Heisenberg uncertainty principle -- Questions about a practical experiment

[PeroK]

In chapter 9 “The problem of the interpretation of quantum theory” in his book “The Structure of Physics” (the book is a newly arranged and revised English version of "Aufbau der Physik" by Carl Friedrich von Weizsäcker), Carl Friedrich von Weizsäcker writes in section 9.3.2 “Schrödinger's cat: The meaning of the wave function”:

“Schrödinger had to admit, after the discussions described above, that a wave theory was not suitable for describing particle phenomena. For this reason he remained ever since of the opinion that quantum theory in its present form is not an adequate theory of reality, despite all its successes. He no longer participated in its development, and turned to Einsteinian-type of problems of a unified classical field theory.

In an article from 1935 (see Jammer 1974, pp. 215—218) he treats with irony the Copenhagen point of view by means a thought experiment. Let a living cat be locked up in a box and with it a deadly poison which can be released by a single radioactive atom inside the box. After one half-life of the atom the probability is $1/2$ for the cat being still alive, and $1/2$ for being dead. Schrödinger describes the $\psi$-function of the system at this time with the words: ‘The half-alive and the half-dead cat are smeared out over the entire box.’

The answer is trivial: the $\psi$-function is the list of all possible predictions. A probability $1/2$ for the two alternative possibilities (here: "living or dead") means that the two incompatible situations must now be considered equally possible at the instant of time meant by the prediction. There is no trace of a paradox.

Schrödinger's reason to consider the situation as paradoxical lay in his hope to interpret the $\psi$-function as an ‘objective’ wave field. In the implied deterministic description, he saw no reason to take seriously the difference between the present and the future. I have seen from a letter he once wrote to me (after the war) how foreign the idea was to him, as well as to many other physicists, that this difference was something to be taken seriously physically, and not merely ‘subjectively’……….”

You posted this once before and it seems to me that Weizsäcker missed the point. You could replace the cat by a person and the poison by a simple signal. When the experimenters open the box, the person can tell them what happened and can clearly recount the entire time in the box. And we can see that what was perceived inside the box is much the same as what was perceived in the lab. The sealed box can't have added a new layer to the observation of physical phenomena. This is, IMO, definitely something that requires an explanation.

 

[Fra]

@PeroK , @phinds, @Nugatory Now please check whether I am correct or not.

In Schrödinger cat experiment, the cat is either alive or dead is not in a state of quantum superposition.

At the heart of the problem of understanding how "QM interactions" work... which we don't know yet

What is the meaning of "the cat is dead or alive" or for that matter, if a spin is "this way or that way"?, until we actually measure it?

It is more well defined to speak about if we know, after having made a measurement.

So both a complex/QM superposition and a classical probability distribution represents our uncertainty or incomplete knowledge of what we know.

The difference is that in a classical probability distribution the meaning of the uncertainty or incomplete knowledge is simply that the value is definite, and rules what happens as per the prior mechanisms, it's just that WE (or the observing context) are ignorant about it. In classical probability there are no non-commutative information. This meaning is what what is implicit in the Bell theorem, and by know we know that this classical understanding of uncertainty can not be true, it can not explain QM interactions.

So the non-commutative elements in our state of information or knowledge, is the part which is hard to grasp, and there is no current explanation for this. In QM as it is formulated, the conjugate momenta and HUP are introduced somewhat axiomatically, just showing some classical correspondence in the macro limit.

To "learn" QM as in accpeting the axioms, and the mathematical formalism which is essentially linear algebra applied to functional spaces is much easier than trying to understand or explain it, which means motivating the axioms as why are they a good way to describe nature?

But learning the basic formalism, helps distinguishing between the interesting yet unsolved problems with some beginners confusion of categorization which can smear solved and unsolved problems into one big haze. The problem is that in order to be "pedagogical" some QM textbooks, don't highlight conceptual problems, but instead focus on ether heuristic or axiomatice building of the topics. So the understanding you then gain IMO has built-in holes in understanding; but I think everone has the same problem. Some have easier to let go, and other prefer to obsess on things until its resolved.

/Fredrik

 

[phinds]

@PeroK , @phinds, @Nugatory Now please check whether I am correct or not.

In Schrödinger cat experiment, the cat is either alive or dead is not in a state of quantum superposition.

The simple answer is, yes, you are correct, but as has been pointed out extensively above, QM is more complex than something as simple as the cat experiment.

 

[L Drago]

The simple answer is, yes, you are correct, but as has been pointed out extensively above, QM is more complex than something as simple as the cat experiment.

Yes, you are right. QM is complex but not as weird as pop-sci has made it in YouTube videos

 

[L Drago]

Thank you @phinds and @PeroK for correcting my mistake about that cat experiment . Thank you @Nugatory for providing me authentic sources to read from.