Undergrad MWI and path of single electron

[PeterDonis]

What happens to the other awareness where you see other hits?

This should be obvious; just do the same thing for subsequent measurements as we did for the initial measurements.

For example, suppose we measure the spins of two electrons (call them electrons 1 and 2) in succession, both in the up/down direction. The total evolution looks like this (hopefully the notation is clear):

$$
\Psi_0 = \left( a_1 \vert u_1 \rangle + b_1 \vert d_1 \rangle \right) \left( a_2 \vert u_2 \rangle + b_2 \vert d_2 \rangle \right) \vert R_1, R_2 \rangle \vert O_{R1}, O_{R2} \rangle
$$
$$
\rightarrow \Psi_1 = \left( a_2 \vert u_2 \rangle + b_2 \vert d_2 \rangle \right) \left( a_1 \vert u_1 \rangle \vert U_1, R_2 \rangle \vert O_{U1}, O_{R2} \rangle + b_1 \vert d_1 \rangle \vert D_1, R_2 \rangle \vert O_{D1}, O_{R2} \rangle \right)
$$
$$
\rightarrow \Psi_2 = a_1 a_2 \vert u_1 \rangle \vert u_2 \rangle \vert U_1, U_2 \rangle \vert O_{U1}, O_{U2} \rangle + a_1 b_2 \vert u_1 \rangle \vert d_2 \rangle \vert U_1, D_2 \rangle \vert O_{U1}, O_{D2} \rangle \\ + b_1 a_2 \vert d_1 \rangle \vert u_2 \rangle \vert D_1, U_2 \rangle \vert O_{D1}, O_{U2} \rangle + b_1 b_2 \vert d_1 \rangle \vert d_2 \rangle \vert D_1, D_2 \rangle \vert O_{D1}, O_{D2} \rangle
$$

In other words, each time a measurement happens, it creates another entanglement. So after two measurements, we have an entangled state containing four terms, one corresponding to each possible combination of the results of the two measurements.

 

[mieral]

That's because the MWI, at least in the form in which it purports to explain our everyday observations, in which we observe measurements to have definite single results, has to explain how that can be the case given the entangled state that comes out of a measurement. The explanation is that, when we write down such an entangled state, for example, this one:

$$
\Psi_\text{final} = a \vert u \rangle \vert U \rangle \vert O_U \rangle + b \vert d \rangle \vert D \rangle \vert O_D \rangle
$$

where $u, d$, $U, D$, and $O_U, O_D$ are, respectively, the eigenstates of the electron (up/down), the measuring device (measured up/measured down), and the observer (observed up result/observed down result), the observer states have to include conscious experience--so, for example, $O_U$ has to mean "the observer consciously experienced seeing the measuring device give an up result", and similarly for $O_D$ with down. So this entangled state describes an entanglement that includes two different conscious experiences in it, which are separate and cannot communicate at all with each other, but it's still one single state of the overall system. That's what the MWI has to claim, in order to explain our everyday experience of measurements. (And it's also where all the talk about "splitting of worlds" and so forth comes from.)

You mentioned this critical passage: "So this entangled state describes an entanglement that includes two different conscious experiences in it, which are separate and cannot communicate at all with each other, but it's still one single state of the overall system".

There are two different conscious experiences within the single state of the overall system. Yet you don't want to say the persons are duplicated. So it's the same person can both feel sad and happy but the overall system is still one single state. Let's say if the hit of the double slit detector screen in the left half side.. you are sad, if the hit of the screen is in the right half side, you are happy. And the result is right half side detector hit, so you are happy. However, the other you is sad because it's left half side hit. Yet you don't believe you are duplicated. Maybe the rule is this. Potential/Hamiltonian can never be duplicated, yet it can experience different entanglement. So you as Peterdonis is never duplicated.. yet there is another side of you that is sad because of the left side hit that you didn't see (because you are seeing right side hit which made you happy). This is bewildering. Hope other Many Worlders can come and state if they agree with this. I can't imagine another side of me having other experiences in other branches yet I'm still one person and not duplicated. This seems contradictory. I'm still absorbing it though.. so don't worry.

Dear other Many Worlders, what do you think?

No.
Any author that says that the MWI can explain our everyday experience of measurements. See above.

 

[PeterDonis]

There are two different conscious experiences within the single state of the overall system. Yet you don't want to say the persons are duplicated.

Because as far as the physics we know is concerned, the person--the quantum state--is not duplicated; it's just entangled. I'm personally not a proponent of the MWI, so I'm not saying I agree with the claim about conscious experience. I'm just saying that the claim about conscious experience is necessary to reconcile the MWI with our actual observations. We don't have a quantum theory of consciousness, so nobody has any way of knowing whether the claim about conscious experience is actually consistent with the quantum state being entangled. If it turns out it isn't, then something will have to give--either the MWI will be falsified, or something about the quantum state must be different from what we've been saying. (The second alternative, however, would require a wholesale change in all aspects of QM, because what we've been saying about the quantum state is a simple consequence of unitary evolution, which is one of the most fundamental aspects of QM as we understand it.)

 

[mieral]

Let's uncomplicate it by treating an atom... the electrons in the atoms are entangled to the nucleus. So you are right the different engenvalues don't mean the atoms are duplicated many times. There is only one nucleus and one electronic cloud and the potential and Hamiltonian don't get duplicated. So entangled electrons are something unclassical because each component don't have a state and only the whole system has state and we can't imagine what it would be like to be entangled electrons. That's understandable.

But we complicate it when we used a camera to view the atoms. We can say the camera is entangled to the atoms such that the equivalent of say spin up and spin down would form different branches. But this shouldn't happen.. it's more logical you can't make the camera become entangled to the atoms eigenvalues. Why do we believe it is possible at all for the camera and atoms to get entangled? Therefore the correct interpretation is one where they shouldn't be able to get entangled in the first place.

Imagine entangled electrons looked like smeared ghosts. Since a camera and atoms can't be smeared ghost.. then no entanglement should be possible between camera and atoms. What interpretation disallowed such entanglement?

 

[zonde]

There are two different conscious experiences within the single state of the overall system. Yet you don't want to say the persons are duplicated. So it's the same person can both feel sad and happy but the overall system is still one single state.

This phrase "within the single system" doesn't seem quite right. I think it should be more like this:
There is single Hilbert space where two conscious experiences are two different directions in that Hilbert space. If state vector is not exactly in one of those two directions we can write the state vector as superposition of two conscious experiences. Then two conscious experiences get fractional probability amplitudes. So if we want to claim that both possibilities are realized then we have to give different interpretation for probability amplitudes squared. Some kind of interpretation that allows for both states to coexist with reduced weight.

 

[bhobba]

No, it isn't. We don't observe the position of every atom in the cat..

Of course we don't - but, as you allude to, we can observe parts like the heart, blood, and lung and they have positional behavior entirely different in alive and dead cats. But point taken - its very hard to disentangle a cat from its environment (eg it must breathe air) and that is at the atomic level which we don't directly observe.

This is self-contradictory.

Hmmmm. I was thinking in terms of a mixed state ∑p1|a><a| + p2|d><d| where |a> is the alive state and |d> the dead state. The decoherence inherent in being a cat (ie its entangled with the environment) leads to the mixed state. It also leads to the rather 'interesting' issue of exactly what is the alive state and dead state because of that entanglement ie it can't be alive unless it breaths air. It reminds me of Feynmans discussion on the surface of a table in his lectures. The closer you examine it the less clear exactly what that surface is becomes. Or have I somehow goofed here?.

Thanks
Bill

 

[bhobba]

Leave them there. One good textbook is what you need. The different terms never go away - that's what makes MWI what it is.

For the OP, just as a simple example you have two systems that can be in state |a> and |b>. If system 1 is in state |a> and system 2 in |b> then that is written as |a>|b> and conversely we have |b>|a>. Now according to the principle of superposition you can have a superposition of these two states say 1/root(2) |a>|b> + 1/root(2)|b>|a>. The systems are called entangled. If you chug through the (the reference I give at the end does it) math you find something interesting - suppose we observe just system 1 then it behaves as if its in the following mixed state 1/2 |a><a| + 1/2 |b><b|. Mixed states are different to superposition's. One way to create a mixed state is to present states for observation with the probability of the number in front of the terms in the mixed state. In the forgoing that would mean the system 1 is in state |a> 1/2 the time and state |b> the other half. But that is not how this mixed state was created - it was created from entanglement. The thing is we can't tell the difference. The system taken as a whole is still in superposition - that never goes away - but the subsystems behave differently due to the entanglement. This is a very simple illustration of decoherence (its not true decoherence which involves entanglement with such a large number of things it can't be disentangled) but helps understand what's happening.

This thread is at the I level, THE reference at that level where all this is explained in detail is:
https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20

Thanks
Bill

 

[bhobba]

Dear other Many Worlders, what do you think?

I am not a MW'er but simply out of interest have studied it.

If you want to study the detail here in the book I studied:
https://www.amazon.com/dp/0198707541/?tag=pfamazon01-20

Its very theorem, proof, theorem proof in style.

Its also very very elegant.

What do I think of what Peter says - from my study its pretty well spot on, although rather non intuitive.

Thanks
Bill

 

[PeterDonis]

We can say the camera is entangled to the atoms such that the equivalent of say spin up and spin down would form different branches. But this shouldn't happen.

Why not? In order for the camera to tell us anyting about the atom, it has to become entangled with the atom. That's how measurement works.

the correct interpretation is one where they shouldn't be able to get entangled in the first place.

No, because on this interpretation, measurement would be impossible, and we could never have any information about anything.

Imagine entangled electrons looked like smeared ghosts.

No, don't "imagine" anything. Look at the actual math. Trying to "imagine" how things are in the quantum world, when you don't understand the math, is a fool's errand.

 

[PeterDonis]

I was thinking in terms of a mixed state

Mixed states can't be produced by unitary evolution from pure states, and according to the MWI, the state of the entire system is always pure. So that's the viewpoint I have been taking in this thread. You are correct that experimentally we can't tell whether the state after a measurement is the pure superposition state I have been using here, or the mixed state you were thinking of. But the MWI says that the state is the pure one.

 

[PeterDonis]

The OP question has been answered, multiple times. Thread closed.