The Instantaneous Creation of Infinite Space

OK. So I can type faster than I can think.
Here's my CORRECTION:

The Instantaneous Creation of Infinite Space

The 3-space in which we live is one of an infinite variety of possible
geometries. http://arxiv.org/PS_cache/gr-qc/pdf/9804/9804006.pdf. No
mortal can identify the right spatial form. The Big Bang creation
story comes in two incomprehensible versions. No human knows which
version is correct. This thread is a request that knowledgeable
mathematicians answer questions as simply as possible on the very
essence of mathematical cosmology and what is knowable and provable.

The most delightful creation story is that, in an instant, out of
nothing, infinite space suddenly came to be. The infinite and
everywhere appeared instantly, inexplicably; and time was also born.
The second creation story is a plain and simple alternative to the
first. Space (the everywhere) was born finite, with zero volume and
grew from that; and time also came to be.

The birthing of geometry in time has associated with that space and
time, a flow of idealized, mathematical trajectories. Each trajectory
is easily pictured as the spatial trace of an abstract idealized clock
moving effortlessly through that geometric space, parameterized by its
own clock time. Each clock, therefore, is defined by a timelike
geodesic.

The most glaring fact that I see in the simultaneous emergence of
space and time is the existence of the above mentioned global flow of
abstract coordinate clocks, all initially synchronized by God Himself.
Obviously, attempting mathematical physics by coordinatizing space
and time, if space is infinite and flat, can not produce the Lorentz
transformation. It isn't the Creator's choice. It doesn't harmonize
with creation. Going the route of conventional special relativity
would imply that imagining an event at some time in one frame of
reference would necessarily translate to the same event happening
in another frame before time even began. It's against nature.

Imagine the second creation story and the birthing of a hypersphere
(or projective 3-space if you prefer) from an initial inexplicable
point. The symmetry of this space demands a corresponding symmetry
in the global multidirectional flow of abstract coordinate clocks.
To understand this symmetry physically, I wish to understand motion
generally. My most stubborn and longstanding expectation is that
all motions in spatially compact spacetimes have extremely absolute
characteristics, whereas, all motion in spatially infinite spacetime
is relative.

Therefo I would like to define a geodesic coordinate system in
space as a flow of our abstract idealized clocks such that all those
clocks travel the same distances as a function of clock time. I also
like the requirement that nearby clocks in the flow all move in
approximately the same direction. What are all the global geodesic
coordinate systems for an expanding circle, sphere and hypersphere?

Eugene Shubert
http://www.everythingimportant.org

Perfectly Innocent wrote:
The most delightful creation story is that, in an instant, out of
nothing, infinite space suddenly came to be. The infinite and
everywhere appeared instantly, inexplicably; and time was also born.
The second creation story is a plain and simple alternative to the
first. Space (the everywhere) was born finite, with zero volume and
grew from that; and time also came to be.

Within FRW cosmological models you have those two choices (with a
sub-choice for the first: flat or hyperbolic 3-space). But who's to say
those models are all there is? In particular, it is expected that a real
theory of quantum gravity will have major things to say about this, and
presumably the evolution of the cosmos at early times will be
significantly different in such a theory....


The birthing of geometry in time has associated with that space and
time, a flow of idealized, mathematical trajectories. Each trajectory
is easily pictured as the spatial trace of an abstract idealized clock
moving effortlessly through that geometric space, parameterized by its
own clock time. Each clock, therefore, is defined by a timelike
geodesic.

Sure. You can imagine such clocks.


The most glaring fact that I see in the simultaneous emergence of
space and time is the existence of the above mentioned global flow of
abstract coordinate clocks, all initially synchronized by God Himself.

Huh??? Those clocks "exist" only in your imagination, and it is up to
YOU to synchronize them. Go ahead -- it's easy to IMAGINE how to do
that.... But the only "God" here is YOU.


Obviously, attempting mathematical physics by coordinatizing space
and time, if space is infinite and flat, can not produce the Lorentz
transformation.

I have no idea what you mean by that. The Lorentz transformation holds
between any pair of locally-inertial coordinates. That, of course, is
true in any Lorentzian manifold.


It isn't the Creator's choice.

Speak for yourself -- because YOU are the "creator" here. This whole
discussion is about figments of your imagination. That is, of course,
what all mathematical models of physics are....


It doesn't harmonize
with creation.

Why not? -- You don't like your own creation?


Going the route of conventional special relativity
would imply that imagining an event at some time in one frame of
reference would necessarily translate to the same event happening
in another frame before time even began.

But you're imagining a manifold that is not consistent with the
requirements of SR, so why should one be concerned that attempting to
apply SR yields nonsense?


It's against nature.

"Nature" of course has nothing whatsoever to do with this, as you are
not discussing the world we inhabit, you are discussing a figment of
your own imagination.


Imagine the second creation story and the birthing of a hypersphere
(or projective 3-space if you prefer) from an initial inexplicable
point. The symmetry of this space demands a corresponding symmetry
in the global multidirectional flow of abstract coordinate clocks.

Why?

In particular: all you have specified is that space is
a 3-sphere; that is a topological condition, and is not
"symmetry" in any usual sense, which is normally expressed
as a set of Killing vectors, which obviously require a
connection on the manifold.


To understand this symmetry physically, I wish to understand motion
generally. My most stubborn and longstanding expectation is that
all motions in spatially compact spacetimes have extremely absolute
characteristics, whereas, all motion in spatially infinite spacetime
is relative.

Here your "most stubborn and longstanding expectation" is clearly wrong.

Counterexample: consider the flat and hyperbolic FRW manifolds. Just as
in the spherical FRW manifolds, the cosmic time coordinate is expressed
in the proper time since the initial singularity of each and every dust
particle. That cosmic time coordinate is "absolute" in the sense that it
is unique and the same for all observers, and yields a similarly
"absolute" spatial structure relative to which all motion can be referenced.


It is true that certain manifolds of GR have an "absolute" spatial
structure wrt which motion can be referenced. This is invariably due to
those manifolds having appropriate symmetries (e.g. a timelike Killing
vector), or appropriate other structure (e.g. a congruence of timelike
geodesics as in the FRW manifolds). Note that topology alone is not
sufficient for this, you need some additional structure to have any sort
of "absolute" reference (and beware of that word -- it has meanings
which don't apply here).

Topology constrains the metric applied to a manifold, but
does not determine it. In your SxR toy model you can apply
a metric that determines a specific "absolute frame". But
I could apply a different metric to the same manifold that
determines a different "absolute frame". The topology
requires there be such an "absolute frame", but does not
in any way determine which frame is the "absolute" one.


Therefo I would like to define a geodesic coordinate system in
space as a flow of our abstract idealized clocks such that all those
clocks travel the same distances as a function of clock time.

That is the usual thing to do in FRW manifolds, and is called "cosmic
time". Note it applies in all FRW manfiolds, including those with
non-compact 3-spaces.


I also
like the requirement that nearby clocks in the flow all move in
approximately the same direction.

That is also true in the FRW manifolds for those "cosmic clocks".


What are all the global geodesic
coordinate systems for an expanding circle, sphere and hypersphere?

There are none. It simply is not possible to cover S^n with a single
coordinate system, for any n0. Note this is a topological theorem,
unrelated to any metric.


If you are truly interested in topics like this, you
need to study geometry. For starters I suggest:
Frankel, _The_Geometry_of_Physics_.


Tom Roberts

Tom Roberts wrote in message ...
Perfectly Innocent wrote:
The most delightful creation story is that, in an instant, out of
nothing, infinite space suddenly came to be. The infinite and
everywhere appeared instantly, inexplicably; and time was also born.
The second creation story is a plain and simple alternative to the
first. Space (the everywhere) was born finite, with zero volume and
grew from that; and time also came to be.

Within FRW cosmological models you have those two choices (with a
sub-choice for the first: flat or hyperbolic 3-space).

Physicists are stuck on the FRW cosmological models and they won't let
go because 1) legends are sacrosanct and 2) they're insulted by the
infinite variety of equally reasonable geometries that mathematicians
are familiar with. http://arxiv.org/PS_cache/gr-qc/pdf/9804/9804006.pdf

But who's to say those models are all there is?

Albert Einstein wished to exclude every other realistic option without
offering reasonable justification.
http://arxiv.org/PS_cache/gr-qc/pdf/9804/9804006.pdf

In particular, it is expected that a real
theory of quantum gravity will have major things to say about this, and
presumably the evolution of the cosmos at early times will be
significantly different in such a theory....

Please understand that I'm referring to the basics of the creation
story. Space being created either infinite or finite is the only
essential point that I'm alluding to.

The birthing of geometry in time has associated with that space and
time, a flow of idealized, mathematical trajectories. Each trajectory
is easily pictured as the spatial trace of an abstract idealized clock
moving effortlessly through that geometric space, parameterized by its
own clock time. Each clock, therefore, is defined by a timelike
geodesic.

Sure. You can imagine such clocks.

The most glaring fact that I see in the simultaneous emergence of
space and time is the existence of the above mentioned global flow of
abstract coordinate clocks, all initially synchronized by God Himself.

Huh??? Those clocks "exist" only in your imagination, and it is up to
YOU to synchronize them. Go ahead -- it's easy to IMAGINE how to do
that.... But the only "God" here is YOU.

My use of the word _God_ was meant to be flexible enough to include
the initial conditions decided by Creation itself. I was kindly
accommodating both the actual and philosophical pantheism made popular
and acceptable by such notable physicists as Albert Einstein and
Stephen Hawking.

http://members.aol.com/Heraklit1/einstein.htm
http://www.harrison.dircon.co.uk/wpm/index.htm

It isn't the Creator's choice.

Speak for yourself -- because YOU are the "creator" here. This whole
discussion is about figments of your imagination. That is, of course,
what all mathematical models of physics are....

Thanks for that acknowledgement about mathematical models of physics.

It doesn't harmonize with creation.

Why not?

Going the route of conventional special relativity
would imply that imagining an event at some time in one frame of
reference would necessarily translate to the same event happening
in another frame before time even began.

But you're imagining a manifold that is not consistent with the
requirements of SR, so why should one be concerned that attempting to
apply SR yields nonsense?

I believe that if you think about this carefully, you will see that
Einstein's postulates of Special Relativity work perfectly fine on an
instantaneously created, flat, infinite space but that the Lorentz
transformation is not a natural law for that space. In this universe,
as a consequence of instantaneous creation, there must have existed a
natural initial synchronization for all idealized coordinate clocks in
all frames of reference. t=0 everywhere. I believe that this is a
straightforward counterexample to a false philosophy in relativity
that I was combating recently on another thread.

Eugene Shubert
http://www.everythingimportant.org

On 3 Jul 2004 22:13:54 -0700, (Perfectly
Innocent) wrote:

In this universe,
as a consequence of instantaneous creation, there must have existed a
natural initial synchronization for all idealized coordinate clocks in
all frames of reference. t=0 everywhere.

Simply put, the universal process as we know it , started.

On 3 Jul 2004 22:13:54 -0700, (Perfectly
Innocent) wrote:

In this universe,
as a consequence of instantaneous creation, there must have existed a
natural initial synchronization for all idealized coordinate clocks in
all frames of reference. t=0 everywhere.

Simply put, the universal process as we know it , started.

In sci.astro Perfectly Innocent wrote:
[...]

Physicists are stuck on the FRW cosmological models and they won't let
go because 1) legends are sacrosanct and 2) they're insulted by the
infinite variety of equally reasonable geometries that mathematicians
are familiar with. http://arxiv.org/PS_cache/gr-qc/pdf/9804/9804006.pdf

The paper you cite is by a physicist, not a mathematician. Furthermore,
the "exotic" topologies Luminet talks about are all FRW cosmological
models -- specifically, quotient spaces of standard simply connected
FRW models by finite groups. In particular, they have the same general
"history," starting with an initial big bang singularity.

Your claim that physicists ignore these topological possibilities is simply
wrong. See, for example, the September 1998 issue of _Classical and Quantum
Gravity_, which is entirely devoted to this subject, or the review article
by Lachieze-Rey and Luminet, Phys. Rept. 254 (1995) 135, which contains
165 references and has itself been cited over 100 times.

In fact, there is an extensive observational effort to look for topologies
of the type discussed by Luminet. The results so far have been negative:
see Cornish et al., Phys. Rev. Lett. 92 (2004) 201302; Phillips and Kogut,
preprint astro-ph/0404400; Uzan et al., Phys. Rev. D 69 (2004) 043003.

Steve Carlip

wrote in message ...
In sci.astro Perfectly Innocent wrote:
[...]

Physicists are stuck on the FRW cosmological models and they won't let
go because 1) legends are sacrosanct and 2) they're insulted by the
infinite variety of equally reasonable geometries that mathematicians
are familiar with. http://arxiv.org/PS_cache/gr-qc/pdf/9804/9804006.pdf

The paper you cite is by a physicist, not a mathematician.

Correct. Jean-Pierre Luminet, Observatoire de Paris-Meudon,
Departement d'Astrophysique Relativiste et de Cosmologie.
But that doesn't mean that Luminet's survey paper has anything
commendable to say about Einstein or the majority of 20th century
relativists.

Furthermore, the "exotic" topologies Luminet talks about are all FRW
cosmological models -- specifically, quotient spaces of standard simply
connected FRW models by finite groups.

There is nothing "exotic" about the FRW cosmological models according
to Luminet. He writes:

"Such fruitful ideas of cosmic topology remained widely ignored by the
main stream of big bang cosmology. Perhaps the Einstein-de Sitter
model (1932), which assumed Euclidean space and eluded the topological
question, had a negative influence on the development of the field.
Almost all subsequent textbooks and monographies on relativistic
cosmology assumed that the global structure of the universe was either
the finite hypersphere, or the infinite Euclidean space, or the
infinite hyperbolic space, without mentioning at all the topological
indeterminacy."

Your claim that physicists ignore these topological possibilities
is simply wrong.

I only meant to emphasize what Luminet has already written:

"Until 1995, investigations in cosmic topology were rather scarce."

"Cosmologists must face the fact that a negatively curved space with a
finite volume is necessarily multi-connected."

See, for example, the September 1998 issue of _Classical and Quantum
Gravity_,

How many physicists are reading your journal and how many physicists
still trust their outdated GR textbooks?

Eugene Shubert
http://www.everythingimportant.org

Perfectly Innocent wrote:
wrote in message ...

See, for example, the September 1998 issue of _Classical and Quantum
Gravity_,


How many physicists are reading your journal[...]

Well, considering that C&QG (along with Phys Rev D) is the primary
journal in the field, I'd say a lot.

Perfectly Innocent wrote:
wrote in message ...

See, for example, the September 1998 issue of _Classical and Quantum
Gravity_,


How many physicists are reading your journal[...]

Well, considering that C&QG (along with Phys Rev D) is the primary
journal in the field, I'd say a lot.

In sci.astro Perfectly Innocent wrote:
wrote in message ...

[...]
Furthermore, the "exotic" topologies Luminet talks about are all FRW
cosmological models -- specifically, quotient spaces of standard simply
connected FRW models by finite groups.

There is nothing "exotic" about the FRW cosmological models according
to Luminet. He writes:

"Such fruitful ideas of cosmic topology remained widely ignored by the
main stream of big bang cosmology. Perhaps the Einstein-de Sitter
model (1932), which assumed Euclidean space and eluded the topological
question, had a negative influence on the development of the field.
Almost all subsequent textbooks and monographies on relativistic
cosmology assumed that the global structure of the universe was either
the finite hypersphere, or the infinite Euclidean space, or the
infinite hyperbolic space, without mentioning at all the topological
indeterminacy."

This says nothing either way about whether these topologies are "exotic."
What I meant by the term was that:
1. They have complicated, nonabelian fundamental groups
2. While many examples are known, there is no systematic classification.
3. As far as I know, it is an open question whether these topologies are
*classifiable* -- that is, whether, there is an algorithm that can
determine whether any two given manifolds have the same topology or not.

[...]
See, for example, the September 1998 issue of _Classical and Quantum
Gravity_,

How many physicists are reading your journal and how many physicists
still trust their outdated GR textbooks?

The papers in that issue have a total of more than 250 citations. The issues
are certainly known to most people working in the field. The paper by Cornish,
Spergel, and Starkman on the possibility of actually detecting nontrivial
topology by looking at the CMBR generated a great deal of excitement; it's
been cited more than 70 times, and made Science News, Scientific American,
and a bunch of newspapers. So did the recent observational results that
rule out large numbers of topologies.

This is close to the field I work in, and I know many of the people involved.
It's true that 20 years ago, most people in general relativity and cosmology
didn't pay much attention to three-manifold topologies. But things have
changed *drastically* in the past couple of decades, and now it's a standard
part of research.

Steve Carlip