 |
|
| Science Forum Index » Physics - Research Forum » Is Perfect Reversibility A Myth?... |
|
Page 2 of 2 Goto page Previous 1, 2 |
|
| Author |
Message |
| Juan R." González-Álvarez... |
 Posted: Wed Nov 04, 2009 1:39 am |
|
|
|
Guest
|
Robert L. Oldershaw wrote on Fri, 30 Oct 2009 12:08:59 -0400:
(...)
[quote]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?
[/quote]
*Any* law of physics is a mathematical ideal. One would not confound
reality with our models of her.
For certain systems the production of entropy is so low that cannot be
differentiated from zero and are explained using reversible models.
[quote]Did Poincare already discover this during the 1892-1899 period when
modern chaos theory was founded in his "New Methods of Celestial
Mechanics"?
[/quote]
Poincaré showed that not all mechanical systems are integrable due to
presence of resonances.
The so-called Brussels school tries to build models of irreversibility and
to solve the problem of the arrow of time using Poincare theorems.
They think that irreversible systems are LPS (Large Poincaré Systems).
They also think that resonances introduce an arrow of time.
Their work is well explain to broad audiences in the best-seller book
http://www.amazon.com/End-Certainty-Ilya-Prigogine/dp/0684837056
where he explain how to extend reversible theories from particle physics
to general relativity for accounting for irreversible phenomena, including
a resolution of the measurement problem in quantum mechanics as a bonus.
Whereas I agree on motivations, I disagree on the details of their theory.
In my opinion resonances are not the origin of the time arrow.
[quote]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?
[/quote]
It depends. A reversible model of Moon motion is an excellent idealization
and the time-reversible mechanical equations work fine. A reversible model
of dissipation in a fluid would be artificial.
[quote]What are the best examples of candidates for truly and ideally
reversible systems?
[/quote]
The second law says: reversible systems are those for which production of
entropy is zero.
In thermodynamics we compute the production of entropy (using the
well-known product of forces and fluxes) for checking irreversibility.
Microscopically we have the dissipative quantum equation
d(rho)/dt = L rho + D
when D is zero the production of entropy is also zero and the resulting
dynamics is reversible and described by the Liouville equation
d(rho)/dt = L rho
When the state can be approximated by a pure state
rho = |Psi><Psi|
then the Liouville equation reduces to the Schrödinger equation
d|Psi>/dt = H |Psi>
Therefore one computes D and it if it is zero or close to zero, the
dynamics is reversible.
The big question is what is the new term D? Nobody knows for sure.
Each School propose a diferent D. Some people has proposed
phenomenological terms in wait for a theory of irreversibility.
Zubarev School proposes D = epsilon (rho - rho_R)
where epsilon is a positive infinitesimal and rho_R an auxiliary state
postulated according to certain kernels and phenomenology.
Lindbald proposes another D
http://en.wikipedia.org/wiki/Lindblad_equation
assuming some mathematical properties.
Prigogine School proposes another
http://www.amazon.com/End-Certainty-Ilya-Prigogine/dp/0684837056
where the new term is explained in terms of collision operators
that contain resonances among degrees of freedom.
Byung Chan Eu proposed other based in a generalization of
Boltzmann kinetic theory and the observation of behavior of
hundred of physicochemical systems he studied
http://www.canonicalscience.org/en/researchzone/time.html
Etc.
--
http://www.canonicalscience.org/
BLOG:
http://www.canonicalscience.org/en/publicationzone/
canonicalsciencetoday/canonicalsciencetoday.html |
|
|
| Back to top |
|
|
|
| Juan R. González-Álvarez... |
| Posted: Thu Nov 05, 2009 5:58 pm |
|
|
|
Guest
|
Arnold Neumaier wrote on Mon, 02 Nov 2009 11:51:17 -0500:
(...)
[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.
[/quote]
Untrue. It is not possible to derive irreversibility from reversibility.
As Van Kampen brilliantly noted "One cannot escape from this fact by any
amount of mathematical funambulism".
The open-system approach is totally inconsistent. The subdynamics of a
reversible system is of course reversible. The so-called derivations of
irreversibility are mathematical and physically invalid.
[quote]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).
[/quote]
Those "perfectly noninteractiung universes" that we cannot know belong
to the world of fantasy not to physics.
(...)
--
http://www.canonicalscience.org/
BLOG:
http://www.canonicalscience.org/en/publicationzone/
canonicalsciencetoday/canonicalsciencetoday.html |
|
|
| Back to top |
|
|
|
| Arnold Neumaier... |
| Posted: Fri Nov 06, 2009 11:26 pm |
|
|
|
Guest
|
Juan R. González-Álvarez wrote:
[quote]Arnold Neumaier wrote on Mon, 02 Nov 2009 11:51:17 -0500:
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.
Untrue. It is not possible to derive irreversibility from reversibility.
As Van Kampen brilliantly noted "One cannot escape from this fact by any
amount of mathematical funambulism".
The open-system approach is totally inconsistent. The subdynamics of a
reversible system is of course reversible. The so-called derivations of
irreversibility are mathematical and physically invalid.
[/quote]
As an approximation, there is nothing inconsistent.
All of physics is valid only approximately anyway; so approximations
are legitimate. In particular, one conventionally approximates the
dynamics of a part of a larger system (whether or not the latter is
assumed to be reversible) successfully as that of an irreversible
system.
This approximation process is well understood - see, e.g.,
H Grabert,
Projection Operator Techniques in Nonequilibrium
Statistical Mechanics,
Springer Tracts in Modern Physics, 1982.
It is often applicable with much success.
In all serious applications of physics, one reduces a system description
to something manageable by replacing its interaction with the unmodelled
environment, using some approximation that accounts for its influence
without having to model it. This makes the system open, but amenable to
a stochastic description. Or, with further approximation, even to a
deterministic description.
If one does not allow for that, one cannot do any physics at all.
[quote]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).
Those "perfectly noninteractiung universes" that we cannot know belong
to the world of fantasy not to physics.
[/quote]
We cannot even know whether they are fantasy or physics.
They might exist, and still we could never find out. But of course,
one can ignore them completely without losing anything of
predictive value. This is why I put the statement in parentheses.
Arnold Neumaier |
|
|
| Back to top |
|
|
|
| Robert L. Oldershaw... |
| Posted: Mon Nov 09, 2009 10:52 am |
|
|
|
Guest
|
On Nov 4, 6:39 am, "Juan R." González-Álvarez
<juanREM... at (no spam) canonicalscience.com> wrote:
I am also troubled by AN's comment that: "it follows from the
assumption that the universe as a whole is reversible..."
(1) There is considerable confusion over what the term "universe as a
whole" actually means. In fact, the phrase is scientifically undefined
at this point.
(2) Assuming this undefined thing is "reversible" just adds insult to
injury. Who says it must be so? Where is the evidence?
I realize that AN was just speaking in the vernacular, but woe be to
science when assumptions are treated as facts and and used as such in
reasoning.
RLO
www.amherst.edu/~rloldershaw |
|
|
| Back to top |
|
|
|
| Phillip Helbig... |
| Posted: Mon Nov 09, 2009 12:24 pm |
|
|
|
Guest
|
Arnold Neumaier wrote on Sat, 07 Nov 2009 09:26:11 +0000:
[quote]Juan R. wrote:
Arnold Neumaier wrote on Mon, 02 Nov 2009 11:51:17 -0500:
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.
Untrue. It is not possible to derive irreversibility from
reversibility. As Van Kampen brilliantly noted "One cannot escape
from this fact by any amount of mathematical funambulism".
The open-system approach is totally inconsistent. The subdynamics
of a reversible system is of course reversible. The so-called
derivations of irreversibility are mathematical and physically
invalid.
As an approximation, there is nothing inconsistent.
All of physics is valid only approximately anyway; so approximations
are legitimate. In particular, one conventionally approximates the
dynamics of a part of a larger system (whether or not the latter is
assumed to be reversible) successfully as that of an irreversible
system.
This approximation process is well understood - see, e.g.,
H Grabert,
Projection Operator Techniques in Nonequilibrium Statistical
Mechanics,
Springer Tracts in Modern Physics, 1982.
It is often applicable with much success.
In all serious applications of physics, one reduces a system
description to something manageable by replacing its interaction
with the unmodelled environment, using some approximation that
accounts for its influence without having to model it. This makes
the system open, but amenable to a stochastic description. Or, with
further approximation, even to a deterministic description.
If one does not allow for that, one cannot do any physics at all.
[/quote]
Evidently both Van Kampen (one of most respected physicists
in the field)
http://www.amazon.com/Views-Physicist-Selected-Papers-Kampen/dp/
981024357X
and myself (not at his level of course) are aware of the importance
of approximations. You missed the whole point
I agree with him on that the claimed 'derivations' of irreversibility
from reversibility are based in some "amount of mathematical
funambulism".
His remark is totally general and also applies to the claimed
'derivations' using PO techniques.
PO techniques introduced in NESM in early 60s are rather useful [#].
But its lack of usefulness beyond the weak limit (more exactly in
regimes where the reduced kinetic equation is not closed) is also
well-known.
Moreover, PO techniques are only a clever and *fast* technique to
decompose the so-named "relevant" and "irrelevant" subspaces.
PO techniques do not provide a foundation for NESM neither solve
the problem of the arrow of time.
A more modern and rigorous discussion of those issues was given in a
recent Solvay conference devoted to the problem. Contributions were
published in the next volume
http://www.amazon.com/Resonances-Instability-Irreversibility-Advances-
Chemical/dp/0471165263
I agree on their motivations and welcome their attempt to substitute
"mathematical funambulism" by a more rigorous and axiomatic approach.
However, I want to remark that I disagree with all the theories
presented there.
[quote]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).
Those "perfectly noninteractiung universes" that we cannot know
belong
to the world of fantasy not to physics.
We cannot even know whether they are fantasy or physics. They might
exist, and still we could never find out. But of course, one can
ignore them completely without losing anything of predictive value.
This is why I put the statement in parentheses.
[/quote]
That in your own words "set of perfectly noninteractiung universes -
of which we can of course know only the single one we are in" do not
belong to physics.
[#] I want to reproduce here an interesting episode. It is often
acknowledged in NESM literature that PO techniques were introduced
by Nakajima, Zwanzig, and Mori. However, in a personal
communication with Prigogine coworker, Gonzalo Ordonez, he said me
that Prigogine had introduced PO techniques during a talk he gave
and Zwanzig attended. Some time after Zwanzig published his
foundational paper on the PO method. Gonzalo said me that Zwanzig
gave a more elegant formulation but the original idea was from
Prigogine!
--
http://www.canonicalscience.org/
BLOG:
http://www.canonicalscience.org/en/publicationzone/
canonicalsciencetoday/canonicalsciencetoday.html |
|
|
| Back to top |
|
|
|
| ... |
| Posted: Mon Nov 09, 2009 12:30 pm |
|
|
|
Guest
|
Arnold Neumaier wrote on Sat, 07 Nov 2009 09:26:11 +0000:
[quote]Juan R. wrote:
Arnold Neumaier wrote on Mon, 02 Nov 2009 11:51:17 -0500:
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.
Untrue. It is not possible to derive irreversibility from
reversibility. As Van Kampen brilliantly noted "One cannot escape
from this fact by any amount of mathematical funambulism".
The open-system approach is totally inconsistent. The subdynamics
of a reversible system is of course reversible. The so-called
derivations of irreversibility are mathematical and physically
invalid.
As an approximation, there is nothing inconsistent.
All of physics is valid only approximately anyway; so approximations
are legitimate. In particular, one conventionally approximates the
dynamics of a part of a larger system (whether or not the latter is
assumed to be reversible) successfully as that of an irreversible
system.
This approximation process is well understood - see, e.g.,
H Grabert,
Projection Operator Techniques in Nonequilibrium Statistical
Mechanics,
Springer Tracts in Modern Physics, 1982.
It is often applicable with much success.
In all serious applications of physics, one reduces a system
description to something manageable by replacing its interaction
with the unmodelled environment, using some approximation that
accounts for its influence without having to model it. This makes
the system open, but amenable to a stochastic description. Or, with
further approximation, even to a deterministic description.
If one does not allow for that, one cannot do any physics at all.
[/quote]
Evidently both Van Kampen (one of most respected physicists
in the field)
http://www.amazon.com/Views-Physicist-Selected-Papers-Kampen/dp/
981024357X
and myself (not at his level of course) are aware of the importance
of approximations. You missed the whole point
I agree with him on that the claimed 'derivations' of irreversibility
from reversibility are based in some "amount of mathematical
funambulism".
His remark is totally general and also applies to the claimed
'derivations' using PO techniques.
PO techniques introduced in NESM in early 60s are rather useful [#].
But its lack of usefulness beyond the weak limit (more exactly in
regimes where the reduced kinetic equation is not closed) is also
well-known.
Moreover, PO techniques are only a clever and *fast* technique to
decompose the so-named "relevant" and "irrelevant" subspaces.
PO techniques do not provide a foundation for NESM neither solve
the problem of the arrow of time.
A more modern and rigorous discussion of those issues was given in a
recent Solvay conference devoted to the problem. Contributions were
published in the next volume
http://www.amazon.com/Resonances-Instability-Irreversibility-Advances-
Chemical/dp/0471165263
I agree on their motivations and welcome their attempt to substitute
"mathematical funambulism" by a more rigorous and axiomatic approach.
However, I want to remark that I disagree with all the theories
presented there.
[quote]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).
Those "perfectly noninteractiung universes" that we cannot know
belong
to the world of fantasy not to physics.
We cannot even know whether they are fantasy or physics. They might
exist, and still we could never find out. But of course, one can
ignore them completely without losing anything of predictive value.
This is why I put the statement in parentheses.
[/quote]
That in your own words "set of perfectly noninteractiung universes -
of which we can of course know only the single one we are in" do not
belong to physics.
[#] I want to reproduce here an interesting episode. It is often
acknowledged in NESM literature that PO techniques were introduced
by Nakajima, Zwanzig, and Mori. However, in a personal
communication with Prigogine coworker, Gonzalo Ordonez, he said me
that Prigogine had introduced PO techniques during a talk he gave
and Zwanzig attended. Some time after Zwanzig published his
foundational paper on the PO method. Gonzalo said me that Zwanzig
gave a more elegant formulation but the original idea was from
Prigogine!
--
http://www.canonicalscience.org/
BLOG:
http://www.canonicalscience.org/en/publicationzone/
canonicalsciencetoday/canonicalsciencetoday.html |
|
|
| Back to top |
|
|
|
| Arnold Neumaier... |
| Posted: Sat Nov 28, 2009 12:15 pm |
|
|
|
Guest
|
Robert L. Oldershaw wrote:
[quote]On Nov 4, 6:39 am, "Juan R." González-Álvarez
juanREM... at (no spam) canonicalscience.com> wrote:
I am also troubled by AN's comment that: "it follows from the
assumption that the universe as a whole is reversible..."
(1) There is considerable confusion over what the term "universe as a
whole" actually means. In fact, the phrase is scientifically undefined
at this point.
[/quote]
It can be easily defined precisely as the smallest closed and isolated
physical system that contains the earth.
[quote](2) Assuming this undefined thing is "reversible" just adds insult to
injury. Who says it must be so? Where is the evidence?
[/quote]
According to the mainstream theory, this system is governed by a
reversible dynamics; but there are a significant number of dissenters
who take this into doubt.
Therefore I called the reversibiliy an assumption.
[quote]I realize that AN was just speaking in the vernacular, but woe be to
science when assumptions are treated as facts and and used as such in
reasoning.
[/quote]
Without making assumptions and stating them clearly, no science is
possible.
Arnold Neumaier |
|
|
| Back to top |
|
|
|
|
|
All times are GMT - 5 Hours
The time now is Mon Nov 30, 2009 1:03 pm
|
|