Exploring Sparse Many Worlds: Is a Compact Representation of Existence Possible?

[Jarvis323]

TL;DR Summary

Is a sparse many worlds representation possible?

Is a sparse many worlds representation possible? Or in other words, is it compatible that existence is informationally compact, in that branching is not global? As a crude example, take two worlds, one where I had coffee and one where I had tea; would it be possible that those two versions of me are looking at the same moon (or sharing parts of the world which are causally isolated from the choice of beverage)?

 

[.Scott]

1) I think that there may be an issue with "global". Certainly, when I observe an interference pattern, I am seeing one pattern of many possible patterns. I can take a photograph and communicate that information widely. And it would seem that you could peruse any variation of that photograph as either the coffee-drinker or the tea-drinker. So, at least in many cases, the only restriction seems to be the causality light cone. And as that light cone intersects the light cones from other MWI split events, each would seem to eventually achieve pretty global effects.

But this doesn't mean that each of these events do not remain independent in some other way - or that they are somehow never independent to begin with. So perhaps there are many versions of the photo - but you only get one if you are drinking coffee and another if it's tea.

2) At the quantum level, time is reversible. So it would make sense to me that with MWI we should expect to see worlds both split and recombine. You stopped off at a restaurant in August 2000 - was it coffee or tea that you ordered - are you sure you remember - is there any record at all?

So ...
Certainly yes - but for what purpose.
Since Hugh Everett created this interpretation, the life of MWI seems to operate under its own rules - splitting off into enumerable variations.
Given that a version of MWI is a genuine "interpretation", it's point would not be to create new Physics but to put existing Physics in a different light.
So would constraining MWI to limit the information inflation help in describing or understanding something? It might.

 

[PeroK]

Summary:: Is a sparse many worlds representation possible?

Is a sparse many worlds representation possible? Or in other words, is it compatible that existence is informationally compact, in that branching is not global? As a crude example, take two worlds, one where I had coffee and one where I had tea; would it be possible that those two versions of me are looking at the same moon (or sharing parts of the world which are causally isolated from the choice of beverage)?

You could start by defining, under MWI:

a) "I that had coffee".

b) "I that had tea".

c) "The Moon"

 

[Jarvis323]

Certainly yes - but for what purpose.

Carroll seems to think that "taking quantum foundations seriously" is a good first step towards figuring out how QM leads to gravity. But he then admits he might be deluding himself.

Given that a version of MWI is a genuine "interpretation", it's point would not be to create new Physics but to put existing Physics in a different light.
So would constraining MWI to limit the information inflation help in describing or understanding something? It might.

Whether or not the interpretation makes a difference, I guess, depends on whether the many-worlds are assumed to be "real", as opposed to just part of a conceptual model for understanding the math and logic behind Schrodinger's equation. I understand this is a matter of disagreement between physicists.

But if the many worlds interpretation is correct, and in the "real" sense, and this interpretation is useful for explaining gravity as Carroll hopes, then the issue I bring up would be important wouldn't it; maybe necessitate a different way to incorporate information theory?

I would expect that the structure of information (how it's bound/causally connected) isn't changed/deformed without some type of exchange. So if MW is a real thing, and if we connect it with gravity and information somehow, I would naively expect something like Noether's theorem to apply.

Maybe I am way off the mark with these thoughts.

 

[PeterDonis]

would it be possible that those two versions of me are looking at the same moon (or sharing parts of the world which are causally isolated from the choice of beverage)?

To answer this question, you need to be very clear about what the "worlds" actually are in the MWI. Remember that the MWI says that the wave function is the only reality: that's all there is. And the wave function is not a function in ordinary 3-dimensional space. It is a function in Hilbert space. For a universe that includes "subsystems", i.e., things like cups of coffee, cups of tea, people who drink things, and the Moon, the subsystems, as far as the MWI is concerned, are sets of degrees of freedom in Hilbert space. They are not regions of ordinary 3-space.

The "worlds" are simply individual terms in a wave function in which at least some of the subsystems are entangled. In your beverage example, the "cup of coffee", "cup of tea", and "drinker" subsystems would be entangled, with two "worlds" (terms in the wave function):

Term #1: cup of coffee drunk by drinker, cup of tea not drunk, drinker drank coffee

Term #2: cup of coffee not drunk, cup of tea drunk by drinker, drinker drank tea

Notice that neither of these contains the Moon; so if we have the Moon as another subsystem, it would not be entangled with any of the others at this point. So it would be reasonable to say that both "worlds" contain the same Moon, or that both "copies" of the drinker are looking at the same Moon, at the instant the drinking is completed.

However, that won't last very long, because it only takes about 1 1/4 seconds for photons from the Moon to reach the Earth. So by 1 1/4 seconds after the drinking is completed, each "copy" of the drinker will have interacted with the Moon after drinking, so the Moon will now be entangled with each "copy" of the drinker after the drinking. Once the Moon is entangled with the drinker after drinking, we can no longer say it's the same Moon in both worlds, because the Moon is now part of the entanglement that makes the worlds separate.

Of course all of the above is highly oversimplified. In a real scenario, the drinking takes time and the Moon is interacting with the drinker during that time, so in fact the inclusion of the Moon in the split of worlds would happen well before the drinking was completed (except perhaps in the highly unlikely case that the drinker can down an entire cup of coffee or tea in less than 1 1/4 seconds). Also, in a real scenario it wouldn't even be necessary for the drinker to be looking directly at the Moon; the drinker is always interacting with his environment, and so is the Moon (since all it takes for the latter is for photons to arrive at the Earth from the Moon), so the drinker is always entangled with the Moon via some pathway or other, and this entanglement is always being "updated" as new interactions occur. So in a real scenario there is practically never any meaningful sense in which two "worlds" in the MWI are "sharing" anything.

 

[PeterDonis]

it would make sense to me that with MWI we should expect to see worlds both split and recombine.

Not when decoherence is taken into account. See below.

You stopped off at a restaurant in August 2000 - was it coffee or tea that you ordered - are you sure you remember - is there any record at all?

It doesn't matter whether your not you remember. Decoherence means that the universe "remembers"--the entanglement that was created when you ordered coffee or tea never goes away. It gets spread farther and farther through the universe by ongoing interactions and can never be undone. So worlds can never recombine once they've split.

 

[Jarvis323]

To answer this question, you need to be very clear about what the "worlds" actually are in the MWI.
...
The "worlds" are simply individual terms in a wave function in which at least some of the subsystems are entangled. In your beverage example, the "cup of coffee", "cup of tea", and "drinker" subsystems would be entangled, with two "worlds" (terms in the wave function):

There is something I feel needs to be considered:

(1) Simple MWI is just a direct interpretation of Schrodinger's equation and limited in that way.
(2) MWs may be "real" so to speak.

If (2) is correct, the "real" MWs need not be the MWs from (1).

So in a real scenario there is practically never any meaningful sense in which two "worlds" in the MWI are "sharing" anything.

If we look at it from an information theoretic perspective, it would be surprising to me if a timeline splitting on an electron having one spin or another, immediately brings into existence multiple distinct descriptions of different universes, with no mutual information between any of them.

 

[PeterDonis]

If (2) is correct, the "real" MWs need not be the MWs from (1).

I have no idea what this means. If we're discussing the MWI, then we're discussing the MWI, and any "worlds" are the ones the MWI describes, i.e., (1).

If we're not discussing the MWI, then you need to explain what we are discussing and give appropriate references for the theory you are using. Otherwise we can't even make sense of (2).

If we look at it from an information theoretic perspective, it would be surprising to me if a timeline splitting on an electron having one spin or another, immediately brings into existence multiple distinct descriptions of different universes, with no mutual information between any of them.

Go back and read my post again. You evidently do not understand what the MWI actually says.

 

[Jarvis323]

I have no idea what this means. If we're discussing the MWI, then we're discussing the MWI, and any "worlds" are the ones the MWI describes, i.e., (1).

If we're not discussing the MWI, then you need to explain what we are discussing and give appropriate references for the theory you are using. Otherwise we can't even make sense of (2).
Go back and read my post again. You evidently do not understand what the MWI actually says.

(1) is the "worlds" which are terms in the wave function.
(2) is the "worlds" which are assumed by some to be things that exist in reality.

My question is about (2). If we assume there actually are multiple timelines, and not just useful equations, then is there a reason those worlds need to be wholly separate/exclusive.

 

[PeterDonis]

maybe you didn't understand my post?

Maybe you don't understand the MWI?

(1) is the "worlds" which are terms in the wave function.

Yes, that's what the MWI says.

(2) is the "worlds" which are assumed by some to be things that exist in reality.

Not "assumed"--the MWI says the worlds in (1) are things that exist in reality, because they are terms in the wave function, and the MWI says the wave function is all that exists in reality.

My question is about (2).

Your question was about (2) somehow being different from (1). That's not what the MWI says; the MWI says (2) and (1) are the same. See above.

 

[.Scott]

It doesn't matter whether your not you remember. Decoherence means that the universe "remembers"--the entanglement that was created when you ordered coffee or tea never goes away. It gets spread farther and farther through the universe by ongoing interactions and can never be undone. So worlds can never recombine once they've split.

In order to refute the notion that MWI worlds can recombine, you would need to assert that there is always enough information retained in the world to unambiguously differentiate every possible historic MWI split leading up to the present. I don't think you would be willing to do that. It would suggest that every MWI world has a huge information storage capacity. Or, that MWI splits are largely dependent of each other.

 

[PeterDonis]

In order to refute the notion that MWI worlds can recombine, you would need to assert that there is always enough information retained in the world to unambiguously differentiate every possible historic MWI split leading up to the present. I don't think you would be willing to do that.

I already did that. The "information retained in the world" is the entanglement spreading further and further throughout the universe through ongoing interactions. The details are in the literature on decoherence.

It would suggest that every MWI world has a huge information storage capacity.

It does. The Hilbert space describing a spatially infinite universe has an infinite number of degrees of freedom. The entanglement through ongoing interactions can ultimately spread out to all of them.

 

[Jarvis323]

But isn't the Hilbert space an abstract mathematical object, not an information storage medium? If the information is stored, then it stands to reason that something goes into embedding it, and it would be surprising to get unlimited information storage capacity and transformation for free.

 

[.Scott]

I already did that. The "information retained in the world" is the entanglement spreading further and further throughout the universe through ongoing interactions. The details are in the literature on decoherence.

You are ignoring the "unambiguously differentiate every possible historic MWI split" part of the statement.
I can record every possible chess position in about 200 bits - including whether pawns are en passant, whether each rook still qualifies for castling, and how recently there was pawn move or piece take. But that is not sufficient information to reconstruct the history.
Every chess move has an indelible affect on the rest of the game - but not necessarily a permanent and uniquely distinguishable effect.

It does. The Hilbert space describing a spatially infinite universe has an infinite number of degrees of freedom. The entanglement through ongoing interactions can ultimately spread out to all of them.

But the "addressing information" for each possible world needs to be containable within that 3D world. So you can have the equivalent of a chess "Hilbert Space" that describes all possible chess games, but the chess position for any given move of any given chess game needs to be contained within a "game state" (those 200 bits I mentioned above). Your Hilbert Chess Space may tell you that there are 1000 ways of reaching a specific game state, but given only the game state you cannot back out which history the game has followed. This would be a case where multiple chess lines recombine.

 

[PeterDonis]

isn't the Hilbert space an abstract mathematical object, not an information storage medium?

Not according to the MWI. The MWI says the wave function is real, and the wave function is in Hilbert space, so Hilbert space also has to be real.

You are ignoring the "unambiguously differentiate every possible historic MWI split" part of the statement.

No, I'm not. In each of the different MWI worlds, different information is stored by the entanglement relations. That's what differentiates the worlds, and that differentiation includes every interaction that has ever happened.

Your Hilbert Chess Space may tell you that there are 1000 ways of reaching a specific game state, but given only the game state you cannot back out which history the game has followed.

And that is not how the MWI works. The "state" in a particular world in the MWI does not just contain the analogue of the current "chess game state". It includes the analogue of the entire sequence of moves that led to that state.

 

[Quanundrum]

This question is moot if you consider the approach of 'Diverging Worlds' by Simon Saunders, David Wallace, David Deutsch, Alastair Wilson, Anthony Aguirre, etc. I.E. All world lines are spawned at the dawn of existence itself and are always qualitatively separated.

 

[.Scott]

And that is not how the MWI works. The "state" in a particular world in the MWI does not just contain the analogue of the current "chess game state". It includes the analogue of the entire sequence of moves that led to that state.

So, as the universe gets older and older and splits over and over, this history information keeps accumulating.
If this happens within a BH, as it accumulates historic information, it would grow to the limits of the Bekenstein Bound.
If it doesn't happen within a BH, when do you stop the tally as something is falling in - when an object crosses the EH or when it reaches the singularity?

Or perhaps this is a different type of information which is exempt from the normal ties to gravity.

This question is moot if you consider the approach of 'Diverging Worlds' by Simon Saunders, David Wallace, David Deutsch, Alastair Wilson, Anthony Aguirre, etc. I.E. All world lines are spawned at the dawn of existence itself and are always qualitatively separated.

Interesting Interpretation: So all of this "which way" information came as a complete package. As time passes, more and more of it is revealed to us. If the universe ever "finishes", we will finally know exactly which universe was the one we were created within.
Basically, time passes as information leaks into our universe from a prewritten history.

 

[PeterDonis]

So, as the universe gets older and older and splits over and over, this history information keeps accumulating.

No, it doesn't. Unitary evolution preserves information; it neither creates it nor destroys it. So there is no additional information being created that accumulates or needs to be stored anywhere.

All that is happening is that the unitary evolution of the wave function, since it includes interactions, will propagate entanglement relations, so that degrees of freedom that started out not entangled become entangled. Those entanglement relations contain all of the "information" about the "history of chess moves" in any particular branch. But the "bits" that store whether or not a particular pair of degrees of freedom are entangled were already there in the wave function at the start; they have to be, since, as above, the evolution of the wave function is unitary, so it can't create (or destroy) information, hence the number of "bits" can't change. All that happens as interactions take place and entanglements propagate is that "bits" change state (and the state they are in can be different in different branches).

all of this "which way" information came as a complete package. As time passes, more and more of it is revealed to us. If the universe ever "finishes", we will finally know exactly which universe was the one we were created within

I'm not sure that's what the interpretation @Quanundrum is referencing is actually saying.

the approach of 'Diverging Worlds' by Simon Saunders, David Wallace, David Deutsch, Alastair Wilson, Anthony Aguirre, etc.

Can you give a reference?

 

[Jarvis323]

But the "bits" that store whether or not a particular pair of degrees of freedom are entangled were already there in the wave function at the start; they have to be, since, as above, the evolution of the wave function is unitary, so it can't create (or destroy) information, hence the number of "bits" can't change.

I admit I am a little confused, because I have been probably misapplying concepts from classical information to quantum information.

I guess it is not possible for quantum information to be compressed when talking about MWI worlds? It seems you are saying that a fixed number of bits, determined exactly by what is physically possible, must have been here from the start, and each with a strict predesignated purpose; so they cannot be "reused" to store different information. E.g. there are bits out there signaling that I in one world had coffee, and others signaling I in another had tea. Those bits, from inception were designated to only signal that information, and have only been storing the information prior to the event that the event hadn't happened yet, and after the events, those bits remain constant for the rest of eternity? And those bits are real physical things. And these are or aren't qbits we are talking about?

Am I misinterpreting about your assertions?

Of course if you write out the evolution of the wave equation on paper, that could be compressed, but this is a classical description.

I know quantum information can be compressed in some sense.
https://physicsworld.com/a/quantum-data-are-compressed-for-the-first-time/

Your question was about (2) somehow being different from (1). That's not what the MWI says; the MWI says (2) and (1) are the same. See above.

I won't try too hard to defend what I said here, I got the idea that there is a debate about the interpretation of the worlds as real from Wikipedia, and that's not a good source. I don't have access to the books that are referenced, but it is claimed that Steven Hawking said,

"MWI is "trivially true", and

"But, look: All that one does, really, is to calculate conditional probabilities—in other words, the probability of A happening, given B. I think that that's all the many worlds interpretation is. Some people overlay it with a lot of mysticism about the wave function splitting into different parts. But all that you're calculating is conditional probabilities."

Gardner, Martin (2003). Are universes thicker than blackberries?. W.W. Norton. p. 10. ISBN 978-0-393-05742-3.

Ferris, Timothy (1997). The Whole Shebang. Simon & Schuster. pp. 345. ISBN 978-0-684-81020-1.

And it claims that Hawking's said, referring to Penrose,

"He's worried that Schrödinger's cat is in a quantum state, where it is half alive and half dead. He feels that can't correspond to reality. But that doesn't bother me. I don't demand that a theory correspond to reality because I don't know what it is."

Hawking, Stephen; Roger Penrose (1996). The Nature of Space and Time. Princeton University Press. pp. 121.

What you seem to be claiming is that there can be no separation (in the case of MWI) from the theory and reality, so that either MWI is true and exactly corresponds to reality in every literal sense, or MWI is incorrect. I'm not sure so I just left the issue open.

 

[jartsa]

So, as the universe gets older and older and splits over and over, this history information keeps accumulating.
If this happens within a BH, as it accumulates historic information, it would grow to the limits of the Bekenstein Bound.
If it doesn't happen within a BH, when do you stop the tally as something is falling in - when an object crosses the EH or when it reaches the singularity?

Nothing can store more bits per kilogram than a BH. So if we try to exceed Bekenstein Bound by dropping something into a BH, then a BH is the best possible choice for the thing to be dropped.

It's easy to check that dropping a BH into a BH does not cause Bekenstein Bound to be exceeded.
Oh, the question was about new history being made while falling inside a black hole. Well, isn't this the Schrodingens cat situation where the BH is the box and the infallers are the cat? The contents of the box evolve unitarily.

 

[PeterDonis]

I have been probably misapplying concepts from classical information to quantum information.

I suspect you have, yes.

I guess it is not possible for quantum information to be compressed when talking about MWI worlds?

To even address this question, we would first have to be clear about what "compression" means with classical bits. I think that would take us too far afield. I also don't think it's necessary to address your actual question. See below.

there are bits out there signaling that I in one world had coffee, and others signaling I in another had tea.

No. I probably should have insisted on using the term "degrees of freedom" (which I'll abbreviate as "DOF") instead of "bits". Think of it this way: in the coffee/tea/drinker scenario, we have the following DOF:

Coffee subsystem
Tea subsystem
Drinker subsystem

These DOF are what are there in the wave function of the universe from the start and never change. What differs in each "world" in the MWI is what state these DOF are in: for example, in the given scenario, after the drinker chooses what to drink, we have the following two worlds:

World #1:
Coffee subystem in the "drunk" state
Tea subsystem in the "not drunk" state
Drinker subsystem in the "drank coffee" state

World #2:
Coffee subsystem in the "not drunk" state
Tea subsystem in the "drunk" state
Drinker subsystem in the "drank tea" state

But, and here is the key, the "information" stored in the overall wave function, which is what is conserved, is not either of these worlds separately, but both of them together. In other words, the complete state is a superposition of World #1 and World #2, and that state has evolved unitarily from the previous state, which was:

World #0:
Coffee subsystem in the "not drunk" state
Tea subsystem in the "not drunk" state
Drinker subsystem in the "deciding what to drink" state

The worlds branch based on the drinker subsystem's decision about what to drink, which we are here assuming to be a quantum interaction with two possible outcomes, "drink coffee" and "drink tea", that entangles the drinker subsystem with the coffee and tea subsystems. It is no different in this respect from an electron going through a Stern-Gerlach magnet and coming out with its spin and momentum DOF entangled. (The only difference in the coffee/tea/drinker case is that there is no way to reverse the interaction because of decoherence.)

I know quantum information can be compressed in some sense.

This is a different concept of "compression" which has nothing to do with what we are discussing here.

 

[PeterDonis]

What you seem to be claiming is that there can be no separation (in the case of MWI) from the theory and reality, so that either MWI is true and exactly corresponds to reality in every literal sense, or MWI is incorrect.

The interpretation of QM that is normally referred to as the MWI is like this, yes.

What the quotes you give appear to be describing is a different interpretation of QM, which strictly speaking should not be called "MWI" but something else. However, physicists can be as sloppy as anyone else in their use of terminology.

 

[Demystifier]

As a crude example, take two worlds, one where I had coffee and one where I had tea; would it be possible that those two versions of me are looking at the same moon (or sharing parts of the world which are causally isolated from the choice of beverage)?

I think it's impossible, because the two experiences of watching the Moon (one during drinking a coffee, the other during drinking a tea) are not exactly identical. The two different experiences correspond to two different states in the Hilbert space.

 

[timmdeeg]

I think it's impossible, because the two experiences of watching the Moon (one during drinking a coffee, the other during drinking a tea) are not exactly identical. The two different experiences correspond to two different states in the Hilbert space.

But regardless of "two different states in the Hilbert space" wouldn't the moon look the same for both? I mean it doesn't seem to make sense that the coffee drinker in contrast to the tea drinker seas a meteorite hitting the moon.

 

[Halc]

As a crude example, take two worlds, one where I had coffee and one where I had tea; would it be possible that those two versions of me are looking at the same moon (or sharing parts of the world which are causally isolated from the choice of beverage)?

Simply put, you'd have to have had coffee or have had tea, including any part influencing the decision making process, in the space of probably under 3 seconds. If over 3 seconds, then the moon you see has measured an Earth with either you having tea or having coffee, and the moon that measures one is different than the moon that has measured the other, therefore no, these two worlds you describe are not sharing the same moon.

Try it with Venus. Far more plausible that both of you share the same Venus, assuming the decision to have one drink or the other did not have a root cause that goes too far back. Make both drinks, then measure the spin of one particle, and then immediately consume one of the drinks based only on the outcome of that measurement. That takes a minute or so, far under the several minutges that both of you might share the same Venus.

 

[PeterDonis]

regardless of "two different states in the Hilbert space" wouldn't the moon look the same for both?

You might not be able to perceive any difference, but that doesn't mean there isn't one. We are talking about the microscopic quantum state, not what you can macroscopically perceive. The microscopic quantum state "coffee drinker observes Moon" is different from "tea drinker observes Moon". Since the Moon is entangled with the drinker, there is no way to put the difference in either one individually.

 

[Jarvis323]

Simply put, you'd have to have had coffee or have had tea, including any part influencing the decision making process, in the space of probably under 3 seconds. If over 3 seconds, then the moon you see has measured an Earth with either you having tea or having coffee, and the moon that measures one is different than the moon that has measured the other, therefore no, these two worlds you describe are not sharing the same moon.

Try it with Mars. Far more plausible that both of you share the same Venus, assuming the decision to have one drink or the other did not have a root cause that goes too far back. Make both drinks, then measure the spin of one particle, and then immediately consume one of the drinks based only on the outcome of that measurement. That takes a minute or so, far under the several minutges that both of you might share the same Venus.

So as soon as a photon travels between you and the surface of the moon, then you've interacted with/become entangled with the whole moon? Or in general, by proxy, everything the version of the moon you're looking at was already entangled with is now necessarilly unique to your world as well?

Despite that there is one moon that sees you drinking tea, and another one that sees you drinking coffee (and the distinguishing entanglement relations), couldn't both still have some overlapping 'existence'? Like a git repository, you have different/separate branches, but internally it's one data structure that is storing differences. Is it completely able to be ruled out that entanglement relations can't be factored out of some form of shared existence? E.g, some time after the me that would go on to drink tea had split from the me that would drink coffee, the position of the moon would not have changed more than one plank length.

The next question, which I think I already got an answer on, is can't the the wave function as we know it/represent it mathematically, be an abstraction of a real wave function-like thing, which fits the model of the wave function in so far as the wave function demands, but be different in reality in significant ways beyond that? To which I think the answer is that now we aren't talking about MWI anymore. And if we talk about this in the context of what is compatible with MWI, then we first need to at least view MWI as a less realist interpretation (if this is possible)? If so, I wanted to ask if, to whatever form the thing that the wave function models takes on in reality, information theory can be applied in some way; but it seems, even if this is possible, it would be something beyond both classical information theory and quantum information theory, since quantum information theory sits on top of the wave function? So we would need a new concept of information to ask about an accounting of the information that represents the wave function (or Hilbert space) itself? And that might be beyond physics?

Is anything I've been asking relevant to how one would think about the conjecture that space-time acts as a quantum error correcting code, alongside MWI?
https://www.quantamagazine.org/how-space-and-time-could-be-a-quantum-error-correcting-code-20190103/

 

[PeterDonis]

as soon as a photon travels between you and the surface of the moon, then you've interacted with/become entangled with the whole moon?

Yes, because the moon's particles are all entangled with each other.

everything the version of the moon you're looking at was already entangled with is now necessarilly unique to your world as well?

Yes, because a photon from you interacting with the moon is different from no photon from you interacting with the moon. And a photon from a "you" who drank coffee interacting with the moon is different from a photon from a "you" who drank tea interacting with the moon.

Of course these differences are way, way below our ability to distinguish with the technology we have, now or in the foreseeable future. But we're talking in this thread about what is true in principle according to a particular interpretation of QM, not about what we can actually distinguish with our current limited technology.

Like a git repository

No. You cannot use any ordinary analogy for this; all such analogies are wrong. A quantum superposition is not like anything you are familiar with. The only accurate way to think about it is to look at the math.

can't the the wave function as we know it/represent it mathematically, be an abstraction

Not according to the MWI. According to the MWI, the wave function of the entire universe is real, and is the only real thing, and the thing we call a "wave function" in the math is an exact representation of the real thing.

 

[Jarvis323]

No. You cannot use any ordinary analogy for this; all such analogies are wrong. A quantum superposition is not like anything you are familiar with. The only accurate way to think about it is to look at the math.

But MWI is already a step beyond math. By looking at the math, you're only understanding the thing which is being interpreted, not the interpretation. The concept of 'real' is not mathematical.

 

[Jarvis323]

Not according to the MWI. According to the MWI, the wave function of the entire universe is real, and is the only real thing, and the thing we call a "wave function" in the math is an exact representation of the real thing.

Are you sure it is true that "it says the only thing that exists is the wave function", rather than "it only says that the wave function exists" (e.g. doesn't claim anything else exists, or require anything else to serve its purpose)? There would be a difference, and I would be surprised if it was really the former, because it would be making quite a leap beyond what is necessary. It would be like throwing in that god exists as part of the Copenhagen interpretation. Is there a reference on this?

 

[PeterDonis]

MWI is already a step beyond math.

Yes, but you still have to understand the math and use that as the foundation for interpretation. You can't use intuitive analogies.

Are you sure it is true that "it says the only thing that exists is the wave function"

That's my understanding of what the MWI says, yes.

There would be a difference

Yes, there would: saying that other things besides the wave function exist would require you to have some mathematical model for them, and there isn't one. Remember that the MWI says there is only unitary evolution of the wave function, all the time. Saying that anything else exists would require there to be something else going on besides unitary evolution of the wave function.

 

[Jarvis323]

Saying that anything else exists would require there to be something else going on besides unitary evolution of the wave function.

Does this include the possibility that the wave function is made up, or emerges, from something at a lower level?

 

[PeterDonis]

Does this include the possibility that the wave function is made up, or emerges, from something at a lower level?

No, since there is no such thing in the math of QM. We are talking about the interpretation of QM here, not the interpretation of some speculative theory that adds other elements beyond QM.

 

[Halc]

So as soon as a photon travels between you and the surface of the moon, then you've interacted with/become entangled with the whole moon?

More like the moon has interacted with me. The moon has taken a measure of me, and I'm no longer in superposition of drinking coffee and tea. From my own point of view, I was never in superposition since I've measured my decision and seem to be aware of what I'm drinking. So once the moon measures me, it becomes entangled with those two states and is now two different moons instead of one moon with me in superposition.
It takes about 1.5 seconds for that to happen, and 1.5 seconds for me to measure the moon subsequently, and thus have the coffee drinking Halc no longer share a common moon with the tea drinking Halc.

Or in general, by proxy, everything the version of the moon you're looking at was already entangled with is now necessarilly unique to your world as well?

If I read that right, I think I agree.

Despite that there is one moon that sees you drinking tea, and another one that sees you drinking coffee (and the distinguishing entanglement relations), couldn't both still have some overlapping 'existence'?

Two states are never entirely separate according to MWI, but at the point you're describing, they functionally are. I don't think you could possibly get those two states to measurably interfere with each other. They're not even close anymore. Having had coffee or tea are two very macroscopically different states that diverged some time ago, which is why I didn't really think it could happen with the moon at all in that limited couple of seconds. The difference diverged far further back than 3 seconds.

Like a git repository, you have different/separate branches, but internally it's one data structure that is storing differences.

That's an analogy to a point, but a git change doesn't interact with another unless there is overlap in the parts of the structure changed, and it isn't ever an analogy of entanglement. There is no analogous propagation over time to more distant parts of the structure. Git has no speed of light.

Is it completely able to be ruled out that entanglement relations can't be factored out of some form of shared existence? E.g, some time after the me that would go on to drink tea had split from the me that would drink coffee, the position of the moon would not have changed more than one plank length.

The position of the moon has not likely changed due to your choice, but the measured state of the atoms most certainly has. A photon was emitted from here instead of there. No going back if that photon is measured, and moon photons are always being measured.
Schrodinger's box is an unrealistic hypothetical idea. There is no way even in principle to not measure a live and dead cat in a box in a lab. The box would have to be immune to inertial changes of the smallest sort. Certainly the live cat puts out different gravitons than the dead one. If those gravitons make any change to the environment outside, the cat is no longer in superposition relative to the lab guy. It's merely collapsed to a state of the lab guy not knowing, and epistemological state, not a state of superposition any longer.
But distance makes a great box. A cat on Venus can be in superposition of live and dead relative to Earth. We cannot have measured it because information cannot yet have reached us. Venus locally may have split into Venus-with-live-cat and Venus-with-dead-cat, but Earth is still one Earth, unsplit, with one Venus with a cat in superposition of live and dead.
A non-local interpretation would assert otherwise, but I've not heard of a non-local version of many worlds with FTL information transfer that immediately splits the universe when entangled measurements are taken. Somebody should suggest it.

The next question, which I think I already got an answer on, is can't the the wave function as we know it/represent it mathematically, be an abstraction of a real wave function-like thing, which fits the model of the wave function in so far as the wave function demands, but be different in reality in significant ways beyond that? To which I think the answer is that now we aren't talking about MWI anymore. And if we talk about this in the context of what is compatible with MWI, then we first need to at least view MWI as a less realist interpretation (if this is possible)?

I'm kind of losing you. In a way, MWI typically is presented as the one universal wave function being real. A lot depends on one's definition of 'is real' there. Tegmark's mathematical universe posits that such a function IS reality, not just a model of it. In that sense, there would be no difference between the wave function and the reality it represents.
I'm more of an RQM guy, not MWI, so being real is a relation to me, not a property. A mathematical universe works with RQM as well, but I don't think Tegmark views it like that.

If so, I wanted to ask if, to whatever form the thing that the wave function models takes on in reality, information theory can be applied in some way; but it seems, even if this is possible, it would be something beyond both classical information theory and quantum information theory, since quantum information theory sits on top of the wave function? So we would need a new concept of information to ask about an accounting of the information that represents the wave function (or Hilbert space) itself? And that might be beyond physics?

Not sure if I can answer this. I've not seen the whole thread, but I seem more going down this line of questioning. I think there are others more capable of giving coherent answers to this.

Haven't read the ECC link yet. I'll give it a shot.

 

[Jarvis323]

No, since there is no such thing in the math of QM. We are talking about the interpretation of QM here, not the interpretation of some speculative theory that adds other elements beyond QM.

No, it seems MWI is speculating that there is nothing beyond the mathematical elements of QM. I am asking about compatibility. If there were a version of MWI that didn't impose unnecessary limitations/barriers, I don't know why we would be talking about the original.