Can Quantum Mechanics be postulated to exclude humans?

[AndreiB]

The fundamental problem is that we tend to think of the world around us as made up of "objects", be they planets or electrons. But electrons must be "objects" in a very different sense.

Can you be more specific here? In what sense are electrons objects?

It is misleading to think of them as objects (particles), because the term carries too many inappropriate connotations.

OK, how one should think of them?

For example that objects have properties, that an electron must always have a position.

Are you saying that electrons don't have properties? Why are you calling them electrons then instead of neutrinos or pink rabbits?

 

[vanhees71]

They are the result of evolution. Unsuccessful theories have been forgotten along with the concepts that they relied on.

Very good question! In my view the focus on the wave function is misguided. The Heisenberg picture with its focus on operators (ensembles) is a much better starting point. The wave function is but a single piece of a bigger mathematical apparatus (and is always traced over, except in situations involving idealized experiments).

I agree that too much focus on pure states can be misleading. Particularly it is hard to make clear that not Hilbert space vectors (or wave functions in the wave-mechanics formulation) are the states but unit rays in Hilbert space. 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. The same holds for using the Dirac approach, i.e., using "canonical quantization" with abstract operators and representation-free Hilbert-space formalism using the Heisenberg picture of time evolution. Though I think that this is the most "natural" approach, but that's true provided you have a good understanding of the formulation of classical mechanics in terms of the Hamiltonian formulation with Poisson brackets with an emphasis on its algebraic structure and its natural relation with the Lie groups underlying the space-time symmetries (Galilei symmetry, which however is not so easy too, and you cannot start an intro lecture in QM with Lie group and algebra representation theory, needing complicated concepts as unitary ray representations and central extensions). With all this experience I'm back at the old-fashioned heuristic approach via wave mechanics, using the de Broglie approach postulating the free-particle dispersion relation for the wave via the energy-momentum relation and then discussing wave mechanics in position and momentum representation first. This works quite well as a heuristic, and the math is well known from the electrodynamics lecture the students had just one semester before the QM lecture. Then you can introduce the abstract Hilbert space formalism a la bras and kets later as a generalization. Of course then you naturally have the Schrödinger picture of time evolution first.

 

[WernerQH]

I think part of the issue here is that there are two possible attitudes towards our experiences and observations of macroscopic objects that are in tension.
[...]
So if QM ends up telling us that macroscopic objects don't have properties, or only have them in some approximation, that means that QM cannot be viewed as a complete fundamental theory.

I think that's going a bit too far. :-)
QM cannot be telling us that macroscopic objects don't have properties.

Nobody doubts that electrons have a mass of 511 keV and spin 1/2, whereas properties like position and spin direction are questionable (at least not permanent, or "uncertain"). The former properties are better viewed as properties of the Dirac propagator, whereas the latter arise in interactions with detectors and should perhaps be better called attributes (or observables), because they depend on the detector as much as on the "object" being measured. I think that at the fundamental level it is best to avoid the talk of "objects" altogether.

 

[vanhees71]

In classical physics, position, momentum and classical spin components (for extended bodies) also take different values in different "states" and only intrinsic properties like their mass don't change. If nothing would change, we'd not have any kinematics and dynamics. Of course, also in quantum theory systems have properties, described by the state.

 

[WernerQH]

So, where's the difference between classical and quantum mechanics in your opinion?
Is it just that c-values are replaced by q-values, and one has to be careful in interpreting the "states" of systems? I'm interested to understand the physical, not the formal differences.

 

[vanhees71]

The difference is that in classical physics we assume a deterministic behavior, i.e., in classical physics all observables always take determined values, no matter in which state the system is "prepared" in. In quantum theory the state determines, which observables take determined values. The physical content of the quantum state is probabilistic and only probabilistic, i.e., for each observable it gives probabilities for the outcomes of measurements and nothing else. An observable's value is determined if and only if with probability 1 you measure this one value.

 

[WernerQH]

I agree that quantum physics is fundamentally probabilistic. In my view the difference to classical physics is not due to "measurements", but to the actual discreteness of the microscopic processes. Photons can be counted. The continuity of classical physics is lost.

 

[vanhees71]

But not all states of the electrodynamical field have a definite number of photons like thermal radiation and coherent states.

 

[WernerQH]

Agreed. I didn't mean to imply that the number of photons is always definite. The underlying microscopic processes can be non-markovian, and photons are not created or absorbed in an instant. But there is some actual "graininess" that is absent in the classical picture.

 

[Demystifier]

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

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.

 

[EPR]

There is no cut and the difference between QM and CM amounts mostly to brain structure and aspects of perception.

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.

 

[gentzen]

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.

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.
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 exercise from such a book which highlights how bad one can misappreciate the statistical operator:

Try to understand where that exercise 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.

 

[vanhees71]

WHAT? Where is this from (Nolting?). $\hat{\rho}$ is a pure state if and only if it's a projection operator, i.e., it must fulfill $\hat{\rho}^2=1$. Also it's obviously not self-adjoint. So the right answer without any need for calculation is that it cannot be a statistical operator to begin with.

 

[physika]

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

...maybe not so much

Reconstruction of Gaussian quantum mechanics from Liouville mechanics with an epistemic restriction​

https://arxiv.org/abs/1111.5057
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.86.012103

Quantum mechanics as classical statistical mechanics with an ontic extension and an epistemic restriction​

https://arxiv.org/abs/1711.01547
https://www.nature.com/articles/s41467-017-01375-w

.

 

[CelHolo]

I'd say there are various limits where the observer can be essentially removed but they're not the general case.

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.