Science > Physics > A Treatise On Quantum Theory (was: Textbook on quantum mechanics)
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09 Feb 2005 12:06:30 PM |
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A Treatise On Quantum Theory (was: Textbook on quantum mechanics) |
Peter Craven wrote:
Could you please advise me which is the textbook that
you think most correctly explains quantum mechanics.
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;
bringing all simultaneously under a common foundation, a' la the
Landsman 1998 epitome "Mathematical Topics Between Classical and
Quantum Physics".
The Big Picture
===============
[Stuff about Olbers' paradox -- why the sky isn't hot white -- deleted]
.... Why is space black, then?
In fact, it's not.
We're bathing in the afterglow of a brilliant flash which was so
enormous that even today it heats the entirely of outer space to a
temperature that is 3 degrees above absolute zero [or about 5 degrees,
Fahrenheit above absolute zero]; and colors outer space with a faint
and, to the naked eye invisible, glow in the microwave spectrum so that
it is, in fact, still not entirely black. The occurrence of the event
was long ago, but is still directly in the line of sight of where we
are today. In fact, it is the one and only place and time in the
universe that is in the line of sight of all other places in the
universe, at all other times -- visible in all directions at once.
For, you see, the visible universe is actually a projection of the
past. The Earth (as well as each other place and time everywhere else)
is surrounded by a nested series of spheres -- exactly as apprehended
by philosophers of old. But they are not spheres of substance, rather
they are spheres that envelope all those places a set distance from
Earth which existed a set time in the past and are, only now, becoming
visible to us by their light. The sphere of radius 4.3 light years,
which crosses the neighborhood of the nearest star, comprises events
that are 4.3 years ago. Likewise, the projection seen of Andromeda --
our nearest (regular) galaxy -- is of 2,000,000 years past.
Going further out, the image seen of galaxies more distant, or other
exotic objects like quasars, whose appearance steadily become more and
more primitive the further out we go are of time yet more remote.
Eventually you reach a point where is visible nothing more than a shell
-- of enormous size -- of nearly uniform but diffuse glow: the Cosmic
Microwave Background or CMB. That's the glow, mentioned at the outset,
which still illuminates the entire universe, but only faintly.
It represents the last moment that outer space was opaque, and the
first moment it became transparent. The times following form smaller
spherical shells within, and all that's visible lies on one of these.
The times preceding lie outside the CMB and are largely obscured by the
opaqueness of outer space at these remote times. Though nearly
uniform, ever so slight variations show up in the CMB -- lumps and
regions slightly more sparse than the surround background -- that are
directly tied to what later became the -- visible -- structure formed
by the galaxies in the large: the vast network of filaments and cosmic
gaps that these galaxies do (or do not) lie along.
Beyond the CMB shell lie other shells, further remote in time, and
further out. They, too, are directly in the line of sight, though
obscured and cloaked by the CMB. Going far enough, ultimately, one
reaches the outermost shell, at which lies the earliest point in time,
and the brilliant occurrence alluded to -- that, which Cosmology calls
the Big Bang.
But this "shell", in fact, is NOT a shell at all. It's a point! It is
the same point in space and time that lies on every part of this outer
shell. All directions lead to the point.
Before reaching this outermost shell, at some point along the process,
the nested series of shells actually quit getting larger and larger and
actually start to curve the other way around and get smaller and
smaller! Though we appear to be on the inside of them, they curve the
OTHER way, and we are on the outside; as are all other places and times
following the moment these shells existed at. Indeed, the CMB itself
may even be curved the other way around.
[Picture of the famous Medieval painting, also illustrated in Rudy
Rucker's 'Infinity and the Mind' here. This shows the outermost
sphere, "Empyrean" as a single point, lying at the antipode of a
hyperspherical universe -- and represents one of the earliest
expressions of a non-Euclidean geometry].
-- 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.]
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| User: "" |
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| Title: A Treatise On Quantum Theory II (was: Textbook on quantum mechanics) |
15 Feb 2005 03:24:16 PM |
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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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| User: "" |
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| Title: Re: A Treatise On Quantum Theory II (was: Textbook on quantum mechanics) |
18 Feb 2005 06:53:35 PM |
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wrote:
Not to plug new or upcoming books, but [oops too late],
I'm only putting out the Prologue here, to try and lay out the general
direction I'm heading in, not an entire treatise itself! The rest of
the Prologue explains, in part, what I'd like to cover.
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...]
Finite Temperature
==================
Of course, it is entirely possible that both a Big Bang and Big Crunch
exist, that both the Past and Future have such events, but that the one
with the Future is as of yet far more remotely situated. Then one may
see a very faint and partial illumination of the Future, along with
sporadic snippets of memories of events postdating the memories
themselves. Or it may still be the case that, despite the apparent
assymmetry in the sky, and the assymmetry in time that seems consequent
upon it, that memories of the future are still possible, but simply
more sporadic, rarely ever registering beyond the noise of the
background noise within a person's head (or within other physical
systems, such as computers).
it's almost a folk cliche' nowadays, that some of the snow seen on a TV
set, when attuned to a channel that has nobody on it, is actually
background radiation of the Big Bang, itself straight out of the CMB.
This, then, should make a key point all the more clear: no large-scale
physical system can be completely isolated from its environment. It is
an axiom, then, that the Universe is a heat bath, at the present time
at a temperature of about 3 degrees Kelvin above absolute zero, and
that everything is immersed in it. The only proper foundation of
Quantum Theory, therefore, is one at finite, non-zero temperature.
This distinction will make itself readily apparent when we find
ourselves back at the question of the Big Picture, when discussion of
negative energy particles and the 'vacuum state' of a quantum field.
It will also make itself felt, even more acutely in fact, when
discussing the question of what meanings ought to be given to the
various objects appearing in a formalism of quantum theory. In
particular, the question of where the probabilistic behavior of a
quantum system arises from must, at some point, be addressed;
particularly since there really is nothing at the bottommost level of a
formalism of quantum theory that calls forth this property.
This latter question will, in fact, assume a central importance here.
The classical foundation of quantum mechanics has, in essence, two
postulates. The first is the Evolution Postulate, which states that
the "observables" of a system and its "states" evolve in accordance,
respectively, with the Heisenberg equation of motion and the
Schroedinger equation. [Which yields, in turn, respectively, the
Heisenberg and Schroedinger pictures.] The other -- however -- runs
antithetically to this, asserting in effect that despite this
progression in time, there are instances (called "Measurements") where
information is extracted from a system. The information is
probabilistic -- it may be one outcome or another, each with set
probabilities of occurring, and the state the system is in immediately
afterwards is one that is known cannot be described by anything arising
from the first postulate. It's entirely from the second postulate that
the notion of probability enters into play. Without it, quantum theory
would involve probabilities in any way.
Yet, there is a serious incongruity. The second postulate lies totally
at odds with the first, and there is no clearly delineated set of rules
indicating at which instances it may be applied (i.e., which events in
space and time actually comprise what are called "measurements"?) The
picture painted is of a system running along normally minding its own
business, when suddenly and sporadically it suffers "measurements"
inflicted upon it that causes it to spew out random information (more
so than a treatise does) and jump at random into another state
completely unrelated to anything that would have arisen by the first
postulate alone. Yet, without the second postulate, you're no longer
able to account for the fact that quantum systems *do*, in fact, behave
as if they did this very thing.
So, it is almost universally accepted that the second postulate is in
no way fundamental. This shifts the burden of explanation onto the
shouldners of the fhirst, which has already shown its incapacity to
handle the weight. Various approaches have been adopted to try and
remedy the defect or "explain it away" -- Consistent Histories,
Decoherence, Everett, Deutsch's Multiple Universes, etc. Indeed, all
have had a measure of success in crossing at least part way and even
bringing up new issues and perspectives. But all have failed to close
the deal. For, no matter how you look at it: There. Are. No.
Probabilities. In. The. First. Postulate. They can NOT come from
there, nor from ANYTHING -- no matter how argued -- that uses only this
postulate. They may bring us close to the deal, but cannot close the
deal and get in bed with it.
Some people, notable Heisenberg, have thrown their hands up in the air
and simply admitted defeat, even going as far as to assert (like
Deutsch and Everett) that the quantum world does NOT, in fact, exhibit
any probabilistic behaviour at all. It's all in the head. Even your
consciousness is under the umbrella of quantum theory, so it too
exhibits all the weirdities of quantum theory (superposition of states,
etc.) so that the notion of You in the singular is rejected.
That can never be empirical, and (to say the same thing twice) nothing
in the physical world can ever single out this precept as its sole
explanation.
In all these deliberations, it somehow failed to dawn on just about
everyone that there already is a source of randomness in the universe
at large. Indeed, the approach of Decoherence nearly hits the nail on
the head, calling it the "Environment". But which environment?
When we postulate that the Universe is immersed in a heat bath at
positive temperature, we also mean to assert this with all the modern,
technical, connotations that these terms have accrued. To assert the
Universe is in a thermal state at a set temperature IS a hypothesis on
the fundamental existence of probability in the Universe. For a
thermal state is, itself, probabilistic. What we are assuming is that
were a physical system to settle down into equilibrium with outer
space, it would be at a temperature of 3 degrees Kelvin, and would be
in such a state that the probabilities of it being at an energy E would
be proportional to exp(-beta E) where beta = 1/(k T), k is on the order
of 10^{-23} Joules/degree Kelvin, and T is the 3 degree Kelvin
temperature. That's a probabilistic combination of pure energy states
-- a mixed state.
When a quantum system is immersed in a heat bath, or in any large
system in a probabilistic state, it will exhibit the very states and
probabilistic properties that one associates with quantum systems. The
Second Postulate is not needed, for we have another more fundamental
one that subsumes it: the Universe is, in effect, an open system -- a
heat bath of positive temperature. This is what closes the remaining
10% of the deal that Decoherence only brought us part way along.
The significance of such expectations cannot be underscored. It is
common practice, in Quantum Cosmology, to assume the Universe is in a
PURE quantum state, which flies directly in the face of the
overwhelming reality, just described here. Someone forgot about the
CBE. If it were truly in a pure state, then -- at least going by the
account given in Canonical Quantum Gravity -- there would be absolutely
no concept of any such thing as time flow: not in reality, not even in
perception by those subsystems (including humans) contained in this
universe. The state would be eternally the same. Literally, nothing
would ever be seen to happen. Reality would be completely timeless.
The rather obvious paradox -- the Problem of Time -- should make it
clear that the Universe is in anything BUT a pure state. It is in a
mixed, thermal, state. And a mixed state, being the probabilistic sum
of pure states, automatically entails the omnipresent reality of
probability.
To the degree one commits to the notion of a mixed state, one is
reintroducing a measure of classical physics back into the world. The
reason for the traditional insistence on pure states is one wants to
assert the universality of the quantum hypothesis. This states that
all systems, in all the degrees of freedom they exhibit, accord with
quantum theory. Everything, both large and small, is equally subject
to the laws of quantum physics: even the Universe, in its entirety.
Now, I don't know about you, but that assertion -- especially that last
part -- is a little brash. While there is clear evidence that systems
with quantum degrees of freedom EXIST, there's no evidence -- nor can
there ever by any -- that ALL degrees of freedom, even of the Universe
in the large, are quantum! In particular, to the extent that the
structure of a large system, such as the Universe, deviates from this
hypothesis of universality, it may indeed show mixed states -- such as
the one the Universe is actually in!
We assert, in contrast, that the Universe at large exhibits both
classical and quantum degrees, and that in the neighborhood of
infinity, it is classical. More specifically: the CMB is a classical
thermal state.
Among other things, this means that a proper foundation of Quantum
Theory must not only include some notion of thermodynamics or
statistical physics at its foundation -- putting these branches of
Physics on par with General Relativity and Quantum Field Theory as
fully equal pillars of foundation -- but that it must bridge the gap
between classical and quantum physics, transcending the distinction
between the two, into an enveloping formalism that has both pure
quantum and pure classical physics as subsets.
[... to be continued ...]
[Note: all 3 parts were copied from 2 sides of a page of a 6" by 9"
notebook. Feynmann, eat your heart out.]
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| User: "" |
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| Title: Re: A Treatise On Quantum Theory II (was: Textbook on quantum mechanics) |
22 Feb 2005 03:47:48 PM |
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wrote:
I'm only putting out the Prologue here
[...]
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...]
Finite Temperature
==================
[continued]
One of the primary tasks of the treatise, therefore, is not just to
dispel the myth that quantum and classical physics are so radically
different as to actually require radically different formalisms (as
opposed to, say, of radically different formalisms being merely the
effects of different tastes and styles differentially applied to one
branch of physics vs. the other) but that their differences are in fact
far smaller and of far less physical content than is normally regarded,
and that they can be secured on a common foundation that in large
measure applies equally to both.
This foundation is the algebraic approach, and the state-space approach
adopted by von Neumann, coupled with the foundation of statistical
physics. In it, the Heisenberg picture stands at the center, rather
than the Schroedinger picture that is more commonly used. All three
branches of physics [quantum physics, classical physics, statistical
mechanics], therefore, will enter equally into the mix in this
treatise. We approach them indiscriminately in a unified treatment
that transcends them all.
The other main task of the treatise -- closely related to the foregoing
-- is to provide an introductory to intermediate level coverage of the
field, but with a complete point of departure on nearly every item of
coverage from the past. Just for starters: there is a lot that has
normally only been seen or done in the Schroedinger picture that has
not seen much air play in the Heisenberg Picture; not even the Hydrogen
or Helium atom!
What we offer is a new perspective for a new century that is, in large
measure, divorced from the more immediate historical roots. Though we
will invoke the ghosts of the past, we will not be following the
well-trodden paths laid out by threatments of the subject overdone to
the point of predictability and cliche' -- over the past century.
Among other things, the ghose of Einstein, one of the greatest
engineers of statistical mechanics, shall return to have one final
laugh.
Literally, everything will be new or rarely seen within monographs or
textbook treatments: from the treatment of perturbation theory, to the
general treatment of the Kepler problem in the Heisenberg picture
(including such elegant notions as Hydrogen SO(4) and H-quarks); from
the invocation of a Galilean analogue to the Wigner classification that
even includes massless particles, spin and a semblance of time
dilatation(!), to the modern rendition of the ossified periodic table,
which will also include an Element 0; from the nearly ab initio
derivation of Heisenberg, to the return of Maxwell's "displacement
current" hypothesis in the new guise of a new version of the Standard
Model.
Maxwell's theory of vacuum polarization and the vacuum dielectric
medium (little-known in the present era) -- which very closely
foreshadows the subsequent developments of renormalization theory 80
years later -- will be resurrected (literally) in this new light and in
the larger context of Yang-Mills theory; interacting substantially with
the hypothesis of a thermal vacuum. [FOOTNOTE: stressing analogy on
viewing an electron as a capacitor of capacitance C = e/(2 mc^2), with
pair annihilation corresponding to dielectric breakdown across 1.022 MV
potential, resulting in the emission of light: Maxwell's "glow"] Many
of the arguments, posed even in Maxwell's treatise, itself, that went
into the establishment of the theory transcent the developments of the
past 140 years and apply equally well both to the classical and quantum
domains, yielding the same conclusion. Whereas A,B,D,E,F and H all
have well-known meanings in relation to Maxwell, we will be bringing
back his lesser-known G.
In our treatment, we will dispel the false argument concerning negative
energy states, so that all the states -- both of positive and negative
energy can be consistently treated together, resulting in a consistent
relativistic particle theory, as a semi-classical approximation to
field theory. A significant feature of a field theory in a thermal
vacuum, not present in the zero temperature vacuum, is that the mass
corrections not only become positive, thus, for instance, yielding a
modification and weakening of the Goldstone theorem to one which has
MASSIVE Goldstone bosons; and giving the photon a small effective mass
(on the order of kT/c^2, for T = 3 Kelvin), but one which finds that
the corrections are non-analytic near zero energy and momentum. In a
field theory where the underlying physics requires analyticity, this
results in the condition that a gap must exist near 0 energy and 0
momentum. In turn, this phenomenon carries a close linkage to the 3rd
Law of Thermodynamics.
Needless to say, we will also be addressing the New Era topics, such as
Quantum Computers, Quantum Encryption, Quantum Teleportation,
Entanglement (both quantum *and* classical entanglement) & the Bell
Inequalities; as well as Nanotechnology.
End of Prologue
==============================
A general idea of where this goes in the immediately following context
is below. An actual topic list is still be developed, using much
material already put out on the USENET, so this is as far as it goes so
far.
INTRODUCTION
============
INITIAL CONDITIONS & EQUATIONS OF MOTION
----------------------------------------
(Setting up the background to explain the appearance of 2nd order
equations of motion for a physical system)
STATES: CLASSICAL AND QUANTUM PHYSICS
-------------------------------------
(The state space notion developed, in conjunction with the idea of
initial and final conditions to equations of motion; and the more
general idea of spacetime boundary data).
THE GENERAL STRUCTURE OF OBSERVABLES:
-------------------------------------
HYBRID CLASSICAL-QUANTUM SYSTEMS
--------------------------------
Derivation of the general structure of an operator algebra from the
mere requirement of compatibility with the equations of motion.
Result: a system with a combination of classical and quantum degrees of
freedom, the latter canonically quantized with respect to a Hamiltonian
quadratic in the momenta.
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| User: "Uncle Al" |
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| Title: Re: A Treatise On Quantum Theory II (was: Textbook on quantum mechanics) |
15 Feb 2005 04:10:49 PM |
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wrote:
[snip good stuff]
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.
[snip]
I disagree. Entropy is only a statistical arrow of time. Angular
momentum is an absolute arrow of time.
(Show me how to remove angular momentum given only inertial
observers.) The demo is a large flat motion picture film can with a
port tangential to its edge and a port coming out normal to its flat
surface at its center. The can and its ports are intially entirely
flled with water. Pump water in the middle and out the edge no
problem, low velocity to high velocity. Reverse time and the reversed
observation is ridiculous and impossible. Angular momentum defines
the arrow of time and it cannot be gauged away. (The plethora of
idiot trolls are informed that the can doesn't leak because its seams
are welded.)
Feynman's rotary water sprinkler is another example. Angular momentum
is not symmetric to time reversal.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
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| User: "Creighton Hogg" |
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| Title: Re: A Treatise On Quantum Theory II (was: Textbook on quantummechanics) |
15 Feb 2005 04:26:10 PM |
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On Tue, 15 Feb 2005, Uncle Al wrote:
whopkins@csd.uwm.edu wrote:
[snip good stuff]
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.
[snip]
I disagree. Entropy is only a statistical arrow of time. Angular
momentum is an absolute arrow of time.
(Show me how to remove angular momentum given only inertial
observers.) The demo is a large flat motion picture film can with a
port tangential to its edge and a port coming out normal to its flat
surface at its center. The can and its ports are intially entirely
flled with water. Pump water in the middle and out the edge no
problem, low velocity to high velocity. Reverse time and the reversed
observation is ridiculous and impossible. Angular momentum defines
the arrow of time and it cannot be gauged away. (The plethora of
idiot trolls are informed that the can doesn't leak because its seams
are welded.)
Feynman's rotary water sprinkler is another example. Angular momentum
is not symmetric to time reversal.
I see the point you are making, Uncle Al, but it does seem odd to me then
that physics on a fundamental level appears to be symmetric to time
reversal, i.e. the standard model. Neither orbital nor spin angular
momentum have this arrow of time property as well.
How does one get from reversible single processes to bulk behaviour that
is irreversible?
Come to think of it though, GR obviously does not respect "time reversal"
because that would be a different manifold, yes?
So many questions, but I have so few answers.
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| User: "Andy Resnick" |
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| Title: Re: A Treatise On Quantum Theory II |
16 Feb 2005 07:57:49 AM |
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Uncle Al wrote:
whopkins@csd.uwm.edu wrote:
[snip good stuff]
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.
[snip]
I disagree. Entropy is only a statistical arrow of time. Angular
momentum is an absolute arrow of time.
(Show me how to remove angular momentum given only inertial
observers.) The demo is a large flat motion picture film can with a
port tangential to its edge and a port coming out normal to its flat
surface at its center. The can and its ports are intially entirely
flled with water. Pump water in the middle and out the edge no
problem, low velocity to high velocity. Reverse time and the reversed
observation is ridiculous and impossible. Angular momentum defines
the arrow of time and it cannot be gauged away. (The plethora of
idiot trolls are informed that the can doesn't leak because its seams
are welded.)
Feynman's rotary water sprinkler is another example. Angular momentum
is not symmetric to time reversal.
Here's one that's even simpler- macroscopic and easily reproduced. Take
a drop of fluid on a slightly irregular, non-wetted surface. If the
drop is induced to move, the contact angles at the leading and trailing
edges are different. Thus, the time-reversed motion is not similar to
reversing the direction of motion of the drop.
There's also some relevant discussions regarding Faraday isolators and
the bidirectional reflectance function of rough surfaces.
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
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| User: "" |
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| Title: Re: A Treatise On Quantum Theory II (was: Textbook on quantum mechanics) |
18 Feb 2005 06:07:40 PM |
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[On the notion that a universe with a Big Crunch has time flowing the
other way]
Uncle Al wrote:
I disagree. Entropy is only a statistical arrow of time. Angular
momentum is an absolute arrow of time.
Yes, but the *universe*, itself, is a thermal state at positive
temperature. That, in itself, gives you an arrow of time!
Consider the consequences of that. A system at negative energy (as
explained in the s.p.r. article on the Mass Gap & 3rd Law) would have a
number of states that increases with decreasing energy, so that its
temperature would be negative.
Immersed in a heat bath of positive temperature, it will continue to
absorb energy from it until it reaches equilibrium.
This imposes an assymmetry on any quantum field theory, whereby all the
negative energy states are effectively filtered out (as well as those
of positive, but low energy, like soft photons; thus also avoiding the
Infrared divergence!); while those at positive energy remain.
Instead of postulating this property (as is done in the usual,
Wightmann formalism), it appears it can be derived. In turn, this
imposes an arrow of time on the vacuum state. Further, since this
by-passes the naive folk-argument about "negative energy particles
cascading to negative infinite energy", it , in turn, it opens back up
the ability to deal with negative energy states for particles and to
consistently treat the bosons and fermions in a particle-based setting.
But back to the other issue:
In an expanding universe, all the correlations in a system will tend to
disperse out to the environment, resulting, classically, in an increase
of entropy; and (for quantum degrees of freedom), decoherence. This is
part of how the Decoherence approach explains away the emergence of
classicality (and, also as a result) irreversibility.
In contrast, in a contracting universe, these correlations are squeezed
into tighter and tighter spaces, so that one starts to see the
spontaneous appearance of macroscopic order out of them. So, you
should expect to see all the depictions of backwards running films play
out in such a universe, as described. A quantum theorist in this
universe would then be posing an irreversible theory of "recoherence"
(the Spin Echo experiment and Quantum Eraser, writ large!)
Feynman's rotary water sprinkler is another example. Angular
momentum
is not symmetric to time reversal.
But there is no corresponding assymmetry of angular momentum states in
the universe reflecting the assymmetry of time. Tops don't all spin
one way. [Okay, maybe you can argue the assymmetry for neutrinos, but
I don't think this really changes the conclusion, since this is more a
product of left-right assymmetry than temporal assymmetry].
Angular momentum assymmetry is a reflection of P, not T. (For instance
in 4-D, no such assymmetry exists, but a temporal assymmetry can still
be contemplated -- thus showing that the two concepts are independent).
There's 3 factors in CPT. If you keep one constant, the result is
you'll confuse the other two. But P != T.
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