Science and Technology news... :: View topic - Question regarding coherent states and virtual particles

Alain Stalder · Guest

Let me first expose some considerations before I get to the
specific question.

Coherent states in quantum mechanics and virtual particles
in quantum field theories share a qualitative property,
namely both exhibit a certain form of non-locality.

Results of quantum mechanical measurements are correlated
even in situations where there is a spacelike distance
between the two measurements, so that no real signal could
have signaled a hidden reality between the two measurements.

Virtual particles are not bound by the speed of light either.
As Feynman shows in a booklet called "Elementary Particle
Physics and the Laws of Physics" (Cambridge University Press,
1989), in a lecture called "The Reason for Antiparticles",
there must be a non-vanishing probability amplitude for
intermediate particles in a scattering process that are
outside the light cone, i.e. "faster than light".

This brings me to the question:

Could quantum field theory be reformulated such that virtual
particles (as a mathematical concept) would also describe
quantum mechanical coherence at the same time, unifying the
two concepts into a single one ?

This would be a specific form of a non-local hidden variable
theory in which virtual particles would mediate a real and
hidden reality, but would only allow this to happen in such
ways that no real signals could be observed to propagate
faster than at the speed of light.

Is anybody aware of such or similar theoretical attempts ?
Are there any arguments that would exclude this ?
Or maybe exclude just some forms of it ?
Any other specific ideas or comments ?

Alain Stalder

Igor Khavkine · Guest

On Nov 10, 2:27 pm, Alain Stalder <alain.stal...@exactphilosophy.net>
wrote:
[quote]Let me first expose some considerations before I get to the
specific question.

Coherent states in quantum mechanics and virtual particles
in quantum field theories share a qualitative property,
namely both exhibit a certain form of non-locality.

Results of quantum mechanical measurements are correlated
even in situations where there is a spacelike distance
between the two measurements, so that no real signal could
have signaled a hidden reality between the two measurements.
[/quote]
Entanglement, which is the property of quantum states you are
referring to, is different from non-locality. So, right away, you are
starting with a false premise.

[quote]Virtual particles are not bound by the speed of light either.
As Feynman shows in a booklet called "Elementary Particle
Physics and the Laws of Physics" (Cambridge University Press,
1989), in a lecture called "The Reason for Antiparticles",
there must be a non-vanishing probability amplitude for
intermediate particles in a scattering process that are
outside the light cone, i.e. "faster than light".
[/quote]
Virtual particles are not bound by the speed of light just like love
isn>t. In either case, velocity is an inapplicable concept. Virtual
particles don>t exist for their velocity to be measured.

Unfortunately, the interpretation of the amplitude that Feynman had in
mind as "something" travelling faster than the speed of light is overly
simplistic and basically wrong. Unfortunately, there doesn>t seem to be
an end for this meme in sight, with Feynman among others to blame.

[quote]This brings me to the question:
[/quote]
For the record, your question is already based on two false premises,
so the odds of it making sense or having a positive answer are slim to
none.

[quote]Could quantum field theory be reformulated such that virtual
particles (as a mathematical concept) would also describe
quantum mechanical coherence at the same time, unifying the
two concepts into a single one ?
[/quote]
Highly unlikely. There are well defined mathematical concepts behind
virtual particles and coherence, and they don>t have much to do with
each other.

[quote]This would be a specific form of a non-local hidden variable
theory in which virtual particles would mediate a real and
hidden reality, but would only allow this to happen in such
ways that no real signals could be observed to propagate
faster than at the speed of light.

Is anybody aware of such or similar theoretical attempts ?
Are there any arguments that would exclude this ?
Or maybe exclude just some forms of it ?
Any other specific ideas or comments ?
[/quote]
I>m sure that non-local hidden variable theories have been considered
as realistic (that>s a technical term) foundations of quantum
mechanics. I don>t know whether any have succeded, but I doubt it. In
fact, Anthony Leggett (recent Nobel prize winner) has published some
work showing that even non-local realistic hidden variable theories
cannot reproduce quantum mechanics.

A.J. Leggett, Nonlocal Hidden-Variable Theories and Quantum Mechanics:
An Incompatibility Theorem.
Foundations of Physics 33 (2003) 1469-1492

Hope this helps.

Igor

Oh No · Guest

Thus spake Alain Stalder <alain.stalder@exactphilosophy.net>
[quote]Let me first expose some considerations before I get to the
specific question.

Coherent states in quantum mechanics and virtual particles
in quantum field theories share a qualitative property,
namely both exhibit a certain form of non-locality.

Results of quantum mechanical measurements are correlated
even in situations where there is a spacelike distance
between the two measurements, so that no real signal could
have signaled a hidden reality between the two measurements.

Virtual particles are not bound by the speed of light either.
As Feynman shows in a booklet called "Elementary Particle
Physics and the Laws of Physics" (Cambridge University Press,
1989), in a lecture called "The Reason for Antiparticles",
there must be a non-vanishing probability amplitude for
intermediate particles in a scattering process that are
outside the light cone, i.e. "faster than light".
[/quote]
yes, but remember that, as I am sure Feynman also explains, that this is
cancelled to zero by the probability amplitude for the process of an
intermediate antiparticle going the other way.
[quote]
This brings me to the question:

Could quantum field theory be reformulated such that virtual
particles (as a mathematical concept) would also describe
quantum mechanical coherence at the same time, unifying the
two concepts into a single one ?

This would be a specific form of a non-local hidden variable
theory in which virtual particles would mediate a real and
hidden reality, but would only allow this to happen in such
ways that no real signals could be observed to propagate
faster than at the speed of light.

Is anybody aware of such or similar theoretical attempts ?
Are there any arguments that would exclude this ?
Or maybe exclude just some forms of it ?
Any other specific ideas or comments ?

[/quote]
Quite a number of people, including myself, have thought about this.
None of the thoughts ever get far enough to dignify with the phrase
"theoretical attempt". The problem is that these are chalk and cheese
situations. The mathematics of entanglement leading to correlations
between space-like separate events is so different from the mathematics
of intermediate virtual particles that it is impossible to see any
mechanism which would relate the two.

Regards

--
Charles Francis
moderator sci.physics.foundations.
charles (dot) e (dot) h (dot) francis (at) googlemail.com (remove spaces and
braces)

http://www.teleconnection.info/rqg/MainIndex

Alain Stalder · Guest

Igor Khavkine wrote:
: Entanglement, which is the property of quantum states you are
: referring to, is different from non-locality. So, right away, you are
: starting with a false premise.

That depends on the particular interpretation of quantum
mechanics. Interpretations in which there is a reality
that exists independently of observation, usually do not
get away without non-locality, and the reason they do not
is entanglement. My previous statement "Coherent states
in quantum mechanics [...] exhibit a certain form of non-
locality" was meant to alude to that and I consider it
"correct" to the degree to which it is exact.

Legett>s paper that you mentioned does not exclude non-
local hidden variable theories in general, just a certain
class of them (which is certainly an interesting result).

Alain Stalder

Alain Stalder · Guest

Charles Francis wrote:
: Quite a number of people, including myself, have thought about this.
: None of the thoughts ever get far enough to dignify with the phrase
: "theoretical attempt". The problem is that these are chalk and cheese
: situations. The mathematics of entanglement leading to correlations
: between space-like separate events is so different from the mathematics
: of intermediate virtual particles that it is impossible to see any
: mechanism which would relate the two.

Thanks. Too bad though, I was hoping there had maybe
something new come up in recent years. :(

Quantum mechanics is very difficult to supersede,
probably for at least these two reasons:

a) No disagreement with experiment.
b) In many aspects a very simple and minimal theory.
(Linear, makes only statistical predictions about
things that can be measured)

I remain curious...

Alain Stalder

Oh No · Guest

Thus spake Alain Stalder <alain.stalder@exactphilosophy.net>
[quote]Charles Francis wrote:
: Quite a number of people, including myself, have thought about this.
: None of the thoughts ever get far enough to dignify with the phrase
: "theoretical attempt". The problem is that these are chalk and cheese
: situations. The mathematics of entanglement leading to correlations
: between space-like separate events is so different from the mathematics
: of intermediate virtual particles that it is impossible to see any
: mechanism which would relate the two.

Thanks. Too bad though, I was hoping there had maybe
something new come up in recent years. :(

Quantum mechanics is very difficult to supersede,
probably for at least these two reasons:

a) No disagreement with experiment.
b) In many aspects a very simple and minimal theory.
(Linear, makes only statistical predictions about
things that can be measured)

Indeed. Imv, this is the key to understanding quantum theory. Being a[/quote]
minimal theory, the implication is that if any aspect of our intuition
appears to be in conflict with it (viz. remote correlations), we should
think that perhaps our intuition is causing us to make hidden, and
false, assumptions. You might be interested in the statements I give of
causality and locality at

http://www.teleconnection.info/rqg/Paradox

These statements are not in conflict with Bell>s theorem.

Regards

--
Charles Francis
moderator sci.physics.foundations.
charles (dot) e (dot) h (dot) francis (at) googlemail.com (remove spaces and
braces)

http://www.teleconnection.info/rqg/MainIndex

Igor Khavkine · Guest

On Nov 12, 6:11 pm, Alain Stalder <alain.stal...@exactphilosophy.net>
wrote:
[quote]Igor Khavkine wrote:

: Entanglement, which is the property of quantum states you are
: referring to, is different from non-locality. So, right away, you are
: starting with a false premise.

That depends on the particular interpretation of quantum
mechanics. Interpretations in which there is a reality
that exists independently of observation, usually do not
get away without non-locality, and the reason they do not
is entanglement. My previous statement "Coherent states
in quantum mechanics [...] exhibit a certain form of non-
locality" was meant to alude to that and I consider it
"correct" to the degree to which it is exact.
[/quote]
Practice has shown (including the results of Leggett) that it is
realism that is incompatible with entanglement, rather than locality
or lack thereof. So, your assertion is still on shaky footing.

[quote]Legett>s paper that you mentioned does not exclude non-
local hidden variable theories in general, just a certain
class of them (which is certainly an interesting result).
[/quote]
As far as I understand, this class is fairly large. Do you know of a
candidate interpretation that is not excluded?

Igor

Alain Stalder · Guest

Charles Francis wrote:
: >Quantum mechanics is very difficult to supersede,
: >probably for at least these two reasons:
:
: >a) No disagreement with experiment.
: >b) In many aspects a very simple and minimal theory.
: > (Linear, makes only statistical predictions about
: > things that can be measured)
:
: Indeed. Imv, this is the key to understanding quantum theory. Being a
: minimal theory, the implication is that if any aspect of our intuition
: appears to be in conflict with it (viz. remote correlations), we should
: think that perhaps our intuition is causing us to make hidden, and
: false, assumptions. You might be interested in the statements I give of
: causality and locality at
:
: http://www.teleconnection.info/rqg/Paradox
:
: These statements are not in conflict with Bell>s theorem.

Thanks for the link. Actually lead me also to the interpretation
called "relational quantum mechanics", which I had never heard of.

There is one more point that speaks for the minimal elegance of
quantum mechanics, namely decoherence, since it explains already
*within* the theory why quantum interference usually disappears
for macroscopic objects.

In January 2003 I posted a Gedankenexperiment here that combines
decoherence with EPR and Schroedinger>s Cats or Wigner>s Friends,
and hopefully explains what decoherence can explain and what not
with regard to measurement in quantum mechanics:

--- START QUOTE ---

* Subject: Re: Some questions on decoherence and QM.
* From: Alain Stalder <astalder@exactphilosophy.net>
* Date: Mon, 13 Jan 2003 22:30:49 +0000 (UTC)
* Message-ID: <astalder-A850F5.13133713012003@news.bluewin.ch>

In article <3E1C9025.A2D5A6CB@uni-essen.de>,
Urs Schreiber <Urs.Schreiber@uni-essen.de> wrote:

[quote]Frank Hellmann wrote:

A measurement of the quantum system described by rho in generally still
has a propability for both classically exclusive states though, so we
still have a superposition of classically exclusive states.

The last phrase must read: "a *mixture* of classical states".

Using the density operator one is bound to talk about
statistics only. Decoherence cannot and does not explain "how"
a system chooses from the possible outcomes a specific one
when we measure it. Decoherence only explains how the "quantum
probability" becomes a "classical probability", very roughly
speaking, but it still only gives probabilities.
[/quote]
It is worthwhile to explain what exactly "classical" means in
this context. This is maybe most easily seen if Schroedinger>s
Gedankenexperiment is combined with the experiment for testing
Bell>s Inequality:

Two entangled photons fly in opposite directions and then each
pass through polarization filters. A photon detector after each
filter either kills or does not kill a cat on each side,
depending on whether the respective photon has passed through
the polarization filter.

Decoherence tells us that each cat quickly ends up in a state
with a density matrix that is practically diagonal. Or, more
loosely put, the cat is "either dead or alive, but not both".
Can we conclude that whether the cat is dead or alive is already
determined, that an experimentator who looks inside to discover
either a dead or a living cat will only note what was already
determined before ?

No, because Bell>s Inequality excludes any local hidden variable
theories in which for both cats it would already be determined
whether the cats are dead or alive. In other words, "classical"
means in this context only that you cannot do interference with
Schroedinger>s cats, i.e. that they statistically behave like
measured cats, but not that measurement has already occured
through decoherence.

Hence some of the "strangeness" of quantum mechanics remains,
especially if you modify the above Gedankenexperiment to include
what is typically called "Wigner>s Friend". Replace each cat by
an experimentator who looks at the detector, and place two other
experimentators outside the respective labs.

Now, when does measurement occur ? When the inner experimentators
look at the detectors, or when the outer experimentators open the
doors to the respective labs and ask the guys inside about what
they have measured ? At least decoherence tells us that we cannot
distinguish experimentally between the two possibilities, because
in both cases all experimentators behave statistically classical.

In conclusion, decoherence is a big step towards understanding
measurement in quantum mechanics, but does not go all the way,
at least not yet.

Alain Stalder

--- END QUOTE ---

Defies intuition again, I guess. Picturing an individual cat as
losing all its coherence almost immediately by contact with its
environment would naively seem to exclude that a *pair* of cats
can maintain a relevant, measurable correlation.

I remain curious...

Alain Stalder · Guest

Igor Khavkine wrote:
: Practice has shown (including the results of Leggett) that it is
: realism that is incompatible with entanglement, rather than locality
: or lack thereof. So, your assertion is still on shaky footing.

Just like your first sentence above ;)

You make it sound like the measurement problem in
quantum mechancis was actually solved...

Until then this remains an open question and a matter
of taste. :)

See my other post in reply to Charles Francis for a few
more concrete ruminations that involve a different aspect
of relatively recent "practice", namely decoherence.

Alain Stalder

Oh No · Guest

Thus spake Alain Stalder <alain.stalder@exactphilosophy.net>

[quote]
Thanks for the link. Actually lead me also to the interpretation
called "relational quantum mechanics", which I had never heard of.
[/quote]
There is a wiki article by that title.

http://en.wikipedia.org/wiki/Relational_quantum_mechanics

This is an interpretation due to Carlo Rovelli. It starts from pretty
much identical precepts as my own notions, though relational quantum
gravity was developed separately, imv to a much greater degree, and more
successfully unifies the principle of relativity with qm.
[quote]
There is one more point that speaks for the minimal elegance of
quantum mechanics, namely decoherence, since it explains already
*within* the theory why quantum interference usually disappears
for macroscopic objects.

In January 2003 I posted a Gedankenexperiment here that combines
decoherence with EPR and Schroedinger>s Cats or Wigner>s Friends,
and hopefully explains what decoherence can explain and what not
with regard to measurement in quantum mechanics:
[/quote]
Decoherence is a somewhat subtle notion. See

http://en.wikipedia.org/wiki/Quantum_decoherence

It is not actually the same thing as wave function collapse, but is
easily confused with it.

Regards

--
Charles Francis
moderator sci.physics.foundations.
charles (dot) e (dot) h (dot) francis (at) googlemail.com (remove spaces and
braces)

http://www.teleconnection.info/rqg/MainIndex

Igor Khavkine · Guest

On Nov 14, 5:53 pm, Alain Stalder <alain.stal...@exactphilosophy.net>
wrote:
[quote]Igor Khavkine wrote:

: Practice has shown (including the results of Leggett) that it is
: realism that is incompatible with entanglement, rather than locality
: or lack thereof. So, your assertion is still on shaky footing.

Just like your first sentence above ;)
[/quote]
If that>s true, then you should have no problem providing an example
of a realistic (whether local or non-local) interpretation of/
alternative to quantum mechanics. In fact, I already requested such an
example in my previous post.

[quote]You make it sound like the measurement problem in
quantum mechancis was actually solved...

Until then this remains an open question and a matter
of taste. :)
[/quote]
Umm, this is a giant non-sequitur.

[quote]See my other post in reply to Charles Francis for a few
more concrete ruminations that involve a different aspect
of relatively recent "practice", namely decoherence.
[/quote]
A non-sequitur once again. However, specifically on the topic of
decoherence, I do find that it is a good approach to recovering
classical behavior from quantum systems, with many interesting results
to its name. On the other hand, decoherence has nothing to do with
either realism or non-locality.

Igor


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