QM Interpretations: Most Popular & Why?

[ConradDJ]

Just to put in a word for Rovelli's Relational QM... which probably has no large following among physicists. But I think it's the most straightforward interpretation of quantum experiments, in particular the "quantum eraser" experiments.

The idea is that the "collapse" is a real physical event, but not an "objective" (observer-independent) event. The superposition "collapses" exactly to the extent that information about a system S is communicated to any other system O. However the collapse is "relative to O". For another system P, the combined S-O system remains in an entangled superposition until information about its state gets communicated to P.

I don't think this has much significance for physics, yet, but I think it should. It shifts the picture from --

A) systems exist in a paradoxical superposition of states, and then at some point are transformed... not exactly into a single determinate state, but a state which is more determinate with respect to some parameters and less determinate with respect to others; to --

B) at bottom the world consists not of things-in-themselves but of "the information systems have about other systems." The world is not a structure of things, but of communcations.​

However, this interpretation is useful only if you want to head into almost unexplored conceptual territory -- i.e. considering how "communication of information" actually happens, in physics... how the world actually works, as a communications system.

That the world in fact does this is beyond dispute -- that it communicates information about itself through physical interaction. The strength of Relational QM is that it allows every interaction to be a "measurement"... instead of assuming that some "cause a collapse" and others don't. But it's not very clear what this implies, for physics.

Even so, for me it's more interesting to think about what we know actually happens in the world, than to explore notions like the splitting of the universe into infinitely many universes.

 

[Bob_for_short]

We don’t need to 'assume' that they exist: their existence is an unavoidable result of unitary evolution. On the contrary, to deny their existence you need to provide some mechanism. For example, in Copenhagen that elimination mechanism is called ‘collapse’... So the burden of proof is on those who claim that only one branch exists.

Let us consider a lotto. Its results are probabilistic. All different results form the ensemble of events describe this lotto as a system. Each particular result is an element of the ensemble rather than a collapsed probability.
In QM each particular result (point) is considered as a collapsed wave-function. Why? The wave function does not describe a specific event but ensemble of them. Make many elementary measurements: one-by-one in a sole installation or one in many different but similar installations, whatever, and you will determine the system properties. The system properties are not reduced to one point. There is no a WF collapse in an elementary measurement.

 

[Fredrik]

The axiomatic system of MWI is very simple: there is only unitary evolution of the waves and nothing else Period. In that sense it is NULL interpretation and very close to 'shut up and calculate'

Is the usual probability rule of QM included in the axioms or not? If it is, then what exactly distinguishes the MWI from the ensemble interpretation? If it isn't, then the theory is crippled and can't make any predictions at all. It's not even a theory anymore.

...many people get an impression that the wordy stuff about the branches is a part of axiomatics of MWI. it is not.

That's precisely why I've been suggesting that the MWI is a failed attempt to interpret QM, and that it's only giving us a rough idea about what sort of things are actually happening. An interpretation should at least be able to make a claim (that may or may not be correct) about what exactly is happening.

I really haven't been able to figure out what MWI proponents think is really happening, or what they consider a mathematical representation of a "world". I know that they think it makes sense to consider the Hilbert space of possible states of the entire universe. Penrose calls it the "omnium" rather than the "universe", since it's the physical system that contains all the worlds. I'll call it that from now on.

I think the Born rule is essentially equivalent to the assumption that a Hilbert space of states of a physical system can be expressed as a tensor product of component systems. We can decompose the omnium into subsystems in many different ways. When we decompose it into only two subsystems, we can call one of them "the system" and the other "the environment". The state of the omnium can be expressed as

$$\sum_{\alpha, \beta}c_{\alpha\beta}|S_\alpha\rangle\otimes|E_\beta\rangle$$

where the S states are eigenstates of some observable and the E states are basis vectors for the Hilbert space of the environment. Decoherence theory tells us that any interaction between the system and the environment will transform the state (by unitary time evolution) into the form

$$\sum_\alpha c_\alpha|S_\alpha\rangle\otimes|P_\alpha\rangle$$

where the P states are "pointer states" of the environment. Now each term of this expression can be interpreted as representing the state of a different "world". But note that each of these terms is a vector in the Hilbert space of the omnium. So the Hilbert space of a "world" is the same as the Hilbert space of the omnium, and that means they're actually the same physical system. Every world is the same physical system as every other world. So why do we call them "worlds"?

Apparently we do because the systems that include at least one human observer always perceive themselves as a term in the second mathematical expression above, rather than as the sum of the terms. Note however that nothing in the MWI explains why, or even states explicitly that they do. Even decoherence can't really explain it. I'm sure decoherence can tell us that the eigenstates of some observable of my brain must be correlated with pointer states of my environment, but it can't tell us why every experience I have is represented by an eigenstate of that observable. So maybe we do need to talk about consciousness?! It seems that we need to prove that all conscious experiences are represented by eigenstates of some observable. What observable would that be? Is there a consciousness observable? Do we need a better theory of consciousness to answer that? It seems to me that as long as these issues haven't been worked out, the MWI is just a set of loosely stated ideas rather than an actual interpretation.

The fact that the decomposition into "the system" and "the environment" is arbitrary seems to mean that two different subsystems of the universe can't agree on what the worlds are. Each subsystem would describe what it considers "the world" from its own point of view. We're entering the territory of the "relational interpretation" here. I think that the MWI also needs to be supplemented by a set of statements similar to a "relational interpretation" before we can consider it an actual interpretation.

 

[Fredrik]

We don’t need to 'assume' that they exist: their existence is an unavoidable result of unitary evolution. On the contrary, to deny their existence you need to provide some mechanism.

Only if you have assumed that QM really describes the world, but this assumption is naive and unjustified. A set of statements only needs to be falsifiable to qualify as a theory, and for that it's sufficient that it tells us the probabilities of possible results of experiments. It doesn't have to include a model of the real world. MWI proponents believe that Hilbert space together with the Schrödinger equation is a mathematical structure that's approximately "isomorphic" to the real world. We "ensembleists" believe that this isn't true. It's only if we assume that your unjustified belief is correct that what you're saying in the quote is true.

QM doesn't look like a description of anything to me. It looks like a toy model that mathematicians would come up with if we ask them to think of the simplest possible theory that predicts non-trivial probabilities (i.e. not always 0 or 1) of possible results of experiments.

 

[Count Iblis]

It seems that we need to prove that all conscious experiences are represented by eigenstates of some observable. What observable would that be? Is there a consciousness observable?

I think that's true. Formally it is easier to replace a biological human by an artificial intelligence and then consider the classical bits of the computer. Whatever consciousness really is, the operators that descibe it will be diagonal in the basis spanned by the classical bit states.

 

[Hurkyl]

Let me make a statement about qubits, which is hopefully nontrivial enough to serve as an analogy that says something interesting.


The algebra of "observables" of a qubit is generated by the three "spin about the * axis" operators. IIRC, the set of all states for this algebra can be arranged into a geometric object: the Bloch sphere and its interior.


Now, suppose for some reason I do not have access to all observables -- let's say I only have access for the spin about the x-axis observable. The state space for this algebra is just the interval [-1,1]. The endpoints are the only pure states.

My algebra doesn't have enough observables to tell apart the points on/in the Bloch sphere: on any of my observables, (x,y,z) and (x,y',z') have the same expectation.

Algebraically restricting the operator algebra just to what I have available has the geometric effect of projecting the Bloch sphere onto the x axis.

On the pure states on the Bloch sphere, if you grind through the process of mapping it to the Bloch sphere, projecting down to [-1,1], then rewriting it as a statistical mixture of the pure states, the result is that the ket

a |x^-> + b |x⁺>​

is converted into the statistical mixture

x^- with proportion |a|²
x⁺ with proportion |b|²​

So while the "true" state space of our qubit is the Bloch sphere, the fact I only have access to a limited algebra of observables means that I only see a restricted view of the quantum state. The Born rule pops out of the partial trace. There is no arbitrary choices, artificial decomposition, or anything like that involved.




Local quantum field theory incorporates this. Two different kinds of locality are involved here.

The first kind of locality is that we may want to restrict our attention merely to a particular region of space-time, rather than the entire universe -- and so we get a restriction of the full state space, much as in my example of the qubit.

The second kind of locality says that if the region V is causally determined by the region U (e.g. the past light-code of every point in V has a cross-section lying entirely in U), then the quantum state local to V is completely determined by the state local to U -- time evolution is local.

In particular, this means that if the quantum state local to U is a statistical mixture of some pure states, then time-evolving to V is required to preserve this mixture!

 

[Fredrik]

I think that's true. Formally it is easier to replace a biological human by an artificial intelligence and then consider the classical bits of the computer. Whatever consciousness really is, the operators that descibe it will be diagonal in the basis spanned by the classical bit states.

That's a good point. I've heard it before, but I had forgotten about it. Even if we don't know the best possible definition of consciousness, it's safe to say that conscious experience involves changing memory states. I think that answers my concerns about consciousness. Suppose e.g. that we consider a physicist measuring S_z of a silver atom. In this case, all the "pointer states" of the environment (of the silver atom) have the physicist's memory in a state in which the stored information about the result of the experiment is well-defined (i.e. it's either "up" or "down", not a superposition of both), and that's why he can only experience the pointer states of the environment that he's a part of.

 

[Fra]

The following are the interpretations of QM:

Bohmian · CCC · Consistent histories · Copenhagen · Ensemble · Hidden variable theory · Many-worlds · Pondicherry · Quantum logic · Relational · Transactional

Which is the most accepted by the theoretical physics community? Obviously all have some supporters but I'm interested in finding out which is the most popular and why?

When this has been debated before it's clear that there is different ideas about "point" of an "interpretations".

(A) The I think most common point of an interpretation is as a way to come to a consensus with yourself, in the sense of finding a logically coherent view that incorporates what we know. A way to find a way to mentally handle factual weirdness.

As we know, there are many self-consistent views that corresponds to a finite set of knowledge. Ie. the interpretation is not unique.

(B) The other point is to consider what expectations a given choice of view, induces on the extension of the theory. Here I picture unification of forces and unification of GR and QM.

The latter points is the more interesting in my view, and the reason for my preferences. It seems to me that some of the interpretations doesn't not relaly have a clear ambition beyond the first (A) point. This is why these interpretation has not predictive value.

So I'm quite indifferent to the "interpretation-only" discussion. For me, the interpretations reflects my expectations for extendign the theory.

In this respect my "interpretation" of QM, is that it is a special limiting case (and thus an approximation) to a not yet found theory.

I would like to keep from QM the ambition of keeping it a "measurement theory". This is the distinguishing feature from classical realist physics. However, the physical realisation of measurements and possible state spaces are insufficiently understood. Somehow it's obvious that the QM structures like state space are observer dependent, but the evolution of the observer is not acknowledged. The only accounts for this is the decoherence style views where you picture an external observer, or the environment as an observer, where you can have both the observer andthe observed system as part of the system, and then apply the same QM. But this construct is fundamentally missing the point IMO. It just repeats the mistake. In particular does these imaginary observers vioalte the information capcity of arealy observer, and thus fails to explain the how to evaluation the action of a real observer because it unavoidably capture physical redundancies in evaluation the action.

This doens't fit in any of the major interpretation though. But it shares traits of rovellis' relational QM + smolins objection to reality of law + ariel catichas and ET Jaynes attempt to abstract the laws of physics as rules of inductive inference.

/Fredrik

 

[Fredrik]

Let me make a statement about qubits, which is hopefully nontrivial enough to serve as an analogy that says something interesting.

It's interesting, but I'm not sure it's relevant here. I was talking about decomposing a physical system into subsystems, and you chose a system that can't be decomposed. The Hilbert space of the larger system is supposed to be the tensor product of the Hilbert spaces of the subsystems. In your example the Hilbert space of the "large" system is 2-dimensional, so it can't be the tensor product of two Hilbert spaces.

On the pure states on the Bloch sphere, if you grind through the process of mapping it to the Bloch sphere, projecting down to [-1,1], then rewriting it as a statistical mixture of the pure states, the result is that the ket

a |x^-> + b |x⁺>​

is converted into the statistical mixture

x^- with proportion |a|²
x⁺ with proportion |b|²​

So while the "true" state space of our qubit is the Bloch sphere, the fact I only have access to a limited algebra of observables means that I only see a restricted view of the quantum state. The Born rule pops out of the partial trace. There is no arbitrary choices, artificial decomposition, or anything like that involved.

I don't quite follow you here. Can you post some details?

Local quantum field theory incorporates this. Two different kinds of locality are involved here.

The first kind of locality is that we may want to restrict our attention merely to a particular region of space-time, rather than the entire universe -- and so we get a restriction of the full state space, much as in my example of the qubit.

The second kind of locality says that if the region V is causally determined by the region U (e.g. the past light-code of every point in V has a cross-section lying entirely in U), then the quantum state local to V is completely determined by the state local to U -- time evolution is local.

In particular, this means that if the quantum state local to U is a statistical mixture of some pure states, then time-evolving to V is required to preserve this mixture!

I understand even less of this, but maybe I'll have to wait until I get around to reading Haag's book. It's been on my bookshelf for a year, and it's on the list of the next ten books I'd like to read.

 

[Hurkyl]

It's interesting, but I'm not sure it's relevant here. I was talking about decomposing a physical system into subsystems, and you chose a system that can't be decomposed.

That was half out of convenience, and half intentional -- I think decomposition is a special case.

I don't quite follow you here. Can you post some details?

I'm not sure what part specifically you're asking about. But I do notice I fibbed (kinda) at one place!

(IIRC) In the Bloch sphere picture, the quantum state $\rho$ corresponds to the point $(\rho(S_x), \rho(S_y), \rho(S_z))$ whose coordinates are the 'expectation' values (where I use $S_x$ as the operator with eigenvalues $\pm 1$ for spin about the x direction).

So when projected onto the interval, then, $\rho$ gets mapped to $\rho(S_x)$ -- the (mixed) state representing

Spin up with weight $(1 + \rho(S_x)) / 2$
Spin down with weight $(1 - \rho(S_x)) / 2$​

The part I fibbed about is the Born rule doesn't appear when projecting; it appears in the correspondence between the Bloch sphere and the more usual kets-in-a-Hilbert space representation of the pure quantum states.

I think the point I wanted to make was that one doesn't need to make any reference to the Born rule to analyze how the quantum state projects from the Bloch sphere down to the interval.

 

[Fredrik]

I'll start with a quick summary of some of the technicalities. The most general qubit state is

$$|\psi\rangle=\cos\frac\theta 2|0\rangle+e^{i\varphi}\sin\frac\theta 2|1\rangle$$

The corresponding density matrix, in the |0>, |1> basis, is

$$\frac 1 2(I+\vec r\cdot\vec \sigma)$$

where $\vec r=(\sin\theta\cos\varphi,\sin\theta\sin\varphi,\cos\theta)$. By "projecting", I assume that you mean e.g. to replace $\vec r$ by $(0,0,\cos\theta)$. This is a projection onto the z axis. The density matrix becomes

$$\frac 1 2(I+\cos\theta\ \sigma_3)=\frac 1 2\begin{pmatrix}1+\cos\theta & 0\\ 0 & 1-\cos\theta\end{pmatrix}=\begin{pmatrix}\cos^2\frac\theta 2 & 0\\ 0 & \sin^2\frac\theta 2\end{pmatrix}$$

and the corresponding density operator is

$$\cos^2\frac\theta 2|0\rangle\langle 0|+\sin^2\frac\theta 2|1\rangle\langle 1|=|\langle 0|\psi\rangle|^2\ |0\rangle\langle 0|+|\langle 1|\psi\rangle|^2\ |1\rangle\langle 1|$$

It took me a while to work out these technical details, but I understand them now. What I still don't understand is how you interpret results of this kind, and why you think they're relevant to the MWI. These are some of my thoughts:

The Born rule says that $\langle A\rangle_\rho=\mbox{Tr }(\rho A)$ when $\rho$ is a pure state. From this we can easily show that when $\rho=\sum_n a_n|n\rangle\langle n|$, with $\sum_n a_n=1$, $\mbox{Tr }(\rho A)$ takes the form $\sum_n a_n\langle n|A|n\rangle$. This is a weighted average of pure state expectation values, so this result is what tells us to interpret $\sum_n a_n|n\rangle\langle n|$ as a representation of an ensemble with $a_n$ of the systems in state |n>.

What does the qubit calculation really tell us? It tells us that a projection onto an axis will change the state in exactly the same way that the Born rule tells us the state will change. So it tells us that a measurement is a projection onto an axis. But there's one important detail that we must not forget. The reason why we can interpret the projected state as the statistical mixture that the Born rule predicts...is the Born rule! So it's not like we can derive the Born rule from an axiom that says that a measurement projects a point in the geometrical representation of a state onto an axis. We need the Born rule to interpret the result of the projection.

 

[Fredrik]

I'm starting to come around a little bit about the MWI. For a long time, it just seemed more nonsensical the better I understood it, but it's been going in the other direction while I've been writing my posts in this thread. I still think the terminology is confusing at best and idiotic at worst, and the same goes for the statements that MWI proponents make about the MWI, but I think it's possible to make sense of some of their ideas.

These are some of my thoughts:

There's no way to define the MWI without including the Born rule in some form. The idea that defines the MWI isn't that every system evolves according to the Schrödinger equation. It's that there actually exists a physical system (the omnium) with the properties defined by the Dirac-von Neumann axioms of QM. (The alternative is that QM is just a set of rules that we can use to calculate probabilities of possibilities). It's not a crazy idea, but it's really weird to call it "the many-worlds interpretation". It should be called "realism" or something like that (and it sometimes is). Sure, if we think about the consequences of the defining assumption for a while, taking into account the results of decoherence theory, it's pretty clear that this physical system will include both a dead cat and a living cat at the end of a Schrödinger's cat experiment. But it's really hard to make more specific statements about these things.

I think I made a mistake before when I suggested that the MWI must point out the exact mathematical structures that represent the various worlds. It already does, via the Born rule (which tells us that we must be able to reconstruct the Hilbert space of the omnium as the tensor product of the subsystems). There's no preferred way to decompose the omnium into subsystems, and that means that all of the decompositions are equally valid. If we choose one particular decomposition, we end up with a specific set of worlds. If we choose another decomposition, we get a different set of worlds. This is analogous to how different inertial frames in special relativity disagree about simultaneity and many other things.

Note that the picture of the universe as constantly "branching" into more and more "worlds" doesn't even come close to accurately representing the MWI. The time evolution of the state of the omnium is represented by a curve in its Hilbert space. That curve doesn't have any branches. When we decompose the omnium into "the system" and "the environment", the time evolution is represented by two curves (one in each Hilbert space), but neither of them has any branches. They don't even split during those times when the states of the system develops correlations with macroscopically distinguishable states of the environment.

So what happens when e.g. a physicist measures a spin component of a silver atom, using a Stern-Gerlach apparatus, from the point of view defined by the decomposition of the omnium into "the spin of the atom" and "the environment". The first thing that happens is that the interaction between the atom and the Stern-Gerlach magnet causes a correlation between spin states and position states. This is not a measurement, because the position states are not "pointer states" of the environment, in decoherence theory terminology. The moment after that, correlations will start to form between the position states of the atom, and states of the detectors. These detector states are pointer states, so now we have measured the spin, by allowing these correlations to form.

Nothing funny happens to the curves that represent the time evolution of the omnium in the Hilbert spaces of the subsystems, but as soon as the correlations with the pointer states have formed, we assign a new meaning to their projections onto the subspaces in which the spin and position have definite values. We now think of each of the projections in the atom's Hilbert space as representing the state of the atom as described by an environment in the corresponding pointer state. The worlds in this decomposition are just different projections of the two time evolution curves. There may be other decompositions in which it isn't possible to find anything at that time that resembles these two worlds.

The "environment" can be decomposed further into smaller subsystems. We can take one of them to be the physicist performing the experiment. At some point in time, the environment (that includes the physicist) has developed correlations with the atom, but the information hasn't yet reached the physicist. At this time, the physicist needs both of the projections of the atoms state vector to describe its state from his point of view. To him, the atom is now in a mixed state. This is the type of situation in which one physical system needs a mixed state operator to describe the state of another physical system. At a later time, the memory states of the physicist are correlated with the atom's spin states, and we can now talk about worlds that contain physicists with different memories of what just happened, but only given this decomposition into subsystems.

I still feel that the name "the many-worlds interpretation" should refer to a set of statements about the sort of things I've been talking about here, and not to the simple statement that the omnium is an actual physical system. Instead, people claim that the MWI is defined by statements that can't possibly define an interpretation, and they call the only set of statements I have heard of that's about how subsystems view other subsystems "the relational interpretation".

Note that as long as we're talking about a formulation of QM based on the Dirac-von Neumann axioms, there are only two interpretations: The realist interpretation (a.k.a. the MWI) which merely states that the omnium exists, and the anti-realist interpretation (a.k.a. the statistical interpretation or the ensemble interpretation) which states the opposite, i.e. that QM is just a set of rules that tells us how to calculate probabilities of possibilities. Any other interpretation of this axiomatic framework can only be a clarification of what the MWI is about.

There are of course other axioms that we can take as the starting point, e.g. the path integral formulation. There are two mutually exclusive possibilities in this case too. Either the math describes what actually happens or it doesn't. I'm not sure what the realist interpretation says here. Maybe the realist interpretation of these axioms isn't the MWI, but the transactional interpretation? (I only have a rough idea about what the transactional interpretation is aobut, so I can't really tell). In that case, the name of the MWI is justified. We need to call it something other than "realism" because the realist interpretations of different formulations of the theory can be very different.

 

[Dmitry67]

Fredrick, cool
For you, what was a set of axioms of MWI?

Because if you say that there is just unitary evolution of omnium, then it is not takes seriously because 'it does not describe the classical world'

When you explain it, you get into the wordy stuff, and other people complain that 'MWI is just a long blah-blah-blah'

 

[Fredrik]

Fredrick, cool
For you, what was a set of axioms of MWI?

The same as the axioms for the statistical interpretation (Link), plus the additional assumptions that it makes sense to consider the Hilbert space of the universe (even though it includes yourself), and that a state vector in that Hilbert space is a representation of all the properties of a physical system (the omnium). (The statistical interpretation doesn't assume that, and it never includes the observer in the Hilbert space).

Because if you say that there is just unitary evolution of omnium, then it is not takes seriously because 'it does not describe the classical world'

The classical world is explained by what I said about decoherence, correlations between states of subsystems, and how the subsystems describe each other. The reason why we never experience superpositions is that consciousness involves changing memory states. Each pointer state of the environment (which you're a part of) has your brain in a well-defined memory state, not a superposition. Decoherence ensures that the distinguishable memory states of your brain are correlated with the eigenstates of the observable you're measuring. (Hm, I know that there's something called the "many-minds interpretation", but I have no idea what it says. We may be entering its territory here. If that's the case, then "many-minds" is one of the interpretations that can be described as just a clarification of what the MWI is actually saying).

When you explain it, you get into the wordy stuff, and other people complain that 'MWI is just a long blah-blah-blah'

Yes, it gets wordy, but I have never really had a problem with the amount of words required to explain the consequences of the assumptions that define the intepretation. My objections have been against the lack of a clear explanation of what the MWI says, or against really bad explanations like the infamous Everett FAQ. Max Tegmark came pretty close to defining the MWI properly, but he blew it (in my opinion) by failing to realize the significance and importance of the Born rule.

It's of course still possible that I have misunderstood something fundamental, and that I'm wrong about a lot of this. I still don't know decoherence very well for example, so when I talk about pointer states and stuff like that, I only have a rough idea about what they are.

 

[hamster143]

You've correctly grasped the essence of MWI. Once you admit the possibility that the observer is a quantum object that may be in a superposition of states with different sets of memories, you're more than halfway there.

Note that as long as we're talking about a formulation of QM based on the Dirac-von Neumann axioms, there are only two interpretations: The realist interpretation (a.k.a. the MWI) which merely states that the omnium exists, and the anti-realist interpretation (a.k.a. the statistical interpretation or the ensemble interpretation) which states the opposite, i.e. that QM is just a set of rules that tells us how to calculate probabilities of possibilities. Any other interpretation of this axiomatic framework can only be a clarification of what the MWI is about.

There are also varying degrees of positivism/agnosticism and varying points of view. An observer "out of the universe" would be able to tell the difference, but an internal sentient observer would be perfectly able to describe his own history and experience using, say, Copenhagen and wavefunction collapse, and treat everything about splitting of himself as Occam razor violating nonsense.

I wonder if it's possible to set up an experiment that creates a superposition of a human being in different states.

Note that the picture of the universe as constantly "branching" into more and more "worlds" doesn't even come close to accurately representing the MWI.

This all depends on what you mean by "world". There's a definite branching of sentient beings and of classical worlds. There isn't any branching of the whole state of the universe in the big Hilbert space - that one simply evolves according to Schrodinger's equation.

 

[Count Iblis]

I think that in the MWI, the Born rule can be derived from the weaker assumption that measuring an observable of a system that is in an eigenstate will yield the corresponding eigenvalue with certainty.

 

[Fredrik]

I think that in the MWI, the Born rule can be derived from the weaker assumption that measuring an observable of a system that is in an eigenstate will yield the corresponding eigenvalue with certainty.

That's what Wikipedia claims (here), and their reference for that is this 1968 article by James Hartle. I checked it out some time ago and he's clearly also assuming that the Hilbert space of a physical system is the tensor product of the Hilbert spaces of its subsystems. That's a very strong assumption. I don't have all the details figured out, but it seems to me that this assumption is essentially equivalent to assuming that the Born rule holds. The weak assumption that you mentioned is probably just the piece that needs to be added to make them completely equivalent.

 

[Fredrik]

...an internal sentient observer would be perfectly able to describe his own history and experience using, say, Copenhagen and wavefunction collapse, and treat everything about splitting of himself as Occam razor violating nonsense.

I still don't think that QM is anything more than a set of rules that tells us how to calculate probabilities of possibilities, but I think that using Occam's razor as an argument against the MWI makes about as much sense as using it against special relativity because it includes more than one inertial frame. If (the Dirac-von Neumann version of) quantum mechanics actually describes reality (which is hard to dismiss based only on Occam, considering that no other theory does a better job), this reality clearly must include many worlds. Even if some other version of QM is an accurate description of the world, then why would we consider it "simpler"? I don't think e.g. Bohm or a realist intepretation of the path integrals formulation is any simpler. The worlds are only "points of view" in the linear and deterministic evolution of a single point in a vector space, and I think the people who try to use Occam against the MWI have completely failed to understand this point.

I wonder if it's possible to set up an experiment that creates a superposition of a human being in different states.

I think every human is always in a superposition in most decompositions into subsystems, but the only decomposition that mattters to that human is the one that describes the universe as consisting of his memory and everything else, and in that decomposition, his memory states keep developing correlations with eigenstates of whatever he observes. Conscious experience is the development of such correlations. An important detail here is that the correlations form so quickly that the human won't ever notice that he failed to experience the time of decoherence.

This all depends on what you mean by "world". There's a definite branching of sentient beings and of classical worlds. There isn't any branching of the whole state of the universe in the big Hilbert space - that one simply evolves according to Schrodinger's equation.

Good point. I agree.

 

[Gerenuk]

What's the advantage of the MWI?
(What's the aim of any interpretation in general?)

To me it seems MWI makes an even more abstract mess than what we had before with "conventional" thinking.

 

[Fredrik]

What's the advantage of the MWI?

(What's the aim of any interpretation in general?)

It's a way to interpret QM as a description of what actually happens, instead of as nothing more than a set of rules that tells us how to calculate probabilities of possibilities. That's exactly what interpretations are about.

To me it seems MWI makes an even more abstract mess than what we had before with "conventional" thinking.

What do you consider conventional?

 

[Gerenuk]

Hmm, then I personally prefer the set of rules without the complicating extension like MWI around it.

Conventional I consider the Copenhagen interpretation I suppose.

Actually I do favour interpreting the set of rules of QM as to make the picture either more intuitive or so that one can grasp QM effects better in the mind or make the picture more well defined so that one has never doubt about what the result of a question might be. I cannot see MWI achieving either of these two. I also believe a good interpretation will give as a more correct and complete version of QM.

Admittedly I don't understand MWI fully, but that also shows that it doesn't simplify so much?

What is your opinion? Why do we need an interpretation and what should it achieve?
(I repeat that my opinion is that it should make QM either easier or extend it)

 

[zenith8]

Actually I do favour interpreting the set of rules of QM as to make the picture either more intuitive or so that one can grasp QM effects better in the mind or make the picture more well defined so that one has never doubt about what the result of a question might be. I cannot see MWI achieving either of these two. I also believe a good interpretation will give as a more correct and complete version of QM.

Hi Gerenuk,

Hmmm... you seem to be describing de Broglie-Bohm..

I found the following on-line lecture course helpful: http://www.tcm.phy.cam.ac.uk/~mdt26/pilot_waves.html

 

[Gerenuk]

Thanks a lot for the link. These kind of interpretation are actually really my favourite, but I also haven't studied them yet. So I've collected information and books and will study them soon.
My first impression was that the pilot wave is still a bit awkward.

Are there any less-known interpretations that are similar to that?

 

[zenith8]

Thanks a lot for the link. These kind of interpretation are actually really my favourite, but I also haven't studied them yet. So I've collected information and books and will study them soon.
My first impression was that the pilot wave is still a bit awkward.

Are there any less-known interpretations that are similar to that?

No there aren't - as far as I know.

Your impression that the de Broglie-Bohm pilot wave approach is awkward, I would respectfully suggest, is not true.

Tell you what. You don't have to go through the full Cambridge de Broglie-Bohm course. I note that the guy recently added a popular lecture to the bottom of his slides page. Why don't you read that (should take half an hour) then, if you still think it's awkward, we can talk.. (the many worlds guys have had their four pages).

 

[Fredrik]

Why do we need an interpretation and what should it achieve?

We don't need one, but it would be nice to have one, if it really does describe what actually happens.

Hmm, then I personally prefer the set of rules without the complicating extension like MWI around it.

I do too.

I also believe a good interpretation will give as a more correct and complete version of QM.

A correct interpretation would certainly do that, but I doubt that there is such a thing.

Conventional I consider the Copenhagen interpretation I suppose.

I don't think there's a universally accepted definition of the Copenhagen interpretation, but most people would say that it asserts that the laws of QM do not apply to measuring devices(!) even though it applies to the components they're made of(!), and that measurements "collapse" wave functions into eigenstates. The problem with this is that it's complete rubbish that no one has ever believed is true. The first assumption introduces an obvious inconsistency into the theory, and the second implies that we have not one, but two rules that specify how systems change with time. That makes another inconsistency possible.

I would say that the MWI must be defined by the assumption that QM actually describes something, and that all that stuff about "worlds" follows logically from that assumption. (Those logical arguments are quite complicated, as you can see in my posts above). We may not like it, but it's certainly better than the version of the Copenhagen interpretation that I described above.

 

[Hurkyl]

Hmm, then I personally prefer the set of rules without the complicating extension like MWI around it.

The main epistemological point of MWI is that it is essentially the only interpretation that is not an extension.

The extra "complication" is mainly because it looks different. Also, it's partly because it does not use any extensions -- like collapse -- that could be used to simplify things.

 

[Hurkyl]

For Fredrik:

There may be a higher-level difference in how we picture QM.

I prefer something more like the C*-algebra picture. The main thing is the algebra of observables. Quantum states are functions that map observables to complex numbers that satisfy certain properties. (we might call the value of such a function the "expected value" of the observable on the state)

For any particular state, we can apply the GNS construction to create a Hilbert space in which our state is represented by a ket. The Born rule simply comes from the definition of what it means for a ket to represent a quantum state -- i.e. that $\rho(O) = \langle \rho | O | \rho \rangle$.

While the ket picture is useful for some calculations, it obscures what's happening when we want to restrict to subsystems or whatever.

 

[hamster143]

That's what Wikipedia claims (here), and their reference for that is this 1968 article by James Hartle. I checked it out some time ago and he's clearly also assuming that the Hilbert space of a physical system is the tensor product of the Hilbert spaces of its subsystems. That's a very strong assumption. I don't have all the details figured out, but it seems to me that this assumption is essentially equivalent to assuming that the Born rule holds. The weak assumption that you mentioned is probably just the piece that needs to be added to make them completely equivalent.

Perhaps I'm missing your point, but how could the Hilbert space of a physical system NOT be the tensor product of its subsystems? That seems axiomatic to me.

using Occam's razor as an argument against the MWI makes about as much sense as using it against special relativity because it includes more than one inertial frame. If (the Dirac-von Neumann version of) quantum mechanics actually describes reality (which is hard to dismiss based only on Occam, considering that no other theory does a better job), this reality clearly must include many worlds.

The observer is never able to experience a splitting of himself, because he's always in a state of definite memory. In places where MWI says that the observer is split, the observer instead observes wavefunction collapse. So, from the point of view of the observer, those "other" states of him are unobservable and do not exist. From his point of view, the Occam-minimal, positivist interpretation is Copenhagen and not MWI. Even if MWI is the proper description of the totality of the universe.

It would be more interesting to design an experiment that "proves" to an observer that he did, in fact, split, but, short of quantum suicide, nothing good comes to mind.

 

[Fredrik]

Perhaps I'm missing your point, but how could the Hilbert space of a physical system NOT be the tensor product of its subsystems? That seems axiomatic to me.

There's more than one way to use two Hilbert spaces to construct a third. We use the tensor product because we want to make sure that the probability of obtaining two specific results in two independent measurements on two non-interacting systems is the product of the two probabilities assigned by the Born rule. See this post for a few more details about this, and this one for more about the tensor product in general.

 

[Fredrik]

I prefer something more like the C*-algebra picture.

I think I will too when I have learned it. I have bought the books already. 1, 2. I just need to get through them. It looks like it will take a long time. I'm going to finish another book (3) before I get deep into these two.

Nothing in your summary was new to me, but it covers most of what I know already, which is just the "big picture" and none of the details. One of the things I feel that I do understand is that there isn't a huge difference between the C*-algebra formulation and the Dirac-von Neumann (Hilbert space) formulation. It avoids superselection rules, but those aren't relevant here since we can consider a quantum theory that doesn't have any. It may be a better starting point for derivations of rigorous theorems, but that doesn't seem to be very important here either. It's prettier, but...you get the idea.

While the ket picture is useful for some calculations, it obscures what's happening when we want to restrict to subsystems or whatever.

OK, that's a statement I haven't heard before. How does the C*-algebra formulation deal with subsystems, and how is it relevant? Does it imply that something I said is wrong?

By the way, I'm quite fascinated by the fact that there are so many different approaches that lead to essentially the same thing. The Dirac-von Neumann approach defines a mathematical structure (a complex separable Hilbert space) to represent the states of a physical system. The C*-algebra approach defines a mathematical structure (a non-abelian C*-algebra) to represent the observables, and the quantum logic approach defines a mathematical structure (a something something orthomodular lattice that something something ) to represent experimentally verifiable statements. OK, I know even less about quantum logic than about C*-algebras, but I've bought a book about that too. 4. If I can get through all of these by the end of 2010, I'll be quite pleased with myself.

 

[hamster143]

There's more than one way to use two Hilbert spaces to construct a third. We use the tensor product because we want to make sure that the probability of obtaining two specific results in two independent measurements on two non-interacting systems is the product of the two probabilities assigned by the Born rule. See this post for a few more details about this, and this one for more about the tensor product in general.

In order for the tensor product construction to work, all we need is for the two Hilbert spaces to be orthogonal, which is automatically true in all interpretations of QM as long as two systems are non-overlapping.

 

[Fredrik]

In order for the tensor product construction to work, all we need is for the two Hilbert spaces to be orthogonal, which is automatically true in all interpretations of QM as long as two systems are non-overlapping.

The subsystems aren't represented by orthogonal subspaces. For example, if you take the tensor product of a 2-dimensional and a 3-dimensional Hilbert space, the result is 6-dimensional, not 5-dimensional. The choice to use the tensor product is definitely non-trivial.

(I'm going to bed now, so I won't be writing any more replies for at least 8 hours).

 

[Dmitry67]

Returning to the Born rule… I am keeping to have some kind of internal dialog with myself, and can't escape this trap. May be someone can help me. As a reminder, I like MWI, but the Born rule… personally, I think for MWI it must be interpreted differently. So:

“I am driving to work. But there is a branch where (because my brain malfunctioned) I killed/attacked people and ended in a jail/got killed”
“Yes, such branch exists, but the probability is very very low”
“But our sense of “being real” does not depend of “intensity” of a branch!”
“How is it possible?”
“Generate 1000 random decimal digits and read this number. Now you are on one of 10^1000 branches. Do you feel 10^1000 times less real after you did it?”
“Definitely not. Then intensity is not important. Even if we have Frequent event (90%) and Rare event (10% probability), and we make 100 tries, then all combinations are possible, like FFFFFFFFFFFF… (100 Fs), and RRRRRRRRR (100Rs which is also rare). All 2^100 branches must exist! There are 2^100 observers observing all these branches”
“Lets make that experiment. I bet we get about 85-95Fs and 5-15Rs. What is a prediction of MWI?”
“Hmmmm…. Everything is possible…”
I am blocked at this point.

 

[Dmitry67]

P.S.
If anyone claims that Born rule is proven in MWI first I need to know, how Born rule is defined, because there is NO probability MWI. It must be defined is other terms, like, total number of observers observing X divided by the total number of observers in some subbranch on a given basic...

 

[Fra]

What is your opinion? Why do we need an interpretation and what should it achieve?
(I repeat that my opinion is that it should make QM either easier or extend it)

I think this is a motivated question. I posed the same in post 43, where I gave my view.

(I guess an addition would be to note that my interpretation is also somewhat related to the version of MWI called "many minds" instead of many worlds; which is basically the idea that the different worlds are simply the different views the actual observers have that populate our one universe. The problems with this appoach, are then solved by letting the popultion and thus worlds evolve - in this picture the different worlds do interact; which is why it's better seen as many minds rather as many worlds, and from where I see it, this view gives a very good stance for expansion and unification of current theory - in line with my "pet views")

Edit: To respond again in little more detail to the point with my preffered view - it apparently holds the potential of unification since INTERACTIONS can probably be inferred from the rational player analogy (where in economy the dynamics of the economical system is inferred from the assumption of each player acting rationally) where each subsystem of the universe acts originally at will, but an evolution where selection for rational actions takes place. This is my motivation for my view. It is a vision, not finished theory, but the rationality for my preference lies in that I see it as a very natural and promising stance for extending current models and solving some of the open problems.

What the point is with the regular standard MWI I don't know. I don't see it either :)

/Fredrik