# Proof of correctness of MWI

• Count Iblis

#### Count Iblis

This is similar to an argument made by David Deutsch. The argument appeals to artificial intelligence that can be implemented by a quantum computer. So, the first part of the argument is that however the brain works, it is ultimtely formally describable using a finite number of bits. Therefore it can be implemented by a computer and thus also by a quantum computer.

The different branches of the observer correspond to the different projections of the quantum computer in the |0>, |1> basis of the qubits. Suppose that this observer measures the state of a qubit in the |0>, |1> basis. Let's call this qubit a "spin" to avoid confusion with the qubits that are part of the observer.

Then what we can achieve is the following.

1) We start with the spin in state |0>, then we rotate it to
1/sqrt(2) [|0> + |1>]

2) The observer then does a measurement in the |0>, |1> basis, which causes a qubit (that was initiallized to |0>) of his memory to be entangled with the state of the spin. This is performed using the controlled NOT gate. Also another qubit of his memory that was initialized to |0> is flipped to |1>. That qubit detects that a measurement has taken place (but not the result of the measurement).

3) The observer then applies the controlled NOT gate again, reversing the measurement. Then he flips another qubit that was initialized to |0> to |1>, which records the fact that the memory qubit that registered the spin has been erased.

4) At this stage the spin is back in the state 1/sqrt(2) [|0> + |1>]. The observer can verify this by applying the inverse rotation that he appied to the spin at the start, rotating it back to the state |0>. A measurement of the spin by the observer (or some other observer) will yield zero with 100% probability.

Now, the fact that the observer knows that he measured the spin in the |0>, |1> basis when it was rotated to 1/sqrt(2) [|0> + |1>] means that in the CI interpretation, the spin's state should have collapsed to either |0> or |1>. Only one of the branches really exists. Then, applying the inverse rotation won't bring the spin back to the state |0>, instead it will be a mixed state of

1/sqrt(2) [|0> + |1>]

and

1/sqrt(2) [|0> - |1>]

Measuring the spin again in the |0>, |1> basis must thus yield a 50% probability of finding it to be |0>.

So, the CI interpretation makes a different prediction than the MWI. Moreover, since the spin can be measured by an external observer, the CI interpretation predicts non-unitary time evolution for an isolated system that can be verified by an external observer.

The obvious CI rebuttal would seem to be
Sure, you can call it a measurement, but that doesn't mean it actually is one. In fact, it's reversibility is proof that it isn't.​

I can also envision CI proponents making the additional claim
Observers and measuring devices aren't within the domain of validity of QM, so your toy example doesn't really say anything about them.​

The obvious CI rebuttal would seem to be
Sure, you can call it a measurement, but that doesn't mean it actually is one. In fact, it's reversibility is proof that it isn't.​

I can also envision CI proponents making the additional claim
Observers and measuring devices aren't within the domain of validity of QM, so your toy example doesn't really say anything about them.​

But how does the CI proponent explain the fact that he himself can have a memory of having measured the wavefunction of a spin that verifiably hasn't collapsed in the basis he measured it?

But how does the CI proponent explain the fact that he himself can have a memory of having measured the wavefunction of a spin that verifiably hasn't collapsed in the basis he measured it?
He wouldn't; he would accuse you of asking a loaded question. He has not agreed with your hypothesis that your experiment constitutes (what CI calls) a measurement.

Why do you think 'artificial intelligence', human memory, simulations thereof, computer simulations, or quantum computers would be the least bit relevant here? I think you're just obfuscating the issue to an extent where you've managed to confuse yourself.

They're called 'interpretations' for a reason; they're not scientific theories because they're not testable. The MWI in particular is untestable by definition since a universe external to our own can never be proven or disproven. You might as well say 'God did it.' (which is popular, but not a scientific theory either).

He wouldn't; he would accuse you of asking a loaded question. He has not agreed with your hypothesis that your experiment constitutes (what CI calls) a measurement.

Will the CI proponent say that a perfectly isolated quantum computer will always under a unitary time evolution?

Why do you think 'artificial intelligence', human memory, simulations thereof, computer simulations, or quantum computers would be the least bit relevant here? I think you're just obfuscating the issue to an extent where you've managed to confuse yourself.

They're called 'interpretations' for a reason; they're not scientific theories because they're not testable. The MWI in particular is untestable by definition since a universe external to our own can never be proven or disproven. You might as well say 'God did it.' (which is popular, but not a scientific theory either).

The MWI does not postulate "many worlds", it merely postulates unitary time evolution ("many worlds" is how we can visualize the unitary tme evolution, but it is not a priori assumed). The CI postulates non unitary time evolution associated with the interaction of humans with physical systems.

So, this is a clear difference that can in principle be measured.

They're called 'interpretations' for a reason; they're not scientific theories because they're not testable.
The untestability is not for the reason you think -- it's simply a matter of practicality. CI predicts that "measurements" cannot be reversed. MWI predicts that all interactions can be reversed. (Including those interactions CI would call a "measurement") In principle, this divergence could be tested -- the only reason it has not is that the experiment would be far too difficult to engineer.

The toy example of using a CNOT gate as a "measuring device" is an experiment that is not too difficult to engineer -- and I'm pretty sure it has been done, conclusively demonstrating that it does not invoke a collapse.

Of course, that does not disprove CI -- CI is somewhat vague about what is and is not a "measurement", and all this experiment would prove is that a CNOT gate is not one.

And, of course, such an experiment would do nothing to distinguish between MWI and other decoherence-based interpretations.

since a universe external to our own

The MWI does not postulate "many worlds", it merely postulates unitary time evolution ("many worlds" is how we can visualize the unitary tme evolution, but it is not a priori assumed). The CI postulates non unitary time evolution associated with the interaction of humans with physical systems.

So, this is a clear difference that can in principle be measured.

I'd prefer to not mix the two different views.

- The collapse is the inside view, it is what the observer sees.
- A second observer, observing observer 1 + the environment does would for sure describe it differently.

Another opinion on the consistency of different observers descprition of "reality", Dmitry67 alsed a good question here, which relates to this indirectly:
"The role of false info in the Copenhagen Int. "

I'm not a strict CI, but I think I am closer to CI than some others here. My view is more than interpretations, it suggest a reformulation of QM, where QM is emergent. But the collapse isn't the problem.

/Fredrik

I think questions like "is <X> real?" does not make any sense.
Especially if you believe in MUH

true MWI'ers are denialists, claim their interpretation is a representation of a realist interpretation, howver it really breaks down easy.
It can't deal with probability, so all our observations really contradicticts MWI at this point.
No preferred frame.
all these problems, it's a retarde dinterpretation.

A mix between Bohm and some ensemble view is more likely.

1 It can't deal with probability, so all our observations really contradicticts MWI at this point.
2 A mix between Bohm and some ensemble view is more likely.

Regarding 1,
http://en.wikipedia.org/wiki/Many-worlds_interpretation
The many worlds interpretation has, controversially, been seen by some as offering the possibility of deriving the Born rule and the appearance of quantum probabilities from simpler assumptions. In fact, this was first attempted by Everett and DeWitt in the 1950s. In a September 2007 conference[11] David Wallace reported on what is claimed to be a proof by Deutsch and himself of the Born Rule starting from Everettian assumptions[12].

Regarding 2, in case if you like Bohm
http://en.wikipedia.org/wiki/Bohm_interpretation#Isomorphism_to_the_many_worlds_interpretation
Explicitly non-local. Bohm accepts that all the branches of the universal wavefunction exist. Like Everett, Bohm held that the wavefunction is real complex-valued field which never collapses. In addition Bohm postulated that there were particles that move under the influence of a non-local "quantum- potential" derived from the wavefunction (in addition to the classical potentials which are already incorporated into the structure of the wavefunction). The action of the quantum- potential is such that the particles are affected by only one of the branches of the wavefunction. (Bohm derives what is essentially a decoherence argument to show this, see section 7,#I ).

The implicit, unstated assumption made by Bohm is that only the single branch of wavefunction associated with particles can contain self-aware observers, whereas Everett makes no such assumption. Most of Bohm's adherents do not seem to understand (or even be aware of) Everett's criticism, section VI [1][10], that the hidden- variable particles are not observable since the wavefunction alone is sufficient to account for all observations and hence a model of reality. The hidden variable particles can be discarded, along with the guiding quantum-potential, yielding a theory isomorphic to many-worlds, without affecting any experimental results.

First off I got to laugh at you for citing randomly written wikipedia pages obviously biased...

Anyways, yes Deutsch prestented what HE claimed was a proof, which has been thoroughly critized and disproved.
(don't believe the hype).

Also Deutsch's desperate attempts at claiming BM is MWI in denial has been disproved too:
http://arxiv.org/PS_cache/arxiv/pdf/0811/0811.0810v2.pdf

In this paper by Antony Valentini, David Deutsch's claims are raped, there's also a counter argument against MWI.

Currently there exist no MWI that can arrive at the born rule:

http://arxiv.org/abs/0808.2415

There have been many attempts over the years to derive the Born Rule from the wave equation since Everett's Many Worlds Interpretation was proposed; however, none of these have been satisfactory as shown when critics pointed out loopholes and unsupported assumptions. In this paper the case is made that the currently fashionable decision-theoretic approach founded by David Deutsch and explicated by David Wallace is likewise unsatisfactory. A more fundamental computationalist approach is advocated.

Hilary Putnam, David Z Albert and other's have also written a lot of good work on this.

Not to mention this is far from the biggest cirticism of MWI.

What makes MWI so appealing to you personally?

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true MWI'ers are denialists, claim their interpretation is a representation of a realist interpretation, howver it really breaks down easy.
It can't deal with probability, so all our observations really contradicticts MWI at this point.
No preferred frame.
all these problems, it's a retarde dinterpretation.

A mix between Bohm and some ensemble view is more likely.

MWI is deterministic. The wavefunction of the universe satisfies the equation:

H|psi> = 0 (1)

The question is then what the meaning of |psi> is and how one gets to the Born rule. In my opinion people are making things far too difficult for themselves. One can intepret |psi> exactly as on would interpret the eigenvector of a row to row transfer matrix of a lattice model, e.g. the 2d Ising model.

There is absolutely no ambiguity here and the Born rule is what you would expect if |psi> is analogous to an eigenvector of a transfer matrix.

You are saying that a mix between Bohm and some ensemble view is more likely. But then, people are tackling important problems in theoretical physics using Eq. (1) (e.g. Black hole evaporation), while your favorite Bohm theory has yet to be properly formulated to be able to deal with quantum field theory.

It looks like the annihilation operator has been applied to |QMessiah>.

I didn't fully understand the argument in #1, but I'm not posting to ask about that. I just wanted to say that I wouldn't consider a process that entangles the eigenstates of a qubit with the eigenstates of another qubit a "measurement". To me a "measurement" is a process that entangles the states of the system with macroscopically distinguishable states of a system that (at least in the particular experiment we're considering) can be treated as classical. For example if someone bets \$1000 that the result of a measurement will be|0>, the time evolution of the qubit-gambler system is (approximately, and ignoring normalization factors)

(|0>+|1>)|:shy:> → |0>|>+|1>|>

We can "measure" this system just by looking at the gambler's face. I'm not assuming a collapse here. I'm assuming that there are other terms on the right, but I expect them to be extremely small because of decoherence, so there's no point in including them.

Unfortunatley, I don't have an exact definition of what it means for a system to be effectively classical, and I don't think anyone else does either. I suspect that it just isn't possible to define the concept in a way that draws a sharp line between systems that are effectively classical and systems that are not. And I believe that this means that it isn't possible to draw a sharp line between the two situations "a measurement has been performed" and "a measurement hasn't been performed". I find that both confusing and disturbing.

I just wanted to say that I wouldn't consider a process that entangles the eigenstates of a qubit with the eigenstates of another qubit a "measurement". To me a "measurement" is a process that entangles the states of the system with macroscopically distinguishable states of a system that (at least in the particular experiment we're considering) can be treated as classical.
So, in your opinion, it's only a matter of scale. That's fine -- the point of the original argument is an attempt to refute the hypothesis that a measurement is a fundamentally different physical process, rather than quantum mechanics operating at large scales.

Unfortunatley, I don't have an exact definition of what it means for a system to be effectively classical, and I don't think anyone else does either.
I thought it was rather clear in decoherence-based interpretations of QM -- a system is 'effectively classical'* if and only if its (relative) state is approximately a purely mixed state.

I suspect that it just isn't possible to define the concept in a way that draws a sharp line between systems that are effectively classical and systems that are not.
You don't want there to be a sharp line. (At least, it's a bad thing if you want macroscopic behavior to be the by-product of quantum mechanics applied to a huge number of particles) You simply want "obviously nonclassical" and "obviously classical" to be widely separated.

* I don't think that's a technical term

Why do you think 'artificial intelligence', human memory, simulations thereof, computer simulations, or quantum computers would be the least bit relevant here? I think you're just obfuscating the issue to an extent where you've managed to confuse yourself.

They're called 'interpretations' for a reason; they're not scientific theories because they're not testable. The MWI in particular is untestable by definition since a universe external to our own can never be proven or disproven. You might as well say 'God did it.' (which is popular, but not a scientific theory either).

MWI in relation to Decoherence can be testable, and is routinely tested. People have seen interference patterns on double-slit experiments where instead of photons they used C_60 molecules which are like huge planets compared to a single photon. Decoherence theory survived many of these experiments, and is well on track to be falsified further in the future.

There is going to be an adopted "interpretation" in the future, and treating them on equal footing because the current day scientific community hasn't adopted one is a big scientific sin.

And preaching people to stop thinking about the interpretations and telling them to "shut up and calculate" is an even bigger sin!

Copenhagen, with its kitsch wavefunction "collapse" assumption is SURELY going to be replaced.

Although we may not get to see it.

MWI in relation to Decoherence can be testable, and is routinely tested.
Sure -- and these experiments support MWI in favor of non-quantum theories. But they have nothing to say regarding whether MWI should be favored over CI. (or Bohm, or RQM, or ...)

Sure -- and these experiments support MWI in favor of non-quantum theories. But they have nothing to say regarding whether MWI should be favored over CI. (or Bohm, or RQM, or ...)

I don't know anything about any non-quantum theory being clashed with a quantum interpretation. That doesn't make sense to me. Can you provide some examples or references?

And No. They do say MWI should be favored over CI. MWI does not need wavefunction collapse --- which is an ugly artifice added to the theory by hand.

Similarly Decoherence theories try to explain the classicality emergence and they favor MWI because of its lucid approach.

What says Occam?

The simpler the better.

And No. They do say MWI should be favored over CI.
What prediction of CI was violated by these experiments? If you cannot give a satisfactory answer to that, then you're wrong.

Hurkyl said:
MWI predicts that all interactions can be reversed.
Does this imply that the 'arrow of time', or apparent irreversibility of the evolution of our universe, isn't driven by some fundamental universal dynamic(s)? If so, then what?

Count Iblis said:
The question is then what the meaning of |psi> is and how one gets to the Born rule.

Does the Born rule have a dynamical basis?

Does this imply that the 'arrow of time', or apparent irreversibility of the evolution of our universe, isn't driven by some fundamental universal dynamic(s)? If so, then what?
This question seems vague enough that I can't make heads nor tails of it. I will point out that classical mechanics is also reversible, and apparent irreversibility is a thermodynamical issue (both in classical and in decoherence-based quantum mechanics).

What prediction of CI was violated by these experiments? If you cannot give a satisfactory answer to that, then you're wrong.

IF a new theory simplifies and/or removes the assumptions of an older theory, while still making ALL the predictions of the old theory, then scientific method replaces the old theory with the new one.

And what does CI have to say about wavefunction collapse?

"An electron obeys the Schrodinger equation except when it doesn't."

I showed this in brackets because it's a brilliant insight from Max Tegmark.

If you cannot explain the wavefunction collapse from a fundamental standpoint using CI, you are wrong.

IF a new theory ...
You failed to present empirical evidence violates CI, therefore you lose -- you have absolutely nothing to back up your claim that experiment favors MWI over CI.

I agree that there are strong reasons to favor MWI over CI, but experimental evidence is not one of them. You do a great disservice by pretending the preference is actually grounded in experiment.

This question seems vague enough that I can't make heads nor tails of it.
You said that "MWI predicts that all interactions can be reversed." So, is this a reason to not adopt the MWI as the 'correct' interpretation of quantum theory, since observations suggest that no interactions can be reversed?

You failed to present empirical evidence violates CI, therefore you lose -- you have absolutely nothing to back up your claim that experiment favors MWI over CI.

I agree that there are strong reasons to favor MWI over CI, but experimental evidence is not one of them. You do a great disservice by pretending the preference is actually grounded in experiment.

: ) First of all, I think you are the "losing side" here.

For those who can tolerate to at least read the full remark:

IF a new theory simplifies and/or removes the assumptions of an older theory, while still making ALL the predictions of the old theory, then scientific method replaces the old theory with the new one.

Tutorial:

new theory = decoherence
old theory = Copenhagen

extra assumptions/specifications in old theory = wavefunction collapse

Could somebody give a reasonable explanation for that under Copenhagen? = No.

Could decoherence do that? = Yes.

And I think you very well got it.

So I have made my service by - at least - disclosing the truth without prejudice and personal bias.

If you think there's anything wrong/biased or fallacious in this very post, please let me know and I'll delete it.

(Edit: Plus, your misconception that a theory is only discarded against empirical evidence is very wrong. Theories just like biological organisms compete and survive. Very much like evolutionary processes... And this "selection" is based not only on empirical support but also on many other parameters that define the "better" theory. And everybody would agree that "simplicity" ( See Murray Gell-Mann's TED talk) is one of these parameters)

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Technically Hurkyl is right. But let me ask him, why do we give equal rights to CI and MWI but not to SR and LET?

If you think there's anything wrong/biased or fallacious in this very post, please let me know and I'll delete it.
Nothing in it has to do with empirical evidence, and thus has no bearing on your previous claim that empirical evidence favors MWI over CI.

thus has no bearing on your previous claim that empirical evidence favors MWI over CI.

I never claimed that. You wanted to see it that way. My point is crystal clear.

It doesn't mean that CI is wrong. It means that it is NOT as competitive as MWI or any other, if it cannot be simpler.

And yes, it's a fact.

Good luck,

(Just FYI: "[URL [Broken])[/URL]

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Did Bohr and Heisenberg actually say that the "collapse" in their interpretation must be exact? I mean, why would anyone actually think that it is? They were certainly smart enough to realize that if the component parts of the measuring device obey QM, the whole thing can't be completely classical. So it's likely that what they had in mind was a kind of "classical limit", sort of like obtaining non-relativistic physics from SR by taking the limit c→∞. The message they were trying to get across was that going from a small and simple system to a large and complicated one is analogous to making c absurdly large in SR.

Of course I'm just speculating here. If there's evidence for the claim that Bohr and Heisenberg meant that the collapse was complete, then feel free to use it to prove me wrong.

If I'm right, then decoherence doesn't favor either the CI or the MWI. In the CI, it's the mechanicsm that (approximately) collapses the wave function, and in the MWI it's the mechanism that (approximately) chooses the preferred basis of the Hilbert space which defines the "worlds".

It seems to me that the difference between the CI (the version of it that isn't crazy) and the MWI is just that they disagree about which one of the two interpretations of a density operator they should take seriously. I mean, we know that we can use a density operator

$$\rho=\sum_i w_i|\psi^{(i)}\rangle\langle\psi^{(i)}|$$​

both to represent an ensemble of systems prepared in many different states, and to represent a single system in an unknown but specific state. It seems to me that the CI and the MWI are just saying that one of those options is right and the other wrong in the specific situation when the density operator represents a combined system "measured object + measuring apparatus" right after a measurement.

Technically Hurkyl is right. But let me ask him, why do we give equal rights to CI and MWI but not to SR and LET?

No he isn't.

And we do not give equal rights to any of them because they are different.

Currently, there's only heuristic evidence -- in the future, there will be an exact branching to one of these (or even a newer one)

You are asking the wrong question, the question is:

Why should we give equal rights to all the interpretations considering that they are predicting entirely different physical mechanisms ?

Considering the current difficulties in distinguishing them, scientists are being cautious and are not ruling out any of these,

but just because some wiki article treats them on equal footing DOESN'T mean they are equal or not being tested.

I am MWI fan :)
AFAIK Hurkyl prefers it too. You see, we are all on the same side!

But the sad truth is that we don't have anything to disprove CI - not for us - we all know that it is insanity: conscious observers, knowledget et cetera - but for those who still think in CI terms.

Technically Hurkyl is right. But let me ask him, why do we give equal rights to CI and MWI but not to SR and LET?
Because special relativity is easier to work with than Lorentz (a)ether theory, and easier to generalize to a theory of gravity.

(I don't know Lorentz's theory. I'm assuming that their predictions are the same, just because that claim has been made in this forum without getting shot down).

Did Bohr and Heisenberg actually say that the "collapse" in their interpretation must be exact? I mean, why would anyone actually think that it is? They were certainly smart enough to realize that if the component parts of the measuring device obey QM, the whole thing can't be completely classical.

Fredrik, there's historical evidence that they thought exactly the way you described above.

Murray Gell-Mann, in his book ( Quark and the Jaguar ) relates this to the fact that the founders of QM were coming from a classical physics school and they just could not comprehend the fact that the universe is governed by QM and QM only...

In fact, Bohr thought there must be (invariably) a classical object around when making a measurement. These ideas might seem weird, you even go as far as saying "Why would anyone actually think this is the case?"... But they did. The best minds of the worl d at the time thought that.

But we know that QM governs the entire universe now, thanks to the recent developments culminating in the works of Zurek, Hartle, Everett, Gell-Mann and many others.

Founders of QM were very smart people but they didn't "certainly realize" that as you say.

And wavefunction collapse; as ugly and as alien as it seemed, survived all the way up to these days. Because nobody had a better explanation, so these discussions must have been made in thousands of equivalent "physics" forums before. The good news is, the "collapse" is reaching its "collapse". (with MWI or something else!)

A few years from now, these ideas will be flowing in the mainstream layman forums and people will not choose their favorite interpretation based on their taste.

So yes, MWI may not be the correct replacement, but CI is definitely not "exact"

And no interpretation is treated equally, at least in scientific circles. People know that there are problems with CI and they are working on clearing those up.

Assuming that they are all equal is naive. Why so?

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Fredrk, there's historical evidence that they thought exactly the way you described above.
I assume that you meant that they thought a measuring apparatus is completely classical. That's more consistent with what you said next. (If it wasn't for that I would have interpreted the text I just quoted in the exact opposite way).

In fact, Bohr thought there must be (invariably) a classical object around when making a measurement. These ideas might seem weird, you even go as far as saying "Why would anyone actually think this is the case?"
I think it's clear that there must be an object around that for all practical purposes is classical. A measurement is an interaction that entangles the eigenstates of the measured system with macroscopically distinguishable states of the f.a.p.p. classical system.

And no interpretation is treated equally, at least in scientific circles. People know that there are problems with CI and they are working on clearing those up.
Only the version with an exact collapse has problem, so the easiest way to clean it up is to replace the assumption of exact collapse with an assumption of approximate collapse.