Hawking believes "God confuses us throwing dice....", why?

[stevendaryl]

That's fundamentally wrong! Please, provide a time dependent Schroedinger equation which comprises a physical process that allows to “cut” the wave function of the considered system into “real” pieces, viz. which leads to an increase in entropy and, consequently, to a physical conversion of a pure state into a mixed state.

You cannot trick quantum theory because of your feeling of what “reality ought to be”!

I'm sorry. I don't understand what you're saying is wrong. It's just a fact that whatever you consider the system of interest, eventually, that system will interact with the rest of the universe. So you're faced with a choice: Either you have a wave function for the rest of the universe, or you somehow have to switch to a nonpure state for the description of the system of interest.

What are you disagreeing with?

 

[stevendaryl]

I'm sorry. I don't understand what you're saying is wrong. It's just a fact that whatever you consider the system of interest, eventually, that system will interact with the rest of the universe. So you're faced with a choice: Either you have a wave function for the rest of the universe, or you somehow have to switch to a nonpure state for the description of the system of interest.

What are you disagreeing with?

I'm unsure about the level at which you are disagreeing. I was assuming that you understood the mathematics of pure and mixed states. Bill Hobba explains it. If you start with a pure state for a composite system, and you perform a "trace" to eliminate the degrees of system that you are not interested in, then the result is a mixed state. There is no assumption being made that there is any nonunitary collapse going on, it's purely a mathematical transformation that is necessary to keep your focus on the system of interest, as opposed to the entire universe.

 

[stevendaryl]

He didn't talk about it in terms of decoherence, but the mathematics of how mixed states arise from pure states by considering subsystems was described in Everett's original paper on Many Worlds (which is not the name that he used---that was Bryce Dewitt).

Suppose that you have a composite system described by a wave function |\Psi\rangle = \sum_{\alpha, j} C_{\alpha, j} |\alpha\rangle |j\rangle, where |\alpha\rangle is a complete set of states for the first subsystem, and |j\rangle is a complete set of states for the second subsystem. You can think of |\alpha \rangle as describing the system of interest--maybe an electron--while |j\rangle describes everything else in the universe. Now K be some operator that only affects the first component. That means that its affect on the composite state |\alpha\rangle|j\rangle is this:

K |\alpha\rangle |j \rangle = \sum_{\alpha'} K_{\alpha' \alpha} |\alpha\rangle |j\rangle

Since operators correspond to observables, K represents an observable of the first subsystem alone. Now, let's compute the expectation value of K in the composite state |\Psi\rangle:

\langle \Psi|K|\Psi \rangle = \sum_{\alpha, \alpha', j, j'} C^*_{\alpha', j'} C_{\alpha, j} \langle \alpha' | \langle j' | K | j \rangle |\alpha\rangle
= \sum_{\alpha, \alpha', j, j'} C^*_{\alpha', j'} C_{\alpha, j} K_{\alpha' \alpha} \delta_{j j'}
= \sum_{\alpha, \alpha', j} C^*_{\alpha', j} C_{\alpha, j} K_{\alpha' \alpha}

Now, if we define \rho_{\alpha \alpha'} to be: \sum_j C^*_{\alpha', j} C_{\alpha, j}, then we have:

\langle \Psi|K|\Psi\rangle = \sum_{\alpha, \alpha'} \rho_{\alpha \alpha'} K_{\alpha' \alpha} \equiv Tr(\rho K)

So for measurements only involving the first subsystem, the density matrix \rho is all that we need for computing expectation values. It's a mixed state, in general.

 

[Mario Rossi]

And so, does God confusing us throwing dices (indeterminism)? Does an electron exists when nobody looks at it? If no, why the wave function collapses (maybe this is too difficult for me like you said, if it is, skip it)?

 

[bhobba]

There is no assumption being made that there is any nonunitary collapse going on, it's purely a mathematical transformation that is necessary to keep your focus on the system of interest, as opposed to the entire universe.

Exactly, and that is why it doesn't solve the measurement problem - it just does FAPP - but that is not the same thing.

Still progress has been made in identifying the exact problem.

Thanks
Bill

 

[PeterDonis]

what do you think about this

It's a speculative proposal in an active, ongoing area of research. Which means discussion of it doesn't belong in this subforum. It might possibly be discussible in a new thread in the Beyond the Standard Model forum, if you're careful to limit discussion to how the proposal might be tested.

 

[PeterDonis]

Just want to convince myself everything is map

Who said that? "Everything" doesn't just include our physical models; it includes the things they are models of. The models are maps. What they are models of is territory.

Part of the problem here is vagueness in ordinary language. Consider the word "electron". Does it refer to a particular theoretical model--a part of the Standard Model of particle physics? Or does it refer to the thing, whatever it is, that the theoretical model is modeling? The word is used both ways, so the question "is an electron a map or territory?" doesn't have an answer until you specify what you are referring to by the word "electron". And, of course, once you've specified that, the answer to the question is obvious.

Physics consists of our models; that's why I said all physics is maps. But those models are models of something--or at least they are intended to be. (The models don't always turn out to be accurate, so it's possible that they don't actually refer to anything--for example, back when people thought combustion was due to phlogiston, "phlogiston" was an object in the models--the map--but there was nothing in the territory corresponding to it.)

The reason the map-territory distinction is made is to make it clear that our physical models are distinct from the things they are trying to model. That let's us take a step back, so to speak, and keep ourselves from making commitments based on our models that might be too broad. For example, quantum physics is a model--a map: it can be used to make very accurate predictions about the results of experiments. But there are multiple, mutually inconsistent interpretations of QM, which amount to multiple, mutually inconsistent claims about exactly what kind of territory the map is modeling. Those claims can't be resolved by experiment (because all of the interpretations make the same predictions for all experimental results), so they are off topic for discussion here, because here we focus on claims that can be resolved by experiment.

 

[Lord Jestocost]

And so, does God confusing us throwing dices (indeterminism)? Does an electron exists when nobody looks at it? If no, why the wave function collapses (maybe this is too difficult for me like you said, if it is, skip it)?

Up to now, no serious physicist can answer these questions. Maybe, you will get various answers, depending on the respective interpretation which the responding one is adhering to (very often some implicit, unprovable assumptions are even not disclosed). Nevertheless, all interpretations of quantum theory are myths, or crutches, which should help us to form ideas and conceptions about what’s occurring at the quantum level and which might, perhaps??, help us to make experimentally provable predictions. Myths which - to my mind - centre at the end around one single question: “Which came first — the observer or the particle?” (Vanna Bonta, in "Flight: A Quantum Fiction Novel").

With respect to this, the instrumentalist’s attitude is the most honest one: The formalism of quantum theory provides nothing but calculational recipes to predict the probabilities of various directly observed macroscopic outcomes; the theory is thus about relations and correlations between – so to speak – observable spatial and temporal patterns of “clicks”; about the linkage of pointer readings with pointer readings.

 

[Mario Rossi]

“Which came first — the observer or the particle?”

Yes, this is the main answer. If we try to make an hypothesis on the "came first the observer", what can we think? The universe is prior to the observers, right? If not, so the Big Bang theory is wrong and we must search not the beginning of the universe but the beginning of the observer.

 

[Mario Rossi]

I found a theory made by Penrose and Hameroff, it's called ORCH-OR, what do you think about it?

 

[PeterDonis]

I found a theory made by Penrose and Hameroff, it's called ORCH-OR, what do you think about it?

Please give a specific reference.

 

[Mario Rossi]

Please give a specific reference.

https://en.wikipedia.org/wiki/Orchestrated_objective_reduction

 

[PeterDonis]

https://en.wikipedia.org/wiki/Orchestrated_objective_reduction

This is a speculative proposal which has not been confirmed. There have been some experiments which the proponents claim support their proposal, but as far as I can see those claims are not generally accepted.

 

[PeterDonis]

This thread is veering off into philosophy and speculation and is now closed.