A system's wave function is uniquely determined by its underlying physical state
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| License | CC Attribution 3.0 Unported: You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. | |
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Transcript: English(auto-generated)
00:06
In the early days of quantum theory there were many discussions between eminent physicists about the fundamental nature of the theory. A lot of correspondence was exchanged over many years, but some of the deepest questions remained unanswered.
00:23
In particular, what is the meaning of the central object in quantum theory, the wave function? Is it a real thing? Does it represent a state of knowledge about the parameters of some underlying reality? Or is it at all used to make predictions about the outcomes of future measurements with no deeper significance?
00:44
In our work we give an argument that rules out the second of these cases. We consider a state creation device that, according to quantum theory, generates a state of psi. Suppose there is a hypothetical higher theory in which the state would instead be represented by some other parameter lambda.
01:03
So when a system is created in state psi, the higher theory ascribes a state lambda instead, where lambda is distributed according to some probability distribution. We want to think of the parameter of the higher theory as representing reality. If psi is uniquely determined by the parameter, we can think of psi as real.
01:25
The alternative is that two devices that generate different wave functions could generate the same real state lambda. To investigate this, we consider the predictions we can make about the outcomes of measurements.
01:41
Let us call the measurement outcome X. Because lambda is supposed to represent the state of reality, if we know lambda, psi doesn't help us to make predictions. In other words, the conditional probability of X given lambda and psi is the same as the conditional probability of X given lambda. We say lambda is complete.
02:05
This is related to the concept of psi being complete, where if psi is known, lambda doesn't help us make predictions. Completeness of psi is not something we assume in this work. Here is an illustration of four possible roles the wave function can have.
02:21
Each graph shows the probability distribution over the parameters lambda of a hypothetical higher theory for three possible psi, each represented with a different colour. In the top row, for each possible value of lambda, there is only one possible psi, while conversely, in the bottom row, for some values of lambda, more than one psi is possible.
02:45
In the left column, the distributions have support on only one value of lambda, so psi uniquely determines lambda, while on the right, a given psi may give rise to a range of possible values of lambda.
03:00
The main result of our paper is that it rules out the bottom row using the assumption of free choice with respect to a natural causal order. In other words, the wave function is uniquely determined by the parameters of any real theory. This is the same conclusion as obtained by Pussy, Barrett and Rudolph, but with free choice, replacing their assumption of preparation independence.
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