Interpritations of Quantum Mechanics

[Mike2]

...And if someone trys to intercept the message it produces more noise for any subsequent receiver. What can that be except entropy, no process (of measurement) without causing an increase in entropy (loss of information). So it would seem that the act of covertly gathering information means reducing the emount of information (increasing entropy) in the rest of the signal. Which again leads me to ask: Is entropy conserved, noise somewhere because information gained somewhere else?

I don't understand why this is not more interesting. Does this not match the concept of entropy - events and interactions increase entropy which means they reduce the emount of information in the world? Only those events which increase entropy can occur, at least in the average.

But we cannot know how entropy has changed (increase or decrease) unless we make two measurement of a system and see how the state has changed. We take before and after readings; we measure the initial and final states. In the act of making the first measurement, we gain information about the system. The system is then assumed to proceed in a manner of increased entropy. Then we make the final measurement. And we expect that less information is available since the entropy of the system has increased.

How does the emount of available information that can be gained about a system effect the expectation values? Expectation values are probabilistic and so is information. If a measurement randomizes the system, then you'd expect that any measurement would make any subsequent measurement less accurate. You wouldn't know it was less accurate unless you also tried to reverse the order of the two measurements. If the two measurements do not commute, then you'd expect that there would be a limit to the accuracy of the both measurements. Is h-bar a measure of information? Any thoughts or corrections, gentlement?

 

[vanesch]

decoherence!

Thus, the fundamental question seems to be, what picks out the basis in which we are to regard the state as a mixture. It seems to be dependent on what measurement we perform. This is indeed one possible answer, which has a distinctly Copenhagen flavour.

Be careful ! There is a fundamental difference between a superposition of states (which is in fact nothing else but "choosing the wrong basis") and a statistical mixture in the classical sense. The state |dead>+|alive> is a pure state, while the statistical mixture 50% dead and 50% alive is a statistical mixture, and this distinction is INDEPENDENT of the choice of basis, as can easily be seen using the density operator rho: if trace rho^2 = 1, then it is a pure state, else it is a mixture (and this is of course independent of basis).

I would even say that the whole difficulty of QM resides in this distinction (all quantum weirdness comes from superpositions, not from mixtures).

It is exactly the merit of decoherence theory to show under what circumstances the density matrix always evolves into a statistical mixture a la Ballantine when coupled to a macroscopic system (a "thermal bath"), and the preferred basis is the one of the "coherent states".

cheers,
Patrick.

 

[slyboy]

Be careful ! There is a fundamental difference between a superposition of states (which is in fact nothing else but "choosing the wrong basis") and a statistical mixture in the classical sense. The state |dead>+|alive> is a pure state, while the statistical mixture 50% dead and 50% alive is a statistical mixture, and this distinction is INDEPENDENT of the choice of basis, as can easily be seen using the density operator rho: if trace rho^2 = 1, then it is a pure state, else it is a mixture (and this is of course independent of basis).

That is exactly my point. The statistical interpretation of Ballentine seems to want to interpret all states as statistical mixtures rather than superpositions. This is only possible if the measurement basis for the state is somehow fixed (by dechoherence or some other mechanism).

 

[meteor]

I've been always curious about what was exactly Quantum logic, this approach originated in the 30's by Birkhoff and Von Neumann, so I've printed today this paper
"Quantum logic. A brief outline"
http://arxiv.org/abs/quant-ph/9902042
to add to my collection of quantum papers. Although I still don't understand the Hasse diagrams and Greechie diagrams that appear in it, I'm giving to it a try

 

[Feynman]

Hi Alem ur question is too hard

 

[Alem2000]

Yeah i kinda noticed

 

[slyboy]

I've been always curious about what was exactly Quantum logic, this approach originated in the 30's by Birkhoff and Von Neumann, so I've printed today this paper

Quantum logic is the structure that arises by taking the algebra formed by projection operators (or closed subspaces of a Hilbert space) to be the quantum analog of classical boolean algebras.

For a while it was fashionable to try and resolve the problems of QM by saying that they arise from using classical logic and that they could be resolved by replacing it with quantum logic. Putnam was a famous advocate of this view. Naturally, this leads to the question of whether quantum logic can be derived from a natural set of principles or axioms rather than deriving it from the Hilbert space formalism. The Geneva School, lead by Jauch and Piron, attemped to do this, but the program ran into serious mathematical difficulties and has largely been abandoned as a serious approach to quantum foundations.

However, quantum logic has had a significant influence on other approaches to quantum foundations, notably consistent histories. Also, it still attracts considerable interest from mathematicians, who are interested in the structures regardless of whether they have any significance to physics.

An interesting question is whether quantum logic has any application to quantum information and computation, particularly given the central role that boolean algebra plays in classical computer science. This is a difficult issue, because quantum logic does not have a clear-cut analog of truth values, which are central to the application of boolean algebra in computer science. I have been spending a bit of time thinking about this question recently.

 

[sol2]

I would think that if Smolin and the archetypes at PI were to hold the principals of teleportation, then quantum information would have revealled consideration, in an axiom of sphere orientation, from one location to the other automatically.

Even Greene speaks to this, in his example of entanglement in the Fabric of the Cosmo.

Shall we take examples from the issues of Numerical relativity here in discriptve values?

 

[meteor]

Zurek's Existential interpretation:
http://arxiv.org/abs/quant-ph/9805065

 

[Eye_in_the_Sky]

How "classical" can QM be construed to be?

This is a first step at attempting to get a better understanding of the various "interpretations" of QM.
_____________________

Below are three basic tenets from the ontology of Classical Mechanics. The third of these, 1c), is somewhat ambiguous, but its intended meaning should become clear. (Note: I am assuming that the total force acting on the particle is derivable from a potential, which may be time-dependent; also, I am limiting my discussion of "attributes" to only position and momentum.)

1a) Definite Values for Attributes: The attributes of position and momentum are "properties" which objectively "belong" to the particle. That is to say, at any moment in time, the particle is situated at some definite point in space moving with some definite momentum.

1b) Classical "Type" of Trajectory: In the course of time, the particle follows a definite trajectory given by the "classical equations of motion" once those equations have been supplied with an appropriate "potential" from which the total force acting on the particle can be derived.

1c) Classical "Rule" for the Potential: The potential to be used in solving the "classical equations of motion" is that given by a "naïve classical analysis" of the situation.

Note that these principles are "laddered" in the sense that 1a) is required for 1b), and 1b) is required for 1c).

Observe that to say "all three are true" is inconsistent with QM. Thus, at least, 1c) is false - this must be the case for all (consistent) interpretations of QM.
_____________________

Now, what is an example of an interpretation in which 1a) and 1b) are both true? Well ... Bohm's interpretation. For Bohm, only 1c) is false - and that is so by virtue of the "quantum potential".
_____________________

Here is my question:

Apart from Bohm's interpretation, are there any other interpretations for which at least 1a) is said to be true?

(Note: Here, I am asking only about "position" and "momentum". At this stage, I am not addressing the possibility of some other "types" of "attributes" (i.e. "hidden variables") which could conceivably assume definite values.)

 

[Eye_in_the_Sky]

A comment on Bohm's interpretation

The version of Bohm's interpretation in which 1a) and 1b) [see previous post] are true in the "full" sense - i.e. in which the classical equations of motion are solved subject to arbitrary initial conditions for position and momentum - requires the introduction of another potential in addition to the so called "quantum potential". However, in that case, the theory ceases to be "identical" to QM.

For the version of Bohm's interpretation which "reproduces" all of QM's predictions, the initial momentum cannot be arbitrarily specified. Specifically, it must satisfy the following constraint:

p = grad S(x) ,

where S(x) is given by the phase of the wavefunction,

psi(x) = R(x) e^iS(x)/h_bar .

Now that I have understood this, I see that QM - without any modification - cannot be construed to be as "classical" I as I thought it could be ... at least in so far as Bohm is able to "classicalize" it for me.

________________________

Now that I have understood this, I see that QM - without any modification - cannot be construed to be as "classical" I as I thought it could be ... at least in so far as Bohm is able to "classicalize" it for me.

I retract my statement. At the time I didn't quite understand this "pilot-wave" notion ... and I still don't.