Such theories have 4 main problems:

"That said, we presently have no theoretically good reason why the parameter [exact rate of collapses per particle] should be in the range that allows this explanation to work. It might seem a little conspiratorial of nature to give us the impression that quantum theory is correct, while tuning the equations so that the crucial features that give rise to a definite physical reality are – with present technology – essentially undetectable."

Quantum mechanics has is strange, twisted but coherent way to satisfy these conservation laws.

But with physical mechanisms of spontaneous collapse, these logical necessities may be broken. As this article reports "

Since the core of the mathematical contradiction in the idea of a violation of conservation laws is a matter of how it relates with gravity, this would suggest a link between spontaneous collapse and quantum gravity. Penrose had that kind of suggestion. But the nature of such a link and how it can resolve the above problem, is far from clear. In particular, physical quantities would suggest that quantum random outcomes can be consciously observed by humans (imagine, just a pack of photons coming on a retina and then just a nerve impulse reaching the brain ! and a nerve impulse is a very microscopic move, much lighter than a Planck mass) before they make the first graviton of difference.

This leads us to the philosophical problem:

Maybe, would the motivation to see the idea of a slow collapseThe other constraint — that macroscopic superpositions should collapse quickly — is harder to quantify.(...)

How quickly should they collapse? Proponents of dynamical-collapse theories (...) generally require that the speed of collapse should be chosen so as to prevent “the embarrassing occurrence of linear superpositions of appreciably different locations of a macroscopic object”. But it is unclear exactly when a given superposition counts as “embarrassing”. One natural criterion is that the superpositions should collapse before humans have a chance to observe them. But the motivation for this is open to question.

Now suppose that the collapse is much slower, taking several seconds to occur. Then the cat-observer system enters the superposition

α |dead cat> ⊗|observer sees dead cat> + β |live cat> ⊗|observer sees live cat>.

Who knows what it is like to be in such a state? But no matter: in a few seconds the state collapses to

|dead cat> ⊗| observer sees dead cat> or | live cat>⊗|observer sees live cat>.

Once again, the agent is in a state where he remembers seeing either a live or dead cat, and the probability is|α|^{2}that he remembers seeing a dead cat — since his memories are encoded in his physical state, he will have no memory of the superposition. So the fast and slow collapses appear indistinguishable empirically.

But we can go further : since the condition of decoherence is emergent and cannot be explicitly written in the fundamental equations of laws, and the collapse needs to be slow to not be measurable, the collapse "mechanisms" that were proposed are not 100% effective : alternative possibilities, not "chosen" by the collapse, only see their "probability" (or "amount of reality", as with the many-worlds) fall to a value that is close to zero but not exactly zero. Now, here is a thought experiment I propose to analyze : do you think that the following proposition can make any sense, and why:

An ontology in fact very close to that of the many-worlds, to be compared to what we can tell there about "shrinking the size of neurons".The next experiment has 99% chances to give "yes" and 1% to give "no"... Now done, let us look at the result. We get... "No". Hum, but the collapse of the wave function is slow and not complete yet, so we are now in a branch of the multiverse that has 1% chance of staying real and 99% chance of being annihilated in the next minute. So, just wait a minute and the branch of reality we are now in, is most probably going to be annihilated... One minute later... Uh what, we still exist, what happens ? Ah of course, it is because the collapse is not totally complete, the amplitude of our branch of reality most probably fell but not exactly to zero, only to 10^{-100}, but so our annihilation is probably almost done, and thus most likely to become... even more close to completeness, still one minute later.

One reference I found: Killer Collapse: Empirically Probing the Philosophically Unsatisfactory Region of GRW by Charles Sebens

- If the slow collapse hypothesis has any problem, then which problem is it exactly ?
- If the slow collapse does not have any problem, then can you be happy with the many-worlds interpretation as well (as it is the limit of very large collapse times), otherwise what is the problem with it ?

- If yes then do you agree that, as a result, the collapse has "strictly no effect for all practical purposes", in the sense that, then, the Many-worlds interpretation just fits to "explain" probabilities, and therefore should be favored, by Occam's razor, eliminating any assumption of collapse as artificial ?
- If no, then it would seem to imply indeed that we can "observe that the collapse is fast" by the fact that otherwise, at any time, existence would be spread out across recently appeared branches of possibilities not conform to Born's rule and not yet eliminated by the collapse process obeying Born's rule. But then wouldn't it be reasonable to reply to such an observation report by the following objection : "So, I see you as having written a moment ago, that you noticed all things kept behaving in conformity with Born's rule, but this is only because, while that time actually blossomed with versions of you with a dominance of some where you actually saw everything wildly running upside down, all those of the latter kind finally turned out to vanish from existence before I had a chance to observe your report of them; only the then lucky versions closest to Born's rule made it to me, or maybe I'm just myself in such a lucky branch of existence, the one you're going to read back from me, while the rest of the versions of me with opposite observations, and myself also seeing all things wildly running upside down, are going to vanish from existence until then".

Please answer this question in Quora

I cannot find this answer satisfactory because of the gross contingencies it is based on, unworth of the much more fundamental nature of the question. Namely, what if by some super new nanotechnologies we could engineer a system working like a brain but much smaller and faster ? Is there any fundamental impossibility for another universe to exist with different laws of physics, or different values of physical constants, working much the same as our universe except that it would lead to slow collapse ?

Does the wavefunction in Quantum Mechanics collapse instantaneously when we measure an observable or is there a transition time between states?

How do measurements collapse quantum wave functions?

What exactly does it take to collapse a wave function?

Why does observation of a quantum wave function cause it to collapse into a discrete quantum state? QBist answers there

Can you uncollapse the wave function by killing an observer who did the measurement?

What is currently the best
explanation for how and why the quantum wave function
collapses?

What is the difference between quantum decoherence and wave function collapse?

What hypothesis explain the collapse of a wave function?

If an observer is required to collapse a wave function, how does the observer exist?

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