A Treatise On Quantum Theory II (was: Textbook on quantum mechanics)

whopkins_at_csd.uwm.edu
Date: 02/15/05 

Date: 15 Feb 2005 13:24:16 -0800

whopkins@csd.uwm.edu wrote:
> Not to plug new or upcoming books, but [oops too late],
> I've been working through the basic topics of a treatise,
> as per the subject header, for quite some while. The
> initial draft of the Prologue addresses some of the
> issues and also shows the general direction the
> treatise will be headed in.
>
> The basic point of departure (and there are many) is
> to firmly cast the foundation in the realm of finite
> temperature physics; and closely integrate it with
> statistical mechanics and classical physics, itself;
[...]
> The Big Picture
> ===============
[... explanation showing that the observable universe (i.e.
the past light cone) is a hypersphere with the Big Bang on
the other end; recalling the famous medieval painting of Dante's Divine
Comedy; and is in a thermal state at a positive
temperature ...]
>
> -- to be continued --
> [why this tack is taken on in the prologue will become
> clear in the following articles, provided I have time to
> post them.]

Continuing on with the Prologue ...

The situation is somewhat analogous to having a polar map of the Earth.
 The North Pole, in this example, lies at the center. And around it
are a concentric series of circles, each marking off a latitude.
Eventually you reach a point where the circles are as flat as any can
get on the Earth -- the equator. Beyond this point, they start curving
the other way -- with the North Pole outside of them -- even through
they appear on the map as circles yet larger than the Equator,
encompassing it. The outermost circle is merely a point: the South
Pole. Those circles just inside of it are actually tiny circles around
the South Pole.

So it is that the visible universe -- all those places and all those
instants of time newly directly visible to us here and now; which forms
the projection called the "sky" or "heavens" -- is the 3-dimensional
analogue of a sphere: a hypersphere. And at the opposite end is the
Big Bang, itself.

The difference from the example with the Earth map is that "polar" maps
centered on different regions would not all have the South Pole on the
outer periphery. The corresponding map centered on Chicago, for
instance, would have Australia on the outside. [Though, it is possible
to devise a conformally warped variant of polar projection that has the
South Pole on the outside].

In contrast, the sky from every point of the Universe since the first
moment outer space became transparent, maps the past into a concentric
series of (equal-time) spheres, the outermost one which is the Big
Bang. The same point is at the opposite pole of the hypersphere of
every other point at all times.

The Past is illuminated in a way that the Future may not likewise be.
If there were, indeed, a future analogue of the Big Bang -- a Big
Crunch -- we'd expect that the before-glow of this event would,
likewise, be present int he sky and that the sky, itself, would then
project not merely an afterimage of remote places past, but also a
before-image of remote places future. We'd also expect that the Future
would, likewise, be more visible to us in all other regards, more
memorable, so that the concept of "remembering the future" would simply
be an everyday occurrence, rather than a phenomenon seeming so out of
the ordinary as to merit the term "supernatural".

For, it is indeed the case that all the known laws of Physics, all of
its fundamental processes, make no distinction between Past and Future.
 They work equally well and are the same for events depicted in films
running backwards as well as events going forwards in time. Indeed,
despite the appearance of broken vases spontaneously jumping off the
ground onto a table and reassembling themselves, dead bodies
recomposing themselves and jumping off the morgue table and proceeding
to walk on the street (walking backwards), everything that happens in
this depiction is in accord with the basic laws of Physics.

Yet the difference between the two pictures is obvious, and even the
most casual observer will always be able to tell whether a movie is
running forwards or backwards. The only clear assumption that stands
out that could be at the root of all of this is the Big Picture just
described. Indeed, those people living in the backwards running
universe would be in a world where all of outer space would be
collapsing to a point. There would be no Big Bang, no afterglow.
Instead, there would be only a Big Crunch. The sky would probably
project images of events yet to be, the concentric series of spheres
would be of times more and more into the future. The one at 4.3 light
years would show the nearest star 4.3 years into the future. Everyone
would remember the future, nobody would remember the past. They would
perceive time as a "flow" going the opposite way than it "actually
does".

In other words, it would look exactly like our Universe.

FINITE TEMPERATURE
Of course, it is entirely possible that both a Big Bang and Big Crunch
exist...
[... to be contined (spelling out the essential hypothesis underlying
the treatise that the universe is NOT in a pure quantum state, but a
mixed thermal state at positive temperature; the occurrence of the
mixture ultimately yields the classical degrees of freedom needed to
complete the transition from the quantum to the classical world that
Decoherence gets you 90% of the way to; and the positivity of the
temperature, among other things, ultimately being the origin of the
positivity of energy in quantum fields)...]

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