# Postulates of many worlds interpretation of QM

1. Apr 21, 2009

### ueit

I am interested to see a clear enumeration of the postulates of this interpretation. There seem to be something fuzzy about how MWI describes what we call "reality". It might be a problem with the theory or, more probable, a misunderstanding of my part.

Here is a list I found on Google:

http://vergil.chemistry.gatech.edu/notes/quantrev/node20.html" [Broken]

Tell me if you agree with this list, and if not, what needs to be rejected/added/modified or give a link to a better one. Thanks.

Last edited by a moderator: May 4, 2017
2. Apr 21, 2009

### Dmitry67

3. Apr 21, 2009

### jensa

I usually avoid interpretational questions but I am also trying to avoid work right now so here goes:

I never really understood the argument that Many worlds theory reduces the number of axioms by dropping the measurement postulate. I mean I understand that it assumes the observer becomes entangled with the system in a way that the combined system is in a superposition |observer_a>|eigenstate a> + |observer_b>|eigenstate_b> but I still feel like there needs to be some postulate that tells us how the observer experiences being in such a superposition.. I mean, so I do an experiment and I evolve into a superposition.. then why do I only experience one result? and what determines the probability of experiencing this result? I suppose the answer to these questions is the subject of the interpretation, but something must still be said (postulated) about how the probability of experiencing one or the other result is related to the superposition (i.e. amplitude of eigenstate a/b squared).
Or am I missing something?

4. Apr 21, 2009

### Dmitry67

You experience BOTH results
So YOU (observer_a) is asking "But why I observe eigenstate a, not eigenstate b?"
Observer_b is asking "But why I observe eigenstate b, not eigenstate a?"
The total picture is deterministic and symmetrical in terms of the result.

Regarding the probability check the same Wiki article

5. Apr 21, 2009

### jensa

Thanks for the reply Dimitry, although I am not sure it addressed the point (or maybe it did).

This quote illustrates the question... So I exprience both results but at the same time only one???

I understand that from a birds view it can be interpreted that the observer experiences both results since he/she is in a superposition but since I am the observer it makes it suddenly very unclear what being in a superposition means... what can I expect to observe? It seems to become somewhat of a philosophical question. I don't see how anything about what I can expect to experience follows logically from the mathematical result of me being in a superposition without some extra postulate/interpretation. IMHO this is precisely what the "measurement postulate" is for... whether it is thought of as a collapse of the wave-function or if it is a recipe for the interpretation of being in a superposition... I still think one needs it.

EDIT: I should point out that when I say "measurement postulate" I don't refer to the collapse of the wave-function but simply the recipe for finding the probability of observing result a or b. I am pretty sure that it can be stated in a interpretation-unspecific way.

I suppose I should read the reference Hartle[35] someday when I have time. Maybe all the answers are there. Anyway, thanks for help.

Last edited: Apr 21, 2009
6. Apr 21, 2009

### Dmitry67

There are 2 YOU's. Each YOU observes only one result, not a superposition

7. Apr 21, 2009

### jensa

Well, I feel like this is getting nowhere, so I will drop my question. thanks anyway.

8. Apr 21, 2009

### Fredrik

Staff Emeritus
This is a good article about axioms of many-worlds interpretations.

9. Apr 22, 2009

### Dmitry67

Frederick, BOTH articles were published in 1997.

Before major improvement in the understandig of the Quantum Decoherence
And before
In fact, both articles are very pro-MWI because it appears that 1997 is the last year when there were any anti-MWI articles :)

---------------

But it appears that since Sept 2007, MWI was able to get rid of TWO, not ONE axiom: both apparent "collapse" AND Born rule can be derived from the pure QM.

10. Apr 22, 2009

### ueit

In the above link there is no clear statement of the MWI postulates. So, I will repeat my question:

I understand that you will not add anything but remove one postulate. It's OK. Can you tell me if you agree to the rest of them? Are they correctly formulated as far as MWI is concerned?

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11. Apr 22, 2009

### Dmitry67

It does not work.
At least now, I will check later

12. Apr 22, 2009

### ueit

Sorry, this is the good one:

http://vergil.chemistry.gatech.edu/notes/quantrev/node20.html" [Broken]

Last edited by a moderator: May 4, 2017
13. Apr 22, 2009

### Fredrik

Staff Emeritus
Other articles have pointed out that the reasoning used in Zurek's derivation of the Born rule was circular. He derived the Born rule using the technique of "tracing out" other degrees of freedom, but the justification for that technique is...the Born rule.

The "tracing out" technique is also used in derivations of the apparent collapse of the wave function. This means that you can't take the MWI axioms to be what you get by taking the Copenhagen axioms and removing the collapse axiom including the Born rule. It seems to me that what you can do is to take the Copenhagen axioms and just weaken the collapse axiom a bit. Instead of postulating that the collapse is exact, you postulate that it's approximate. But you absolutely have to keep the Born rule in the axioms of the MWI.

Now, if you do this, the existence of "many worlds" is not implied by the axioms. It's just one of several possible interpretations of the statement that a measurement entangles the eigenstates of the measured system with macroscopically distinguishable states of a system that can be described as classical to a very good approximation. A measurement of an observable B changes the density matrix $\rho=|\alpha\rangle\langle\alpha|$ according to

$$\rho\rightarrow\sum_b P_b\rho P_b$$

where $P_b$ is the projection operator onto the eigenspace of B corresponding to eigenvalue b. If the spectrum is non-degenerate, we have $P_b=|b\rangle\langle b|$.

I don't think decoherence has weakened Kent's arguments against the various MWIs in any way.

14. Apr 22, 2009

### Fredrik

Staff Emeritus
I didn't notice this before, but Tegmark actually included a few comments about Kent's paper in his. (There's no link to the Tegmark paper in this thread, so I'm putting one here. His article is actually a very good). This one is interesting:

I don't think this is correct. The "preferred" basis is defined as the one in which the density matrix is approximately diagonal. You find this basis by "tracing out" the environment's degrees of freedom, but that's a move that's justified by the Born rule, which is an axiom that we had supposedly dropped.

I haven't been through the details of the arguments and counterarguments, so it's possible that I'm wrong. Let's just say that I'm unconvinced, and that the anti-MWI argument above seems plausible to me. (Note that it's not really an argument against many worlds. It's an argument against dropping the Born rule).

I want to make it clear that I'm not advocating an exact collapse of the wavefunction. I'll try to explain how I think about QM: We should weaken the Copenhagen axioms by assuming that the collapse (as seen from the perspective that Tegmark calls "the inside view") is only approximate. This is sufficient to guarantee that the Born rule axiom doesn't contradict the axiom that Tegmark takes as the definition of the MWI: Any isolated system evolves according to the Schrödinger equation. So we keep the Born rule as an axiom, along with an approximate collapse. The real significance of decoherence is that it tells us what a measurement is: It's an interaction that entangles the eigenstates of some observable, selected dynamically by the interactions between the system and the environmen, with macroscopically distinguishable states of a system that's approximately classical. This process (which only exists in the theory if the axioms include the Born rule) defines the preferred basis, which defines the worlds in the MWI.

All of this is perfectly consistent with the idea of many worlds, but it doesn't imply that many worlds exist. A measurement turns a pure state into a mixed state, represented by a density matrix which is almost diagonal in the preferred basis, but this density matrix can be interpreted in many different ways. One of them is as an ensemble of systems (many worlds). Another is as a single system in a specific but unknown state. I actually prefer a third option: For a theory to be scientific, it's not necessary that it describes reality. It's sufficient that it tells us how to compute the probabilities of possible results of experiments. It's actually rather naive to expect that if science has something to say about a phenomenon, it's always in the form of a model with the property that every concept in the model has a counterpart in the real world. I just think QM is the first example of a theory that's non-trivial in the sense that it isn't a description of reality. (And no, this isn't quite the same as "shut up and calculate". It's a bit more sophisticated than that ).

15. Apr 23, 2009

### Dmitry67

Frederick,

Regarding the circularity issue, it does not mean that it is wrong. As a reminder, the very first (naive) explanations of HUP (using a though experiment with a microscope) were also circular: lets assume that the particles (say, photons) have the following dependency of momentum/position. Now we are trying to measure a position and momentum of another particle (a photon). We find the same HUP. Now we assume that ALL particles have the same property...

So I agree with you, it might not be a proof but it is a good indication that the theory is self-consistent. In order to finalize a proof, one need to assume that born rule is violated and show that it leads to incosistency.

Last edited: Apr 23, 2009
16. Apr 23, 2009

### Dmitry67

Frederick,

I dont think that you can ever make a theory where other worlds are NOT real. This is because the Quantum Decoherence is a GRADUAL process. 2 systems exchage, say, the photons and they gradulally decohere (in each branch we observe this process as they become somehow 'synchronized' in terms of macroscopic reality - they become 'diagonal')

Based on experiments, to completely decohere you need several photons, about 5. I hope you dont want to claim that say after an exchange of 3 photons ohter branch is real, but then, after some treshold is reached it 'suddenly' becomes non real? This looks very artificial, right?

17. Apr 23, 2009

### Dmitry67

If we dont discuss for not Born's rule (Sept 2007 issue) then most of these axioms are valid, except the word "measurement", because MWI explains what the measurement is hence it is not an 'atomic' operation and it CAN NOT be included in the axiomatic.

To be more specific, check Postulate 2. There are no 'observables' except the states of the measurement systems. So in MWI you cant simply say 'This is momentum'. instead, you need to show, that a measurement device, built to measure a what we call a momentum, after interaction with a particle will show on it's indicator the value we call a momentum and it is the same defined by the operator. What is more difficult, you need to show that ALL different apparatus designed to measure the momentum will do the same.

It is very close to the 'Physics from scrach' approach by Max Tegmark, so MWI can make his (and mine) dream come true.

Last edited by a moderator: May 4, 2017
18. Apr 23, 2009

### Fredrik

Staff Emeritus
It only means that there's still no proof of the claim that in QM without the Born rule as an explicit axiom, interactions between the system and the environment make the density matrix of the combined system approximately diagonal in a basis selected dynamically by the interactions.

What we would need to do (What Zurek claimed to have done) is to prove that the Born rule* follows from the other axioms.

*) To be more specific: A version of the Born rule that says that the collapse is only approximate.

I don't follow your argument here. If decoherence had been absolute and instantaneous instead of gradual, we would still have at least two possible interpretations: Wavefunction collapse, and many worlds. What the gradual nature of decoherence suggests is just that the collapse isn't absolute, and the universe doesn't actually split into many copies. It's more subtle than that.

I assume that what you mean by "completely" is "approximately". Otherwise it would contradict what you said about dechoherence being gradual. Of course I don't want to claim anything like what you're suggesting here. The "branches" are either never real or always real, even before the measurement.

By the way, I took a look at the 'Against "Against many worlds interpretations" ' preprint that Tegmark referenced. It looks like a bunch of incoherent nonsense. I wonder if Tegmark ever tried to understand a single sentence in that paper except for the ones that claimed (incorrectly) that Kent doesn't even understand what the MWI is. Sakaguchi didn't seem to understand what he was talking about, and this paper was never published anywhere as far as I can tell, so it's really weird that Tegmark used it as a reference.

19. Apr 23, 2009

### Fredrik

Staff Emeritus
Regarding the derivation of the Born rule...This article looks interesting. I just found it, so I haven't read it yet, but I intend to.

Last edited: Apr 23, 2009
20. Apr 25, 2009

### Fredrik

Staff Emeritus
According to Tegmark, the only axiom of many-worlds QM is that all isolated systems evolve in time according to the Schrödinger equation. But seriously, that can't possibly define a theory. I'm not referring to the fact that he didn't mention the usual stuff about how states are represnted by unit rays and so on. (He's obviously just thinking that that's so standard that it's not even worth mentioning). I'm talking about the fact that there are no axioms that tell us how to interpret the mathematics as predictions about results of experiments.

Let's say that we know that the "outside view" of the evolution of the universe (decomposed into the subsystems qubit+observer+environment) is

|q>|>|X> → |0>|>|X'>+|1>|>|X''>

Now what exactly is the justification for the claim that the first term describes an observer who's happy because she found the qubit to be in state |0>? I really don't see any. I don't even see any justification for the decomposition of the universe into subsystems. Maybe there's some theorem about Hilbert spaces that gurantees that it can be expressed as a tensor product of a bunch of subsystems, but even if that's the case, it only solves one of the smaller problems.

Kent pointed out that there's no mechanism that can select the basis that defines the "worlds". Tegmark dismisses Kent's arguments as if they were the incoherent ramblings of a madman, and references an unpublished article to support this. But that article is really bad and doesn't make much sense. That's probably why it wasn't published.

Tegmark claims that decoherence is the mechanism that dynamically selects the basis, but it seems to me (and to this guy) that decoherence relies on additional axioms. In particular, we need to be able to express the Hilbert space as a tensor product of the Hilbert spaces of subsystems, and to compute the reduced density matrix of the qubit+observer system by "tracing out" the environment's degrees of freedom. The justification for these things is the Born rule, i.e. the axiom that says that if we measure an observable B when the system is in state |u>, the probability that we'll get the result b is |<b|u>|2.

So I think I have to metaphorically join the club of people who think that there is no many-worlds theory. It seems that no one has been able to properly define Everett's MWI, and the foreword to the 1997 version of Kent's article suggests that other many-worlds theories like consistent histories have similar problems.

One more thing...The many-worlds axiom is somewhat ill-defined, since the term "isolated system" hasn't been defined in advance. It seems more natural to take corollary 1 as the axiom (the universe evolves according to the Schrödinger equation) and then define a subsystem to be "isolated" if it evolves according to the Schrödinger equation.