Smolin was here - statistical vs. quantum probabilities
I.Vecchi
instances of probabilities are just squared moduli of quantum
amplitudes, which the observer is often unable or unwilling to track.
This was the result of some deconstructive argument on the distinction
between proper and improper mixtures, which plays a key role in
decoherence theory's conceptual mess. One of the further supporting
arguments is the irrelevance of the distinction between classical and
quantum probabilistic devices, since any "classical" chaotic device
will quickly pump quantum-scale initial indeterminacies up to
macroscopic level (cf. [3] ), making any statistical vs. quantum
distinction empty. Such probabilistic model is required by my
RQM+DeFinetti-inspired intersubjective quantum framework ([1],[4]) and
should be testable once and if macroscopic superpositions will be
detected (e.g. as interference patterns of dice throws).
Now, I found out that a related idea had been proposed by Smolin in
1986 ([5], cf. [6]), although his arguments and his setting are quite
different (starring the Unruh effect, of all things):
"A new point of view towards the problem of the relationship between
gravitational and quantum phenomena is proposed which is inspired by
the fact that the distinction between quantum fluctuations and real
statistical fluctuations in the state of a system seems not to be
maintained in a variety of phenomena in which quantum and gravitational
effects are both important. One solution to this dilemma is that
quantum fluctuations are in fact real statistical fluctuations, due to
some unknown, but universal, phenomena".
Interesting, huh?
IV
[1] http://xxx.lanl.gov/abs/quant-ph/0206147
[2]
http://groups.google.com/group/sci.physics.research/msg/9bc5d5052b349946
[3]
http://groups.google.com/group/sci.physics.research/msg/19562781a8ccfeff?
[4]
http://groups.google.com/group/sci.physics.research/msg/f5d535f8f4b645e8?
[5] L. Smolin "On the nature of quantum fluctuations and their
relation to gravitation and the principle of inertia" , Class. Quantum
Grav., 3 347-359 (1986) at
http://www.iop.org/EJ/abstract/0264-9381/3/3/009
[6] R.M Wald "III. Are statistical probabilities truly distinct from
quantum probabilities?" p. 18 in "Gravitation, Thermodynamics, and
Quantum Theory" at
Benjamin Schulz
> Now, I found out that a related idea had been proposed by Smolin in
> 1986 ([5], cf. [6]), although his arguments and his setting are quite
> different (starring the Unruh effect, of all things):
> "A new point of view towards the problem of the relationship between
> gravitational and quantum phenomena is proposed which is inspired by
> the fact that the distinction between quantum fluctuations and real
> statistical fluctuations in the state of a system seems not to be
> maintained in a variety of phenomena in which quantum and gravitational
> effects are both important. One solution to this dilemma is that
> quantum fluctuations are in fact real statistical fluctuations, due to
> some unknown, but universal, phenomena".
>
> Interesting, huh?
>
Smolin had some inspiration from Edward Nelson [1], who showed in 1960
in phys.rev. [2] that the Schroedinger equation can be produced from
F=m*a particles when they act under reversible pair forces, which give
them energy and restore the old energy afterwards. This is in
mathematical formulation, a special brownian motion process without
dissipation.
Nelson was also able to show that these nondeterministic theories
violate the Bell uncertainties as quantum mechanics does. His doctorate
student Dankel proved, that one also can do a spin quantisation which
leads to correct half integer and integer spins[3].
This gives also correct results of the Stern-Gerlach and Aspect
experiments although it is only brownian motion[4].
Nelson proved some theorems to explicitly show, that it violates
locality, but has no effects with information exchange over the speed of
light (Nelson therefore proved in fact a deeper version of Bells
theorem, which begins with lower premises and distinguishes between an
active form of locality (sending signals over lightspeed) and a passive
one (only simulatenaous events happen at the same time), where the last
one is well suited for his theory [5]).
His theory therefore "solved" some paradoxes as the measurement problem
and that of the wave function collapse[1].
But hovever, no lorentz covariant formulation has been found for this
theory till now.
Enjoyable a recent, and very readable article (which analyzes the
physical meaning of the stochastic process and its nonlocality
properties) is in Annalen der Physik 2003 [6]
Since no relativistic version was found, the theory was given up. But
this is not due to the "stranginess" of the postulate from Nelson, it is
only because Nelson's idea relies on brownian motion and even for a gas
of particles like molecules in a hot plasma, we have no relativistic
generalisation of the theory of brownian motion till today. If you find
one, tell it to me. I would be very interested.
There are, however some slowly motivated efforts to work with
gravity[7]. But they are wrong as long as the stochastic process
constructed for the special relativity is not motivated physically. When
one has found such a theory in special relativity, it would be easy to
go to general relativity.
1) http://www.math.princeton.edu/~nelson/books/qf.pdf
2) E. Nelson, Derivation of the Schrodinger equation from Newtonian
mechanics, Phys. Rev. 150 1079 (1966).
3) Work of Nelsons doctorate Dankel
http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JMAPAQ000018000002000253000001&idtype=cvips&gifs=yes
4)W.G.Farris Spin correlations in stochastic mechanics, found. phys.
12,1982,1-26
5) E. Nelson, lecture notes in physics 262, springer 1986, stochastic
processes in classical and quantum systems, pp 438
a better description of nelsons theorems might be in the appendix of
W.G. Faris in Dawid Wicks book
http://www.amazon.com/exec/obidos/tg/detail/-/0387947264/104-6390766-1213566?v=glance.
It is more readable than the very advanced mathematics Nelson prefers in
this lecture (this writing style is one reason why his theorems are not
much known)
6) a nice summary in Annalen der Physik of what this theory is about
http://www3.interscience.wiley.com/cgi-bin/abstract/104544152/ABSTRACT
jarek korbicz
> violate the Bell uncertainties as quantum mechanics does.
Violating Bell inequalities is not enough to fully reproduce quantum
correlations - there are states that do not violate Bell inequalities,
but nevertheless possess non-classical correlations [1]. Do you know if
Nelson=B4s theory is able to reproduce fully quantum entanglement, not
just states violating Bell ineq=B4s ? Sounds very interesting.
[1] R. Werner, Phys. Rev. A 40, 4277 (1989).
Best,
jarek
Benjamin Schulz
Yes. it does.
Nelson's stochastic begins with random fluctuations and (at least) in
the Annalen paper [1]. It derives the Quantum Potential of Bohmian
Mechanics. The Bohmian trajectories are there, however only ensemble
averages of possible trajectories in this theory (That explains why they
are not observable as trajectories in for example in [2]).
The only problem of Nelson was, that his formulation starts with a
classical Wiener Process. This is due to that Nelson feared to introduce
a real hidden variable theory (because he believed in 1960 that the
wrong proof of v.Neumann was correct).
The nonlocality theorem of Nelson (which is very interesting and
valuable itself) states that there are two forms of locality. Active
(whith information exchange over lightspeed) locality. And passive
locality (simultaneous events happen at the same time, due to the
stochastic process). And to violate Locality in Bell's sense, one must
violate only one condition.
Since Bohmian Mechanics is an active-non-locality violating theory with
over lightspeed effects, Nelson stopped in his famous book at the point,
where he says:
> The classical Markov Process he hat thought of only violates active locality and has to be abandoned.
Since Nelson did not find a suitable and physically motivated stochatic
process, he gave up.
But this is exactly, what is done in the Annalen paper of 2003 [1].
Moreover, the stochastic process is much physically motivated.
Since one has the Bohmian Mechanics as ensemble average, one gets the
same as Quantum mechanics.
Entanglement with spins is done in [3]. But, however, in the "old
formulation" Nelson had begun, which only deals with the ensemble
averages. (thinking on this ensemble averages as trajectories, would
mean, it is an active nonlocal theory. But in the context of the new
work in Ann.Phys. this is clearly wrong and it is passive nonlocal).
1) Annalen paper
http://www3.interscience.wiley.com/cgi-bin/abstract/104544152/ABSTRACT
2) summary about surrealistic bohmian trajectories
http://www.physica.org/xml/article.asp?article=t076a00041.xml
3) Spin correlations, Stern Gerlach and Entanglement (EPR) W.G.Farris
Spin correlations in stochastic mechanics, found. phys. 12,1982,1-26
Benjamin
jarek korbicz
> same as Quantum mechanics.
I think Bohm mechanics is not able to reproduce entanglement. Hence my
question.
Best,
jarek
LEJ Brouwer
> But hovever, no lorentz covariant formulation has been found for this
> theory till now.
Quite a lot of work has been done on finding a lorentz covariant
formulation. See for example:
http://arxiv.org/abs/quant-ph/0108139
> Since no relativistic version was found, the theory was given up. But
> this is not due to the "stranginess" of the postulate from Nelson, it is
> only because Nelson's idea relies on brownian motion and even for a gas
> of particles like molecules in a hot plasma, we have no relativistic
> generalisation of the theory of brownian motion till today.
It is the conservative interactions between the particles which lead to
the Brownian motion, and there is no reason why relativistic
conservative interactions should not exist (of course they do). The
ensemble motion of such self-interacting particles will lead to a
conservative diffusion process (which will be a generalisation of
Brownian motion) which is Lorentz covariant, so I am not sure why this
has been such a mystery. I think the link to Brownian motion may be
something of a red herring which is distracting people from the main
issue, which are the relativistic non-dissipative interactions
underlying the relativistic conservative diffusion.
Best wishes,
Sabbir.
Benjamin Schulz
> Benjamin Schulz wrote:
>
>>But hovever, no lorentz covariant formulation has been found for this
>>theory till now.
>
> Quite a lot of work has been done on finding a lorentz covariant
> formulation. See for example:
>
> http://arxiv.org/abs/quant-ph/0108139
Yes of course. But these theories have all problems in the foundation
of the stochastic process (and nonlocality therefore. A theory which is
passively nonlocal must be a non-markovian process). Here is another
publication that goes straight forward to gravity, but has the same
problems:
> http://arxiv.org/abs/gr-qc/0407076
> Title: Classical Gravity as an Eikonal Approximation to a Manifestly Lorentz Covariant Quantum Theory with Brownian Interpretation
When one looks at the methods used by the Annalen paper
http://www3.interscience.wiley.com/cgi-bin/abstract/104544152/ABSTRACT
to get a passively nonlocal theory, then these new papers, which use the
same methods with relativistic brownian motion should be of interest:
> http://arxiv.org/abs/cond-mat/0411011
> http://arxiv.org/abs/cond-mat/0505532
But one has a non-constant diffusion coefficient here.
And now, this author seems to have a constant:
> http://www.arxiv.org/abs/cond-mat/0310113
> http://www.arxiv.org/abs/cond-mat/0310022
> http://www.arxiv.org/abs/cond-mat/0310102
Can some expert on diffusion look at the three papers above if they are
correct? This would be interesting since there are some "nice" claims in
it, but I'm too uneducated to proofread them.
> It is the conservative interactions between the particles which lead to
> the Brownian motion, and there is no reason why relativistic
> conservative interactions should not exist (of course they do).
This is of course true. Only one does not know how to describe it.
> so I am not sure why this
> has been such a mystery.
This is explained in the two papers of Dunkel above. The problems are
"only" mathematical ones. Unsolved for almost 100 Years now.....
> "relativity theory and diffusion seem not to like each other" (Edward Nelson)
Benjamin
Benjamin Schulz
>
> I think Bohm mechanics is not able to reproduce entanglement. Hence my
> question.
>
> Best,
> jarek
>
OK. I must say I'm not an expert of Bohmian Mechanics.
I've read some lines again and indeed, there seem to be, some
differences between those theories, when watching multy particle systems
closely, for example (The Stochastic seem to reproduce BM only in the
one and many particle Schroedinger Equation without spin).
However, for stochastic mechanics, there are some articles related to
entangled states:
> http://www.iop.org/EJ/abstract/0305-4470/33/33/304
> We work out in detail an example with entanglement and rigorously
> prove that Stochastic Mechanics and quantum mechanics agree in
> predicting all the observed correlations at different times.
Of course the work of Farris discusses also the classical example with
entangled spin systems
> Spin correlations, Stern Gerlach and Entanglement (EPR) W.G.Farris
> Spin correlations in stochastic mechanics, found. phys. 12,1982,1-26
Best Benjamin.
Benjamin Schulz
OK. I must say I'm not an expert of Bohmian Mechanics.
I've read some lines of my cited papers again and indeed, there seem to
be, some differences between Stochastic Mechanics and BM, when looking
at multy particle systems, for example (The Stochastic seem to reproduce