Can QM be derived from classical physics?
Rock Brentwood
theory, allow for interactions and/or propagation along spacelike
intervals and then pose a "no information condition" which restricts
the ability of space-like propagation to transmit information.
The general idea is that the "no-information" condition will force the
condition that spacelike propagation be randomized in just the right
way to recover quantum theory.
The result should not be precisely equivalent to quantum theory, but
an upwardly compatible generalization of it. The really interesting
part of this question is what will the generalizations entail;
particularly when this is cross-applied to classical field theory and
to relativistic dynamics?
p.ki...@ic.ac.uk
Something like Ekert's http://arxiv.org/abs/0806.0485 ? ...
mind you I don't recall it being relativistic.
--
---------------------------------+---------------------------------
Dr. Paul Kinsler
Blackett Laboratory (Photonics) (ph) +44-20-759-47734 (fax) 47714
Imperial College London, Dr.Paul...@physics.org
SW7 2AZ, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/
gehrab
> The question, more precisely, is this: starting out with classical
> theory, allow for interactions and/or propagation along spacelike
> intervals and then pose a "no information condition" which restricts
> the ability of space-like propagation to transmit information.
>
> The general idea is that the "no-information" condition will force the
> condition that spacelike propagation be randomized in just the right
> way to recover quantum theory.
Why not just begin with special relativity and assume that
relativistic ED is in effect?
I have wondered about this prospect for many years, but have never set
out to do it.
My question, for what it is worth, is, "Given a relativistic version
of classical physics,
that is with the Minkowski spacetime, can we build QM?
George
enders
Unfortunately, I don't fully understand your idea of randomization.
But I can answer your question "Can QM be derived from classical
physics?" with 'yes'. There are several ways from CM to QM. I
favourize those fulfilling Schr�dinger's requirements (1926, Commun. 2
and 4).
- The use of the classical expressions for V(r,t) and T(p,t) should be
justified;
- It should outcome uniquely that the energy and not the frequency is
discretized;
- The maths used should correspond appropriately to the quantum nature
of the objects investigated (eigenvalue methods belong to classical
objects).
Unfortunately, I know only one aproach doing so, viz., the one
developed by Dieter Suisky and myself, see Int. J. Theor. Phys. 2005
or my book (Springer 2006).
Best wishes and good luck with your idea!
Peter
Hendrik van Hees
what one means by "derived". I think there's no way to "derive" a physical
theory whatsoever from pure logics like in math, where you build
your "universe" by postulating some basic axioms and then just deduce with
pure logic what might follow from such a axiomatic structure.
I guess it is impossible to derive quantum mechanics from classical physics,
be it relativistic or non-relativistic, because quantum mechanics is the
more general model, i.e., it describes more phenomena and contains
classical mechanics as a limiting case. So it is (at least to a certain
extent) possible to derive classical behavior of, e.g., many-body systems
which interact with the environment from quantum theory (decoherence), but
it's not possible, without hidden assumptions, to derive quantum theory
from classical theory.
To find a more general theory (QM in our contect) of nature than is present
at the time (classical electron theory within Maxwell's electromagnetics),
is more an intuitive act considering all the empirical facts which
contradict the previous theory, than a question of logical deduction.
Rock Brentwood wrote:
--
Hendrik van Hees Institut f�r Theoretische Physik
Phone: +49 641 99-33342 Justus-Liebig-Universit�t Gie�en
Fax: +49 641 99-33309 D-35392 Gie�en
http://theory.gsi.de/~vanhees/faq/
Thomas Heger
That approach is called 'structured spacetime' and e.g. done by David
Heestenes.
But someting even more interesting is this paper:
http://arxiv.org/ftp/arxiv/papers/0810/0810.0224.pdf
Greetings
Thomas Heger
CarlBrannen
Foundations
of Physics that may have something to do with this:
http://www.brannenworks.com/Gravity/EmergSpin.pdf
The basic idea is that position and spin are both attributes of
elementary
particles, but they act differently. When you measure spin you get a
result, and then measuring it again gives the same value. For
instance,
if you measure an electron as spin-up, then another, later, spin
measurement will also give spin-up.
But measuring position (to sufficient accuracy) causes a random
momentum, and that changes the position, so if you wait a little
while, and measure position again, you're likely to get a completely
different result.
So the paper proposes that if you could measure spin accurately
enough (in the sense of a measurement of spin over a very short
time interval) you would also find that spin acts like position, it
would not be consistent when you measured it twice.
The connection to the concept of a classical behavior underneath
quantum is that the measurement of spin that is implied by the
idea is less quantum and more classical than the usual spin-1/2.
My intuition says that if you want to get classical behavior under
the quantum, you are going to have to still have linear superposition,
but my suspicion is that this is enough.
Carl
enders
giessen.de> wrote:
> It's a pretty difficult question to answer. First of all one has to define,
> what one means by "derived". I think there's no way to "derive" a physical
> theory whatsoever from pure logics like in math, where you build
> your "universe" by postulating some basic axioms and then just deduce with
> pure logic what might follow from such a axiomatic structure.
Hello Hendrik,
I agree (with Huygens) that the methodics of posing axioms as well as
of axiomatic conclusions in physics is different from that in
geometry. It is not as week, however, as it might seem from your
rather sceptical assessment :-)
> I guess it is impossible to derive quantum mechanics from classical physics,
> be it relativistic or non-relativistic, because quantum mechanics is the
> more general model, i.e., it describes more phenomena and contains
> classical mechanics as a limiting case. So it is (at least to a certain
> extent) possible to derive classical behavior of, e.g., many-body systems
> which interact with the environment from quantum theory (decoherence), but
> it's not possible, without hidden assumptions, to derive quantum theory
> from classical theory.
I see it differently (in agreement with Bohr and Landau). As I wrote
in my foregoing posting, a derivation has been presented by Dieter
Suisky and myself, see Int. J. Theor. Phys. 2005
or my book (Springer 2006). An essential point is that we start not
from Newton's representation (Heisenberg) or Hamilton-Jacobi theory
(Schr�dinger), but from Euler's representation of CM. The decisive
advantage consists in that here the change of state (motion) is not
axiomatically fixed, so that other manners of motion become possible,
not only motions along pathes.
In case you see flaws or gaps in our conclusion chain, I would be
happy to discuss them with you :-)
Best wishes,
Peter
PS:
> To find a more general theory (QM in our contect) of nature than is present
> at the time (classical electron theory within Maxwell's electromagnetics),
> is more an intuitive act considering all the empirical facts which
> contradict the previous theory, than a question of logical deduction.
The microscopic Maxwell eqs. and the Maxwell-Lorentz force can be
deduced using the kind of forces in the 'Principia' (chs.
'Definitions' and 'The Laws of Motion') and Helmholtz's analysis of
the relationships between forces and energies (copies of my
publications are available at requests).
======= Moderator's note =====================================
I'll have a look at your paper next week, when I can print it out.
I suppose the full citation is
Int. J. Theoret. Phys. *44*, 161 (2005)
DOI: 10.1007/s10773-005-1491-5
Uncle Al
>
> I've just finished the 2nd version of a paper under review at
> Foundations
> of Physics that may have something to do with this:
> http://www.brannenworks.com/Gravity/EmergSpin.pdf
> But measuring position (to sufficient accuracy) causes a random
> momentum, and that changes the position, so if you wait a little
> while, and measure position again, you're likely to get a completely
> different result.
>
> So the paper proposes that if you could measure spin accurately
> enough (in the sense of a measurement of spin over a very short
> time interval) you would also find that spin acts like position, it
> would not be consistent when you measured it twice.
[snip]
A linear polarizer makes an unambiguous measurement - but it doesn't.
Cross "perfect" linear polarizers, 90 degree relative rotation, to
obtain 0% transmission. Interpose a third linear polarizer rotated 45
degrees and suddenly obtain 25% transmission (less real world
interface reflections and inefficiencies), {[cos(45)]^2}^2 for the two
45 degree interfaces (Malus' law),
<http://www.physicsphotons.org/linear_polarization.pdf>
<http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/polcross.html>
Suppose we instead interposed a train of 8 perfect polarizers each
sequentially rotated 10 degrees? Run the train,
http://www.codehappy.net/calculator.htm
(angles in radians)
{[cos(45)]^2}^2 = 25.0000% transmission
{[cos(10)]^2}^8 = 78.2750% transmission
{[cos(1)]^2}^89 = 97.3252% transmission
{[cos(0.1)]^2}^899 = 99.7265% transmission
{[cos(0.01)]^2}^8999 = 99.9726% transmission
{[cos(0.001)]^2}^89999 = 99.99726% transmission
{[cos(0.000001)]^2}^89999999 = 99.99999726% transmission
By making more and more smaller and smaller orientation meaurements we
overall end up making no orientation measurement at all.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2
student
This is an interesting question!
I don't think the classical theory could be a phase space
theory, as the classical algebra of Poisson brackets is
not isomorphic to the quantum commutator algebra. But
perhaps this is partly what you mean when you say "the
results should not be precisely equivalent to quantum
theory"?
There are two contexts to try and impose your "no
information" condition - expectation values for one
system shouldn't change under
(i) a canonical transformation applied to another
system (a 'local' evolution)
(ii) a measurement carried out on another system.
Analysing the first case is probably the easiest. It
would seem to imply that the average of any
interaction potential should be zero under all local
canonical transformations. This condition
presumably places a combined restriction on
(a) the form of interaction potentials, and
(b) the allowed physical ensembles over
which averages are taken.
Ilja
> On Oct 1, 10:23 am, Rock Brentwood <markw...@yahoo.com> wrote:
> > The general idea is that the "no-information" condition will force the
> > condition that spacelike propagation be randomized in just the right
> > way to recover quantum theory.
>
> > The result should not be precisely equivalent to quantum theory, but
> > an upwardly compatible generalization of it.
> This is an interesting question!
>
> I don't think the classical theory could be a phase space
> theory, as the classical algebra of Poisson brackets is
> not isomorphic to the quantum commutator algebra.
If one considers such questions, de Broglie-Bohm pilot wave
theory is a good starting point: It has a preferred frame with
hidden information transfer FTL, but one can in so-called
quantum equilibrium derive QM with it's no information
result. One idea would be to try to find another
axiomatization of this theory, with the "no information"
condition not as derived from qu. equilibrium, but as an
axiom. If this gives much even if possible is not clear to me.
dBB is not a phase space theory, but a configuration
space theory, which is IMHO more natural.
enders
...
> If one considers such questions, de Broglie-Bohm pilot wave
> theory is a good starting point: �It has a preferred frame with
> hidden information transfer FTL, but one can in so-called
> quantum equilibrium derive QM with it's no information
> result. One idea would be to try to find another
> axiomatization of this theory, with the "no information"
> condition not as derived from qu. equilibrium, but as an
> axiom. If this gives much even if possible is not clear to me.
Since dBB is Schr�dinger theory + assigning particle trajectories to
psi, I would think that one possible axiomatics of dBB consists in an
axiomatics of the former + 1 axiom containing the pilot wave
interpretation.
> dBB is not a phase space theory, but a configuration
> space theory, which is IMHO more natural.
Why "more natural"?
i) The Hamiltonian is the "natural" generalization of Newton's
description of (stationary) states in terms of the momentum to bodies
in external force fields.
2) Gibbs' (Principles, 1902, Ch. I) derivation of the equilibrium
condition of canonical ensambles would work not so "natural" in
configuration space.
Thank you and best wishes,
Peter
Surfer
wrote:
These may be of interest.
=================
Quantum Fluctuations
Edward Nelson
http://press.princeton.edu/titles/2357.html
"......Stochastic mechanics is a description of quantum phenomena in
classical probabilistic terms...."
=================
Scale relativity and fractal space-time: theory and applications
Laurent Nottale
http://arxiv.org/abs/0812.3857
Derivation of the postulates of quantum mechanics from the first
principles of scale relativity
Laurent Nottale, Marie-Noëlle Célérier
J. Phys. A: Math. Theor. 40 (2007) 14471-14498
http://arxiv.org/abs/0711.2418
Numerical simulation of a macroscopic quantum-like experiment:
oscillating wave packet
L. Nottale, T. Lehner
http://arxiv.org/abs/quant-ph/0610201
=================
maxwell
Thanks for the reference, Thomas. Peter Rowlands' paper appears to
contain a lot of useful physics & is written clearly and with powerful
algebra. A worthy follow-on to the British tradition in theoretical
physics (exemplified by Dirac) where the physical ideas come first and
then the math follows - unlike the American/European approach.