Provide references and I'll see if I have the time to study it. — Rich
Still, quantum theory remains probabilistic though in Bohm's model there are real causal agents - including "information". — Rich
So I want to ask you. You keep saying that the Mach-Zehnder interferometer experiment would be inexplicable under any interpretation other than the Everett interpretation. So what do you think the result of the experiment would look like if the Bohm or the Copenhagen interpretation was true? — SophistiCat
According to such interpretations, the photon always turns up at the same detector (with certainty), but without a sufficient cause. So God not only plays dice but he always rolls a six. — Andrew M
I don't understand. If an interpretation gives us the correct result (i.e. the result predicted by the formalism and validated by experiments), then where is the problem? Or are you under the impression that a "non-deterministic interpretation" is contractually obligated to give a non-deterministic result for every conceivable measurement? — SophistiCat
Bohmian is causal but not deterministic — Rich
Are you suggesting that there is an interpretation that doesn't use the same Schrodinger/Bohmian equations and is getting better predictions? — Rich
What is the difference between causal and deterministic here? — Andrew M
Why do you continue to insist that quantum theory = randomness? — Rich
Nonetheless a photon has a specific position and momentum and follows one specific trajectory as governed by the pilot wave. — Andrew M
No. It is in principle possible that Alice could roll a dice a million times and get a six every time. That result is no less likely than any other string of results for a million rolls. But her non-random-looking result begs for an explanation in a way that random-looking results don't.
So the Copenhagen interpretation correctly predicts that a photon in the standard MZI experiment will always end up at the first detector despite passing through beam splitters. But that raises the question as to why. What is the causal explanation for that non-random-looking result?
For the Copenhagen interpretation, the Schrodinger equation is equivalent to asserting that Alice just always rolls sixes. Each formalism gives the correct predictions and no causal explanation exists.
The problem is with the plausibility of that idea. — Andrew M
It is necessary to discard the concept of "things" (as determinists continue to insist on) and treat quantum as a process that is in continuous flux. How does a process become a thing? That is exactly the role of the mind as it seeks to create a canvas to create on. — Rich
n the MZI experiment the standard quantum mechanics calculation gives the probabilities at the detectors as 0 and 1. Any interpretation of quantum mechanics had better yield the same probabilities, otherwise it doesn't even qualify as an interpretation. Are you saying that the Copenhagen interpretation predicts probabilities other than 0 and 1 in this case, or fails to predict anything specific? — SophistiCat
(As an aside, this very special case where probabilities neatly collapse into all or nothing is uniquely favorable to the Everett interpretation, which otherwise faces a prima facie problem with specific observed frequencies of outcomes. In contrast to the Copenhagen interpretation, which happily assumes the reality of probabilistic outcomes as a matter of principle, the Born rule is difficult to justify in the context of Many Worlds. When they are not making popular presentations, like the one by David Wallace that you linked, Everettians tie themselves into knots trying to make sense of these probabilities. And this is where, I am afraid, the prima facie appeal of the MWI as the "no-interpretation" interpretation dissipates.) — SophistiCat
The Copenhagen interpretation makes the same prediction but it denies that there is a causal explanation for the probabilities. But, if causality is assumed, then the MZI experiment shows that a beam splitter cannot be sending a photon exclusively one way or the other with 0.5 probability (or else a photon would arrive at either detector with 0.5 probability, not 0 and 1). — Andrew M
But try to think of an idea you've had that was completely brand new, and not based on a combination of knowledge and experience of past events... — CasKev
You do not need to assume causality, or anything else besides the operation of standard quantum mechanics, in order to obtain that result. You said so yourself: the Copenhagen interpretation makes the same prediction. It follows the standard solution all the way up to the moment of detection, at which point it says that the superposition state collapses into one of the eigenstates - acausally, as you say, but following the Born rule for probabilities. And since in this case the superposition is degenerate, the result is perfectly predictable, even assuming the Copenhagen interpretation: the wavefunction has to collapse into one particular position eigenstate with probability 1, simply because there is only one non-zero eigenvalue. — SophistiCat
So where do you get probability 0.5? And what does this have to do with causality? I don't understand. — SophistiCat
The point is that everything that went into your decision is based on something that existed prior to the decision. Even seemingly random events have a preceding chain of events leading up to them. — CasKev
I agree with all you say above but would add that the probabilities themselves also have no causal explanation under the Copenhagen interpretation (i.e., the Born rule is postulated). — Andrew M
This is when considering a single beam splitter in isolation. When one photon is sent into a beam splitter, there are two position eigenstates - one for the reflection path and one for the transmission path with 0.5 probability for each.
The MZI experiment shows that this cannot be the scenario at the second beam splitter. If only one photon were entering the second beam splitter, then a photon should be found at the second detector half the time. But it's not. This is what I was trying to convey with the "Alice rolling sixes" analogy. It is highly improbable that on multiple runs a single photon entering the second beam splitter would always be found at the first detector purely by chance.
But this is what the Copenhagen interpretation is committed to by denying causality. The results that it predicts are inherently inexplicable on its own premise. — Andrew M
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