Why are there no clear experiments describing the exact boundary between classical and quantum sizes?

Question

Why are there no clear experiments describing the exact boundary between classical and quantum sizes? Assuming we believe in interpretations of quantum mechanics (QM) that state during measurement (interaction with a classical object), the wave function collapses, i.e., it no longer follows the Schrödinger equation. In all the textbooks describing this process, I haven't found an explanation of what happens if we start to decrease the size of the classical measuring object. At what exact size does it stop being large and classical and become quantum? What exactly happens at sizes when the object is neither fully classical (to collapse the wave function) nor fully quantum?

I do understand that there are interpretations of QM that don't assume the wave function collapses and instead propose that everything always follows the Schrödinger equation.

But my main question is: Why aren't there clear, precise experiments describing the interaction for these “intermediate-sized” objects? If we assume that the wave function does indeed collapse, such experiments might reveal very interesting details.

Answer 1

Why are there no clear experiments describing the exact boundary between classical and quantum sizes ?

There are no clear experiments because there is no exact boundary.

Although we think of quantum effects as being typically short-lived and acting on a very small scale, they can in fact be persisted over long timescales and magnified to produce macroscopic effects. This is the whole basis of quantum computing, although the engineering required to prevent the quantum effects being swamped by noise from the environment is challenging. This Scientific American article says that quantum entanglement has been observed on a macroscopic scale with photosynthesising bacteria. And this Physics World article says that quantum entanglement has demonstrated with vibrating membranes that are $10$ microns across.

Answer 2

Collapse is supposed to be a process that takes a quantum system in a superposition and somehow selects just one of the states in the superposition: $$\sum_a\alpha_a|a\rangle\to|a\rangle$$

This process isn't compatible with the equations of motion of quantum theory. Some "interpretations" of quantum theory postulate such a process without bothering to give an explicit account of it, such as the Copenhagen interpretation. Others, such as spontaneous collapse, explicitly change the equations of motion of quantum theory

https://arxiv.org/abs/2310.14969

These theories can't currently reproduce any of the predictions of relativistic quantum theories, i.e. - almost all actual experimental results involving quantum theory:

https://arxiv.org/abs/2205.00568

Some physicists have worked out the consequences of quantum theory without such modifications. When information is copied out of a quantum system, interference is suppressed - this is called decoherence:

https://arxiv.org/abs/1911.06282

Any object you see around you in everyday life will evolve a lot slower than the timescales over which information is copied out of them and so they will show negligible interference. The result of decoherence is that there are a bunch of different versions of the decohered system that evolve independently to a good but not perfect approximation:

https://arxiv.org/abs/1111.2189

https://arxiv.org/abs/quant-ph/0104033

This is often called the many worlds interpretation of quantum theory, but it is just a consequence of the theory when it is taken seriously as an account of what is happening in reality. In the MWI there would be a version of me sitting one millimetre to my left that doesn't interfere with me, but if you get down to differences around the size of an atom interference is no longer negligible and the different versions can't be safely regarded as independent.

We have already seen decoherence in action and measured and controlled it for systems about the size of molecules: accounts can be seen in the review linked above. So then if collapse is a significant effect it must happen for larger systems. Almost any interaction will cause decoherence and that includes even internal vibrational modes so it is very difficult to prevent decoherence for most large systems. So if collapse happens it is very difficult to observe. It is also unclear what problem such theories are supposed to solve since decoherence already explains the lack of quantum effects for large systems.

Answer 3

In fact, there are. The field that deals with the intermediate regime is called mesoscopic physics. The way you determine whether a system is best described by quantum mechanics or classical mechanics is by comparing the length/time/energy scales of the system with certain characteristic length/time/energy scales, like e.g. the Thouless energy, Fermi wavelengt, coherence length, etc.