- #36
Alem2000
- 117
- 0
Yeah i kinda noticed
Interpritations of Quantum Mechanics
- Thread starter Alem2000
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In summary, the many different interpretations of quantum mechanics are all based on how the theory deals with the same effects as relativity. Some of the more popular ones include the Copenhagen interpretation, the Schroedinger picture with the Copenhagen interpretation, the Bohm-deBroglie interpretation, the many worlds interpretation, and the Everett interpretation.
- #37
slyboy
- 207
- 3
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.
- #38
sol2
- 910
- 2
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?
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?
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- #39
meteor
- 940
- 0
Zurek's Existential interpretation:
http://arxiv.org/abs/quant-ph/9805065
http://arxiv.org/abs/quant-ph/9805065
- #40
Eye_in_the_Sky
- 331
- 4
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.)
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.)
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- #41
Eye_in_the_Sky
- 331
- 4
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) eiS(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.
________________________
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) eiS(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.
________________________
I retract my statement. At the time I didn't quite understand this "pilot-wave" notion ... and I still don't.
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