Posted on 09/14/2006 10:27:24 PM PDT by snarks_when_bored
Quantum Mechanics: The Dreams Stuff Is Made Of
ping
You're wrong. It's a statement about reality.
You're being distracted by the fact that in the case of a cat, the "dead" state does not interfere with the "alive" state. But in the real world, the superposition is one of simultaneous realities and not simply a statement about our ignorance of the state of the system.
Two examples that spring immediately to mind are double-slit diffraction and the Bohm-Aharonov experiment. In each case, there's a measurable interference term caused by the simultaneous realities.
In the case of double-slit diffraction, you get an interference pattern caused by the simultaneous superposition of Schrödinger waves from each slit, which is very different from a mere sum of wave amplitudes from two individual slit sources.
Let's be more specific. Suppose we label one slit the "left" slit and the other the "right" slit. We project electrons through the slits and towards a screen, but we don't know much about their exact trajectories. Classically, they might go through one slit or the other. Quantum mechanically, the wave function is a superposition of the state where it goes through the left slit AND the state where it goes through the right slit.
If the superposition were merely a statement of our ignorance, our mere knowledge of whether each electron went through the left slit ("alive", if you prefer) or the right slit ("dead", if you prefer) wouldn't affect the final distribution of electrons from the slits when projected onto the screen. But the experimental reality--and the mathematical prediction--is that that knowledge matters a great deal. If we add up the cases where we remain in ignorance, we see a series of light and dark bands on the screen: interference fringes. If we add up the cases where we know which path the electron took, we see the sum of two Gaussians. No fringes.
Quantum mechanically, what is happening is that, by knowing the trajectories, we are collapsing the electron trajectory eigenstates into either "left" or "right". The interference between the slits then disappears; it's as if the slit not used were simply covered up. Classically, there is no analogue.
Now, you might think that perhaps the interference effect has nothing to do with individual wave functions or trajectories. Perhaps if you get a cloud of electrons flying through two slits, they'll bounce off each other, block each other, and knock one another to this or that side in such a way as to produce the interference fringes, even though each individual electron took a definite, well-defined path through one slit or the other. But that's not the case: the interference effect works even if we send the electrons through one at a time, so that each electron can't have any contact or "knowledge" of the rest of the ensemble. Any simple interpretation will have to say that each electron went through both slits, taking both paths simultaneously.
The Aharonov-Bohm experiment is more technical, but it involves two (field-free!!) paths around a magnetic solenoid, and the shifting of interference fringes as the field within the solenoid is altered. The principle is one of gauge symmetry: there's a phase angle associated with the difference in integrated vector potential along each path.
OK, that was a mouthful, but the key is this: BOTH paths have to contribute simultaneously for each electron, or the effect disappears. It cannot be said that each electron passed either to the right or left of the solenoid.
I'm giving special heed to Bohr's remarks. Wikipedia notes that one can speak of the "collpase", or simply say that the theory makes predictions without granting any kind of physical reality to wavefunctions ( or propagators. )
"Niels Bohr emphasized that it is only the results of the experiments that should be predicted, and therefore the additional questions are not scientific but rather philosophical."
Taking this lead, I've always seen the CI as the "bare bones" interpretation, which contents itself with the predictions made using the theory. Bohr emphasized that we are constrained to speak and understand in everyday terms, and the theory itself is part of our everyday experience of pencils and paper and apparatus.
Even allowing that the condition of the cat is "undefined", we can take this to mean it is undefined by the theory, which is plain to see since its predictions are probabilistic. To put any more into it is mere mystification, as I see it, and I believe I'm following Bohr in this.
... and yet! ... and yet! One can never be very happy with this view, can one? The mystery of QM is ineluctable.
I would also comment that I put a lot of weight on Feynman's remarks on neutron scattering in a crystal in his Lectures Vol. III, 3-3. He contrasts the case of no-spin-interaction, where the scattering nucleus is indeterminate, with the spin-interaction case, where a particular nucleus is affected by the scattering. Thus the crystal itself "observes" the scattering, and localizes the interaction.
"You may argue, 'I don't care which atom is up.' Perhaps you don't, but nature knows; ..."
This obviates the question of an "observer", since after all why may not the cat be regarded as an observer, or what if we put a physicist in there? Or for that matter a clock, or any kind of recording instrument?
I'm not very intelligent, but does communication play a role in all of this stuff? And, I don't mean what you stated in your posts, but the whole of this quantum stuff.
Something (the sender) must tell something else (receiver) to behave or do something. The message sent must both be efficient, in the sense that is received correctly and understood, and effective, in the sense that the response of the receiver is the desired response of the sender.
K. A. Milton, Julian Schwinger (1918-1994) (PDF)
A paragraph with some relevance to the point you were making:
"Schwinger learned from his competitors, particularly Feynman and Dyson. Just as Feynman had borrowed the idea from Schwinger that henceforward would go by the name of Feynman parameters, Schwinger recognized that the systematic approach of Dyson-Feynman was superior in higher orders. So by 1949 he replaced the Tomonaga-Schwinger approach by a much more powerful engine, the quantum action principle. This was a logical outgrowth of the formulation of Dirac [21], as was Feynman’s path integrals; the latter was an integral approach, Schwinger’s a differential. The formal solution of Schwinger’s differential equations was Feynman’s functional integral; yet while the latter was ill-defined, the former could be given a precise meaning, and for example, required the introduction of fermionic variables, which initially gave Feynman some difficulty. It may be fair to say, at the beginning of the new millennium, that while the path integral formulation of quantum field theory receives all the press, the most precise exegesis of field theory is provided by the functional differential equations of Schwinger resulting from his action principle."
The "sending and receiving" stuff that you see in regards to quantum entanglement experiments is heuristic, or philosophical, or whatever. It is definitely not part of Quantum Mechanics!
A striking feature of QM is what Heisenberg called "quantum kinematics". That is, the framework of the theory itself. Many of its amazingly numerous and varied results stem directly from the workings of this framework, and this includes entanglement, degeneracy pressure, and quantum levels themselves, not to mention Light Amplification by Stimulated Emission of Radiation.
Of course, the theory cannot offer any explanation of its own framework, yet traditional heuristics offer many such quasi-classical, and even anthropomorphic explanations. I try to ignore these as much as possible, but you can't get away from them. Note that the term, "stimulated", in the acronym LASER, is just such a heuristic. The laser phenomenon is a pure implication of quantum statistics, and does not involve any sort of postulated "stimulation".
Thank you.
This stuff is hard for the layperson, but extremely interesting. It's like the more I read, the more I understand how much I didn't know.
"You were not made to live like brutes, but to follow virtue and knowledge." - Dante
Wonderful words, dear Pipe. Thank you so much for including me in the ping to them.
Very true. I'm so glad we can share such things in Christ!
LoL.... !Quite funny until the reality of it is considered...
Fascinating. For a layman, I would love to be able to read something that will delve further into this. Got any specific links?
ping for later reading
You know, this is about as far as it goes for laymen until they start digging into the math. But, if you do that you will be doing the real stuff. These made-up examples aren't of much use except to point out that they are mostly nonsense pointing the way to the actual physics. The math isn't really all that bad once you take that step.
Too many people believe that quantum "weirdness" opens a window for the paranormal, supernatural, mystical uncertainty, etc. when in reality, it makes specific physical predictions with a rigor and accuracy unparalleled by any other scientific theory.
The cat was pregnant.
"Any simple interpretation will have to say that each electron went through both slits, taking both paths simultaneously."
Maybe the electron simply swallowed the grid and spit it back out when finished.
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