
#37
Sep1407, 05:37 AM

P: 2,050

Sheesh, get a room.
It's a purely grammatical debate: Zz is saying it's in a superposition. Demy is agreeing it's state is not equal to the first eigenstate, and neither is it's state the second eigenstate. I don't think anyone needs to cite a source for that. 



#38
Sep1407, 06:14 AM

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#39
Sep1407, 06:19 AM

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#40
Sep1407, 10:40 AM

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#41
Sep1407, 11:59 AM

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P: 1,082

StatusX
Mathematicians develop probability as a branch of measure theory for a space of socalled events  a win, drawing a certain hand in poker, measuring an electron arriving at some point in a doubleslit experiment, will there be a recession in three months, and so on. Nowhere in the theory is there any restriction of application. If the shoe fits, .... This abstract approach tells us that classical and quantum probabilities are generically the same  they both can be described by dynamical equations for the probablity distribution the differences between the details, like interference phenomena, are due to the different dynamics, and to generally different initial conditions. In fact, in at least one case the quantum and classical probability distributions are identical  the Rutherford cross section for an electron scattering from a positive point charge at low energies(target at rest)can be derived, as Rutherford did, strictly from classical electrodynamics and mechanics. And the exact same cross section can be derived from nonrel QM. Note that scattering is defined experimentally, as events: a counter indicates yes or no, yes, an electron hit the target. The resulting set of events defines a distribution, which when properly normalized, is a probability distribution in an abstract space of scattering events. That space could care less whether the events are described by QM or classical theory. It makes no difference whether the need for a probability description is due to a lack of knowledge, or is required to make sense of a theory, or involves a highly complex system  perhaps many components,a gas for example, or the nonlinear dynamics that might describe economic phenomena There are plenty of opportunities for interference phenomena outside of quantum physics. When I play the piano and I play middle C, I create a superposition of piano states, basically the overtone series. Changing the overtone structure, changes the sound of the note. In extreme cases, beats are produced, generally caused by two interfering vibrations. Young's experiment is nicely explained classically. Most communication transmitted by electromagnetic means involves superposition of various frequencies, like sidebands "carried" by a carrier wave. The polarization of light, a rowboat crossing a river with a downward current involve superposition The description of anything by a vector space or vector field involves superposition. We use a lot of vector concepts in physics to explain a huge range of phenomena. Finally, don't forget that QM is weird because it was developed to describe, if not explain some very strange phenomena  atomic spectra, electron diffraction, the SternGehrlich experiment, and so on. Indeed, QM is the child of experiments. Regards, Reilly Atkinson ' 



#42
Sep1407, 01:41 PM

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PF Gold
P: 2,197

Real systems are of course always open meaning we still usually need to use statistical quantum mechanics to predict the outcome of experiments, but that is a "technical" detail which rarely changes any qualitative properties of a system; the only difference between Rabi oscillations in a closed and an open system is that they are attenuated in the latter, but there are still oscillations and the basic physics is the same. 



#43
Sep1407, 01:47 PM

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P: 2,566

The reason I addressed your post was because it seemed you were suggesting the schrodinger cat paradox had nothing to do with quantum mechanics. It's true that before quantum mechanics, people could have imagined a similar experiment with, say, a coin flip rather than radioactive decay, and ask what the state of the cat is before we observe it. But this would just be idle philosophizing  there's no practical problem here. The difference in the case where we have a quantum superposition is that the dynamical equations imply that a microscopic superposition, which isn't really much stranger than, say, a superposition of overtones on a piano note, should evolve into a superposition of macroscopic objects, which is something very strange, and not something we seem to observe. The cat paradox is designed to expose this problem. 



#44
Sep1407, 05:56 PM

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PF Gold
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Now, first of all, as I have already pointed out we now DO understand why this never happens to real cats; the theory of open quantum systems as well as measurement theory is now so well developed that there is no real mystery anymore. Hence, there is no 'paradox'. Secondly, we DO observe superposition in macroscopic objects. E.g. superconducting qubits might not be very large but they are certainly macroscopic (a few square microns, you can easily see a flux qubit in an ordinary optical microscope). The interesting thing with modern QIP (=quantum information processing) is that it has taken many problems from the realm of philosophy to what is basically engineering: in order to observe superpositions in a real experiments on superconducting qubits we use good magnetic shields, low noise amplifiers and a lot of filtering; in order to stop the "collapse" (i.e. increase the coherence time) we design the environment of the qubit in such a way as to maximize the impedance it sees (basically microwave engineering) etc. Hence, there is nothing particulary 'esoteric' about QIP anymore. I suspect many of the things we do in the lab nowadays would have shocked Schrödinger. My point is that the cat "paradox" is not really a problem in physics anymore (and I don't think it ever was), in part simply because we got used to the idea; nowadays we instead use these effects to build useful devices. There are obviously quite a few philosophical issues, but these are largely irrelevant to the science. It is worth remembering that thermodynamics and Newtonian mechanics also got their fair share of issues but these are rarely talked about nowadays, simply because we take those theories for granted. 



#45
Sep1407, 08:01 PM

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#46
Sep1407, 08:22 PM

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Dissipation, measurement theory etc are relatively new topics in QM so the concept of decoherence was rather mysterious for a long time (and is still not fully understood). Hence, while it is true that there is no consensus about the interpretation of QM I think it is fair to say that quite a few PRACTICAL issues relating to what you can actually observe in an experiment have been sorted out during the past 20 years or so. Moreover, I am not quite sure I agree that I believe it is all that important to understand what QM really "means", at least not from a scientific point of view. To me physics is all about predicting what I can measure in the lab (I am an experimentalist, in case you haven't guessed that already), the rest is philosophy which means that there is little hope of ever reaching a "correct" answer (but it can still be interesting). 



#47
Sep1407, 11:23 PM

P: 2,050





#48
Sep1507, 02:01 AM

P: 451

Regards, Dany. 



#49
Sep1507, 02:05 AM

P: 451

Regards, Dany. 



#50
Sep1507, 02:15 AM

P: 451

Regards, Dany. 



#51
Sep1507, 02:24 AM

P: 451

You completely correct in all your statements, but “unfortunately” the results of your measurements will be useless since you can’t convince anybody that they are correct. You need another lab to confirm your results. But if you claim that that lab has the same environment, nobody will believe you (it is simply wrong). For information of all respectable contributors in the discussion, I reproduce A.Einstein notion and definition of the objective reality. I guess that A.Einstein even had no chance to read EPR paper before publication. If some stupid idiot taught and convinced you something different when you were students, you were bad students. f95toli don’t worry, the job done. We did it (I am a mathph, in case you haven't guessed that already) Regards, Dany. P.S. 



#52
Sep1507, 06:20 AM

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PF Gold
P: 2,197

One can of course just add the condition that the cat IS insulated (using some mysterious technique) from the enviroment to the gedanken experiment, and then the cat would actually be in a "real" superposition. However, this could never be observed in a real experiment. Hence, the "cat paradox" is only a paradox if you add conditions that are unphysical. It is still an interesting philosophical problem, but I can't see it being very relevant to physics anymore. As I pointed out above wa CAN observe superpositions in macroscopic objects in the lab, but only in systems that can be reasonably well decoupled from the environment; this means that we are now sure that there is no strange "transition" from QM on the microscopic level (atoms) to classical physics on at the macrosopic level (cats). 



#53
Sep1507, 07:58 AM

P: 451

Regards, Dany. 



#54
Sep1507, 01:36 PM

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P: 2,566

f95toli,
You seem to be using decoherence as a mechanism to remove any superposiiton, and thus collapse the cat's wavefunction. My understanding is that decoherence simply renders the alive and dead states in the superposition incoherenet, so that they no longer interact. When we observe the cat, we become entangled with its state in the following way: scientist before>(alive cat> + dead cat>) evolves unitarily into: happy scientist>alive cat>+sad scientist>dead cat> Since these two wavefunctions are incoherent, they evolve independently, as if the other didn't exist. In other words, we get a many worlds interpretation, simply by denying that collapse ever occurs and acknowledging the effect of decoherence. Decoherence by itself does not cause real collapse, only an observed collapse in each world. What are you suggesting really happens, or are you not worried about this? 


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