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It's just some people argue that it's almost MW's last problem and if it's derived,MW would be "over the other interpretations".For me there's no need to derive Born's rule, because it's simply a fundamental postulate of quantum theory.
It surely depends what the derivation is based on. For a long time I too believed that Born"s rule ought to be derivable from Schrödinger's equation. But whenever I studied promising articles, the proof contained an innocent looking assumption that was equivalent to Born's rule (if it wasn't just shrouded in mathematIcs). Now I'm convinced that it is an independent ingredient of QM and even more important than the wave function. (What's observable can always be expressed using operators.)Many articles these years claim that they have derived it.
I don't consider MW an interpretation at all. It claims that Schrödinger's equation and continuous evolution is all there is to quantum theory. I can't believe that discrete events like the clicks of a Geiger counter are tricks played on us by our senses while the underlying reality evolves continuously. MWI glosses over the discrepancy with nothing but hand waving.It's just some people argue that it's almost MW's last problem and if it's derived,MW would be "over the other interpretations".
I agree completely.I must admit that I never understood what MW is good for nor how it interprets quantum states.
Is there any non-minimal interpretation of QM for which you do understand what is it good for?I must admit that I never understood what MW is good for nor how it interprets quantum states.
Every observer with his or her own world. :-)I agree completely.
Many interacting observers - yes, but many worlds? What is the explanatory value and how it helps us forward?
/Fredrik
Not own world Every observer with its own subjectively inferred imperfect expectation of the one common world.Every observer with his or her own world. :-)
The "one common world" is the one which needs proof of its existence, otherwise it's as always assumed that it exists.Not own world Every observer with its own subjectively inferred imperfect expectation of the one common world.
Observer equivalence is the special case of observer democracy where all the observers evolved their views to be in tune as analogous to a Nash equilibrium. Once in tune, the views asymptotically exhibits the symmetries the traditional pardigm sees as timeless constraints.
/Fredrik
The only meaning I assign to the "one common world" is "what you get from all physical observers that are in causal contact with each other". Exactly what this is in detail - the microstructure of observers and their relations - is of course what the whole game of inference is about. It´s also necessarily moving target as I think the inference process itself helps to form and a self-organisation will take place. There will never be a complete answer, because the more complex and observer gets, it´s ability to encode more complex relations increase. The ambition is IMO just to understand the abductive inference mechanisms here.The "one common world" is the one which needs proof of its existence, otherwise it's as always assumed that it exists.
Its not much different from the continuous evolution of a discrete number of corona viruses from 0, to 1,2,3,4, to a huge number.You mean there is continuous evolution from 5, 4, 3, ... down to 0 undecayed atoms? I think there is some actual granularity that theoreticians should not conceal just because differential equations are easier to work with.
It's strange for a mathematician to be lacking in a precise definition of the term "continuous". :-)Its not much different from the continuous evolution of a discrete number of corona viruses from 0, to 1,2,3,4, to a huge number.
This is a physics forum, so I use the term consistent with physics usage. But I presume that the evolution of viruses is governed primarily by classical mechanics, which is continuous even in the mathematical sense.It's strange for a mathematician to be lacking in a precise definition of the term "continuous". :-)
I think what's effectively continuous and what is not is observer-dependent. A binary state always has a discrete transition, but if can consider the probability for the transition of the same state by observing the context as well, it can be almost continous. But the latter description contains MORE information and thus requires a sufficiently complex observer.You mean there is continuous evolution from 5, 4, 3, ... down to 0 undecayed atoms? I think there is some actual granularity that theoreticians should not conceal just because differential equations are easier to work with.
I think such infinite and uncountable amounts of information is likely a fiction that works well for describing atomic phenomena from the perspective of a dominant classical environment.In quantum theory the evolution of the state (statistical operator) is described by a partial differential equation and thus is continuous. So are the probabilities and related expectation values concerning discrete variables
Isn't that about the time evolution only? MWI says that the evolution of the state is given by the Schrödinger's equation, no collapse. It doesn't say that there are no other accpects of QM. At least that is how I always understood it.Right. Schrödinger's equation by itself is not enough; we need the Born rule to obtain measurable quantities from the wave function. Accordingly it is not derivable from Schrödinger's equation. But it seems that MWI supporters disagree and prefer to think that Schrödinger's equation is all that quantum theory is about.
What people have qualms about is how unitary evolution and "measurements" fit together. Schwinger's action principle that led to the closed time-path formalism allows direct calculation of observable quantities. It smoothly joins unitary evolution and "measurements" in one formalism.
The other aspects are the other universes, or branches thereof. The central puzzle is: How does the wave function relate to the real world that we perceive around us?Isn't that about the time evolution only? MWI says that the evolution of the state is given by the Schrödinger's equation, no collapse. It doesn't say that there are no other accpects of QM. At least that is how I always understood it.
But it seems that MWI supporters disagree and prefer to think that Schrödinger's equation is all that quantum theory is about.
How does Schwinger's action principle lead to Born's rule?What people have qualms about is how unitary evolution and "measurements" fit together. Schwinger's action principle that led to the closed time-path formalism allows direct calculation of observable quantities. It smoothly joins unitary evolution and the Born rule in one formalism.
It's the small subsystem seens as an "observer" that has no control, yes. This is my point as well! Yet it has to act without full control. How are its actions caused ? Totally random? By deterministic rules? If so, which ones? Can we get insighgs from pondering about this? (I think yes of course)To the contrary! If you have a small subsystem coupled to a macroscopic "environment", you don't have control
This is from the perspective of the dominany, classical observer - yes. This is statistical description from a different perspective, not a causation.i.e., we average over a lot of unknown degrees of freedom to effectively describe the "relevant observables" of the subsystem.
This extrapolation rules is something I think we can improve. A similar principle could be perhaps that "all agents" have actions causally chosen by a similar logic.Even in cosmology, all we can do is to observe local observables and then extrapolate to the "universe as a whole" assuming the cosmological principle, which is amazingly successful.
This direction of reasoning always seemed conceptually backwards to me. Set aside historical development, how can you start with an equation, and then ask what the dependent variable means? My take on this is to try to first understand in what way the state encodes the observers predictions of the future and how it's inferred. Then ask - what self evolution is implied, when you account for the dependence of some information. I think it's this depencence, that implies the evolution. This is why I interpret the "hamiltonian" as part of the initial information as well. Although it's not the way of standard formalism. In the standard formalism it's just put in there, or considered empirical requiring no explanation.Right. Schrödinger's equation by itself is not enough; we need the Born rule to obtain measurable quantities from the wave function.
It doesn't. Born's rule is needed only when you think of the wave function as the linchpin of quantum theory, as an additional step (to obtain numbers that you can compare with experiment). But with a path integral over a complete time-path you can write down expressions for all measurable quantities directly. One obtains probabilities (rather than probability amplitudes) automatically. Born's rule is built-in, and there's no need to introduce "measurement" as a separate process that somehow disrupts unitary evolution. In my view QM/QFT is just a machinery for calculating correlation functions, and the closed time-path formalism doesn't need a derivation from a set of historical axioms. It works nicely.How does Schwinger's action principle lead to Born's rule?