Re: Creation (short - HA!) (Whatdayamean, ha?)

[David Bowman <dbowman@tiger.gtc.georgetown.ky.us>]

Tom Wayburn wrote:
> ....
> What's not short about my posting?  I just finished an 800 page book,
> which must have influenced my judgment of length (in bytes!).

I didn't mean to imply your posting was not short -- just that my reply was
not.  If I didn't put on the HA! disclaimer the subject line would have been
false advertising.

> How come no one has seen fit to comment on my suggestion that the
> Universe and the rest of existence (the world) might be embedded in
> *something*.

Personally, I like the idea.  My guess as to why you didn't get any comments
is that there is no conceivable experimental test that could be made to test
it.  It is not part of physics (maybe metaphysics but not physics).  Phys-l
people usually comment about things pertaining to physics.

> In the book I noted that we may have a few compact dimensions in and
> around the nuclei of atoms, say.   Is compact a good choice of descriptor?

If that is what you want to say its entirely original with you.  The usual
Kalusa-ish idea about compact dimensions is that spacetime has 4 extended
dimensions whose extent is at least some 10^10 (light) years across (possibly
these dimensions are infinite if the mean density of matter in the universe
is low enough), AND it has (in usual superstring versions) 6 (or so) more
'compact' dimensions that are compact in both the mathematical topological
sense and the everyday sense of being very small.  The circumference of the
universe around these compact dimensions is supposedly of the order of the 
Planck length (~10^(-35) m).  Thus at *each* point (event) of ordinary
spacetime there is supposely a tiny 6-dimensional compact spatial manifold
orthogonal to the usual 4 unit vector directions of spacetime.  Thus the
events of spacetime are not 'points' they are tiny ball-like things extending
into directions orthogonal to the spacetime manifold.  The usual 
lower dimensional analogy for this is to imagine the 2-d surface of a garden
hose.  The one dimension along the hose's length is the analog of our 
4-dimensional submanifold of extended ordinary spacetime.  The other tiny
circular dimension around the hose's diameter is the analog of the
6-dimensional compact submanifold.  When the hose is looked at from a 
sufficient distance it looks like a 1-D line (and our spacetime looks like a
4-D spacetime on a coarse classical scale).  But when the hose is examined up
close on a (quantum Planck) scale comparable to the hose's diameter it is
discovered that the hose is really a 2-D surface rather than a 1-D line.
Similarly, when spacetime is examined on a scale of the Planck length
supposedly the universe would be observed to extend into other dimensions and
would be seen to really have 10 dimensions rather then the just the usual 4.
The theoretical purpose for these extra dimensions is help make a single
gauge group that will unify all the interactions of nature.  The gauge groups
of the Strong, Weak, and EM interactions (SU(3), SU(2), and (U1)
respectively) are all topologically compact and have nothing to do with
spacetime per se.  The gauge group of gravitation is the noncompact group of
diffeomorphisms on the spacetime manifold.  Thus putting in the extra compact
dimensions allows theorists to treat all the gauge interactions on a
comparable footing so they can be unified into one overall symmetry priniple.
So if the extra dimensions exist, they exist everywhere at all events of
spacetime, not just in and around atomic nuclei.

> Are you saying that only the circles of latitude, then, are The Universe?
> at different times, of course.

Yes, if you mean the *spatial* universe at each given instant of (cosmic)
time corresponds to a given circle of longitude.

> ...
> Does this mean that the Lorentz transformation will never create
> confusion with respect to two circles of latitude as to which is closer
> to the North Pole, i.e., which is earlier and which is later?

Yes, after a transforming to a new Lorentz frame originating at some
nonsingular point on the sphere the section curves of constant t' (new time)
are still concentrically ordered wrt each other.  They are just now tilted 
and distorted wrt the previous nice circular sections of the sphere.

>                                                               I was not
> aware of a *cosmic* time parameter.  Also, the term co-moving coordinates
> is new to me.  If I meant two coordinate systems moving with respect to
> one another, I would have said so ;-)

Comoving coordinates in space label points of space relative to the spatial
manifold as a whole.  Observers with fixed comoving spatial coordinates
do not move wrt the underlying rubber sheet or their own local spot on
the expanding balloon, or in this analogy they do not change their longitude.
In this analogy each longitude coordinate around any circle of latitude
labels a fixed place in space in coomoving cordinates.  As the circle expands
and later contracts the tick marks of the longitude labels around the circle
stretch and shrink with it.  (That is why such a coordinate is called 
comoving.)  The comoving coordinates are independent of the overall spatial
scale of the spatial submanifold and only depend on relative position in it.
The 'cosmic time' coordinate is just the timelike coordinate parameter
(unique up to trivial changes in scale) that is orthogonal (wrt the Lorentz
signatured metric of the spacetime) to the spatial comoving coordinates.  The
nice thing about using a coordinate system with this cosmic time parameter is
that it measures the proper time of all observers that are locally at rest
(fixed comoving coordinates) wrt to the 'fabric' of the expanding space.  All
such observers continue to have synchronized watches throughout the whole
history of the universe.  This ongoing cosmic synchronicity is what gives
this timelike parameter the name cosmic time.  In our universe 'cosmic time'
is what observers at rest on all typical planets around all typical stars in
all typical galaxies tend to observe as their own proper time because they
tend to move (even with all their own local planetary rotations, planetary
revolutions around their star, stellar revolutions around their galaxy, and
galactic motions wrt their own local galactic clusters) at speeds much
slower than c wrt the local comoving frame.  Note that cosmic time is not
kept for cosmic ray primary nuclei which travel very close to speed c
wrt a comoving frame.  Also cosmic time would not be kept for any observer
which happened to live on (or in) a neutron star, or happened to be
spiraling with the inner edge of an acretion disk toward the event horizon
of a black hole.

>                                       If the Lorentz transformation does
> not prevent establishing a cosmic time parameter, why do not the two
> observers traveling at 0.9c w.r.t. each other determine contemporaneity
> by means of it and dispense with their disagreement as to which event
> occurred first?   If they cannot, how can anyone else?

If the two observers have fixed comoving coordinates and are separating at
0.9*c because they are so far apart that the Hubble expansion of space is
carrying them apart at this rate then both observers observe time in
identical ways and agree on simultaneous events, etc.  In this case their
watches both keep cosmic time.  If the two observers are very close together
but travelling as a speed 0.9*c wrt each other then as long as their distance
is tiny compared to the 'radius' of the universe and the time intervals
they measure are short compared to the current 'age' of the universe then 
the relationship between how their watches keep time is given by the
ordinary Lorentz transformations of special relativity.  If both observers
are far apart (comparable to the 'radius' of the universe) and the time
intervals they measure are comparable to the current age of the universe and
they are moving at a relative speed of 0.9*c wrt each other where a
significant part of this amount is due to both the Hubble expansion of space
and to large relative motions wrt their local comoving coordinate frames,
then the relationship between the proper times kept by their watches becomes
quite complicated indeed, and sorting out how some events which are
simultaneous in one oberver's frame are observed by the other observer is
a big mess.

>                                                        If no one can,
> why should we accept such an anti-phenomenological concept in these
> post-Copenhagenist times?   After all, everyone is moving respect to
> something.  

The important questions are how fast they moving, and how much of their
motion is due to their changing locations in comoving coordinates, and how
much is due to them passively participating in the overall Hubble expansion
of the universe.

David Bowman
dbowman@gtc.georgetown.ky.us