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This postulate should replace the Born rule as it makes the Born rule precise w.r.t. decoherence:

"If a consciousness is in a superposition $\sum |k_i \rangle$, such that $\langle k_i|k_j\rangle=0$, then there is a probability $\langle k_i|k_i\rangle$ that the consciousness reports/experiences being in the state $|k_i\rangle$"

As an example, $|k_j\rangle$ could represent the possible states of a consciousness after observing the spin of a particle.

Decohered electrons behave as if they're passing through only one slit at a time. But I think this postulate only applies to consciousness, because:

  1. A decohered electron, until observed, evolves unitarily according to the Schrodinger equation. So, we can't say that a decohered electron passes through only one slit.

  2. It would be meaningless to say that an electron experiences/reports passing through only one slit with probability $\langle k_i|k_i\rangle$. This is because electrons have no subjective experience, at least not in a verifiable way.

Consciousness in the only thing that can experience being in a state. This is why I think the Born rule only applies to consciousness. What will be the hurdles of replacing Born rule with this precise version? I think the preferred basis of decoherence, if it hasn't been solved yet, is a big hurdle.

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    $\begingroup$ I guess the main hurdle is that you can't precisely and objectively define consciousness. $\endgroup$
    – rghome
    Commented Sep 16, 2022 at 11:00
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    $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Commented Sep 16, 2022 at 11:07
  • $\begingroup$ @rghome Yes, that is a hurdle too. But leaving it undefined will just make the Born rule completely imprecise. Born rule is verifiably only a fact about subjective experience/consciousness. $\endgroup$ Commented Sep 16, 2022 at 11:10

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Your question is likely to be closed for various reasons. However, I will share my thoughts on what you have said in this question and your earlier one.

It is nonsense to suppose that consciousness- as we normally understand the word- plays a role in determining the outcome of interactions between fundamental particles.

If you perform some kind of experiment that involves a measurement of a property of a particle such as an electron, the experiment has a definite outcome regardless of whether, when or how the outcome might be observed by a human. To take a simple case, pass a series of electrons through some kind of 'two-slits' set up and let them impinge upon a photographic plate. Evidence of the localised arrival of the electrons at the plate will be there without the need for observation by a conscious being.

Your suggestion that 'collapse' of the wave function can be subjective implies that the evidence of the outcome of the 'collapse' might be there for one person but not there for another. Physics does not work like that.

You are treating the concept of collapse in an overly simplistic way. Quantum theory is a mathematical model of reality, a model that is capable of making predictions in good accord with experimental results. However, quantum mechanical modelling of reality is unavoidably based on simplifying assumptions. Specifically, the Schrodinger equation contains a term in which the various forces to which a particle is subject is modelled as a classical potential- almost always the potential is some smoothed approximation of reality, expressed as a function of space and assumed to be constant in time.

If you perform an experiment to determine the spin direction of an electron, you arrange for the electron to be passed through a suitable magnetic field and place a detector in its subsequent path. The spin direction is not measured directly but is inferred from where the electron is detected- the 'measurement' of spin is actually a measurement of the electron's position.

If the above experiment is performed 'in a box' then yes you could in principle consider the entire contents of the box as evolving according to Shrodinger's equation, but in practice you could not model it precisely because you would not be able to define the potential term in the equation at a sufficient level of detail to account for the intimate interactions between the countless particles involved.

When you perform a two-slits experiment, say, you assume the incoming electron is free. However, as the electron approaches the photographic plate it is clearly no longer free but subject to forces that cause it to interact with the chemicals on the plate. The wave function has not really 'collapsed' in the sense you seem to imagine. Instead, what you should really consider is that you model the incoming electron as having a wave function that is a plane wave of some sort, because you assume there is a constant background potential, and that is a simplifying approximation. If you want to model the behaviour of the electron as it hits the photographic plate, you must use a different instance of the Schrodinger equation- one that includes a realistic potential function describing the local environment of the plate.

Quantum mechanics says that if you have a very large number of particles (as would be the case where you have a single particle being 'measured' by a macroscopic detector), then all the particles together have a multi particle wave function that evolves smoothly in time in accordance with a multi particle Schrodinger equation in which there is a potential term that accurately models all of the interactions between the particles. However, if you choose instead to model the system in a drastically simplified way, in which you use a single-particle version of the Schrodinger equation and exclude all the other particles (ie those comprising the detecting apparatus), then the Born rule is applicable.

If you insist that only consciousness can determine the outcome of physical interactions then you must account for how the universe evolves when and where there is no conscious life to observe it. If you try to do that by ascribing some form of consciousness to everything, including elementary particles, then you have strayed outside the realm of physics. We do not yet have an accepted theory about the relationship between consciousness and physics, so the topic is essentially speculative at present.

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  • $\begingroup$ I upvoted your answer because respect your view. I don't like that mainstream physicists ridicule the idea of consciousness collapse. It deserves respect too. The answer that I got on my other post clearly agrees that there either exists a correction term to the Schrodinger equation, or that quantum mechanics involves consciousness. This article agrees too. If you believe that your view is 100% correct, you need to mathematically derive the Born rule.... $\endgroup$ Commented Sep 16, 2022 at 13:50
  • $\begingroup$ .....by mathematically accounting for the approximations that we do. No one has derived the Born rule like that yet. Also, you say that the photographic plates has dots detected on it before it is observed. You have to respect that not everyone agrees with that. From what I know, the photographic plate simply gets entangled with the electron. I don't see anyhow the photographic plate could objectively have dots on it without a correction to the Schrodinger equation. $\endgroup$ Commented Sep 16, 2022 at 13:50
  • $\begingroup$ And no correction term to the Schrodinger equation has yet been verified even in the largest entanglement experiments that we have done so far. Based on this, consciousness collapse deserves to be seen at least on an equal footing as objective collapse.....Are you aware of any derivation of the Born rule by using approximations to unitary evolution? I can't think of any such derivation. Unitary evolution includes every possible state of the measurement device, while Born rule is about the "picking" of a single outcome $\endgroup$ Commented Sep 16, 2022 at 14:18
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    $\begingroup$ Many thanks, LM. I will cogitate on what you have said and try to reply when I have some time free. Best wishes! $\endgroup$ Commented Sep 16, 2022 at 16:48
  • $\begingroup$ I think your answer is really good now. In the spin measurement you wrote about, I understand that the external magnetic field causes the electrons to go one way or the other. But is this only true when all the electrons are a spin eigenstate? What if the electron's spin is initially a superposition? Will it be true that the external magnetic field will evolve the electron's spin into an eigenstate (thereby "collapsing it")? I want to ask the same thing about the photographic plate potential. If we modeled that potential, will it evolve the electron into a position eigenstate? $\endgroup$ Commented Oct 10, 2022 at 13:26