A question on MWI (for Dmitry67)

[Demystifier]

To answer the question precisely we need to find an exact solution of the equation of the wavefunction for the whole universe close to t=0

Completely agree.

 

[Count Iblis]

It is even less clear why a simulation of a human observer (not sharing all physical properties of a true human observer) WOULD qualify as a true human observer.

If you wish you can consider a thought experiment in which you do simulate all the physical degrees of freedom using a quantum computer. The computational states of the quantum computer are then related to the precise physical states of a human being living in some isolated box via a unitary transformation.

 

[Demystifier]

If you wish you can consider a thought experiment in which you do simulate all the physical degrees of freedom using a quantum computer. The computational states of the quantum computer are then related to the precise physical states of a human being living in some isolated box via a unitary transformation.

But then you also simulate decoherence existing in a true human observer. But I don't think that you can simulate decoherence without actual decoherence. So there is decoherence in this quantum computer. Of course, the computer as a whole is unitary and described by a pure state, while decoherence refers to subsystems only. In fact, I don't see any essential difference between this simulation of a human and an actual human. So what is the point of making this simulation anyway?

 

[hamster143]

The definition of a branch is closely tied with slicing up of the Hilbert space of the universe into smaller Hilbert spaces of its interacting constituents (which is, obviously, non-unique). If you view the big Hilbert space as a tensor product of a number of smaller spaces, that gives you a natural set of basis states and an evolution Hamiltonian, which, when applied to any basis state, will likely turn it into a superposition, thus "branching" it.

There is a preferred slicing that identifies conscious beings as basis states. It is convenient because these states are relatively stable. Under the action of Hamiltonian, a conscious being can remain the same (be an eigenstate), evolve in a slow and continuous manner (move), or occasionally undergo discrete branchings when it acquires new knowledge.

 

[Count Iblis]

But then you also simulate decoherence existing in a true human observer. But I don't think that you can simulate decoherence without actual decoherence. So there is decoherence in this quantum computer. Of course, the computer as a whole is unitary and described by a pure state, while decoherence refers to subsystems only. In fact, I don't see any essential difference between this simulation of a human and an actual human. So what is the point of making this simulation anyway?

Suppose that the quantum computer simulates everything that happens inside a hypotetical closed box containing a human on which certain boundary conditions are imposed. There is then no decoherence of the box as a whole. This box can be simulated exactly by a quantum computer. If the box is seen to be unphysical, then you can replace it with an entire closed universe.

Then, the point is that the quantum computer that simulates it can have any preferred basis. For the quantum compoutation to work the decoherence time scale must be much longer than the simulation time. So, any "real" decoherence is irrelevant; you cannot define the sector of the observer by looking at decoherence.

However, the quantum computer does simulate correctly the effective decoherence. If the observer in the box were to make some quantum coherent system, then that system would be represented by some qubits and the environment by other qubits. They would then interact according to a unitary time evolution, leading to effective decoherence of the subsystem.

 

[Demystifier]

Count Iblis, you might be interested in this:
https://www.physicsforums.com/showthread.php?t=347164

 

[Dmitry67]

The definition of a branch is closely tied with slicing up of the Hilbert space of the universe into smaller Hilbert spaces of its interacting constituents (which is, obviously, non-unique). If you view the big Hilbert space as a tensor product of a number of smaller spaces, that gives you a natural set of basis states and an evolution Hamiltonian, which, when applied to any basis state, will likely turn it into a superposition, thus "branching" it.

There is a preferred slicing that identifies conscious beings as basis states. It is convenient because these states are relatively stable. Under the action of Hamiltonian, a conscious being can remain the same (be an eigenstate), evolve in a slow and continuous manner (move), or occasionally undergo discrete branchings when it acquires new knowledge.

So, in the very beginning entropy was very low. We can think about the unitary evolution of the "wavefunction fo the unvierse".

That wavefunction became more and more chaotic in some sense (at the same 'cosmological' time). However, the number of different states was low and matter was very hot. Event we can technically use ANY basis for the decoherence, if did not make any sense because these systems were so hot that they could not posses any stable degrees of memory, which can be considered as 'memory' of that system

We can not talk probably about the decoherence until the very first primitive systems (hardrons, primitive nuclei) emerged. But stillthere were very primitive. As time frame of decoherence depends on the number of degrees of freedom, the decoherence at that time was very slow.

Until some time the whole evolution of the universe should be calculated as unitary and global, without any division to branches.

Is this correct?

 

[Count Iblis]

Count Iblis, you might be interested in this:
https://www.physicsforums.com/showthread.php?t=347164

Thanks, I'll listen to the talk!

 

[Demystifier]

Is this correct?

Perhaps, but not if the initial condition is perfectly symmetric.

 

[Count Iblis]

Nice try! However, a superposition of nontrivial structures does not necessarily need to contain nontrivial structures. Indeed, in the case above it doesn't.

Take for example a constant function
f(x)=1 for all x
You can write this function as a sum of two (or more) very complicated functions. These functions may have nontrivial structures. Yet, the constant function above does not contain nontrivial structures. It is perfectly clear when f(x) represents some classical quantity. And the idea of MWI is that the wave function is also, in a certain sense, a "classical" quantity.

I think one needs to have an unambiguous recipe to define what the "nontrivial structure content" is. My opinion is that one has to expand the function in a certain preferred basis to extract this.

 

[Dmitry67]

Perhaps, but not if the initial condition is perfectly symmetric.

Why perfectly symmetric initial conditions in MWI can not evolve into a symmetric superposition of asymmetric states?

Take a box with 2 neutrons - one on the left and one on the right. The inital state is symmetric.
Now after a while left (or right) neutron decays.
in MWI it means that there are 2 branches (in fact there are much more branches) - left decayed first, right decayed first.

 

[hamster143]

It is perfectly okay to have asymmetry arise out of symmetry. There's even a term for it - spontaneous symmetry breaking :) Think phase transitions.

We can not talk probably about the decoherence until the very first primitive systems (hardrons, primitive nuclei) emerged. But stillthere were very primitive. As time frame of decoherence depends on the number of degrees of freedom, the decoherence at that time was very slow.

Until some time the whole evolution of the universe should be calculated as unitary and global, without any division to branches.

Is this correct?

In some sense, universe itself has a memory. Large-scale structure of the universe depends on fluctuations in inflaton field during inflation. Electroweak angle (and therefore things like Fermi constant and half-lives of most radioactive isotopes) depends on the outcome of electroweak symmetry breaking, which is different in every universe.

I believe that the term "decoherence" is dangerously misleading, imprecisely defined and should not be used too often.

 

[Dmitry67]

It is perfectly okay to have asymmetry arise out of symmetry. There's even a term for it - spontaneous symmetry breaking :) Think phase transitions.

Yes, but the interpretation is the spontaneous symmetry breaking is interpretation-dependent.

In deterministic single history theory it is not possible.
In the deterministic single history theory WIT HIDDEN VARIABLES (BM) assymetry is pre-coded in the initial conditions, but it is undetectable until the actual event.
In non-deterministic theories (CI, TI) initial conditions can be very simple, and randomness is responsible for symmetry breaking.
In MWI the "wavefunction of the universe" is symmetric because theory is deterministic, but different "branches" can break the symettry locally in a globally symmetric way

 

[Demystifier]

I think one needs to have an unambiguous recipe to define what the "nontrivial structure content" is. My opinion is that one has to expand the function in a certain preferred basis to extract this.

There is no preferred basis in MWI.

 

[Dmitry67]

There is no preferred basis in MWI.

Correct

It had recently hit me: while MWI is deterministic and objective, the 'Observer' is not defined in MWI objectively. Loss of realism we witness is not a result of the fact that nature is not realistic, but it is a projection of our own non-realism.

Take an observer Bob. Should we include his hair into the 'state of a system with microscopically many degrees of freedom'? What’s about molecules of H2O evaporating from his skin? A food inside his stomach? All these options give different 'preferred basis'

I would like to say that these bases are macroscopically consistent. Unfortunately it is difficult to define that consistency. It is not only branch-dependent, but branch is defined based on the decoherence, and decoherence uses basis.

 

[Demystifier]

Why perfectly symmetric initial conditions in MWI can not evolve into a symmetric superposition of asymmetric states?

Take a box with 2 neutrons - one on the left and one on the right. The inital state is symmetric.
Now after a while left (or right) neutron decays.
in MWI it means that there are 2 branches (in fact there are much more branches) - left decayed first, right decayed first.

This is not symmetric enough, in the sense that there are MANY DIFFERENT initial states that may lead to branchings of this sort. This is in contrast with your idea that the structures should emerge from a UNIQUE (i.e., much more symmetric, like a ground state) initial condition.

Furthermore, if you allow such a smaller degree of symmetry of the initial condition, then BM can also describe structures.

To remind you, you have argued that MWI is better than MB because the former leads to structures with a very simple initial condition. What I am showing to you is that such an advantage of MWI over BM does not exist.

 

[Dmitry67]

This is not symmetric enough, in the sense that there are MANY DIFFERENT initial states that may lead to branchings of this sort. This is in contrast with your idea that the structures should emerge from a UNIQUE (i.e., much more symmetric, like a ground state) initial condition.

I don't understand your logic.
I say that simple and SYMMETRIC conditions CAN produce the asymmetric state.
You say: there are MANY OTHER initial conditions which can produce the same ASSYMETRY.
I agree. So what?

 

[Count Iblis]

There is no preferred basis in MWI.

What I mean is a basis in which the operators describing conscious experiences for some given observer is diagonal.

 

[Count Iblis]

Correct

It had recently hit me: while MWI is deterministic and objective, the 'Observer' is not defined in MWI objectively. Loss of realism we witness is not a result of the fact that nature is not realistic, but it is a projection of our own non-realism.

Take an observer Bob. Should we include his hair into the 'state of a system with microscopically many degrees of freedom'? What’s about molecules of H2O evaporating from his skin? A food inside his stomach? All these options give different 'preferred basis'

I would like to say that these bases are macroscopically consistent. Unfortunately it is difficult to define that consistency. It is not only branch-dependent, but branch is defined based on the decoherence, and decoherence uses basis.

It is easier if you replace Bob by a classical computer that is assumed to be conscious and able to process information about the real world. Then it is very clear that what counts is (at most) the classical computational state of the computer that you can specify by a string of ones and zeroes.

 

[Demystifier]

You say: there are MANY OTHER initial conditions which can produce the same ASSYMETRY.
I agree. So what?

So you don't know what the initial condition is. So the creator of the universe had a lot of choice. So, contrary to your claim, MWI is not better than BM in this regard.