Spontaneous collapse theories

The Ghirardi–Rimini–Weber theory, or GRW

It has 4 main problems:

Problem with relativistic invariance

According to Precedence and freedom in quantum physics (Lee Smolin, May 2012), spontaneous collapse theories would have troubles to be defined in a relativistic invariant manner.

Problem with conspiracy

Quoted from there:
"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."

Problem with conservation laws

General Relativity proves that the laws of conservation of mechanics are absolute logical necessities.

Quantum mechanics has is strange, twisted but coherent way to satisfy these conservation laws.
But with physical mechanisms of spontaneous collapse, these logical necessities are broken. Indeed this article reports "Another interesting characteristic of all the collapse models is that a narrowed wave function increases its energy because of uncertainty principle: this leads to a violation of energy conservation".

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:

Problem with too slow collapse

In his article The Quantum Measurement Problem: State of Play (p.39), David Wallace wrote the following remark on expected requirements for a spontaneous collapse theory :
The 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.
Maybe, would the motivation to see the idea of a slow collapse “embarrassing”, come from an implicit feeling that the collapse must have something to do with consciousness ?
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:
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.
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".

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