Many-Worlds Interpretation Issue

[Quaoar]

OK, I have a problem with the many-world interpretation, namely the quantum suicide experiment. My problem: How exactly does your consciousness transfer over? When you die in your current "reality," do you just swap randomly to one of the parallel worlds? Or are each of the conscious entities spawned at each instant completely independent from each other?

I'm just wondering if anyone actually has some logical insight into this problem. Basically, I can't see the quantum suicide experiment proving anything, because it's highly unlikely that you're in the one world where the gun doesn't fire after pulling the trigger 100 times. Oh sure, copies of you would persist in various parallel universes, but considering they're probably independent from you, who cares?

 

[setAI]

the idea is that with every event- all possible results of the interaction occur and expand the hermitian matrix- the 'universes' are all branching off from the local event so there is no 'transfer'- it is just that one or some of the transfinite branching possibilities continues while the others die- the 'survivor' in a quantum suicide gedankenexperiment is the physical case were events did not cause the scientist's brain to cease working- if we assume the gun has fired and the bullet is about to enter the skull- the survivor is a branching case where for instance the atoms in the bullet fail to interact with any of the atoms in the skull [or none that cause lethal damage] HIGHLY unlikely but nevertheless this result is a valid one in the Hilbert space-

given the highly unlikelihood of physical survival in such an experiment- or in ANY death [death is a complex process of many interdependent physical events] I personally feel that a corollary to quantum suicide is that it is centillions of orders of magnitude more probable that any dying organism is reconstructed through an archeological resurrection process or 'ancestor simulation' through advanced quantum/hyper computation than through a miraculous survival- the hilbert space would contain an unlimited number of cases where some outside agency ran a quantum computational simulation of the experimenter's world-state and thus those non-local computational processes would by computing the hilbert space of the world-state be directly connected to it as a set of branching possibilities as with the local possibilities- so anyone performing the quantum suicide experiment would just 'wake-up' in a technological reconstruction as with any other dying organism- rather than experience survival of the experiment in the same history- those rare outcomes are still of course in the Hilbert space- but probability shows that any measured outcome would most likely be a non-local archeological reconstruction of the experimenter's state at death

in this view quantum immortality is still the result- but instead of an observer seeming to live forever by always surviving all injuries and illness- then of course somehow surviving aging- instead every observer lives a normal life- then a crucial injury/illness followed by an awakening in some form of technological reconstruction- most likely by a super-intelligent society which evolves in one of the possible futures of the observer's own world [so a resurrection/reconstruction is still more likely even if in some/most futures the world's intelligence goes extinct- there will ALWAYS be futures as well as parallel presents and alternate pasts of ANY world in which limitless godlike technology is achieved and all possible life-histories of any possible observer in the hilbert space of that world are extracted/reconstructed-] after such a reconstruction the options for the eternal continuation of an observer's perspective are limitless and unknowable


there is nothing strange or mystically unscientific about any of this[!]- it may SEEM like fantasy but it is merely what the Schrödinger equation tells us what happens with ANY quantum system: all possible histories occur and the probability of specific types of outcomes determine which sets of histories are observed more- it is just in the case of the highly specialized systems we call conscious minds- that the effect of the Schrödinger equation REQUIRES this odd form of immortality for any conscious observer- an observer can only cease to exist if there are no possibilities of survival in the ENTIRE HILBERT SPACE- and that is not possible- there will always be a tiny few solutions that offer survival- and many solutions which copy/continue the observer's consciousness through reconstruction of their information-

 

[Quaoar]

These are all points that I understand, what I'm not understanding is what someone who performs the quantum suicide experiment experiences. I would think that surviving the experiment 100 times in a row is more probable than any reconstruction by a future civilization (considering the gun is measuring the spin of a single particle).

I guess the question is semi-philosophical. It's my personal belief that your consciousness is attached to yourself. Taking this into consideration, at each time-step, does the consciousness fragment into infinitely many independent copies? Or are they all still intrinsically linked, where if one (or several) of the copies die, consciousness is maintained because the person still lives in at least SOME of the worlds (or they'll be resurrected in the worlds in which they have died).

My feeling is: I will still cease to be conscious at some point in my life, so I would only have "immortality" in that my copies would survive. But since I only experience this one world, that doesn't matter, since I can't suddenly experience those OTHER worlds.

 

[vanesch]

OK, I have a problem with the many-world interpretation, namely the quantum suicide experiment. My problem: How exactly does your consciousness transfer over? When you die in your current "reality," do you just swap randomly to one of the parallel worlds? Or are each of the conscious entities spawned at each instant completely independent from each other?

I'm just wondering if anyone actually has some logical insight into this problem. Basically, I can't see the quantum suicide experiment proving anything, because it's highly unlikely that you're in the one world where the gun doesn't fire after pulling the trigger 100 times. Oh sure, copies of you would persist in various parallel universes, but considering they're probably independent from you, who cares?

In fact, this is a question which is entirely open to your own spiritual inspiration ! The reason is that it is totally impossible to say "when a state has the SAME consciousness as another state". This is like trying to argue for or against re-incarnation. How do you know that you are not in fact the *same* consciousness as, say, Julius Ceasar (but your memory an character being physical aspects of your bodystate, you don't have any memory of it of course).

The issue with quantum suicide is exactly the same, and my personal view is the same as yours in fact. I tend to think that there is a continuity from one state to another for the "same" consciousness, and that you are NOT each time randomly redistributed (as I said before, then there' s no reason you do remain attached to the same body! You could just as well end up the next moment as the "conscious experience" of your neighbour, or your cat, for that matter). So if you want to keep "continuity" in the conscious experience, and at each "branching" you draw (according to the Born rule) in which of the issuing branches you're going to end up, you might as well end up in a dead body state, and then it's over. Or not. Or you might go to heaven, or to hell. Or become Napoleon. There's no sensible way to pick one view over another.

So, next time you're on a spicy party, and one proposes you a game of Russian Quantum Roulette, don't bet on it :-)

 

[vanesch]

My feeling is: I will still cease to be conscious at some point in my life, so I would only have "immortality" in that my copies would survive. But since I only experience this one world, that doesn't matter, since I can't suddenly experience those OTHER worlds.

Yes, my idea too. Of course, like the ancient Egyptians, as long as a copy of you lives on somewhere, you live on too! As long as your name is written somewhere, you live on too. But that's a poetic version of survival. I think - as you do - that you're dead. But hey ! You'll find out ! When you'll be experiencing a 750 years old body, you can take it that the quantum suicide stuff, after all, was correct !

 

[setAI]

as an old-school AI/cog science geek I find that concepts of copies and identity are irrelevant- a human's sense of identity is based on specific neural connections and feedback from the systems the brain has a certain kind of control over- if I were to make such a connection with a fire-hydrant- that hydrant would seem to be as much a part of me as my heart or hand or memories! and even mere non-physical psychological trauma can cause a DISCONNECTION of your sense of self and parts of your body- we see this in those that suffer dissociative identity disorders where they feel that one of their own limbs is 'alien' and must be amputated-

a self is a construct of neural information processing- which is built from a substrate of quantum mechanical matter that is always branching it's histories-

things get even more dicey when you consider that TIME is vital for consciousness- we are aware of our existence because our minds are structured to compare current sensory data with stored records of past sensory experience- yet Time itself is a quantum mechanical concept that is now being understood as not flowing at all- but rather that clock-like systems with records of 'past states' experience a illusory flow of time from that built in comparison to records process- time does not flow- and states are not linked by anything but the probability distribution of possible histories that is formed by their built-in dynamics-


"Philosophically, I would like to add to that that it simply does not make sense to say that there are parallel copies of all particles that participate in microscopic interactions, but that there are not parallel copies of macroscopic ones. It is like saying that someone is going to double the number of pennies in a bank account without doubling the number of Pounds.
" ~David Deutsch

 

[vanesch]

It makes all the difference when you consider issues such as:
"do you prefer your copy to be tortured if this can render you rich" from a non-behavioural viewpoint!

 

[Doc Al]

"copies" in MWI?

Going back to the OP and the notion of "copies" or parallel "universes" in MWI: What are the nature of these "copies"? How are are they formed? How many are they? (Silly questions, I'm sure, but maybe you can straighten me out, vanesch! )

The various branches or copies seem to be somehow tied to human consciousness. Is this true? (Seems rather anthropocentric for a physics interpretation, so I'm sure I'm missing something.)

What about the countless interactions among particles/systems that don't involve "measurements"? Do they provoke branching as well?

As to how many branches form, that completely baffles me. Say I perform a Stern-Gerlach experiment to "measure" the spin of a sodium atom. Are there just two branches, one in which I see spin up, the other in which I see spin down? Or are there countless gazillions of branches? Some in which I measure spin up wearing a red bow tie, some where I have no tie, some where I have two heads (we followed a different evoluntionary path in that branch, apparently), and so on... Please help me understand this. (These examples may sound facetious, but I've seen similar statements.)

 

[vanesch]

Oh no I get half of my peer mentors on my head for this (and the other half isn't interested )

As I pointed out already several times, this "branching" in MWI is often misunderstood. Branches are not objective properties of a wavefunction. MWI only makes one hard formal statement: that is that "objective reality" is described by a unitary structure (to be sliced in a specific reference frame into a wavefunction and a following a timelike evolution described by a unitary operator which is the "time evolution operator"). Of course, one can switch reference frame, then the wavefunction and the unitary operator changes, under a representation of the Lorentz group. But we stil have the same unitary structure. So much for reference frame independence.
I'll now assume we work in a specific reference frame, when talking about the "wavefunction".

In fact, the above is the unitary part of standard "Copenhagen-style" quantum theory. But the projection postulate is left out.

But what has this to do with observation ?
How does a completely formal framework "generate" observations ?
How is this happening in Newtonian theory, say ?

Well, Newtonian mechanics can be described by a flow in phase space. A point in phase space then corresponds to a state (of the entire entity observer + system if you want) and the dynamics is given by a hamiltonian flow over phase space.
Now, there's something special in this Newtonian phase space description, which is that the phase space can be written as the product of a system phase space and an observer phase space, and that a point in the overall phase space corresponds to a pair of points in the two subspaces. It is hence possible to have "a state of the system" and "a state of the observer". We now define "observations" as being different states of the observer, and as, to a single overall state, there only corresponds one state of the observer, once the overall state is given, and once we say what is an observer (as a subspace of the overall phase space) we can associate with each observer state "a definite observation result".

In other words, if we have the Moon-Joe system, and Joe looks at the moon, then the Moon-Joe system will be, through this interaction, in a specific state, which can be split in "a state of the Moon" and "a state of Joe". The state of Joe will contain the specific observation of Joe of the moon. As there is a 1-1 link between the point in the system subspace, and the observer subspace, we usually do not take into account the observer subspace, and we limit ourselves to the phase space of the moon, assuming that Joe's observations will reveal that point.

But you see that there is nevertheless a needed assumption, which is very tiny and straightforward in this case.
One should now, to be complete, associate a "state of consciousness" to each point of the phase space of Joe's body. Well, some points will correspond to "Joe is dead", but some points will correspond to certain conscious experiences by Joe. In this case, there is also a 1-1 relationship between the phase space description of Joe's body, and any conscious experience by Joe.

We could say that we are in a "naive realism" case, where body = conscious experience = observations = reality, because all these different things are in a 1-1 relationship, given a single point in phase space.

Nevertheless, nothing stops us, in Newtonian physics, from considering the INDEPENDENT evolution of SEVERAL points in the phase space. As the Hamiltonian flow is independent of this, we could have "parallel worlds" evolve in one and the same phase space, simply by having several points moving in the same overall phase space, following the same overall dynamics. But, the flows of individual points being independent, there's no way for "one world" to "be aware" of any of the other points. Nevertheless, in Joe's body subspace, we would now have several points evolving, and hence different "parallel conscious experiences" associated to the same body phase space. They'd not know about one another.
In fact, this is not so crazy, and this is an old discussion about whether "alternative possibilities are real". We could even have a DISTRIBUTION of 'worlds' in phase space, which evolves according to the Liouville equation, and which would describe the "density of worlds" evolving in classical phase space.
Nevertheless, the observation is that this has absolutely no observational effect, so these parallel worlds in classical phase space have no influence. That doesn't mean that they aren't there, but they have no purpose. So it remains, in this case, a totally hypothetical concept.
It is nevertheless, a fun exercise in "parallel world thinking": how do we know that our "world" is the only point evolving in classical phase space ?
Once there are these "several points" or this "density of world points", the question is: what does Joe experience ? Which Joe ? If you are "Joe" you are not "Joe's body" but ONE of the points in the phase space of Joe. So there is an association of your subjective, conscious experience, and ONE of the different points in phase space now.
This wasn't an issue when there was only one point. Now, it is. You could say that the one you will experience is "drawn" from the statistical ensemble of points.

MWI quantum theory is faced with a similar situation. We now have our unitary structure. In fact, we could even have several unitary structures, one for each different initial state ! But let's not complicate issues for the moment.
As we saw, even in Newtonian physics, we have to specify the "degrees of freedom of an observer". So in MWI too. This corresponds in picking out the degrees of freedom of Joe's body (as in Newtonian physics).
In QM, this corresponds to a sub-Hilbert space: H_Joe-body
In fact, the overall hilbert space can be written as H_Joe-body (x) H_rest

We now look at H_Joe-body. This hilbert space is spanned by all the different possible microstates of Joe's body. We can "coarse-grain" it, to lump it into subspaces which correspond to different conscious experiences of Joe.
To each of these different states corresponds more or less a lump of points in the classical phase space of Joe's body.

And now we apply a Schmidt-decomposition of the overall state (wavefunction) according to the split H_Joe-body (x) H_rest, but relump terms in the coarse-grained H_Joe-body space.

It turns out that the Schmidt decomposition so effectuated, under the unitary time evolution, usually does not mix the different terms (unless specific quantum experiments are performed).
Now, to each of these terms corresponds also a point (or lump of points) in the classical phase space of Joe, and the time evolution mostly corresponds to the Hamiltonian flow in the classical phase space. So we can say that a branch, or term of such a decomposition is equivalent to considering a "point" in the classical Joe phase space. We could even think of a kind of "distribution" of phase space points, with "weights" given by the Hilbert norm of the term corresponding to the (lump of) points. In other words, the Hilbert norm of each term in the wavefunction decomposition corresponds to the weight in a distribution of classical phase space points in Joe's body phase space.
We seem to be in the "multi - point" situation of classical physics. Each of these points is a "branch" from the point of Joe.However, sometimes, the quantum evolution gives rise to interactions which "split" one phase space point into several (branching). This corresponds, in the classical case, in a lump of weight A to be split in lumps of weight A1 and A2 (so that A = A1 + A2).

This comes about when the quantum evolution does not give rise to a strict hamiltonian flow on classical phase space ; in other words, when Joe observes a typical quantum phenomenon. It also occurs, as a "smearing out" of the "distribution of Joe points" over the phase space, as in classical chaotical Hamiltonian flow: the initial lumps smear out and split.

So, from this PoV, MWI looks a lot like "multiple-point, or better: phase space density" evolution in classical phase space, and "consciousness" or subjective awareness, comes in because you have to PICK one of the Joe-points to be a "particular" Joe. This picking is stochastic, and has to occur according to the density of "Joe points" in the phase space (in other words, proportional to the Hilbert norm --> this is nothing else but the Born rule). The specific point chosen will then give you the corresponding "experience" that goes with it, the "observations" or "memory state" etc...

There is still one difference with the "classical phase space density" in strict classical physics. The Hamiltonian flow in classical physics gives one and exactly one trajectory to a point in phase space. So once a specific point is "you", one can assume that "you" later will be associated with the same point. Things get more subtle in chaotic classical dynamics: a single point still has one and only one trajectory, but a LUMP of points might spread out. Is your conscious experience associated with one point, or with a lump ? What happens when the lump spreads out ? Do you "branch" into several possible states ?
In the quantum case, the Hamiltonian flow is only approximative. Quantum spits happen. So in this case, a "single" observer will see his "blob in phase space" split, and hence will be drawn statistically to go with one or the other. This is the irreducible statistical character we seem to observe in quantum theory and which is not present in deterministic classical dynamics of phase space points.
But it only comes about because of our mapping from the (deterministic) quantum state onto SEVERAL blobs of points on the classical phase space of the observer body, and our association of a conscious experience with these classical phase space points.

The identification between body (= phase space of body) and an experience was only possible when there was one single point in phase space. When there are several points, there is a distinction between an experience (associated to a point) and the body (= a phase space).

So, experiences, or "branches" or "worlds" correspond to POINTS in phase space, or states. If there are many points, well then there are many "worlds".

But note that to consider this, and to even consider "branches" and "worlds", it was necessary to SAY what was an observer (to pick the body degrees of freedom).
So these concepts are observer dependent.

Objectively, there's only the overall unitary structure.

As, in classical physics, objectively, there's only the overall phase space + Hamiltonian flow + point in phase space, or:

overall phase space, + density + Liouville evolution of the density.

 

[Simone Severini]

Dear All,

You may find interesting to read

http://en.wikipedia.org/wiki/The_Garden_of_Forking_Paths

The Garden of Forking Paths by Borges...

Simone

Simone Severini
http://www-users.york.ac.uk/~ss54

 

[Farsight]

Sorry vanesch. You work so hard to give very long explanations, but I just don't buy any of the Multiple Worlds Interpretation.

David Deutsch: "Philosophically, I would like to add to that that it simply does not make sense to say that there are parallel copies of all particles that participate in microscopic interactions, but that there are not parallel copies of macroscopic ones. It is like saying that someone is going to double the number of pennies in a bank account without doubling the number of pounds".

David Deutsche glosses over the "particles" upon which his whole logic stands. It is like saying financial transactions are caused by flying pennies, then when nobody can locate them, using them to build a tower of parallel universes.

 

[vanesch]

Sorry vanesch. You work so hard to give very long explanations, but I just don't buy any of the Multiple Worlds Interpretation.

I don't ask you to buy anything, you know !

The only thing I'm pointing out, is that the cornerstone, the founding principle, of quantum theory is the superposition principle. It is a very strange principle you might object to, but it forms the cornerstone of quantum theory, in the same way as the principle of relativity and the constancy of the speed of light form the cornerstone of SR, and the principle of equivalence and general covariance form the cornerstone of GR.

Given this, the very basic principle of quantum theory tells you already that outcomes will be multiple (that when you flip a coin, that both results happen simultaneously). If you don't buy that, then you don't buy the cornerstone of quantum theory. ** I have no problem with that ** However, people usually have a double standard, and say that quantum theory *is* correct, *is* universally applicable etc... and then refuse to consider the basic, universal application of its founding principle.

It is my conviction that the correct interpretation of quantum theory is to take its founding principles seriously. That doesn't mean that this founding principle of quantum theory is also a principle of *our* universe ; one would in fact be inclined to say it isn't, because of the at first sight absurd conclusion to which it leads.
And then one has to think a bit further, and ask oneself: how would a universe in which this principle WERE correct, look like ? What would be *OBSERVED* in such a universe, by creatures living there ? And then, it turns out, that by making some additional hypotheses about what creatures in a toy universe "experience", that it is not impossible to make this toy universe look exactly like ours. That doesn't prove of course that our universe has anything to do with that toy universe. It doesn't prove that the superposition principle is a correct principle of nature. And it doesn't prove that quantum theory is somehow "correct".

However, it does indicate that the intuitive refusal of considering the superposition principle as even a viable idea, is only that: a gut feeling. It isn't rooted in any observation. It's just rooted in our desire for naive realism. Maybe our desire for naive realism is ultimately correct (in which case the superposition principle is, from the start, excluded, and hence quantum theory is a totally bogus theory based upon a totally crazy idea which doesn't apply). But it is not more than that, and this intuitive gut feeling might just be misled too, in the same way as once, we couldn't accept that man descended from the apes, or that the Earth wasn't flat, or wasn't in the center of the universe. In all these cases, the right way to see that the "crazy proposal" isn't so crazy, was to try to imagine, in a toy universe where said crazy principle WAS postulated to hold, how things would look like. What would the sky and the motion of the planets look like when the Earth turned around the sun ? How come people living in Australia do not "fall off" the Earth ? Why don't we "feel the Earth turn" ? etc...
Now I'm well aware that these items are by far less "intrusive" into our intuition than what is asked for by MWI - it is another scale of denial of naive realism ("we don't feel the Earth move, so it doesn't move", and "we see things turn around us, so we're in the center", and "the world looks flat to us, so it is flat"). But it is only that: a quantitative change.

It is maybe possible to find other principles, and build other theories, that will result in empirically equivalent theories to quantum theory (or at least, empirically equivalent to those parts of quantum theory that have been tested). It is also possible to consider that the superposition principle is not universally applicable, but is an approximate idea that has a limited scope of applicability. But in all these instances, one cannot make the claim that quantum theory is a universal, and correct, theory.
It remains to be seen how natural and powerful these other principles are, and in what way they are not just a cover-up of trying to avoid non-intuitive conclusions.

My point is: it is not because a principle is highly un-intuitive (sounds crazy), that it is necessarily wrong. That doesn't make it right of course.

My second point is: given the superposition principle of quantum theory: if you take it entirely serious, there's no escaping from MWI-like views.
If the superposition principle is applicable to everything, including humans and apparatus, *by definition* there are "weird states" where you are at two places at once, because that is *the very content* of the superposition principle. The nice (or troubling ?) part of MWI is however, that even such "weird states" do not necessarily give rise to any contradiction in what an observer would observe. There are strong indications that an observer *would not notice* most of the time, any of this weirdness.

I often outlined the parallel with general relativity. People don't seem to realize, but in the standard description of GR, yesterday and tomorrow exist on an equal footing with today in GR. Yesterday is not "gone" somehow, and tomorrow is not "still to come". It's all there, fixed in that 4-dimensional manifold.
As such, you can wonder whether there are also not "parallel worlds" in GR, where at the same time, there is *a* you experiencing "today", while another "you" is experiencing "yesterday", and still another you is "experiencing tomorrow".
This, in a toy universe where GR is strictly true, and where there *is* a genuine 4-dim manifold.

Your "you" is just one of the different ones on your world line (in fact, you're changing continuously from one "you" to another "you", all of them being there, statically, on that 4-dim manifold).

It seems that the only world we can intuitively accept (as naively real) is some variant of a Newtonian vision: there's a 3-dim space, there's a special moment in time, which is called "now", and all events that happen are for real, and unique.

We cannot accept, apparently, that "yesterday" and "tomorrow" are just as real as "now" and co-exist, or that the events and their alternatives all happen but we are only aware of one "set". As such, we cannot accept the founding principles of all of 20th century physics.
Maybe this is a good idea, and all of 20th century physics has been build upon totally wrong principles (which nevertheless turn out to crank out formalisms with strong empirical success). Or maybe we are too stubborn to understand that naive realism is, well, naive. Both options are possible, and I don't know which one is ultimately correct.

But, *given* a theory, and asking for an interpretation of it, I always find it a wrong idea to start by saying that the founding principles of said theory are essentially wrong. As such, I find it a wrong idea to say that the superposition principle of quantum theory is wrong when trying to interpret quantum theory. Rather, I prefer to think of a toy universe where these principles are *correct* and then start imagining what this toy universe looks like. That's all I do when considering MWI.

 

[Farsight]

Thanks for that response vanesch. I do appreciate it.

It's not that I don't accept superposition. In fact I think I accept it so much that I'm refuting position, and the particles that go with it. I now think of actions, and position now becomes ambiguous at best. IMHO we don't need MWI to explain superposition, just a different viewpoint. A more rounded viewpoint where we have a better concept of what we're dealing with. We need a glass table for your tossed coin, and then we can see that both results did happen simultaneously, without parallel universes.

 

[MaverickMenzies]

I also have a question regarding MWI (although I'm not sure if its actually a sensible question!). If I understand the interpretation correctly, then every time a system exists in a superposition of eigenstates with respect to a class of commuting observables then the universe splits into many copies such that when a measurement is performed only one eigenvalue is recovered in each universe?

However, one could equivalently regard the original superposition of states as being a single eigenstate of another set of observables (which don't commute with the first). How does the interpretation handle this fact?

 

[setAI]

Thanks for that response vanesch. I do appreciate it.

It's not that I don't accept superposition. In fact I think I accept it so much that I'm refuting position, and the particles that go with it. I now think of actions, and position now becomes ambiguous at best. IMHO we don't need MWI to explain superposition, just a different viewpoint. A more rounded viewpoint where we have a better concept of what we're dealing with. We need a glass table for your tossed coin, and then we can see that both results did happen simultaneously, without parallel universes.

the exponentiating field of quantum computing physically demonstrates every day that the MWI is the only tenable interpretation [that we currently have] because computations can be performed that use far more resources than the number of particles [or 'actions'] in this universe- all the possible states CANNOT be in one universe- there aren't enough observables here to account for the computation

 

[Hurkyl]

all the possible states CANNOT be in one universe- there aren't enough observables here to account for the computation

How do you figure? Even in a universe with one particle, there are infinitely many linearly independent observables... and this is ignoring the complication that observables generally aren't limited to a finite set of possibilities.

 

[CarlB]

the exponentiating field of quantum computing physically demonstrates every day that the MWI is the only tenable interpretation [that we currently have] because computations can be performed that use far more resources than the number of particles [or 'actions'] in this universe- all the possible states CANNOT be in one universe- there aren't enough observables here to account for the computation

I wasted 30 minutes of my time listening to the lecture that gave the "proof" that the MWI was the only possible and I regret it. Zapper gave you a bit too much of a beating for my liking, but the simple fact is that the MWI is an interpretation of quantum mechanics. It gives no results that differ in any way from that of standard quantum mechanics. Nor does quantum computation differ in its predictions from quantum mechanics.

The amount of resources that are used in a quantum computer were also used in the earliest calculations of quantum mechanics of the 1920s. The MWI did not change this in any way.

In standard classical mechanics the condition of a particle is represented by three position variables and three velocity or momentum variables for a total of 6 real degrees of freedom. In quantum mechanics, a particle is represented by a complex valued function (2 real variables) typically defined, for any given moment in time, over a region (\aleph^1 real variables).

The increase in information contained in a quantum description over a classical description is incredible. There is nothing special in MWI in getting that sort of information.

What MWI does is to take a very naive view of what "time" is, and use it to come to very naive conclusions about what the nature of the universe is. Not only does MWI not give anything new over prior theory, its ontology is even more confused than the usual interpretations.

If you want to find out more about MWI, quit reading the crap written by its believers. Go pick up a copy of Bohm and Hiley's "The Undivided Universe", and read their critique of MWI.

As to why QM and the MWI appear to give more degrees of freedom to the world than can possibly fit, I suggest that the answer is in the nature of time. Recall that Feynman once flirted with a theory that there was only one electron in the universe. The idea was that this single electron could go backwards and forwards in time in such a way as to fill out the (Bohmian) trajectories of all the electron wave functions that ever were.

If that's too much, then cut that back down to a single electron. If you want to add up degrees of freedom for an electron, then you should consider the possibility that the electron does not see time in as restricted a way as you do.

The essential mystery of quantum mechanics is that it consists of bundles of trajectories that influence each other. The "bundles of trajectories" is compatible with classical statistical mechanics (phase space and all that), but the "influence each other" is not. This is the central mystery of quantum mechanics, and from my point of view the MWI gives a particularly drunken explanation for it. Far better to suppose that the particle made the traversal many times over the same patch of "spacetime" and thereby influenced itself.

In any case, going around claiming that MWI proves all other quantum mechanics interpretations wrong isn't winning you any converts. There are people out there who have been considering these problems for 75 years. It ain't that simple. If MWI were obviously the only solution, somebody would have a Nobel Prize already and MWI would be taught in school.

Carl

 

[Doc Al]

I wasted 30 minutes of my time listening to the lecture that gave the "proof" that the MWI was the only possible and I regret it.

I applaud your stamina... I only lasted about 15 minutes before throwing in the towel, muttering "give me a break" to myself.

 

[setAI]

I applaud your stamina... I only lasted about 15 minutes before throwing in the towel, muttering "give me a break" to myself.

too bad or you would have seen for yourselves a demonstration of the MWI in the experiment- it'a at 40 minutes into the video where Deutsch SHOWS the experiment- in this experiment the Copenhagen interpretation predicts that BOTH photon detectors at the end will register half the time- MWI predicts that only the right detector will register because the other universes engaged in the experiment provide 'shadow photons' that force them all right- I had to watch this several times before the EUREKA moment sunk in- I suggest you do the same- this experiment is the basis for many types of quantum logic gates being used all over the world in quantum computing research- as of right now it's one of the most succesfully reproduced experiments in physics and is ONLY predicted by the MWI- Deutche's genius in using this simple set-up is nothing short of amazing- he's probably the smartest human being on the planet since Feynman or Minsky

In any case, going around claiming that MWI proves all other quantum mechanics interpretations wrong isn't winning you any converts. There are people out there who have been considering these problems for 75 years. It ain't that simple. If MWI were obviously the only solution, somebody would have a Nobel Prize already and MWI would be taught in school.

pretty ironic considering that David Deutsch IS actually on the fast track right now to winning a Nobel Prize for his multiverse discoveries in QM- and the textbooks ARE going to be changed- I will wager you RIGHT HERE that in 10 years every QM textbook will reflect the verification of the Everttian interpretation-

as ever- I can only suggest that the rest of you get caught up with the state of the field as I have- this news is nearly a decade old now but even I have only been aware of this paradigm shift in QM for about a year and a half- before studying Deutsche's work I would have agreed with your guys for the most part- he will get to you too sooner or later-

 

[setAI]

How do you figure? Even in a universe with one particle, there are infinitely many linearly independent observables... and this is ignoring the complication that observables generally aren't limited to a finite set of possibilities.

Seth Lloyd recently calculated that the observable universe represents 10^90 bits of information- all quantum computers built in the last 9 years up to 10 qubits have performed computations exactly as predicted by theory- this means that we will see how the multiverse must necissarily exist in a decade or two: the first 300 qubit quantum computer to perform Shor's algorithm will perform a computation that surpasses 10^90 classical bits [300 qubits= 2^300 classical bits= 10^90 bits]- 10^90 bits is all that the universe we can interact with can possible represnt- so to go beyond that demonstrates that particle states from other universe that are not part of the observable universe are helping to perform the computation- in fact only 300 bits of the 10^90 total in a 300 qubit quantum computation can be described as part of our universe- all supported by more empirical evidence than just about any scientific concept in human history: http://www.vcpc.univie.ac.at/~ian/hotlist/qc/research.shtml

 

[Hurkyl]

10^90 bits is all that the universe we can interact with can possible represnt

Why do you assume that each particle can only represent one bit of information? That's certainly false, as has already been stated.

in this experiment the Copenhagen interpretation predicts that BOTH photon detectors at the end will register half the time

Only if you make the mistake of making a collapse occur before a measurement is made. (At least, if the experiment at all resembles the impression I get from your description)

 

[Hans de Vries]

The MWI interpretation seems to be clearly falsified by the latest proofs
on two particle interference. MWI needs Dirac's over sited old claim that
particles can only interfere with them self and do never interfere with
other ones.

Hong-Ou-Mandel-type (HOM) interference: http://arxiv.org/abs/quant-ph/0603048
From ZapperZ's thread here: https://www.physicsforums.com/showthread.php?t=124474
This means that the number of distinguishable fields that the vacuum has
to support, at each point in space time, reduces from 10⁸⁰ (The number
of particles in the universe) to a more physical 17 (The number of different
elementary particles) and unitarity is caused by something different than
by distinguishable wavefunctions.

The interference between like particles means for instance that all
identical particles, in all the zillions of different worlds in the MWI
interpretation, all interfere which each other.

Which would simply make one big mess.
MWI is all about unrealistic extrapolations of QM superposition which is
supposed to support all these different worlds existing at the same time.Regards, Hans

 

[setAI]

Why do you assume that each particle can only represent one bit of information?

most atoms represent about 30-40 bits each [one bit for each boolean observable ]:


"...it's been known, ever since the latter part of the 19th century, that every elementary particle, every photon, every electron, registers a certain number of bits of information. Whenever two elementary particles bounce off of each other, those bits flip. The universe computes.

The notion that the universe is, at bottom, processing information sounds like some radical idea. In fact, it's an old discovery, dating back to Maxwell, Boltzmann and Gibbs, the physicists who developed statistical mechanics from 1860 to 1900. They showed that, in fact, the universe is fundamentally about information. They, of course, called this information entropy, but if you look at their scientific discoveries through the lens of twentieth century technology, what in fact they discovered was that entropy is the number of bits of information registered by atoms. So in fact, it's scientifically uncontroversial that the universe at bottom is processing information. My claim is that this intrinsic ability of the universe to register and process information is actually responsible for all the subsequent information processing revolutions.

How do we think of information these days? The contemporary scientific view of information is based on the theories of Claude Shannon. When Shannon came up with his fundamental formula for information he went to the physicist and polymath John von Neumann and said, "What shall I call this?" and von Neuman said, "You'll call it H, because that's what Boltzmann called it," referring to Boltzmann's famous H Theorem. The founders of information theory were very well aware that the formulas they were using had been developed back in the 19th century to describe the motions of atoms. When Shannon talked about the number of bits in a signal that can be sent down a communications channel, he was using the same formulas to describe it that Maxwell and Boltzmann used to describe the amount of information, or the entropy, required to describe the positions and momenta of a set of interacting particles in a gas.

What is a bit of information? Let's get down to the question of what information is. When you buy a computer you ask how many bits its memory can register. A bit comes from a distinction between two different possibilities. In a computer a bit is a little electric switch, which can be open or closed; or it's a capacitor that can be charged, which is called 1, or uncharged, which is called 0. Anything that has two distinct states registers a bit of information. At the elementary particle level a proton can have two distinct states: spin up or spin down. Each proton registers one bit of information. In fact, the proton registers a bit whether it wants to or not, or whether this information is interpreted or not. It registers a bit merely by the fact of existing. A proton possesses two different states and so registers a bit.

We exploit the intrinsic information processing ability of atoms when building quantum computers, because many of our quantum computers consist of arrays of protons interacting with their neighbors, each of which stores a bit. Each proton would be storing a bit of information whether we were asking them to flip those bits or not. Similarly, if you have a bunch of atoms zipping around, they bounce off each other. Take two helium atoms in a child's balloon. The atoms come together, and they bounce off each other, and then they move apart again. Maxwell and Boltzmann realized that there's essentially a string of bits that attach to each of these atoms to describe its position and momentum. When the atoms bounce off each other the string of bits changes because the atoms' momentum changes. When the atoms collide, their bits flip.

The number of bits registered by each atom is well known and has been quantified ever since Maxwell and Boltzmann. Each particle — for instance each of the molecules in this room — registers something on the order of 30 or 40 bits of information as it bounces around. This feature of the universe — that it registers and processes information at its most fundamental level — is scientifically uncontroversial, in the sense that it has been known for 120 years and is the accepted dogma of physics.
" ~Seth lloyd[/color]

Only if you make the mistake of making a collapse occur before a measurement is made. (At least, if the experiment at all resembles the impression I get from your description)

you should watch the experiment a FEW times and listen to Deutsch carefully- he shows that there is no collapse before the final detector by using each branch to perfom the universal CNOT operation-he is performing parallel quantum computing right in front of your eyes! quantum computations don't even work unless pure superposition is maintained until the output-

 

[Hurkyl]

I already know about information theory, and that information and entropy are essentially the same thing. I guess, technically, you answered my question about why you assume the entropy related to a single particle is finite... but the intent of my question is to ask for a reason why that should be true.

Keep in mind that there's no reason that the entropy of a probability distribution should be finite.

 

[Hans de Vries]

too bad or you would have seen for yourselves a demonstration of the MWI in the experiment- it'a at 40 minutes into the video where Deutsch SHOWS the experiment- in this experiment the Copenhagen interpretation predicts that BOTH photon detectors at the end will register half the time- MWI predicts that only the right detector will register because the other universes engaged in the experiment provide 'shadow photons' that force them all right- I had to watch this several times before the EUREKA moment sunk in- I suggest you do the same-

I did watch the first five of David Deutch 40 minute video's a while ago
already and there's nothing there which proves MWI.

The really ironic thing is that the experiment he uses is almost equal to
the two photon interference experiment which is the one most suitable
to falsify the the MWI interpretation.

https://www.physicsforums.com/showthread.php?t=124474
http://arxiv.org/abs/quant-ph/0603048

See preceding post:
https://www.physicsforums.com/showpost.php?p=1021835&postcount=22Regards, Hans

 

[Hurkyl]

you should watch the experiment a FEW times

Watching the experiment won't help me at all. A drawing of what it's doing, or a formal expression of what it's computing would be informative, but irrelevant to this discussion, methinks.

quantum computations don't even work unless pure superposition is maintained until the output-

And since the computations worked, a Copenhagenist would say that the experiment has simply proven that no measurement occurs until we look at the output.

 

[setAI]

I already know about information theory, and that information and entropy are essentially the same thing. I guess, technically, you answered my question about why you assume the entropy related to a single particle is finite... but the intent of my question is to ask for a reason why that should be true.

Keep in mind that there's no reason that the entropy of a probability distribution should be finite.

I recently had this discussion in another forum- how can we be sure that the observed information is ALL of it? as I understand it from reading Deutsch/Lloyd /et al is that any hypothetical information that would be too subtle to detect is TOO SUBTLE TO INTERACT with a quantum system- meaning that according to the Schrödinger equation any hidden 'detail' is by definition in SUPERPOSITION of all possible states and thus is irreleveant and non-existant by every measure of the term- quantum mechanics demonstrates that ideas about classical/continuous systems with boundless detail are nonphysical- only the bits that interact have the quality of 'existence' so a proton is one bit only and absolutely

 

[Farsight]

I watched the lecture all the way through, setAI.

http://www.quiprocone.org/Protected/Lecture_2.htm

David Deutsche assumes that photons are particles of light. He says they must be very small and demonstrates this by passing two laser beams through one another. He depicts photons as red dots passing through the beam splitters, and then builds his mathematics, with the MWI and his qubits upon this presumption.

And yet I can readily find a beam splitter link depicting destructive and constructive interference between two photon waves entering a beam splitter, and the result is one photon wave exiting in one or other direction. This means the location of the beam splitter will affect the output.

http://www.cit.gu.edu.au/~s55086/qucomp/beamsplitterApplet.html

"Light (red wave) is traveling from the left to the beam splitter. 50% of this light is reflected down the page with a 180o phase shift and the rest is transmitted through the beam splitter in phase. Light (red wave) is also traveling down from the top. Again, 50% is reflected to the right and the rest is transmitted through the beam splitter, both in phase. The reflected and transmitted waves interfere and the result is shown as the blue waves..."

Why should I accept exotic MWI based upon point particles whilst rejecting mundane long wave radio and EM interference?

 

[Hurkyl]

Why should I accept exotic MWI based upon point particles whilst rejecting mundane long wave radio and EM interference?

MWI is the rejection of the collapse postulate. MWI is based upon point particles if and only if you are taking it from a formulation of QM based upon point particles.

That said, the meaning word "particle" as used in quantum mechanics only vaguely resembles the meaning of the same word as used in classical mechanics.


Neither the classical notion of a particle nor the classical notion of a wave is adequate to describe light. Instead you need some new quantum mechanical notion capable of resembling (but not being) both!

To wit, the one-"particle" wavefunction does, in the position representation, look something like a classical point particle in a superposition of being in different places.

But, if you take the exact same wavefunction but write it in the momentum representation, it now looks like a superposition of things that look like plane waves.

Representations in other bases will make it look like a superposition of some other sort of thing.

 

[Farsight]

hurkyl: I was just referring to the experiment in the lecture, easily explained by something far simpler than MWI.

 

[Hurkyl]

Using the wave nature of light as the "easy explanation" doesn't work -- that is known to be a flawed explanation.

 

[setAI]

I will give you this- I had thought [and was told by some professional aquaintences in the field] that the idea that MWI has been verified was considered old news amoung quantum physicists and that I was the one that was late in finding out about this development- but it does appear that at least in the USA there is some resistance to accepting that the MWI has been verified-

I was told by more than one UK physicist/student that the MWI IS pretty much accepted in the UK community including Hawking and Rees[ everyone except Penrose who has his own odd notions] as well as japan- but that the US is still 'catching up' [not my words]- given the recent discussions on this forum I guess the matter is not as settled [in the US at least] as I had heard!

 

[Farsight]

hurkyl: whatever the flaws of a wave explanation, I see no justification for offering a "proof" of parallel universes using a particle axiom. Like you said, we should be thinking about something that is neither wave nor particle. I personally like the word "action" for bosons.

PS: I'd be grateful if you could post a link on the flawed wave explanation, I'm particularly interested in beam splitters.

PPS: I recall reading somewhere that the photoelectric effect was not necessarily a particle phenomenum after all. I'll start a separate thread asking if anybody knows about this.

 

[Hurkyl]

we should be thinking about something that is neither wave nor particle.

And we do. Alas, for better or worse, that something has also been given the name "particle".

 

[Hans de Vries]

I was just referring to the experiment in the lecture, easily explained by something far simpler than MWI.

As I remember, the outcome of the experiment in the video is indeed
explained by the applet (which doesn't need more than "classical" waves
to explain the effect)

The experiment on the video uses two beamsplitters, one to "split" the
single photon and the second to merge it again. The wavefunctions
arriving at the second beamsplitter have a fixed phase relation depending
only on the exact path lengths. By adjusting the path lengths one can
arrange the interference at the second beamsplitter so that the photon
goes always left, goes always right, or has any percentage between
these two extremes. The situation at the second beamsplitter is exactly
as in the applet:


http://www.cit.gu.edu.au/~s55086/qucomp/beamsplitterApplet.htmlI can not remember that David Deutsch used this experiment as a "proof
of MWI". This series of video's just demonstrates his way of using spinors
to do calculations involving states which can have a 50:50 probability.
Using spinors is nice for physicists who have mastered them and can
now use them for something completely different.

However, the choice for using spinors is arbitrary, there's nothing
"spin 1/2" involved in the calculations. A computer engineer who is
trying to master this may be rather puzzled where this all comes from
and why it's needed at all. Certainly when the matrices based on the
Pauli spinors blow up when going to multi qubit systems and the
simplest calculations become very tedious.


Regards, Hans

 

[Farsight]

I can not remember that David Deutsch used this experiment as a "proof of MWI".

Sorry to suggest that Hans, no he didn't. It was setAI being bullish.

 

[CarlB]

MWI needs Dirac's over sited old claim that particles can only interfere with them self and do never interfere with other ones.

It was 26 years ago that I was taught QM and my memory of the learning process is fuzzy, but as long ago as I can remember I have always believed that identical particles do interfere with each other. So I'm kind of surprised that this would be up for debate. Was I jumping to conclusions unwarranted in 1979 or something? I guess that I thought it was obvious that this would happen because of the fact that one had to symmetrize or antisymmetrize multi particle wave functions, IF the multiple particles described were identical.

This means that the number of distinguishable fields that the vacuum has to support, at each point in space time, reduces from 10⁸⁰ (The number of particles in the universe) to a more physical 17 (The number of different elementary particles) and unitarity is caused by something different than by distinguishable wavefunctions.

By the way, there is a subtle argument here on the nature of particles, and the way that we should try to unify them.

It is very obvious that two particles that differ in their spin cannot interfere with each other and therefore must require two different sorts of wave functions. But it's not so obvious why it is that nature created more than one "spin-1/2" particle.

In other words, why is it that electrons don't interfere with neutrinos?

On the other hand, spin up electrons do NOT interfere with spin down electrons, so it would seem that nature treats different particle types in a way that is very analogous to that of spin. Which is why I work on classifying preons with Clifford algebra.

Getting back to your observation, I also think that it is great evidence that of the wave particle duality, the wave part is the more important. Of course waves are indistinguishable. What is unusual about quantum mechanics is that upon measurement, the waves collapse down to particles.

But if you remove the measurement from quantum mechanics, then one can rewrite multiparticle wave functions into a pure wave format. It is only in the measurement that we have to do all the complicated manipulation.

This is an argument I remember from a very long time ago. Let \psi(x_1,x_2,t) be a two particle wave function, for two identical scalar particles (spin-0 bosons). By symmetry, we have that
\psi(x_1,x_2,t) = \psi(x_2,x_1,t). Schroedinger's wave equation for two non interacting particles (in one dimensions) is something like:

i\hbar \partial_t\; \psi(x_1,x_2,t) = \partial_{x1}\psi(x_1,x_2,t) + \partial_{x2}\psi(x_1,x_2,t).

Define
\psi(x,t) = \int \psi(x,x_2,t)\; d_{x2}

Then the above is a solution of Schroedinger's wave equation for one particle. Thus we can always convert a two particle wave function into a one particle wave function.

Similarly it is possible to go the opposite direction, but in doing so, there is more than one possible choice of solution. That is, for anyone particle wave equation there is a two particle wave function that maps to that one particle wave function, but that two particle wave function is not unique.

Now the only way you can distinguish between a one particle wave function and a two particle wave function is by counting particles, which is a measurement. This is what I mean when I say that if you eliminate measurement from quantum mechanics, the need for phase space also goes away. In short, the mystery of QM is in the measurement, without that, it's only classical wave equations.

And as far as classical wave equations go, there is plenty of room in them for all the complication seen in the quantum theory of measurement. In other words, the argument for MWI in terms of counting degrees of freedom only applies on the particle side of the interpretation.

Carl

 

[Hans de Vries]

It was 26 years ago that I was taught QM and my memory of the learning process is fuzzy, but as long ago as I can remember I have always believed that identical particles do interfere with each other. So I'm kind of surprised that this would be up for debate.

Well, You're certainly not alone here. It surprised me as well. I suppose
unitarity may be the main argument behind distinguishable wave functions.

This is an argument I remember from a very long time ago. Let \psi(x_1,x_2,t) be a two particle wave function, for two identical scalar particles (spin-0 bosons). By symmetry, we have that
\psi(x_1,x_2,t) = \psi(x_2,x_1,t). Schroedinger's wave equation for two non interacting particles (in one dimensions) is something like:

i\hbar \partial_t\; \psi(x_1,x_2,t) = \partial_{x1}\psi(x_1,x_2,t) + \partial_{x2}\psi(x_1,x_2,t).

Define
\psi(x,t) = \int \psi(x,x_2,t)\; d_{x2}

Then the above is a solution of Schroedinger's wave equation for one particle. Thus we can always convert a two particle wave function into a one particle wave function.

Interesting, Thanks for bringing it up.

And as far as classical wave equations go, there is plenty of room in them for all the complication seen in the quantum theory of measurement. In other words, the argument for MWI in terms of counting degrees of freedom only applies on the particle side of the interpretation.

Carl

Yes, or in other words. The mystery of unitarity.Experimental two photon interference and EPR tests

This 2-photon interference experiment is an extremely interesting one:

If two different (but equally polarized) photons meet at a beam splitter
then their wave functions combine (interfere) and both photons are
always detected at the same detector even though the wavefunction
is split and goes both ways.There's a very interesting link to EPR tests here. It is always assumed that
the choice of going left or right in a beam splitter is random, that is, it may
have an X% chance of coming out left and a 100-X% chance of coming out
right.

Even the Bell-type hidden variables maintain this randomness (That's
why they fail in the first place to predict the measured correlations)

With this experiment it's for the first time that I see a sign of non-random
behavior (correlation) for two particles which are not "entangled" !

I've always had a suspicion that there might be something in the wave-
function which predetermines somehow at which output the photon
will be detected, and this experiment reinforces that: The combined
wavefunction after interference might have a property which pre-
determines at which output both photons are detected...

It is not that hard to find candidates for such a property. Two apparently
equal photons may have completely different V,A potentials. One always
has to define a gauge, typically the transverse gauge.

However. If you look at the radiation pattern of a charge moving up and
down then its easy to see that the A field propagated is always exactly
vertically and generally not transversal to the direction of motion. That
is, only the horizontally propagated radiation is transversal gauge like
(V=0, A= transversal)

The experiment has several more interesting aspects. It's one of the
most interesting ones I've seen in a long time.

http://arxiv.org/abs/quant-ph/0603048Regards, Hans

 

[koantum]

What about the countless interactions among particles/systems that don't involve "measurements"?

There are no interactions that don't involve measurements. Our description of the quantum world is entirely in terms of correlations between measurement outcomes. If two systems interact, it means that their probability distributions over the possible outcomes of possible measurements get correlated.

 

[koantum]

...in a universe with one particle, there are infinitely many linearly independent observables...

A universe with one particle is no universe at all. All positions, all momenta, are relatively defined. In a universe with only one particle there are neither positions nor momenta. And so there is no space. And so there is no universe. Besides, it is time that we learn to distinguish between

• operators, which are useful in characterizing probability distributions over measurement outcomes, by allowing us to calculate their mean values, standard deviations, and higher moments,
• and observables, which are things that can be measured, and that have values only if, when, and to the extent that they are measured.

So you may have infinitely many operators in your disembodied mind, but you won't have observables in a world without things by which they can be measured.

 

[koantum]

MWI is the rejection of the collapse postulate.

MWI is what you get if you reject the symptom (the collapse postulate) without rejecting the underlying disease, which is the belief that quantum states or wave functions represent evolving instantaneous states of affairs. The time dependence of a quantum state is the dependence of an algorithm on the time of the measurement to the possible outcomes of which it assigns probabilities. (Sorry for this convoluted sentence, but the alternative to many worlds is many words. ) A quantum system has its measured properties at the time, and to the extent that, they are measured.

We ought to have the honesty to admit that any statement about a quantum system between measurements is "not even wrong" (Pauli's famous phrase), inasmuch as such a statement is by definition neither verifiable nor falsifiable experimentally. Such a statement is unscientific by Popper's definition, which requires of a scientific statement that it be at least falsifiable. So the story according to which quantum states evolve (or appear to evolve) unitarily between measurements should be seen for what it is - a story. And it is this story which implies that quantum states "collapse'' (or appear to collapse) at the time of a measurement.

That said, the meaning word "particle" as used in quantum mechanics only vaguely resembles the meaning of the same word as used in classical mechanics.

No resemblence whatsover.

Neither the classical notion of a particle nor the classical notion of a wave is adequate to describe light.

Absolutely right.

Instead you need some new quantum mechanical notion capable of resembling (but not being) both!

And what might that be, given that all we have is correlations between measurement outcomes?

if you take the exact same wavefunction but write it in the momentum representation, it now looks like a superposition of things that look like plane waves.

And if you take the wave function of two particles, it looks like one thing spread out over a 6 dimensional space. And so on ad absurdum.

 

[vanesch]

I also have a question regarding MWI (although I'm not sure if its actually a sensible question!). If I understand the interpretation correctly, then every time a system exists in a superposition of eigenstates with respect to a class of commuting observables then the universe splits into many copies such that when a measurement is performed only one eigenvalue is recovered in each universe?

However, one could equivalently regard the original superposition of states as being a single eigenstate of another set of observables (which don't commute with the first). How does the interpretation handle this fact?

I guess I can repeat that a million times and this question will come still back

The simple observation is that "the universe doesn't split".

"Splitting universes" are not objective properties, they are - as you seem to understand - observer-dependent. In other words, the "different universes" are constructs that depend on how you write down the wavefunction from a specific observer point of view ; in other words, what are the "different states of experience" of the individual observer you're considering, and how they entangle with the rest of the universe. Now, there's some hope that these "different states of experience" emerge naturally from a process of decoherence, but nevertheless, they will be different for different observers ; so the "split" in "different universes" will be different for different observers.
"Different universes" is a colloquially used term which is not precisely defined, and is certainly not an objective property. It is unfortunate that many people think about MWI that way. It would be better to talk about "different states of perception" instead of "different universes", then it would be clear that it is an observer-dependent concept.

Now, these "different worlds" DO obtain some independent existence once all considered observers have interacted amongst themselves (exchanged, say, information, or just thermal radiation, or some air molecules), because then they will have entangled their states in such a way that the split according to observer 1 will be the SAME split as the one according to observer 2 etc... So (a la Rovelli) if we say that what is "objective" is what observers interacting with each other agree upon, these observers will agree upon their splits, and hence these splits become "objective" (but still limited to a group of interacting observers ; and maybe not for another group of interacting observers on Andromeda), and we can call them, "worlds". This grouping together of different observer states, which then remain robust through time evolution and remain together, is the entire program of environmental decoherence. I have to say that I don't know up to what point this is established, and up to what point this is what one hopes to establish: I'm still in the process of understanding the recent work done in the domain, because one has to be careful of over-enthousiastic claims.

That solves then the "preferred basis problem" that you touch upon: they are not a free choice, but they are those observables which have robust eigenspaces throughout time evolution (and which are supposed to correspond to "states of experience" for observers). In other words, they are defined by the interaction hamiltonian between systems and their environment.
Now, if this doesn't work out as hoped for, there's always the uglier but surer way of doing things: by POSTULATING a basis of "states of experience", but it would be nice if this simply *emerged* from the interaction with the environment, as decoherence seems to indicate.

 

[vanesch]

the exponentiating field of quantum computing physically demonstrates every day that the MWI is the only tenable interpretation [that we currently have] because computations can be performed that use far more resources than the number of particles [or 'actions'] in this universe- all the possible states CANNOT be in one universe- there aren't enough observables here to account for the computation

You really should stop saying that. In as much as I'm rather pro-MWI as an interpretation of the quantum formalism, all other empirically equivalent formulations are, well, empirically equivalent, and hence there's no lab experiment that proves MWI right.
Hell, even an interference experiment with humans wouldn't prove MWI! You can still consider Copenhagen, but consider that humans are still microscopic, and that the quantum/classical transition only occurs on the level and size, say, of a galaxy.

 

[CarlB]

MWI is what you get if you reject the symptom (the collapse postulate) without rejecting the underlying disease, which is the belief that quantum states or wave functions represent evolving instantaneous states of affairs. The time dependence of a quantum state is the dependence of an algorithm on the time of the measurement to the possible outcomes of which it assigns probabilities. (Sorry for this convoluted sentence, but the alternative to many worlds is many words. ) A quantum system has its measured properties at the time, and to the extent that, they are measured.

Well said. I say "so too!"

Carl

By the way, am I the only one who can't set up an avatar? If it's because of the incident with the naked picture, hey, I'm sorry, it won't happen again.

 

[vanesch]

Well said. I say "so too!"

The problem I have with all these claims about quantum theory being just an algorithm calculating probabilities, is the following. I'm of course not disputing that quantum theory is an algorithm for calculating probabilities of observation, no more than that classical physics is an algorithm for calculating outcomes of measurements. This is the minimum requirement for all scientific theories: they should *at least* be an algorithm to allow you to calculate something that you can compare to experiment.
But the problem with the claim that quantum theory is "just an algorithm" is: what do you think we learn from such a statement ?

I could just as well say that "things happen" in nature, and well, scientific theories are observations of apparent regularities of these things happening, so they are some kind of resume of a catalogue of previously observed regularities and it would be erroneous to try to find any deeper meaning to these observed regularities. So is astrology, btw.

If quantum theory (or for that matter, any scientific theory) is just an algorithm for calculating probabilities (say, regularities) of outcomes, then there's no deeper principle which tells us what form such an algorithm should take on, because the very claim of it being an algorithm which doesn't describe anything underneath means that it can take any form.
As such, there's no reason, nor for the specific form of the algorithm (why this stuff with Hilbert spaces and so on, why a unitary transformation, why Lorentz invariance etc...). All these properties can only leave us wondering, because an algorithm of regularities in a big catalogue of events shouldn't a priori obey any principle.

The power of a good scientific theory has always been that it doesn't ONLY provide an algorithm to calculate outcomes of experiment, but that the algorithm is UNDERSTOOD as following from an underlying ontological description based upon a few fundamental principles. Claiming that scientific theories are now reduced to pure algorithms *without meaning* kills off any explanatory power, or for that matter, any required structure what so ever. So there's no leg to stand on anymore to require whatever principle (like covariance, or superposition, or constancy of the speed of light or whatever), because all these concepts are just applied to "variables in an algorithm with no genuine meaning". So personally, I don't buy the "quantum theory is JUST an algorithm to calculate probabilities of outcomes". Of course it is an algorithm, TOO. But saying that one should think of it as ONLY that is giving up on the essential part of science, because we've switched from investigating the nature of nature, to "stamp collecting".

 

[vanesch]

quantum computations don't even work unless pure superposition is maintained until the output-

Yes, but that would simply mean that the Heisenberg cut has to be applied after you reach the "output". As interpretations of the Copenhagen type don't tell you WHERE and WHAT exactly is a measurement (where the collapse is supposed to occur), you can put it anywhere that fits observation. von Neumann even said that you can put it anywhere *as long as it doesn't make any difference*.

So, again, no amount of experimental result can prove MWI right or wrong over Copenhagen, as Copenhagen can always put the cut AFTER the point where the last visible effect of superposition is observed.

The only thing you could possibly do is the opposite: prove MWI FALSE, by showing an observation where there OUGHT TO BE quantum interference, and where it doesn't happen (after having carefully taken into account all potential sources of decoherence, which is not easy). Copenhagen can accommodate both observations: if no interference is observed, it can tell you that that's normal, because the Heisenberg cut was applied before the interference was supposed to occur ; and if interference is observed, it can tell you that that's normal, because the Heisenberg cut comes in only later. So there's no interference experiment with positive or negative result that is ever going to falsify Copenhagen. However, a negative outcome (where a positive is expected) clearly falsifies MWI.

 

[CarlB]

If quantum theory (or for that matter, any scientific theory) is just an algorithm for calculating probabilities (say, regularities) of outcomes, then there's no deeper principle which tells us what form such an algorithm should take on, because the very claim of it being an algorithm which doesn't describe anything underneath means that it can take any form.

Yes, I agree with you completely here. I think that quantum mechanics points towards the thing that is underneath, but I do not think that quantum mechanics itself is very close to the thing underneath. Quantum mechanics is as good as we've got at this time, but that doesn't mean that it is an accurate description of reality.

As such, there's no reason, nor for the specific form of the algorithm (why this stuff with Hilbert spaces and so on, why a unitary transformation, why Lorentz invariance etc...). All these properties can only leave us wondering, because an algorithm of regularities in a big catalogue of events shouldn't a priori obey any principle.

One can only make one step at a time. The current theory is quantum mechanics. If one tries to interpret QM ontologically, one ends up with inanities like MWI. Instead, what one must do is to walk the cat back one step at a time.

From the point of view of Einstein, QM should all go back to principles of geometry. Thus the next step for understanding QM is to write it in geometric form.

But QM already comes equipped with a geometry, namely the Dirac matrices. Note that I say the Dirac matrices, rather than the Dirac spinors. The reason for distinguishing these is that the Dirac matrices have an immediate geometric interpretation in the Geometric Algebra (Clifford algebra) of David Hestenes. See:
http://modelingnts.la.asu.edu/

So to understand the states in QM, what one must do is to write them in terms of the Dirac matrices. Hestenes wrote the spinors in terms of Dirac matrices (well, Clifford algebra, which amounts to the same thing), and gave a geometric explanation for the imaginary numbers of QM:
http://modelingnts.la.asu.edu/html/GAinQM.html

But there is a much simpler way of attaining the same program. If one wishes to geometrize the states, they are much more easily treated as density matrices then state vectors. For example, let S_z be a spin operator for the Dirac algebra in the z direction, and let S_e be the charge operator for the Dirac algebra so that electron states satisfy S_e|e\rangle = +|e\rangle and positron states satisfy S_e|\bar{e}\rangle = -|\bar{e}\rangle. These operators are easy to write in geometric form given any particular representation of the Dirac algebra.

Given these two (commuting) operators, it is possible to write the density matrices for the states with the four possible cases of spin and charge as follows:
|\pm z\pm e\rangle\langle \pm z\pm e| = \rho_{\pm z\pm e} = (1 \pm S_z)(1 \pm S_e)/4

That is, the above is an eigenvector of S_z with eigenvalue +-1 according to the S_z +-1, and an eigenvector of S_e with eigenvalue +-1 according to the S_e +-1. The "4" is there for normalization.

That's all there is to the density matrix versions of the states (other than the dependence on space and time, which are naturally geometric as well). If you want to read off the spinor state, you can simply take any non zero column out of the matrix \rho_{\pm z\pm e}. But in replacing the matrix with one of its columns, you must make a choice, and that choice amounts to a choice of a sort of gauge. That is, in addition to the U(1) gauge, your choice of a column also amounts to a geometric gauge (that is hidden in the usual spinor version of QM).

Bt the thing to note here is that the density matrix forms are naturally independent of choice of U(1) gauge. To make them also independent of the non Abelian gauges requires that one go yet farther beyond the scope of this thread. But my point here is that understanding quantum mechanics ontologically is not impossible, it's just very very difficult, and the first steps are not in the direction that spinors would point you. I'm busily typing this up into a paper. Some more stuff along this direction is at the website I started a few weeks ago http:www.DensityMatrix.com .

Carl

 

[setAI]

the exponentiating field of quantum computing physically demonstrates every day that the MWI is the only tenable interpretation [that we currently have] because computations can be performed that use far more resources than the number of particles [or 'actions'] in this universe- all the possible states CANNOT be in one universe- there aren't enough observables here to account for the computation

You really should stop saying that.

but I DIDN'T say it: "there are indeed other, equally real, versions of you in other universes, who chose differently and are now enduring the consequences. Why do I believe this? Mainly because I believe quantum mechanics... Furthermore, the universes affect each other. Though the effects are minute, they are detectable in carefully designed experiments... When a quantum computer solves a problem by dividing it into more sub-problems than there are atoms in the universe, and then solving each sub-problem, it will PROVE to us that those sub-problems were solved somewhere - but not in our universe, for there isn't enough room here. What more do you need to persuade you that other universes exist? "

"The quantum theory of parallel universes is not the problem, it is the solution. It is not some troublesome, optional interpretation emerging from arcane theoretical considerations. It is the explanation—the only one that is tenable—of a remarkable and counter-intuitive reality."

-David Deutsch [/color]


so far the only professional scientist that has debated Deutsch's argument [that I have found]- Seth Lloyd- has subsequently conceded and now accepts the MWI as at least trivially true- so if you think the idea that quantum computers physically demonstrate the MWI isn't right then someone should inform the leaders in the field of quantum mechanics that they are wrong and to stop publishing that they do!

-I am just a messenger (^__-)

 

[ttn]

so far the only professional scientist that has debated Deutsch's argument [that I have found]- Seth Lloyd- has subsequently conceded and now accepts the MWI as at least trivially true- so if you think the idea that quantum computers physically demonstrate the MWI isn't right then someone should inform the leaders in the field of quantum mechanics that they are wrong and to stop publishing that they do!

-I am just a messenger (^__-)

This is just the kind of bogus argument that advocates of crazy nonsense always use. Can't you just hear the bible-thumping advocates of "intelligent design" saying "so far hardly any professional biologists have been able to refute me"! The fact is, some ideas are so stupid that to positively engage with them (by debating their advocates or whatever) is at best a waste of time, and at worst an irrational sanction. If nobody's willing to publicly debate David Deutsch, maybe it's because his ideas (as vanesch has repeatedly pointed out, and as is obvious to anyone who understands these issues) are so stupid as to not even deserve to be refuted or debated, not because nobody can find anything wrong with them. Ever think of that?

 

[setAI]

This is just the kind of bogus argument that advocates of crazy nonsense always use. Can't you just hear the bible-thumping advocates of "intelligent design" saying "so far hardly any professional biologists have been able to refute me"! The fact is, some ideas are so stupid that to positively engage with them (by debating their advocates or whatever) is at best a waste of time, and at worst an irrational sanction. If nobody's willing to publicly debate David Deutsch, maybe it's because his ideas (as vanesch has repeatedly pointed out, and as is obvious to anyone who understands these issues) are so stupid as to not even deserve to be refuted or debated, not because nobody can find anything wrong with them. Ever think of that?

of course- except that Deutsche's arguments are backed up by one of the largest empirical efforts in history: the field of quantum computing- and many of the greatest physicists of our age have PUBLICALLY ENDORSED him- such as Gell-Mann/ Rees/ Hawking/ Lloyd/ not to mention that David Deutsch is probably the most respected by his peers and best funded quantum physicist on the planet right now- and a good bet for the recipient of the Nobel http://www.edge.org/3rd_culture/prize05/prize05_index.html

there simply is no exscuse for the bias against his ideas I have seen on this forum- [and ONLY this forum- especially by mentors] when his ideas about the MWI are now nearly universally excepted/corroborated/empiracally repeated by the actual scientists in the field- except I guess for certain isolated regions in the United States [rather like foreign policy it seems]