser pulses to a complete stop in a magnetically
trapped, cold cloud of sodium atoms. Within the spatially localized pulse
region, the atoms are in a superposition state determined by the amplitudes
and phases of the coupling and probe laser fields. Upon sudden turn-off of
the coupling laser, the compressed probe pulse is effectively stopped;
coherent information initially contained in the laser fields is 'frozen' in
the atomic medium for up to 1 ms. The coupling laser is turned back on at a
later time and the probe pulse is regenerated: the stored coherence is read
out and transferred back into the radiation field. We present a theoretical
model that reveals that the system is self-adjusting to minimize dissipative
loss during the 'read' and 'write' operations. We anticipate applications of
this phenomenon for quantum information processing."

RKS:
no single transmission of light is frozen. What is frozen is the "coherent
information initially contained in the laser fields" and not the photons per
se.


C. H. van der Wal, M. D. Eisaman, A. Andr´e, R. L. Walsworth, D.
F. Phillips, A. S. Zibrov,
and M. D. Lukin, Science 301, 196 (2003).
D. F. Phillips, A. Fleischhauer, A. Mair, and R. L. Walsworth,
Phys. Rev. Lett. 86, 783
(2001).
L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature
397, 594 (1999).

Light trapped in a quantum well
http://adsabs.harvard.edu/abs/1998APS..MAR..M301W

http://ostc.physics.uiowa.edu/~prine...forslowing.htm
QUOTE
A unique aspect of the photonic bandstructure of [Bragg spaced
quantum well]s is the presence of a nonpropagating, intermediate
band, which can be used to slow and trap light.
END QUOTE


"Atomic Memory for Correlated Photon States
C. H. van der Wal, M. D. Eisaman, A. André, R. L. Walsworth, D. F. Phillips,
A. S. Zibrov,1,2,3 M. D. Lukin

We experimentally demonstrate emission of two quantum-mechanically
correlated light pulses with a time delay that is coherently controlled via
temporal storage of photonic states in an ensemble of rubidium atoms. The
experiment is based on Raman scattering, which produces correlated pairs of
spin-flipped atoms and photons, followed by coherent conversion of the
atomic states into a different photon beam after a controllable delay. This
resonant nonlinear optical process is a promising technique for potential
applications in quantum communication."

RKS:
Again, it is the state of the photon emission that is stored and not the
photon per se.

And of course you know that charge is (modelled as) virtual
photons, which are certainly trapped (at one end) on a charged
particle.

How about light faster than c?
http://www.vnunet.com/vnunet/news/21...increase-speed

From the comments:-

"Speeding up light
The article refers to the speed of light in an optical fibre. This means the
speed of light in glass, which is closer to 2.10^8 than 3.10^8.

Furthermore the speed of light in various media travels at different speeds
depending on the exact wavelength of the light. So it is possible to speed
up light by, for example, changing the wavelength that travels through the
fibre. You can look at the original article on: http://www.opticsexpress.org
"

The Paper can be downloaded from here.
http://www.opticsexpress.org/abstract.cfm?id=116587
They are, of course, not referring to light travelling faster than c as the
poorly written article claimed nor are they referring to the slowing of an
actual light beam but to scattering ie the absorption and re-radiation of
light. Between each of these events is vacuous space through which light
charges along at c (between each atom in a material is a vacuum like the one
found out there in space).

The science backs me up, the magazine article seems to support you.

One can assume a frame of v=c-1/infinity.

Applies only to massive particles.


Are you saying that it doesn't apply to light? Whist it is not possible to
travel at c, several scientists have observed that at the speed of light the
point of emission and absorption are touching and the transmission interval
is zero (though this is their opinion, as science can not actually probe
these conditions).

As u approaches c the length of the path taken by
high velocity object approaches zero and the interval of
transmission approaches zero.

Only applies to massive particles.


One can not say what happens at c, which is why I can't say that time
definitely stops. But equally one can not make that claim that special
relativistic time dilation and length contraction do not apply to photons.

If your statement is derived from science theory then I would very much like
to know what that theory is - what theory outlines the conditions for a
photon as it travels at the speed of light? If you have no science to back
you up then the statement "Only applies.." is your opinion and should be
stated as such ie "In my opinion, this only applies to massive particles."
I've tried to differentiate between the science, my interpretation of the
science and my opinion.

The path that photons take is the shortest one between
the point of emission and absorption - if spacetime is
curved then the path will be likewise curved. That does
not mean that decisions are made 'in flight'. Indeed,
the very idea is an illusion. As u approaches c the
length of the path taken by a high velocity object
approaches zero and the interval of transmission
approaches zero.

Repeating it does not make it more true.


I don't think you can falsify it.
It is the path through spacetime that is the shortest, not the path through
space (just repeating that in case I hadn't made that point clear
previously).


In any other calculus we would extrapolate to the
infinite point by drawing a graph and noting where the
line passes through zero.

We cannot know what light perceives. But it "responds" to the
space and matter that it passes through / by / around. The LT do
not apply to light, however valid your extraction to faster and
faster massive particles might be. Light obtains finite results
at each end. The LT fails to yield a finite value.


What finite results are you referring to? I am opining that the interval of
transmission at c is zero and that the transmission distance is always zero.
How do you propose to establish that this is not true?

It is either wave *or* particle - you can't mix the metaphors.

No, it is both a wave *and* a particle, and the test you describe
collapses the other behavior. You misunderstood.


Both wave and particle are metaphors - light can not be both. It is more
likely that it is neither but we may never know.

--
Kind Regards
Robert Karl Stonjek

Dear Robert Karl Stonjek:

"Robert Karl Stonjek" wrote in message
news
We are talking about stuff falling into a BH. But rather
than belabor the point...

No, YOU were talking about objects infalling - I was
considering an object already there.

Then we'll drop it, because we are talking past each other.

We have held photons in suspended animation
(BE condensate). We have trapped photons in
quantum wells (we can even "measure" them
there without absorbing them). You seem to be
saying that we will measure c to decrease, if we
are infallers. What did you mean to say?

Let's see a reference to these photons held in
'suspended animation'.
Let's see a reference to photons trapped in quantum wells.

Slowed and/or stopped light
C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, Nature 409,
490
(2001).

Thanks for that. I'll look at each paper in turn.

"Observation of coherent optical information storage
in an atomic medium using halted light pulses
CHIEN LIU, ZACHARY DUTTON, CYRUS H. BEHROOZI & LENE VESTERGAARD
HAU
....
RKS:
no single transmission of light is frozen. What is
frozen is the "coherent information initially contained
in the laser fields" and not the photons per se.

So you have a way in mind of moving information between photons?

C. H. van der Wal, M. D. Eisaman, A. Andr4e, R. L. Walsworth,
D.
F. Phillips, A. S. Zibrov,
and M. D. Lukin, Science 301, 196 (2003).
D. F. Phillips, A. Fleischhauer, A. Mair, and R. L. Walsworth,
Phys. Rev. Lett. 86, 783
(2001).
L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature
397, 594 (1999).

Light trapped in a quantum well
http://adsabs.harvard.edu/abs/1998APS..MAR..M301W

http://ostc.physics.uiowa.edu/~prine...forslowing.htm
QUOTE
A unique aspect of the photonic bandstructure of [Bragg spaced
quantum well]s is the presence of a nonpropagating,
intermediate
band, which can be used to slow and trap light.
END QUOTE

"Atomic Memory for Correlated Photon States
C. H. van der Wal, M. D. Eisaman, A. Andri, R. L. Walsworth, D.
F. Phillips,
A. S. Zibrov,1,2,3 M. D. Lukin

We experimentally demonstrate emission of two quantum-
mechanically correlated light pulses with a time delay that
is coherently controlled via temporal storage of photonic
states in an ensemble of rubidium atoms. The experiment
is based on Raman scattering, which produces correlated
pairs of spin-flipped atoms and photons, followed by
coherent conversion of the atomic states into a different
photon beam after a controllable delay. This resonant
nonlinear optical process is a promising technique for
potential applications in quantum communication."

RKS:
Again, it is the state of the photon emission that is stored
and not the photon per se.

The *readout* is written to another photon beam at a later time.
At which time the original photon's existence ends. The photon
is trapped.

And of course you know that charge is (modelled as)
virtual photons, which are certainly trapped (at one end)
on a charged particle.

How about light faster than c?
http://www.vnunet.com/vnunet/news/21...increase-speed

From the comments:-

"Speeding up light
The article refers to the speed of light in an optical fibre.
This means the speed of light in glass, which is closer
to 2.10^8 than 3.10^8.

And probably phase or group velocity at that...

....
The Paper can be downloaded from here.
http://www.opticsexpress.org/abstract.cfm?id=116587

Thanks.

They are, of course, not referring to light travelling faster
than c as the poorly written article claimed nor are they
referring to the slowing of an actual light beam but to
scattering ie the absorption and re-radiation of light.
Between each of these events is vacuous space through
which light charges along at c (between each atom in a
material is a vacuum like the one found out there in space).

The science backs me up, the magazine article seems
to support you.

Actually, the science doesn't back either of us up. And I am
sorry you are feeling like I am harrassing you.

One can assume a frame of v=c-1/infinity.

Applies only to massive particles.

Are you saying that it doesn't apply to light?

I'm saying "we can't know".

Whist it is not possible to travel at c, several
scientists have observed that at the speed of light the
point of emission and absorption are touching and
the transmission interval is zero (though this is their
opinion, as science can not actually probe these
conditions).

As u approaches c the length of the path
taken by high velocity object approaches
zero and the interval of transmission
approaches zero.

Only applies to massive particles.

One can not say what happens at c, which is
why I can't say that time definitely stops.

It is a reasonable conclusion... for massive particles.

But equally one can not make that claim that
special relativistic time dilation and length
contraction do not apply to photons.

If your statement is derived from science theory
then I would very much like to know what that
theory is - what theory outlines the conditions for
a photon as it travels at the speed of light? If you
have no science to back you up then the statement
"Only applies.." is your opinion and should be
stated as such ie "In my opinion, this only applies
to massive particles." I've tried to differentiate
between the science, my interpretation of the
science and my opinion.

Not so far in this thread. You have provided only your
interpretation.

The path that photons take is the shortest
one between the point of emission and
absorption - if spacetime is curved then the
path will be likewise curved. That does not
mean that decisions are made 'in flight'. Indeed,
the very idea is an illusion. As u approaches c the
length of the path taken by a high velocity object
approaches zero and the interval of transmission
approaches zero.

Repeating it does not make it more true.

I don't think you can falsify it.

I have provided counter evidence, which has so far been
unremarked. From emission to absorption, light "responds" to all
the intervening stuff, curved space and diffraction effects
(which both provide non-Euclidean paths, but diffraction is not
curved space). So between emission and apsorption there are
"intermediate effects", how sure are you that time is not much
more than this?

It is the path through spacetime that is the shortest,
not the path through space (just repeating that in
case I hadn't made that point clear previously).

;)

In any other calculus we would extrapolate to the
infinite point by drawing a graph and noting where the
line passes through zero.

We cannot know what light perceives. But it "responds"
to the space and matter that it passes through / by /
around. The LT do not apply to light, however valid your
extraction to faster and faster massive particles might be.
Light obtains finite results at each end. The LT fails to
yield a finite value.

What finite results are you referring to? I am opining

There is opinion...

that the interval of transmission at c is zero and that the
transmission distance is always zero. How do you
propose to establish that this is not true?

You insist on applying the LT where they cannot go. Obtain a
finite result for the energy of any massive particle you pass.
Yet light, which has a definite momentum, makes a finite effect /
change at both source and destination.

It is either wave *or* particle - you can't mix the
metaphors.

No, it is both a wave *and* a particle, and the test
you describe collapses the other behavior. You
misunderstood.

Both wave and particle are metaphors - light can not
be both. It is more likely that it is neither but we may
never know.

David A. Smith

"Robert Karl Stonjek" wrote in message
...

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.

At the event horizon, the time dilation factor becomes
infinite and I don't think the region within the horizon
maps onto any part of the 3D coordinate system.

Although the resolution of the resulting calculation will
depend on the number of calculations done, one will arrive at the same
result in principle.

No, it isn't a question of approximation. Outside the
horizon there can be a perfect mapping, inside is not
covered by the coordinate patch.

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.

No, I meant space. Distances increase as a function of time
and in the standard GR description space is said to expand.
The uniform homogenous approximation is called the "Hubble
Flow" and individual galaxies have "proper motions" relative
to that mean.

In the simple mapping, space is not expanding (only space-time).

"spacetime" is the 4D view so includes time as an axis, it
cannot expand because that implies a change with time, but
time is inherently part of it. Again, look at the spacetime
diagram or better the one below it with "US" shown:

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

Note the horizontal grey lines which are "space" at different
epochs. The length of those lines between the worldlines of
the galaxies increases as you go up the diagram which is what
is meant by space expanding. Note also the worldlines near the
bottom edge of the diagram slope more than the edges of the
lightcones on our worldline meaning the speeds of those
galaxies are more than the speed of light in that mapping.

On the other hand, if you drew a small box just large enough
to encompass one lightcone, you could approximate that with a
Minkowski patch hence it is a box of spacetime in that sense.
Thus the choice of the worldline for the time axis is a global
preference but is not significant in a local sense.

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 space _does_ result in recession
velocities in excess of c when you try to map to a 3D plus
time view.

Not necessarily.

It is necessary in all the standard models as you could
see from the earlier example.

Objects are not moving inertially ie that are not moving
with respect to the space around them.

Only at relatively low speeds due to gravitational interactions
with other nearby galaxies, that is what is called proper motion.

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.

Inertial has a fairly specific meaning but yes, you can
decompose the speed of any galaxy into a speed relative
to the mean of all its neighbours and that mean relative
to us.

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.

No, that is incorrect. The gravitational redshift due to
a single galaxy is the same regardless of distance, it
depends on it mass and how deep within the galaxy the
light originated. The Hubble redshift is proportional to
distance and is additional to individual gravitational
redshift.

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
mean 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 a common factor in all cosmologies and falls in all
the models I know about except the de Sitter model of an
empty universe, Einstein's original static model and the
old steady state model where new matter was created
continuously counteracting the thinning caused by expansion.

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.

I don't know which earlier model you are thinking of. It is
poosible to form a non-homogenous model which is spherically
symmetric, basically a ball of stars in an empty universe,
but I don't think that has been seen as a realistic model
since GR.

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.

It should decrease as time progresses but looking at greater
distances you look back to the past and expect higher densities
and there is some evidence for that. Be careful though because
often papers discuss co-moving volumes so normalise out the
effects of scale factor.

... 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.

I think you are somehow misreading standard cosmology, that
is the basis of all the models other than the Einstein model
and the pre-expansion phase of the Eddingtom-Lemaitre 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.

That is redshift due to scattering, ..

No, perhaps I wasn't clear. We have a box with particles, I'll
just show four to save typing. A photon is emitted from the left:

+----------------------------+
| * |
| *~ * |
| * |
+----------------------------+

It travels to the right where is it absorbed, but the box is
expanding. The motions are to scale:

+----------------------------------+
| * |
| * ~* |
| * |
+----------------------------------+

The right hand particle is moving away from the source particle
so the frequency is reduced by Doppler, not scattering. It didn't
encounter any other particle on the way.

.. 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.

"norma" should have read "normal". The relativistic Doppler equation
is the same as the product of the geometric term which would apply
in Galilean relativity (i.e. the Doppler equation for sound) and
the SR time dilation factor. It is only a crude analogy but it
satisfies what you asked for.

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.

No but it shows it is not "personal conjecture". Having another look
through D'Inverno, this is basically Weyl's postulate described in
section 22.5. You mention the Friedman equation later and this is
derived from Weyl's postulate in 22.9 where it is specifically noted
that the current pressure term is about 10^5 less than the matter
term hence "the substratum is comprised of dust". See the line
immediately after eqn 22.55.

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.

You said it "smacks of a personal conjecture rather than a reference
to generally agreed cosmological principles or cosmological models."
I think I have shown that is not the case.

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?

No, I am telling you that the standard cosmological models treat
the mean contribution of matter as a dust because the pressure
term is negligible.

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.

In the first paragraph? No, he means space. He is describing
the geometry of "cosmic time slices", in other words a 3D
surface at a uniform cosmic time.

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

The grids you see on the curved surfaces would expand with time,
they show possible geometries at the same epoch.

"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.

I believe I already addressed that.

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.

Not necessarily, but the point was that inflation does not start
from t=0 but after the GUT era.

George