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| Robert L. Oldershaw... |
 Posted: Fri Oct 30, 2009 6:08 am |
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Is it possible that prefect reversibility is a mathematical ideal that
does not apply exactly to any system found the the real world of
nature?
Did Poincare already discover this during the 1892-1899 period when
modern chaos theory was founded in his "New Methods of Celestial
Mechanics"?
Are the examples of revesibility that physicists frequently cite
actually either artificial idealizations, or refer to systems
maintained briefly in periodic states, but whose full, and
unmanipulated, behavior would include the much more extensive behavior
of nonlinear dynamical systems?
What are the best examples of candidates for truly and ideally
reversible systems?
Robert L. Oldershaw
[[Mod. note -- Hmm, elastic scattering of uncharged subatomic particles
or atoms certainly comes very close. "Uncharged" means there shouldn't
be any electromagnetic radiation emitted, although there will still be
(very very *very*) tiny amounts of gravitational radiation emitted.
-- jt]] |
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| Uncle Al... |
| Posted: Fri Oct 30, 2009 10:28 am |
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"Robert L. Oldershaw" wrote:
[quote]
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Is it possible that prefect reversibility is a mathematical ideal that
does not apply exactly to any system found the the real world of
nature?
Did Poincare already discover this during the 1892-1899 period when
modern chaos theory was founded in his "New Methods of Celestial
Mechanics"?
Are the examples of revesibility that physicists frequently cite
actually either artificial idealizations, or refer to systems
maintained briefly in periodic states, but whose full, and
unmanipulated, behavior would include the much more extensive behavior
of nonlinear dynamical systems?
What are the best examples of candidates for truly and ideally
reversible systems?
Robert L. Oldershaw
[[Mod. note -- Hmm, elastic scattering of uncharged subatomic particles
or atoms certainly comes very close. "Uncharged" means there shouldn't
be any electromagnetic radiation emitted, although there will still be
(very very *very*) tiny amounts of gravitational radiation emitted.
-- jt]]
[/quote]
Consider fluxional tunneling between the two equivalent structures of
semibullvalene (in vacuum) around 300 K.
http://pubs.acs.org/doi/abs/10.1021/ja00816a037
Low temp solution kinetics (two interconverting minima)
http://pubs.acs.org/doi/abs/10.1021/ja00544a056
Low temp solid state freeze-out (two minima)
<http://www3.interscience.wiley.com/journal/106588467/abstract>
Stabilized transition state (single minimum)
If you like larger numbers, parent bullvalene has 10!/3 = 1,209,600
fluxional structures - though it must be warmed to about 400 K.
http://en.wikipedia.org/wiki/Bullvalene
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz4.htm |
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| Gordon Stangler... |
| Posted: Fri Oct 30, 2009 9:54 pm |
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On Oct 30, 3:28 pm, Uncle Al <Uncle... at (no spam) hate.spam.net> wrote:
[quote]
Consider fluxional tunneling between the two equivalent structures of
semibullvalene (in vacuum) around 300 K.
http://pubs.acs.org/doi/abs/10.1021/ja00816a037
Low temp solution kinetics (two interconverting minima)http://pubs.acs.org/doi/abs/10.1021/ja00544a056
Low temp solid state freeze-out (two minima)
http://www3.interscience.wiley.com/journal/106588467/abstract
Stabilized transition state (single minimum)
If you like larger numbers, parent bullvalene has 10!/3 = 1,209,600
fluxional structures - though it must be warmed to about 400 K.
http://en.wikipedia.org/wiki/Bullvalene
--
Uncle Alhttp://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)http://www.mazepath.com/uncleal/qz4.htm
[/quote]
What about the quantum harmonic oscillator, or quantum tunneling in a
symmetric atom like ammonia? |
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| Robert L. Oldershaw... |
| Posted: Fri Oct 30, 2009 9:54 pm |
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On Oct 30, 12:08 pm, "Robert L. Oldershaw" <rlolders... at (no spam) amherst.edu>
wrote:
[quote]
[[Mod. note -- Hmm, elastic scattering of uncharged subatomic particles
or atoms certainly comes very close. "Uncharged" means there shouldn't
be any electromagnetic radiation emitted, although there will still be
(very very *very*) tiny amounts of gravitational radiation emitted.
-- jt]]
[/quote]
Interesting. Can you do an actual experiment with neutrons or photons
wherein the particles interact and subsequently are made to retrace
their steps exactly and end up exactly in their original starting
places, states, etc.?
Or can this only be done in the Platonic world of mathematics?
RLO
www.amherst.edu/~rloldershaw |
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| Arnold Neumaier... |
| Posted: Fri Oct 30, 2009 9:58 pm |
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Robert L. Oldershaw wrote:
[quote][ The following text is in the "ISO-8859-1" character set. ]
[ Your display is set for the "US-ASCII" character set. ]
[ Some characters may be displayed incorrectly. ]
Is it possible that prefect reversibility is a mathematical ideal that
does not apply exactly to any system found the the real world of
nature?
Did Poincare already discover this during the 1892-1899 period when
modern chaos theory was founded in his "New Methods of Celestial
Mechanics"?
Are the examples of revesibility that physicists frequently cite
actually either artificial idealizations, or refer to systems
maintained briefly in periodic states, but whose full, and
unmanipulated, behavior would include the much more extensive behavior
of nonlinear dynamical systems?
What are the best examples of candidates for truly and ideally
reversible systems?
[/quote]
Heating and cooling a piece of metal within a moderate range of
temperatures is also generally regarded as a reversible change
of the metal.
Superconductivity is a more truly reversible quantum phenomenon.
But of course, all physical laws are mathematical ideals, so you
may be hunting for the impossible.
Arnold Neumaier |
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| Uncle Al... |
| Posted: Sat Oct 31, 2009 7:42 am |
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Gordon Stangler wrote:
[quote]
On Oct 30, 3:28 pm, Uncle Al <Uncle... at (no spam) hate.spam.net> wrote:
Consider fluxional tunneling between the two equivalent structures of
semibullvalene (in vacuum) around 300 K.
http://pubs.acs.org/doi/abs/10.1021/ja00816a037
Low temp solution kinetics (two interconverting minima)http://pubs.acs.org/doi/abs/10.1021/ja00544a056
Low temp solid state freeze-out (two minima)
http://www3.interscience.wiley.com/journal/106588467/abstract
Stabilized transition state (single minimum)
If you like larger numbers, parent bullvalene has 10!/3 = 1,209,600
fluxional structures - though it must be warmed to about 400 K.
http://en.wikipedia.org/wiki/Bullvalene
What about the quantum harmonic oscillator, or quantum tunneling in a
symmetric atom like ammonia?
[/quote]
Ammonia inversion is reversible, but is it symmetric? It is a general
question pertinent to any two-well "symmetric" oscillator (e.g.,
timekeeping).
Classically, the ammonia umbrella has the same energy before and after
being turned inside out. In QM this is only true to first order.
Even and odd states corresponding to the electronic groundstate of the
NH3 molecule have energies differing by micro-eV, corresponding to a
frequency in the microwave range,
23.6944955 GHz
23.6893348 GHz
A low-loss cavity filled with the antisymmetric form spontaneously
oscillates (ammonia maser). The almost equal populations at room
temperature in a molecular beam can be separated by travel through a
hexapole cylindrical electrostatic field that scatters "gerade"
(quantum state with a negative Stark effect) and focuses "ungerade"
(quantum state with a positive Stark effect) molecules.
<http://ticc.mines.edu/csm/wiki/index.php/The_ammonia_Maser>
Z. Phys. D 37 333 (1996)
<http://www.opus-bayern.de/uni-regensburg/volltexte/2002/57/pdf/diss.pdf>
"Gerade" and "ungerade" re Hund's Paradox are not identical to
geometric chirality, though there is significant overlap,
http://www.ir.ethz.ch/research.htm
"6. Theory of fundamental symmetry principles in chemical reactions
and of parity violation in polyatomic (chiral) molecules"
The two ground states, superositions of "gerade" and "ungerade"
contributors with off-diagonal elements, are then subject to more
rigorous and subtle analysis of their moving positions on an SU(2)
sphere.
================= Moderator's note ================================
Hund's paradox concerning the enantiomeric state of chiral molecules
has been solved only quite recently:
J. Trost, K. Hornberger, Hund's Paradox and the Collisional Stabilization
of Chiral Molecules, PRL *103*, 023202 (2009)
HvH.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz4.htm |
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| Robert L. Oldershaw... |
| Posted: Sat Oct 31, 2009 7:42 am |
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On Oct 31, 3:58 am, Arnold Neumaier <Arnold.Neuma... at (no spam) univie.ac.at>
wrote:
[quote]
Superconductivity is a more truly reversible quantum phenomenon.
But of course, all physical laws are mathematical ideals, so you
may be hunting for the impossible.
Arnold Neumaier-
[/quote]
Yes! That is exactly what I am hunting for: an admission of the
possibility that every system in nature, if studied with unlimited
precision and accuracy, would be found to be a nonlinear dynamical
system that is not ideally reversible or integrable, although the
system could asymptotically approach such an ideal, or be wildly
nonintegrable.
Please Note: I am not trying to convince anyone that nature is built
this way, and certainly I am not saying that I have the required
evidence to prove it. What I hope the reader will take home from this
thread is the idea that nature might be this way. At least until
someone demonstrates that nature could not be this way.
In subsequent discussion it is very important to distinguish among:
perfectly reversible/integrable; approximately reversible/integrable;
mildly irreversible/nonintegrable; strongly irreversible/
nonintegrable.
RLO
www.amherst.edu/~rloldershaw |
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| Robert L. Oldershaw... |
| Posted: Sat Oct 31, 2009 11:05 pm |
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On Oct 31, 1:42 pm, "Robert L. Oldershaw" <rlolders... at (no spam) amherst.edu>
wrote:
[quote]
[/quote]
Refining the general question of whether exact reversibility/
integrability is an idealization or is actually realized in nature,
one could narrow the discussion as follows. Are atoms correctly
characterized by linearity, reversibility and integrability or is this
characterization a good but limited approximation to a more
sophisticated characterization of atoms as nonlinear dynamical
systems.
When chaos theory [aka NLDS theory] was first acknowledged as being
fundamental to modeling much of natural phenomena, it was thought that
its application was limited to the macroscopic domain.
Then one began to see the first papers arguing that period-doubling
and other chaotic phenomena could be observed in the atomic domain, if
one looked hard enough.
In the last decade the application of NLDS modeling to atomic scale
phenomena has been steadily accelerating, especially in regard to
atoms in highly excited Rydberg states.
Now, in the 10/8/09 issue of Nature, we see a potentially paradigm-
changing paper by Chaudhury et al which may herald the advent of a new
era in the modeling of atoms. In this paper the nuclear and electronic
interactions of a single are shown to display a quantum version of
classical chaotic behavior: the kicked top phenomena.
The authors also state: "We ... present experimental evidence for
dynamical entanglement as a signature of chaos.
So it is not unreasonable to ask: are atoms nonlinear dynamical
systems?
RLO
www.amherst.edu/~rloldershaw |
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| Tom Roberts... |
| Posted: Sun Nov 01, 2009 5:35 am |
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Robert L. Oldershaw wrote:
[quote]Are atoms correctly
characterized by linearity, reversibility and integrability or is this
characterization a good but limited approximation to a more
sophisticated characterization of atoms as nonlinear dynamical
systems.
[/quote]
The answer is clearly: nonlinear. After all, at high enough excitation
energies (few eV) atoms ionize, which is not linear at all! And at much
higher energies (MeV), the atomic nuclei transmute into other nuclei,
particle pairs are produced, and a host of highly nonlinear phenomena
occur. When one gets above TeV energies, we simply don't know what
happens....
Bottom line: theoretical concepts like reversibility apply to our
various THEORIES, not to the world we inhabit. For every theory we have,
there is a boundary beyond which it is not applicable, or beyond which
clearly nonlinear phenomena occur.
Tom Roberts |
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| Arnold Neumaier... |
| Posted: Sun Nov 01, 2009 7:36 am |
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Robert L. Oldershaw wrote:
[quote]On Oct 31, 1:42 pm, "Robert L. Oldershaw" <rlolders... at (no spam) amherst.edu
wrote:
Refining the general question of whether exact reversibility/
integrability is an idealization or is actually realized in nature,
one could narrow the discussion as follows. Are atoms correctly
characterized by linearity, reversibility and integrability
[/quote]
Atoms are quantum objects, hence their states (density matrices) satisfy
(to the approximation that the atomic picture of a point charge nucleus
with point charge electrons is valid) the linear quantum Liouville
equations. (And pure states - a further idealization - satisfy the
Schroedinger equation.)
Of course, the nucleus/electron picture is an idealization.
Moreover, linearity only holds for the dynamics of the density matrix,
but not for any reduced dynamics of system of actually observable
quantities. The latter is highly nonlinear, and - no suprise - may
therefore be chaotic.
[quote]Now, in the 10/8/09 issue of Nature,
[/quote]
http://www.nature.com/nature/journal/v461/n7265/full/nature08396.html
[quote]we see a potentially paradigm-
changing paper by Chaudhury et al which may herald the advent of a new
era in the modeling of atoms. In this paper the nuclear and electronic
interactions of a single are shown to display a quantum version of
classical chaotic behavior: the kicked top phenomena.
The authors also state: "We ... present experimental evidence for
dynamical entanglement as a signature of chaos.
[/quote]
I see there nothing indicating a new era in the modeling of atoms.
The Caesium atoms involved are assumed to satisfy the standard linear
quantum laws.
And the experiments are reported to have a 5% error, so they imply
nothing about exact reversibility/integrability.
I also don't understand why you use reversibility/integrability
in this combination as if these were essentially synonymous.
Every (classical or quantum) Hamiltonian system is reversible,
while only very simple or very idealized systems are integrable.
Arnold Neumaier |
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| Arnold Neumaier... |
| Posted: Mon Nov 02, 2009 6:51 am |
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Robert L. Oldershaw wrote:
[quote]On Oct 31, 3:58 am, Arnold Neumaier <Arnold.Neuma... at (no spam) univie.ac.at
wrote:
Superconductivity is a more truly reversible quantum phenomenon.
But of course, all physical laws are mathematical ideals, so you
may be hunting for the impossible.
Yes! That is exactly what I am hunting for: an admission of the
possibility that every system in nature, if studied with unlimited
precision and accuracy, would be found to be a nonlinear dynamical
system that is not ideally reversible or integrable, although the
system could asymptotically approach such an ideal, or be wildly
nonintegrable.
Please Note: I am not trying to convince anyone that nature is built
this way, and certainly I am not saying that I have the required
evidence to prove it. What I hope the reader will take home from this
thread is the idea that nature might be this way. At least until
someone demonstrates that nature could not be this way.
In subsequent discussion it is very important to distinguish among:
perfectly reversible/integrable; approximately reversible/integrable;
mildly irreversible/nonintegrable; strongly irreversible/
nonintegrable.
[/quote]
Actually, it follows from the assumption that the universe as a whole
is reversible that asny subsystem of it (in particular anything we
cannot observe) is not reversible, since it depends on interaction
with the remainder of the universe.
So the only perfectly reversible system (if any) is the universe as a
whole (or a set of perfectly noninteractiung universes - of which we can
of course know only the single one we are in).
The mainstream belief is that, indeed, the universe as a whole is
reversible. But various alternatives have also been suggested, and of
course, perfect reversibility is not experimentally testable.
On the other hand, many small systems that we can observe can be
taken routinely as approximately reversible, with good success.
Arnold Neumaier |
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| Richard D. Saam... |
| Posted: Mon Nov 02, 2009 6:51 am |
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Arnold Neumaier wrote:
[quote]Robert L. Oldershaw wrote:
On Oct 31, 1:42 pm, "Robert L. Oldershaw" <rlolders... at (no spam) amherst.edu
wrote:
Refining the general question of whether exact reversibility/
integrability is an idealization or is actually realized in nature,
one could narrow the discussion as follows. Are atoms correctly
characterized by linearity, reversibility and integrability
Atoms are quantum objects, hence their states (density matrices) satisfy
(to the approximation that the atomic picture of a point charge nucleus
with point charge electrons is valid) the linear quantum Liouville
equations. (And pure states - a further idealization - satisfy the
Schroedinger equation.)
Of course, the nucleus/electron picture is an idealization.
Moreover, linearity only holds for the dynamics of the density matrix,
but not for any reduced dynamics of system of actually observable
quantities. The latter is highly nonlinear, and - no suprise - may
therefore be chaotic.
Yes, actual observable quantities are highly nonlinear[/quote]
but the idealized nucleus/electron picture
represents an elastic (reversible) state
for the majority of the universe mass.
Consider the carbons atoms in your body.
They have maintained
their carbon (nuclear) elastic (reversible) identity
since their super nova creation.
So goes most of the universe
existing in an internally elastic (reversible) state
for billions of years interrupted by infrequent irreversible transitions
to some other time predominate elastic (reversible) condition.
Richard D. Saam |
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| Ken S. Tucker... |
| Posted: Mon Nov 02, 2009 6:53 am |
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On Nov 1, 9:36 am, Arnold Neumaier <Arnold.Neuma... at (no spam) univie.ac.at>
wrote:
[quote]Robert L. Oldershaw wrote:
On Oct 31, 1:42 pm, "Robert L. Oldershaw" <rlolders... at (no spam) amherst.edu
wrote:
Refining the general question of whether exact reversibility/
integrability is an idealization or is actually realized in nature,
one could narrow the discussion as follows. Are atoms correctly
characterized by linearity, reversibility and integrability
Atoms are quantum objects, hence their states (density matrices) satisfy
(to the approximation that the atomic picture of a point charge nucleus
with point charge electrons is valid) the linear quantum Liouville
equations. (And pure states - a further idealization - satisfy the
Schroedinger equation.)
[/quote]
[[Mod. note -- 31 excessively-quoted lines snipped here. -- jt]]
[quote]Every (classical or quantum) Hamiltonian system is reversible,
while only very simple or very idealized systems are integrable.
Arnold Neumaier
[/quote]
Does a hard boiled egg count? (rhetorical).
One heats it, it goes from liquid to solid and there is no way
to get it back to liquid, are we discussing the arrow of time?
Ken |
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| Peter... |
| Posted: Mon Nov 02, 2009 9:03 am |
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On 1 Nov., 18:36, Arnold Neumaier <Arnold.Neuma... at (no spam) univie.ac.at>
wrote:
....
[quote]Moreover, linearity only holds for the dynamics of the density matrix,
but not for any reduced dynamics of system of actually observable
quantities. The latter is highly nonlinear, and - no suprise - may
therefore be chaotic.
[/quote]
It is correct, that the quantum Liouville (von Neumann) equation is
linear in the density matrix. But the interaction enters
parametrically (as in the Schrödinger equation), hence, non-linear.
....
[quote]I also don't understand why you use reversibility/integrability
in this combination as if these were essentially synonymous.
Every (classical or quantum) Hamiltonian system is reversible,
while only very simple or very idealized systems are integrable.
[/quote]
Striking!
Best wishes,
Peter |
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| Robert L. Oldershaw... |
| Posted: Tue Nov 03, 2009 10:59 am |
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On Nov 1, 12:36 pm, Arnold Neumaier <Arnold.Neuma... at (no spam) univie.ac.at>
wrote:
[quote]
I also don't understand why you use reversibility/integrability
in this combination as if these were essentially synonymous.
Every (classical or quantum) Hamiltonian system is reversible,
while only very simple or very idealized systems are integrable.
[/quote]
Well, let's further clarify things with the following impertinent
questions.
Is there a fundamental distinction between the physics of the atomic
microcosm and the physics of the macrocosm that can stand up to
persistent and objective scientific scrutiny?
If there is one physics for all of nature, perhaps not.
Is the current Balkanization of physics due mainly to incomplete and
inadequate modeling?
RLO
www.amherst.edu/~rloldershaw |
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