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- Thread starter dextercioby
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- #37

WernerQH

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WernerQH

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It depends on the interpretation of QM. In some interpretations it's the absence of clear ontology (most interpretations in the Copenhagen spectrum), in others it's very non-classical ontology (many worlds, GRW), and in those with classical ontology (Bohm, Nelson) it's nonlocality.So, where's the difference between classical and quantum mechanics in your opinion?

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- #41

EPR

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Our perception is not equipped to probe below 1/100th of a millimeter, hence we always observe the classical aspect of QT and never noticed in close to a million years of evolution that reality was quantum.

If we had senses equipped to observe at nm scales, we might have seen earlier that fundamental particles don't move in classical trajectories and generally obey different rules. But we always observe the aggregate of statistics of an enormous amount of particles where the mean probability takes the course of a moving classical object.

- #42

gentzen

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My experience a long time ago was that lectures don't live in isolation, but work together with the recommended literature and the literature directly available in the university libraries and bookstores around the university. For me, the lectures often served as motivation to lookup the topics in some books, where I might also find answers to related questions that came to my mind while thinking about the concepts.That's why I think one should introduce statistical operators as the representants of states early and the pure states as the special case, where the statistical operator is the special case of being a projection operator.

I'm not so sure about which approach to QM should be used first. For quite a while I was thinking, that the most simple approach is to start with some finite-dimensional cases like spin 1/2 (problematic for a first encounter, because it's hard to explain what spin is without having a concept of QM first) or polarization of photons (problematic for a first encounter, because you have somehow to introduce the concept of photons, and this all too easily leads to the very wrong idea that photons were in any sense "particles", but it's in principle doable). I've started by intro QM lectures twice in such a way, but my experience is that this is too abstract. The students don't get a good idea what QM is about.

One trap I fell into especially when studying physics where those book-series like Landau-Lifschitz, Feynman, Thorsten Fließbach, (and many lower quality ones I forgot already or at least don't want to mention) ... The trap was that the series which helped me most during previous lectures was not necessarily the best for a lecture on a different topic. (And of course also that books not part of any series might have been a significantly superious choice to begin with, but I was not mature enough yet to understand that.)

In fact, I still fall into this trap today. I want to learn some statistical physics, and instead of trying to find out which would be good recommended books on that subject, I just try a book from Nolting's series and a book from Fließbach's series. They are forced to introduce the statistical operator, but it remains a second class citizen even here. Here is an excercise from such a book which highlights how bad one can misappreciate the statistical operator:

Try to understand where that excercise commits bad mistakes, and how strongly it communicates that the author prefers pure states. And that is my point: I care less about whether the statistical operator is introduced early, or even introduced at all, but about whether it is introduced well when it is introduced.

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- #44

physika

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So, where's the difference between classical and quantum mechanics ?

...maybe not so much

https://journals.aps.org/pra/abstract/10.1103/PhysRevA.86.012103

https://www.nature.com/articles/s41467-017-01375-w

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- #45

CelHolo

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So for example under strong decoherence the probabilities of the theory begin obeying the rules of classical probability and so can be taken as ignorance of an event occurring independent of measurement.

Similarly the notion of particle is shared across all inertial observers in Minkowski space. Also it is possible, due to the presence of PVMs to prepare a unique/objective state of a system in Minkowski space.

However in more general cases like QFT in curved spacetime you get effects where there are no pure states or PVMs, so it's impossible for two observers to completely remove their priors and arrive at the same state in general and thus one is not able to prepare an "objective" state for a system. In the absence of strong decoherence an event cannot be said to occur independent of measurement and so on.

So I'd say removing the subjective/observer dependent aspects of the theory is a limiting case.

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