Questions on Many Worlds Interpretation

[rrw4rusty]

Hi!

I've seen videos depicting the ‘Many Worlds Interpretation’ of quantum physics which show T-Rex stomping through your living room because the K2 Event didn’t take place in that parallel universe, you know the hype you see on the MWI. While probably, no one ‘really’ thinks this is happening, the interpretation somehow assumes other universes are right here all around.

1. Concerning MWI, does the interpretation explain ‘why’ we cannot see these other universes? If the particles (?or atoms?) of these parallel universes are right here all around us… there must be something different with the particles or atoms which ‘hides’ them from us.

2. Again concerning the MWI, when these parallel universes split off (when particles split off on all these different probability waves) does the interpretation indicate what these parallel universes are suppose to be made of? Are our atoms/particles spreading themselves among all of the different universes?

I hope these questions make sense?

Thanks any help you can give me,
Rusty

 

[Fredrik]

There are no books, articles or videos I know of that give any good answers to these questions. Almost everything you hear about the MWI comes from people who don't understand it. (I'm not saying that I do). I don't think there's anyone who can claim to understand it. It starts with the assumption that a state vector actually represents a physical system that we're a part of, and the rest is supposed to follow logically from that and the axioms of QM. But I don't think anyone has ever done a good job of finding out what the logical consequences are. (To everyone: If I'm wrong, let me know, but don't just give me random references to articles with "many-worlds" in the title).

Here's my shot at your questions:

1. I think decoherence does that by telling us that if we describe the universe as decomposed into "system+measuring device+the matter you're made of+everything else" it will always evolve into a state where the eigenstates of the system are strongly correlated with macroscopically distinguishable states of your memory.

I also think that in the MWI, "you" are not the matter you're made of. You're a correlation between memory states and states of the rest of the omnium (the physical system that all the worlds are a part of).

2. All the worlds are part of a single physical system, so the only answer I can give you is that it's all "made of" the same stuff.

 

[Hurkyl]

As I understand it...


For the record, parallel universes as seen in science fiction is only vaguely similar to what's going on in MWI.

If we want to look at you, we take the state of the universe and restrict it just to the subsystem that corresponds to you.

Hypothetically, decoherence suggests that your part of the universe should tend to approximate a probability distribution over a collection of pure quantum states.

So, we say each of those pure states is a "world". And you exist in each of those worlds.

You see everything in each of these worlds. But the catch is that the part of you in world X sees only the stuff in world X, and the part of you in world Y sees only the stuff in world Y.

And there's a whole giant part of the universe that simply doesn't correspond to any of your worlds. Intuitively you might say that these correspond to worlds in which you don't exist, but I'm not sure if that makes sense or not.

 

[rrw4rusty]

Hi!

Thanks for the replies! Fredrik's replay was frankly over my head -- too many words I don't have a feel for yet. I did get that he thought that each world was made from the same matter.

As for Hurkyl's reply...

As I understand it...
For the record, parallel universes as seen in science fiction is only vaguely similar to what's going on in MWI.

I'm not sure I've seen parallel universes in sci-fi (I'm a sci-fi writer and I've attempted to read/view everything and failed but, I've taken in a lot). I really have no clue what you mean.

If we want to look at you, we take the state of the universe and restrict it just to the subsystem that corresponds to you.

Oh boy... by subsystem you mean Earth or San Diego or my immediate surroundings... in any of these cases... how does this restrict the 'state of the universe' and even before that, what it the 'state of the universe'.

Hypothetically, decoherence suggests that your part of the universe should tend to approximate a probability distribution over a collection of pure quantum states.

Hm... what's an 'unpure' quantum state? :-) The above seems to say 'given how things are, that's how things are.' I'm trying, really.

So, we say each of those pure states is a "world". And you exist in each of those worlds.

Yep... but I'm only aware of the one at a time.

You see everything in each of these worlds. But the catch is that the part of you in world X sees only the stuff in world X, and the part of you in world Y sees only the stuff in world Y.

Yeah... as I said... this is basic stuff. The remaining question is 'why'... what separates X and Y.

And there's a whole giant part of the universe that simply doesn't correspond to any of your worlds. Intuitively you might say that these correspond to worlds in which you don't exist, but I'm not sure if that makes sense or not.

Well darn, you told me everything I already knew but did not address either of my questions (that I could see). Thanks for your effort.

I've been researching this on my own and it seems that regarding my OP's question 2, the quantum either 'flits' between these 'worlds' or, and this is more likely, it divides itself between them.

What separates them is still an unknown.

Rusty

 

[hamster143]

The remaining question is 'why'... what separates X and Y.

The principle of linearity of quantum mechanics.

 

[rrw4rusty]

The principle of linearity of quantum mechanics.

Outstanding... I hope! I'm on my way to Google!

Thanks!

 

[Hurkyl]

Consider a qubit.

The state space of a qubit is the ordinary Euclidean three-dimensional unit ball -- that is, the state of any individual qubit in the universe can be described by naming a point on or inside the unit sphere.

What these points represent can vary with the kind of qubit. e.g. one common example is that a point represents the "spin" of a particle, with the North and South poles being spin up and spin down about the z axis respectively.


The points on the sphere are the pure states. The points inside the sphere are the mixed states (your "unpure" states).

However, any point on the inside of the sphere can be written as a convex combination of two points on the surface. (That is, a linear combination whose coefficients are nonnegative and add up to 1)

For example, then point (0, 0, 0.6) is the sum that is 50% of (0, 0.8, 0.6) and 50% of (0, -0.8, 6).

Or, we could choose 80% of (0,0,1) and 20% of (0,0,-1).

The reason the pure states are called pure is that there is only one way to write it as a mixture: as 100% of itself.


If we really don't like the unit ball and instead prefer to express the state of the qubit by points on the sphere, then anytime the state is in the interior, we have to represent the state of the qubit by two points. So, if it ever moves from a pure state to a mixed state, then drawing it in a "points on the sphere" picture requires us to split the qubit from a single point into two points. (We could split into more, if we wanted)

 

[VooDooX]

the way i understand it imagine a sewing needle is an atom and then take paper and space is one on top of the other but 1mm apart then keeping them spaced ram the needle thru them the atom only represents a 2d point on the paper however is a 3d object but we can only precieve it in 2d that's how i understand atoms in our world interact with others i could be completely wrong however

 

[Fredrik]

Hm... what's an 'unpure' quantum state? :-)

It's called a mixed state.

The remaining question is 'why'... what separates X and Y.

I would say "decoherence" but that's a fairly advanced concept in QM. You won't be able to read and understand an article about it until you've taken a couple of QM classes. The basic idea is that given a decomposition of the universe into subsystems (like "you" or "this computer"), we can describe the state of the universe in terms of the correlations between the states of the subsystems. The worlds are the correlations between the subsystems.

The worlds don't exist "out there" in any objective sense, since a different decomposition into subsystems would give us a different description of the state of the universe in terms of correlations between subsystems. In other words, there are infinitely many ways to describe the universe as consisting of many worlds.

I know that you won't understand this (because you said so yourself), but I really don't think there's a way to make this simpler.

 

[rrw4rusty]

In the end this was a great help! Thanks to everyone!

 

[gato_]

Honestly I think multiple universes are just a consequence of a fancy interpretation of the mathematical theory, then promoted by science fiction. QM is a theory on matter waves, and it works great. But what exactly does the wavefunction itself represents and how it is related to "reality", I think is not clear enough. Wavefunctions do not represent particles themselves for sure (relativistic theory with that hypotesis is not consistent). The next interpretation is that of the queantum field, something making particles "be". I somehow feel like we are not yet there with QM and reality

 

[Fredrik]

QM doesn't need an interpretation. It's quite possible that QM can't tell us what "actually happens" during an experiment. The assumption that it can't is called the "ensemble interpretation" or sometimes the "Copenhagen interpretation". (See this thread for a discussion of these terms). But it's still interesting to consider the possibility that QM is telling us what actually happens, and the MWI is easily the most straightforward way to interpret QM as a description of what actually happens. People who claim that Occam's razor is an argument against it haven't got a clue. Occam is an argument for the MWI, not against it.

These two recent threads (1, 2) have some good stuff about the MWI in case someone is interested. At least I think it's good stuff.

 

[gato_]

Yes, QM works no mater what the interpretations is, and I agree with you mwi is no completely refutable. However, I don't agree Occam's argument is in favor of mwi. QM principle mainly says, sum up the "histories" leading to a point, and you get a measure of what happens. Except fot unfortunate term "histories", why is considering each of those paths having a separate existence simpler than assuming that whatever describes reality is wave-like and can add up? I see no necessity for spliting reality, it adds nothing

 

[Fredrik]

From the first of the other two threads:

What the formalism says is that a measurement of an observable A changes a pure state $\rho=|\psi\rangle\langle\psi|$ into a mixed state:

$$\rho\rightarrow \sum_i P_i\rho P_i$$

where the $P_i=|a_i\rangle\langle a_i|$ are the projection operators of the one-dimensional subspaces that represent the possible states after the measurement. If we reject the idea that this describes what actually happens, then we can certainly say that only one of the terms represent the state of the system after the measurement. But if we're going to claim that the above is a description of what actually happens, we're going to have to deal with the fact that there's nothing that even suggests that one of the terms is more real than the others.

So the stuff about worlds isn't an additional assumption. We would need an additional assumption to get rid of the worlds (once we have assumed that QM is telling us what actually happens).

The ensemble interpretation can be considered simplier (and it is the one I prefer), but it seems likely that something does "actually happen", and that whatever that is, it can be described mathematically. So the ensemble interpretation suggests hidden variables, which I think would have to be unobservable or have some other annoying property in order to be consistent with what we know about Bell inequalities and that kind of stuff.

QM principle mainly says, sum up the "histories" leading to a point, and you get a measure of what happens. Except fot unfortunate term "histories", why is considering each of those paths having a separate existence simpler than assuming that whatever describes reality is wave-like and can add up?

You don't add up things in the real world, you add up things in the mathematical model. The result is then associed with a result of an experiment that can be performed in the real world. So it seems that you're just saying that QM (or at least the path integral version of it) doesn't tell us what actually happens.

Everett's MWI doesn't consider the paths in the path integral to have a separate existence. (But I think the consistent histories interpretation does something like that). It's based on the Hilbert space formulation, not the path integral, and it's just what you end up with if you take (that version of) the theory as a description of what actually happens. The "worlds" emerge as correlations between the subsystems through the process of decoherence.

 

[gato_]

You are very clear on explanations, but I still see it as an interpretation. Wether you choose paths, vectors on Hilbert spaces, etc, the thing is you have to superimpose different elements to get to the result. I understand clearly mwi stems from considering each of these elements as something that can exist on it's own. I just don't think so, and still believe quantum represents something about reality which doesn't splits it in multiple ways. Anyway, I think that even if that was the case, decoherence probably would limit the spliting of reality to microscopical realm. I can't imagine two paths in reality interfering (very Terry Pratchett like). String or quantum loop gravity say anything on these?

 

[hamster143]

We all know that multiple elements can exist concurrently and even form interference patterns with each other, at least on the quantum level. MWI just makes a logical step forward and says that observers can get entangled with quantum objects when they do measurements.

 

[gato_]

I don't like to seem stubborn, really. I want to understand the idea: interference patterns DO happen, but isn't it perfectly consistent to say they interfere because whatever interacts, INTERACTS? with that, I mean they have to meet at the same space and time. So why should anyone say they represent different realities?

 

[hamster143]

They interfere, because they coexist, right? In a double-slit experiment, you see interference patterns because paths through the top slit interfere with paths through the bottom slit. The wave function of the photon can be formulated as a superposition of a photon that went through one slit and a photon that went through the other.

So if we park an observer behind one of the slits and shine a photon, we end up with a superposition of an observer who saw the light and an observer who didn't.

 

[gato_]

Ok, so what you suggest is mwi is an alternative to say: observing the photon made the wavefunction collapse to one of the possibilities, and instead there are to observers, each one seeing a possibility? I think I didn't understand mwi well, enough, but I'm still not having it. There is a good chance decoherence explains why you observe the photon in only one state. Did the system not decohere, you would see an interference pattern, including the observer itself. But in the same space. Obviously, our reality would be very strange if quantum applied macroscopically

 

[vanesch]

The main motivation for MWI - as I think it is - is that you can relegate the notion of "observer" to a meta-physical concept again, while in the standard "collapse" view, you need to make a distinction between what is an "observer" and what is not an observer in order to work out the formalism, at least in as much as one wants the wave function to have some or other physical meaning.
In other words, in an MWI-setting, you will never break your head over questions like:
"did the electron 'measure' the position of the photon when it scattered?"
"did the beam-splitter measure the presence of a photon ?" "And if it recoiled ?" "And if it recoiled, but bounced back ? " (I'm referring to the FELIX proposal by Penrose for instance)

Indeed, in any projection-based conception of quantum mechanics, you need to know, in order to find out whether the wave function after this phenomenon is to be considered a probabilistic projection (also described by a mixed state), or just a "normal" wavefunction in the tensor product of hilbert spaces of electron and photon in this case.

You could think that this makes a big difference in the outcome of the experiment, whether somewhere in the middle you "project" or you "superpose".

In fact, decoherence theory let's you understand (but even von Neumann was aware of this), that if this interaction is "sufficiently complex" that it won't affect the final outcome.

However, in some subtle experimental setups, it DOES make a difference. The typical example is the delayed quantum eraser where there was such a "measurement", which was then "erased".

In the MWI view on things, this kind of head ache is eliminated by considering that you NEVER project out. I think it is the main merit of MWI as a tool to help you understand the behavior of quantum mechanics.

Of course, with MWI, you get other kinds of head aches

 

[hamster143]

There is a good chance decoherence explains why you observe the photon in only one state. Did the system not decohere, you would see an interference pattern, including the observer itself. But in the same space. Obviously, our reality would be very strange if quantum applied macroscopically

Decoherence is an overused and a poorly defined word. The observer parked behind a slit can't see an interference pattern. He has to come out in the state "saw the light" or the state "did not see the light", or as a linear superposition of both states (neither aware that the other exists). The question we can ask is whether the photon is in a definite state BEFORE it hits the slits.

 

[rrw4rusty]

Greene strong suggests that... all things do happen in parallel universes... definitely in the quantum world... maybe in the macro world.

See for real player
http://www.pbs.org/wgbh/nova/programs/ht/rv/3012_05.html
or for quicktime
http://www.pbs.org/wgbh/nova/programs/ht/qt/3012_05.html

Yes this is qm for dummies level material, still...

Cheers,
Rusty

 

[gato_]

Thank you, I think I understand better what the theory suggests. However I find the name highly misleading. There are no multiple realities, but a single quantum one. The fact that it sounds like "world splitting" is because macroscopical things are in a quite definite state. I don't think there are parallel universes, what you see is what you get. I would like to understand better how decoherence works. Any suggestions?

 

[Fredrik]

Zurek has written a lot about the subject. A search for "zurek decoherence" at arxiv.org gets 55 hits. These are four of them:

Decoherence and the transition from quantum to classical -- REVISITED
Decoherence, einselection, and the quantum origins of the classical
Environment-Induced Decoherence and the Transition From Quantum to Classical
Deconstructing Decoherence

I have only read small parts of a few of his articles, and I'm not sure which ones. (It was at least 2 years ago). I think the one with "einselection" in the title was one of them.

by a guy named Maximilian Schlosshauer looks good too.

You might want to start with the wikipedia article about the density matrix.

I agree that the name "many-worlds interpretation" is a bit misleading, because we're just dealing with a single physical system. But this system does contain several versions of you with their memories in different states, so the name isn't entirely inappropriate.

 

[Dmitry67]

Thank you, I think I understand better what the theory suggests. However I find the name highly misleading. There are no multiple realities, but a single quantum one.


The fact that it sounds like "world splitting" is because macroscopical things are in a quite definite state. I don't think there are parallel universes, what you see is what you get. I would like to understand better how decoherence works. Any suggestions?

The first part is correct. The name is highly misleading, exactly like the Big bang.

For scrodinger cat experiment decoherence tells us that after you open a box with superposition of dead cat and alive cat, after observer looks at what is inside, there is a superposition of 3 realities:

1. happy observer looking at cat which is alive
2. sad observer looking at dead cat
3. confused observer looking at fuzzy image of alive cat mixed with a dead one.

Decoherence explains how and why the probability of option 3 becomes negligibly small after times about 10^-13s, so only 1 and 2 are left.

But neither cat nor observer are in definite state, as you suggest, their states are just correlated.

 

[Demystifier]

Dmitry, it seems to me that you are no longer convinced that MWI is absolutely the best. Am I correct?

 

[Dmitry67]

I am still convinced that it is the best.
Why are you asking?
Because I asked about the objective collapse? No, it was just pure curiosity.

And are you still convinced that BM is the best? :)

 

[Demystifier]

I am still convinced that it is the best.
Why are you asking?

It was just an impression, I cannot give a good rational argument for that.

And are you still convinced that BM is the best? :)

I would not say that I am convinced, but yes, BM makes more sense to me than any other interpretation. MWI also makes a lot of sense to me, but the Born-rule problem with MWI is the main reason why I still prefer BM over MWI.

 

[gato_]

The first part is correct. The name is highly misleading, exactly like the Big bang.

For scrodinger cat experiment decoherence tells us that after you open a box with superposition of dead cat and alive cat, after observer looks at what is inside, there is a superposition of 3 realities:

1. happy observer looking at cat which is alive
2. sad observer looking at dead cat
3. confused observer looking at fuzzy image of alive cat mixed with a dead one.

Decoherence explains how and why the probability of option 3 becomes negligibly small after times about 10^-13s, so only 1 and 2 are left.

But neither cat nor observer are in definite state, as you suggest, their states are just correlated.

Ok, so exotic quantum like superposition states are ruled out, but certainly, you only see one of the remaining ones. What's mwi answer for that?

 

[Dmitry67]

Answer and simple: both 1 and 2 exist.
And you need to invent ADDITIONAL axioms (like collapse or hidden variables) to claim that only one reality is 'real' and another is not.

 

[Dmitry67]

It was just an impression, I cannot give a good rational argument for that.

Ah, yes, I was totally convinced that BM was true, but it happened in another MWI branch :)

 

[Demystifier]

Ah, yes, I was totally convinced that BM was true, but it happened in another MWI branch :)

Is that a joke? I think it isn't if you honestly believe in MWI. :)

 

[gato_]

So both of them being equaly valid states, they can exist? then, to me it is clear that quantum theory, no mater how precise, is far from being understood (at least, it's relation with reality).

 

[Fredrik]

The theory is well understood. The reasons why it works aren't. Note that this is always the case with the best theory we know, because if we had a theory that explains why it works, that would be a better theory.

 

[Dmitry67]

Yes, they both exist.
'you' are not a line... Some of 'you' are living quite different lives in the other worlds, even they share the same history to some moment of time.

Here is a very good FAQ:
http://plato.stanford.edu/entries/qm-manyworlds/

covering even questions like:
6.4 Social Behavior of a Believer in the MWI
:)