Aspect/Innsbruck Interpretation which respects SR locality

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Put your consciousness also into the wavefunction--what's left now?In fact when you put yourself into the wavefunction,you can't ask your consciousness to stay away!
I realize one can go on and on discussing this issue but never reach a conclusive conclusion.
 

vanesch

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gptejms said:
Put your consciousness also into the wavefunction--what's left now?In fact when you put yourself into the wavefunction,you can't ask your consciousness to stay away!
Well, first I would like to point out that the idea is to find an interpretation that goes with a formalism, so I'm not saying here "what is real", I'm saying only what is a possibly consistent "story" that goes with the usual rules of QM, *if you insist on having such a story*. You can also say that QM is just a theory which describes statistical properties of observations without any interpretation of "what happens physically". I don't really like that approach - although it is a logically possible one - because when you are modelling you QM calculations and so on, you like to think of "physical things out there" you're dealing with, and not some abstract "statistics generator".

When you say "you put yourself in the wavefunction", I can argue that I put my body in the wavefunction, with my brain and everything. But if you consider that a consciousness is a non-material item, then it has no physical description consisting of particles or fields, but is only _associated with a physical system_. And I simply say that *that* non-material item, call it "mind" or "soul" or "consciousness" or whatever, is NOT described by the unitary evolution that describes all matter in the universe, but subscribes to the OTHER postulate of QM, namely the Born rule.
You can write a hamiltonian of your brain, but you cannot write a hamiltonian of your consciousness.

I realize one can go on and on discussing this issue but never reach a conclusive conclusion.
I know, that's the danger. But the nice thing of this approach is that
1) it doesn't contain any inconsistencies, as does the "measurement" versus "physical process" in the "standard" Copenhagen description (namely, why should a physical process sometimes apply the "measurement" postulate, and sometimes the "unitary" postulate ?)
2) you don't need to change anything to the ordinary rules of QM, in that you still have the Born rule, you still have unitary evolution for all physical processes. True Everettians try to _deduce_ the Born rule from the unitary part, but they always have to introduce extra assumptions. And the Copenhagen view should add a theory on why certain physical processes "collapse" the wavefunction, and don't simply work with their hamiltonian.

Ok, the price to pay is that we have to consider now that there is some special physics associated with "mind" and so on, and that we have to consider that what our mind observes is only part of what is "reality" and not all of it.

But there's an extra bonus which I also like: in a MWI like scenario as the one I present, there is no "spooky action at a distance" in the real world, it is just something that is induced by the part of reality which is observed by your mind, and as your mind is attached to a physical structure (say, your brain), it cannot move FTL. As such, there's no reason for any underlying non-locality in physics.

So again, the point is not that I want to talk about what exactly is consciousness or so. It is that it is a story that goes with the standard QM formalism, without any additions, and which permits me to "demystify" a lot of quantum fuzz, such as EPR situations, quantum erasers and so on.
I don't know of any OTHER way of seeing QM where you 1) are not somehow introducing "extra unknown physics you will have to work out later" or 2) some arbitrariness in the concepts you introduce (such as "measurement").

cheers,
Patrick.
 
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vanesch said:
You can also say that QM is just a theory which describes statistical properties of observations without any interpretation of "what happens physically". I don't really like that approach - although it is a logically possible one - because when you are modelling you QM calculations and so on, you like to think of "physical things out there" you're dealing with, and not some abstract "statistics generator".
As I've been learning a little about the decoherent histories approach to quantum theory, I've been reading that the finest-grained description of a series events in quantum theory almost always has interference terms between all the different possible histories. As a result, I'm not entirely sure what the "physical things out there" actually are anymore or even in the theory. :smile:

It seems almost everything is doing the equivalent of the "going through both slits at the same time" trick of the two slit experiment... but a whole lot worse. :bugeye:
 
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vanesch said:
When you say "you put yourself in the wavefunction", I can argue that I put my body in the wavefunction, with my brain and everything. But if you consider that a consciousness is a non-material item, then it has no physical description consisting of particles or fields, but is only _associated with a physical system_. And I simply say that *that* non-material item, call it "mind" or "soul" or "consciousness" or whatever, is NOT described by the unitary evolution that describes all matter in the universe, but subscribes to the OTHER postulate of QM, namely the Born rule.
I am very skeptical about this consciousness thing,but I don't want to enter into a discussion on it right now.I repeat my earlier question which went unanswered.An atom goes from an excited state |e> to the ground state |g>---its state while in transit is a(t)|e> + b(t) |g>,where a(0)=1,b(0)=0.So the atom goes into a superposition(from the initial state |e>) and then leaves the superposition---all via a unitary transformation.So your argument(earlier post) that a unitary transformation can't break a superposition(which though looks reasonable) doesen't seem to hold---kindly comment.
 

vanesch

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gptejms said:
I am very skeptical about this consciousness thing,but I don't want to enter into a discussion on it right now.
I can understand that. It isn't really essential in the discussion, in fact. Replace it by the "observing experience" or something of the kind. Indeed, in a relative-state view, there are no objective observations, and what is experienced as such depends on what entity is supposed to experience the observation. In the rawest state, it is a kind of memory of experienced events.

I repeat my earlier question which went unanswered.An atom goes from an excited state |e> to the ground state |g>---its state while in transit is a(t)|e> + b(t) |g>,where a(0)=1,b(0)=0.So the atom goes into a superposition(from the initial state |e>) and then leaves the superposition---all via a unitary transformation.So your argument(earlier post) that a unitary transformation can't break a superposition(which though looks reasonable) doesen't seem to hold---kindly comment.
That is because you view the atom as a system, while it is interacting with something else. Indeed, you cannot have that an atom in isolation goes from an excited state to a ground state. By definition, a stationary state (such as an excited state) remains forever in that state.
You get transitions because of the coupling to the EM quantum field, and what YOU are describing looks like the local density matrix description, limited to the atom, of the bigger system "atom + EM".

So, "in the beginning" you need at least a photon in your EM field, and an atom in the ground state. What I will write here is "in principle". Nobody (knows how to) do that this way, and uses approximations to do the calculations.

|start> = |1 photon> |g>

Note that this is not a stationary state of the coupled system, otherwise there would be no interaction, and hence no excitation or decay.

So the above state must be rewritten in stationary states which are entanglements between the atom and the field (because you have to diagonalize your total hamiltonian: the |start> state is not an eigenstate of the total hamiltonian of atom + EM + interaction).

So we rewrite this as:

|start> = A |energy 1> + B |energy 2> + C |energy 3> + ....

Where |energy 1> is an entangled state of all the |n photon> states and all the ground and excited states of the atom, and |energy 2> also (but in different proportions)

A = <start| energy 1> ; B = <start | energy 2> ....

This can then evolve into:

|intermediate t> = A exp (i t E1) |energy 1> + B exp(i t E2) |energy 2> ....

and it is NOT (as you seem to suggest) necessarily factorizable in a product of an atom state (such as u |g> + v |e>) and an EM field state. I'm pretty sure you remain in a kind of entangled state, but if you wait long enough, and if the excited state is "rather" stable, you might hope that this evolves into something close to:

|intermediate 2> ~ |0 photon> |e> + small terms.

Now the atom is "excited".

The desexcitation will then be simply a further evolution of the state:
A exp (i t E1) |energy 1> + B exp(i t E2) |energy 2> ....

and for very long times, you will end up again in a state that is close to:

|1 photon> |g>

But note that the whole time, we've never left the superposition:

A exp (i t E1) |energy 1> + B exp(i t E2) |energy 2> ....


If I can give you a rough analogy: if you consider a pulse, which is fourier transformed, it looks a bit as if you're saying: hey, a pulse cannot be composed of sine waves, because a long while before it, I have no signal, so where are your sine waves, and a long while after the pulse, the same. Nevertheless, during my pulse, I can understand that you build it up with sine waves. Well, here it is the same. The sine waves are the stationary states of the overall system, and their composition, all along time, remain the same. Your "initial, intermediate and final" views are particular stretches of your function in the time domain. It can be flat (state |g> or |e>) or a pulse ("superposition a|g> + b|e>"). But all this is just a result of the different phase factors in front of the stationary states of the overall system.

cheers,
Patrick.
 
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Again wonderfully put and very convincing.Can you do an actual calculation for the full system evolution assuming some model (bath of harmonic oscillators coupled to a particle) and show that the wavefunction for the total system actually oscillates in time between different particle states?Even if you can't, nevermind---it looks like the only reasonable thing that can happen.

For the reduced description,do we conclude that the evolution is non-unitary?
 
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[tex]
Let me try to answer my own question:-is the reduced description/evolution unitary?The reduced density matrix description is equivalent to the following quantum Langevin equation:-
\begin{equation}
\frac{dp}{dt} = -V^{\prime}(x) + F(t) - \gamma p,
\end{equation}

where p is the momentum of the particle in potential V(x) coupled to a bath of harmonic oscillators whose fluctuations in the equilibrium state(i.e. when the bath was decoupled from the particle) are encoded in F(t), and the last term gives the average friction the bath exerts on the particle(assuming the memory function to be a delta function).
If F(t) were zero then the commutator [x,p] would decay off in the manner
\begin{equation}
[ x,p ] = \iota \hbar exp(-\gamma t),
\end{equation}
[/tex]

once the coupling between the particle and bath were switched on.So this evolution would be non-unitary.But the term F(t) ensures that the overall evolution is unitary.

In the case of an atom interacting with e.m. field,the constant friction term is its interaction with vacuum(spontaneous decay).F(t), I guess, should be fluctuations of the e.m. field over and above the vacuum.
 
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