Yes, and then what happens when you decide to measure the state of the part of the system that lies in one region of space?
If I had any good idea, I would go pick up my Nobel Prize. The only thing I can really say is that I do not think that the wave function instantly collapses as this would be a non-unitarity evolution of the wave function.
That's irrelevant, because EM is local in physics.
You missed my point, I of course did not want to say that turning on the TV is a non-local interaction, just that it looks like one to humans. So if non-local interaction was all that is going on in quantum mechanics, than it would not be that hard to make sense of it, as we have an intuition for non-local interactions, even though only from things that look like non-local interactions to us but are not actually non-local interactions.
> If I had any good idea, I would go pick up my Nobel Prize.
Well, we already have many ideas, as summarised by the various interpretations of quantum mechanics, some of which have instantaneous non-local interaction.
> The only thing I can really say is that I do not think that the wave function instantly collapses as this would be a non-unitarity evolution of the wave function.
Sure, but many people do think it does, and such an interpretation is totally compatible with QM.
> You missed my point, I of course did not want to say that turning on the TV is a non-local interaction, just that it looks like one to humans. So if non-local interaction was all that is going on in quantum mechanics, than it would not be that hard to make sense of it, as we have an intuition for non-local interactions, even though only from things that look like non-local interactions to us but are not actually non-local interactions.
But it's irrelevant because physics isn't about what things "seem like to humans", it's about what we actually measure and how to create theories that explain and predict it.
Sure, but many people do think it does, and such an interpretation is totally compatible with QM.
The Schrödinger equation and wave function collapse are not compatible. Maybe they could be integrated in some theory, but that will need a lot of additional explaining when and how the evolution changes between being unitary and non-unitary.
But it's irrelevant because physics isn't about what things "seem like to humans", it's about what we actually measure and how to create theories that explain and predict it.
You are still missing my point. Quantum mechanics in general and entanglement in particular are arguably hard to understand because they are unintuitive. If all that was going on were some non-local interactions, than entanglement would not be hard to understand because non-local interactions are intuitive to us because we are familiar with things that look like non-local interactions to us.
Now turn this argument around. We are still having a lot of trouble making sense of quantum mechanics, therefore it seems unlikely that non-locality is at the core of quantum mechanics, because if it was and would explain everything, than it would not be so difficult to grasp quantum mechanics because we have an intuition for non-local behavior. This is obviously no rigoros argument but it was also never was meant to be one.
> The Schrödinger equation and wave function collapse are not compatible.
They don't need to be because they describe totally different phenomena.
> Maybe they could be integrated in some theory,
They already are integrated into the theory of quantum mechanics. Take a look at the postulates of quantum mechanics again, one of the postulates is unitary evolution through time, another is non-unitary collapse with measurement. All the experimental results of quantum mechanics are compatible with those postulates.
> Quantum mechanics in general and entanglement in particular are arguably hard to understand because they are unintuitive. If all that was going on were some non-local interactions, than entanglement would not be hard to understand because non-local interactions are intuitive to us because we are familiar with things that look like non-local interactions to us.
Well, entanglement _is_ intuitive in that sense, which is one of the reasons why seeing entanglement as linked with non-local collapse is so popular.
> We are still having a lot of trouble making sense of quantum mechanics, therefore it seems unlikely that non-locality is at the core of quantum mechanics, because if it was and would explain everything, than it would not be so difficult to grasp quantum mechanics because we have an intuition for non-local behavior.
I don't really buy this, since, quantum mechanics is intuitive and simple if we accept non-local collapse and wavefunction primacy, i.e., if you actually accept the five postulates on face value, it is not difficult to accept quantum mechanics.
As a physicist myself, I don't feel bewildered or confused by quantum mechanics. I have quite a strong intuition for it, in fact.
They don't need to be because they describe totally different phenomena.
In which way are they describing different phenomena? They both describe the evolution of the wave function, the Schrödinger equation while everyone is leaving the system alone, wave function collapse at those special moments when somebody is looking at the system, performing one of those mysterious measurements.
Without explaining more precisely when I should use unitary evolution and when I should collapse the wave function, the Schrödinger equation together with wave function collapse are at the very least an incomplete and maybe even an inconsistent theory.
Again, just take a look at the postulates: Schrödinger equation describes the unitary time evolution of the system under a given Hamiltonian, wavefunction collapse describes the outcome of the non-unitary measurement process.
> Without explaining more precisely when I should use unitary evolution and when I should collapse the wave function, the Schrödinger equation together with wave function collapse are at the very least an incomplete and maybe even an inconsistent theory.
I don't think that QM postulates are incomplete, you just take the set of things that constitute a measurement as a premise.
Let's put it this way, we have never designed an experiment where this has been an issue. So long as we define which part is the measurement beforehand, QM always predicts the results we measure. Usually it will be a photodiode or something of the sort. If QM were incomplete or inconsistent, surely we would be able to find contradictory experimental results?
To summarise, the 5 basic postulates of quantum mechanics, which contains unitary evolution and non-unity measurement collapse, form a microscopic theory which no experiment has ever been able to contradict.
Again, just take a look at the postulates: Schrödinger equation describes the unitary time evolution of the system under a given Hamiltonian, wavefunction collapse describes the outcome of the non-unitary measurement process.
The outcome distribution of a measurement is described by the Born rule, the collapse postulate on the other hand tells us that the wave function will change to the actually measured state. Related but not the same.
For the state |0> + |1> (unnormalized) the Born rule tells us that a measurement will yield |0> or |1> with 50 % probability each. The collapse postulate tells us that the state will change from |0> + |1> to either |0> or |1> depending on the measurement outcome.
This change is non-unitary and therefore incompatible with the Schrödinger equation which tells us that quantum systems evolve unitarily. If you want, consider the combined quantum system of the system under investigation and the measurement device, why should that system not evolve unitarily?
> The outcome distribution of a measurement is described by the Born rule, the collapse postulate on the other hand tells us that the wave function will change to the actually measured state. Related but not the same.
Born rule is also a postulate.
> This change is non-unitary and therefore incompatible with the Schrödinger equation
Yes that's why unitary evolution has a separate postulate
> If you want, consider the combined quantum system of the system under investigation and the measurement device, why should that system not evolve unitarily?
The postulates are roughly quantum system evolve unitarily except when they are measured, then a non-unitary wave function collapse happens. That is inconsistent. For the system under investigation this works, it evolves unitarily until measured, then the wave function collapses non-unitarily. The combined system of system under investigation and measurement device however is never measured, therefore must evolve unitarily. This is a conflict, the combined system can not evolve unitarily and also have some subsystem, the system under investigation, evolve non-unitarily, i.e. undergo a wave function collapse. This problem has been recognized for the better part of a century, that is nothing I am pulling out of thin air.
It is objectively inconsistent, the postulates contradict each other. But for almost a century we did not make any substantial progress, neither resolving the issue theoretically or philosophically, nor experimentally demonstrating any problems. Or at least nothing reached broad consensus.
This seems debatable, but let us assume they are not obviously inconsistent. Those postulates only really mean something if you apply them in some situation, and if you apply them as laid out a few comments before, they make inconsistent claims. If applied to the subsystems, they postulate non-unitary evolution of the combined system, if applied to the combined system, they postulate unitary evolution. If inconsistent is to strong of a claim, I guess this could be changed to incomplete, maybe there are missing postulates resolving the issue.
If I had any good idea, I would go pick up my Nobel Prize. The only thing I can really say is that I do not think that the wave function instantly collapses as this would be a non-unitarity evolution of the wave function.
That's irrelevant, because EM is local in physics.
You missed my point, I of course did not want to say that turning on the TV is a non-local interaction, just that it looks like one to humans. So if non-local interaction was all that is going on in quantum mechanics, than it would not be that hard to make sense of it, as we have an intuition for non-local interactions, even though only from things that look like non-local interactions to us but are not actually non-local interactions.