04 May 14
Originally posted by RJHindsConsider quantum systems where particles can be in a mixing of two states at a time. The Stern-Gerlach experiment is a case in point (see Wikipedia for a full explanation). There the electron is in a mixture of spin up and spin down states. When the electrons are measured nature has to make it's mind up, but until then if P is "the electron is spin up", then -P is "the electron is not spin up" and therefore spin down, we have "P & -P" being true up until an observation is made - at which one of P or -P must be selected. So the law of non-contradiction does not apply to quantum systems. The point I'm making is that logic is no use unless you are certain that the logical rules you are using apply to the system under consideration.
Something can not be TRUE and NOT TRUE at the same time. That would be a contradiction, in my humble opinion. However, depending on what "P" represents "not P" may just be the opposite of "P" and not a contradiction.
04 May 14
Originally posted by DeepThoughtI don't think you can make a sound analogy between formal logic and quantum physics in this context. The initial mixture is neither P nor ¬P. The time evolution of the electrons is (within quantum physics) deterministic until the wavefunction collapse, which involves a complex macroscopic interaction that is not well-understood. The statement "P and ¬P is true" is always false. Empirical science always involves some sort of reasoning by induction, so one cannot (fully) describe it with formal logic. Indeed, if one does restrict oneself to formal logic, the only things one can conclude are trivialities.
Consider quantum systems where particles can be in a mixing of two states at a time. The Stern-Gerlach experiment is a case in point (see Wikipedia for a full explanation). There the electron is in a mixture of spin up and spin down states. When the electrons are measured nature has to make it's mind up, but until then if P is "the electron is spin up ...[text shortened]... ss you are certain that the logical rules you are using apply to the system under consideration.
04 May 14
Originally posted by KazetNagorra
I don't think you can make a sound analogy between formal logic and quantum physics in this context. The initial mixture is neither P nor ¬P. The time evolution of the electrons is (within quantum physics) deterministic until the wavefunction collapse, which involves a complex macroscopic interaction that is not well-understood. The statement "P and ¬P ...[text shortened]... if one does restrict oneself to formal logic, the only things one can conclude are trivialities.
The statement "P and ¬P is true" is always false.
Look up para-consistent logic on Wikipedia.
This has nothing to do with inductive reasoning, which is to do with lack of complete information, but is a point some philosophers have made to cope with various paradoxes such as Russell's set of sets which do not contain themselves.
I don't see any reason not to apply this to quantum theory. From earlier threads I gather that you tend think of quantum mechanics as a classical (deterministic) theory - with normal evolution deterministic and with the expectation of a deterministic theory of quantum observations - such as a many universe interpretation. However, assuming Bell's inequality holds, at observation time I think something non-trivial happens which is non-deterministic and illogical if one insists on classical logic.
04 May 14
Originally posted by DeepThoughtMy bad. I should have been more precise and say that it's always false in standard proposition logic.The statement "P and ¬P is true" is always false.
Look up para-consistent logic on Wikipedia.
This has nothing to do with inductive reasoning, which is to do with lack of complete information, but is a point some philosophers have made to cope with various paradoxes such as Russell's set of sets which do not contain themselves.
I do ...[text shortened]... non-trivial happens which is non-deterministic and illogical if one insists on classical logic.
I don't regard quantum mechanics as "classical" (by definition, it isn't), although it is deterministic to a large degree. My point is mainly that we cannot accurately determine to which degree it may or may not be deterministic, because we don't have an adequate and general theoretical description of wavefunction collapse. Is wavefunction collapse the result of a fundamental, non-deterministic fact of nature? Or is it the result of a deterministic process, which appears non-deterministic?
04 May 14
2 edits
Originally posted by KazetNagorraYes, I know what you are talking about because I did some study into it. Just google "realist interpretation of quantum mechanics" and you get various web links explaining what that is about. for example:
My bad. I should have been more precise and say that it's always false in standard proposition logic.
I don't regard quantum mechanics as "classical" (by definition, it isn't), although it is deterministic to a large degree. My point is mainly that we cannot accurately determine to which degree it may or may not be deterministic, because we don't hav ...[text shortened]... fact of nature? Or is it the result of a deterministic process, which appears non-deterministic?
http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics
http://arxiv.org/abs/0805.1779
It is possible for one of the realist interpretations of quantum mechanics to be true and, if so, one of the implications of that is that the apparent randomness of quantum events could be illusory and in fact be pseudo-random i.e. really actually determined although that still doesn't logically imply there could be a practical way of predicting the outcome of such a quantum event with certainty.
One of the huge bits of misinformation continually spread by the media is that they make out that quantum mechanics says that Niels Bohr interpretation on it is correct -as if his is the only possible valid interpretation of it when it clearly logically is not.
04 May 14
I believe a discussion of quantum mechanics is getting away from topic of the OP. I believe the following debate analysis could get us back on topic.
Ken Ham / Bill Nye Debate Analysis
In a well publicized debate at the Answers in Genesis Creation Museum Ken Ham debated Bill Nye 'The Science Guy' on the topic, "Is creation a viable model of origins in a modern scientific age?"
article at: http://creation.com/ham-nye-debate
05 May 14
Originally posted by KazetNagorraI think I meant deterministic rather than Classical, since classical really refers to the detachment of the observer.
My bad. I should have been more precise and say that it's always false in standard proposition logic.
I don't regard quantum mechanics as "classical" (by definition, it isn't), although it is deterministic to a large degree. My point is mainly that we cannot accurately determine to which degree it may or may not be deterministic, because we don't hav ...[text shortened]... fact of nature? Or is it the result of a deterministic process, which appears non-deterministic?
05 May 14
Originally posted by humyI don't have much beef with the Copenhagen interpretation (although it is more like a set of interpretations rather than a rigid, single one) - it is quite pragmatic. It doesn't really deal with wavefunction collapse though, in the sense that it doesn't attempt to describe it from microscopic principles. On the other hand, the problem with Bohm's interpretation is that it is nonlocal, which is unappealing to most physicists.
Yes, I know what you are talking about because I did some study into it. Just google "realist interpretation of quantum mechanics" and you get various web links explaining what that is about. for example:
http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics
http://arxiv.org/abs/0805.1779
It is possible for one of the realist interpretation ...[text shortened]... ect -as if his is the only possible valid interpretation of it when it clearly logically is not.
05 May 14
Originally posted by DeepThoughtMost commonly, "classical" refers to the mechanics prior to quantum mechanics, i.e. Newtonian mechanics. A common misconception is that quantum mechanics "disproves" Newtonian mechanics, which it does not. Rather, Newtonian (classical) mechanics can be considered a special case of quantum mechanics, from which it can be derived using certain assumptions.
I think I meant deterministic rather than Classical, since classical really refers to the detachment of the observer.
06 May 14
Originally posted by KazetNagorraI agree that "classical" is a somewhat blurry term. Sometimes relativity is regarded as classical and sometimes not, depending on what the speaker wishes to emphasise.
Most commonly, "classical" refers to the mechanics prior to quantum mechanics, i.e. Newtonian mechanics. A common misconception is that quantum mechanics "disproves" Newtonian mechanics, which it does not. Rather, Newtonian (classical) mechanics can be considered a special case of quantum mechanics, from which it can be derived using certain assumptions.
I disagree that Newtonian Mechanics wasn't disproved. Clearly it is fine at "human" scales, so in the limit of small mass, moderate speed compared with the speed of light, and Planck's constant being small compared with the scale one is looking at it will generate the correct answers. But the world view is utterly different.
Newton had an absolute space with time as a parameter and observers who could track particles with infinite precision without disturbing them. Relativity banishes the fibre bundle structure of Newton's picture. Quantum mechanics has observers who cannot make a measurement without disturbing the system they observe. So while I agree theoretical predictions for something like a billiards shot will come out the same; the world views are quite different. Also, whatever the paradigm theory is at the time it is expected to be rigorously true at any scale.
A quick point about your reply to humy - you observed that physicists are uncomfortable with non-local effects - there is a notion that space-time could be an emergent phenomenon. What tells us something is far away is a mixture of geometry and the inverse square law. So in a sense the strength of interaction between particles and the momenta the light reflected off them have determines where they are. While I think the idea should be taken with a fairly generous helping of salt it does solve the EPR paradox quite neatly - in this theory distance doesn't really exist so it is no great surprise that particles appearing far apart can be entangled, they aren't really far apart it's just the way our minds interpret particle interactions.
06 May 14
Originally posted by DeepThoughtIn my opinion, there is too much emphasis on this word "observer." It can be a convenient figure of speech, but in the hands of the layman (or even a trained physicist) it is often confusing. Yes, when an "observer" is measuring some property, there may be a wavefunction collapse, but more generally, the "observation" in quantum mechanics is simply some interaction with a macroscopic object we don't (fully) understand and don't have an adequate, fully quantum mechanical description for.
I agree that "classical" is a somewhat blurry term. Sometimes relativity is regarded as classical and sometimes not, depending on what the speaker wishes to emphasise.
I disagree that Newtonian Mechanics wasn't disproved. Clearly it is fine at "human" scales, so in the limit of small mass, moderate speed compared with the speed of light, and Planck' ...[text shortened]... ngled, they aren't really far apart it's just the way our minds interpret particle interactions.
As for the EPR paradox: I'm not an expert on relativity (I use non-relativistic quantum mechanics exclusively), but from what I understand the instantaneous collapse of entangled particles does not violate relativity as no energy/information/force is transferred faster than light.
06 May 14
Originally posted by KazetNagorraThe magician says that the hand is quicker than the eye of the observer.
In my opinion, there is too much emphasis on this word "observer." It can be a convenient figure of speech, but in the hands of the layman (or even a trained physicist) it is often confusing. Yes, when an "observer" is measuring some property, there may be a wavefunction collapse, but more generally, the "observation" in quantum mechanics is simply some ...[text shortened]... les does not violate relativity as no energy/information/force is transferred faster than light.
07 May 14
Originally posted by KazetNagorraIn classical physics theory the observation is identical to the property. Rather than say: "We observe the particle to be at position x." we say: "The particle is at position x." - the theory allows us to make continuous observations which don't alter the experimental outcome so there is no particular epistemological problem with ignoring the observer.
In my opinion, there is too much emphasis on this word "observer." It can be a convenient figure of speech, but in the hands of the layman (or even a trained physicist) it is often confusing. Yes, when an "observer" is measuring some property, there may be a wavefunction collapse, but more generally, the "observation" in quantum mechanics is simply some ...[text shortened]... les does not violate relativity as no energy/information/force is transferred faster than light.
In quantum theory there is no way of doing this, our means of observing particles are discrete - either bouncing photons off them, or having them leave an ionization trail - in either case the observation is both disturbing of the observed and quantized. Observations are necessarily discrete. This is important since if one prepares a particle in some state and measures it at some later time one gets a different result from the one obtained by adding an intermediate observation. So we have the problem that the particle behaves differently if we observe it. Since most of the time we are interested in either bulk properties or cross-sections this isn't a great practical problem; but it is a foundational problem. I think a consideration of the observer is crucial in quantum mechanics it cannot be brushed under the carpet like in classical physics.
The wave-function collapse interpretation, which is an extension of the Copenhagen Interpretation, is problematic and no one has ever defined what a viable observer is. I agree it's not very clear what the difference between "an observation" and "an interaction" is, except for some reason the measurement produces a definite result whereas the interaction doesn't. So there's a problem.
the instantaneous collapse of entangled particles does not violate relativity as no energy/information/force is transferred faster than light
That is the resolution of the paradox they accepted at the Copenhagen conference (Bohr's I think), essentially stating that the group velocity must be no faster than light, but phase velocities may be. It's not entirely satisfying. The paradox vanishes entirely if the basic quantities are matrix elements and the derived quantities positions.