Does the MWI require "creation" of multiple worlds?

[PeterDonis]

From another thread:

MWI requires the instantaneous creation of a pair (or infinite number) of parallel universes.

I see this claim made fairly often, but it does not seem correct to me. According to the MWI, the dynamics of the wave function is always unitary (there is no collapse), and a unitary process cannot "create" or "destroy" anything. All it can do is entangle things. So, for example, if we consider a measurement with two possible results, under the MWI, unitary evolution induces the state transition (highly schematic since I am ignoring normalization)

$$
\left( |1> + |2> \right) |R> \rightarrow |1>|U> + |2>|D>
$$

where $|1>$ and $|2>$ are the eigenstates of the measurement for the measured system, and $|R>$, $|U>$, and $|D>$ are the "ready to measure", "measured state 1", and "measured state 2" states of the measuring apparatus. The MWI describes this final state as having two "worlds", in one of which the measurement yielded the "1" result and in the other of which the measurement yielded the "2" result; but since the state transition induced by the measurement is unitary, nothing has been "created"; all that has happened is entanglement of the measured system and the measuring device.

Does anyone know of discussions of this in the literature?

 

[akvadrako]

Hi PeterDonis,

I'm not really a physicist, but I have spent a great deal of time reading the research that tries to understand WMI. I'm sure I could find a paper in my notes which get's into this deeper, but the question seems quite basic. In WMI there is only the unitary evolution of the wavefunction without collapse. So indeed, what's "created" is that the split, which now describes two parts of the wavefunction which no longer interfere. But because of the split, those parts can now be described as universes/worlds.

Does that answer the question?

 

[kith]

The MWI describes this final state as having two "worlds", in one of which the measurement yielded the "1" result and in the other of which the measurement yielded the "2" result; but since the state transition induced by the measurement is unitary, nothing has been "created"; all that has happened is entanglement of the measured system and the measuring device.

This seems like semantics to me. If the initial state is described as "having one world" and the final state is described as "having two worlds", it seems sensible to me to speak of the creation of an additional world (or of the splitting of one world into two). But I think the more important question to ask is whether we should ascribe the property of "having a certain number of worlds" to the state alone.

From the bird's-eye view, there's simply a state $|\psi\rangle$ which evolves into a different state $|\psi'\rangle$. In this view, the very concept of multiple worlds doesn't arise. If we insist on introducing it, the number of worlds can be wildly different, depending on which factorization of the Hilbert space we choose.

From the frog's-eye view of an observer, however, there is one world of experience before the measurement and there are two mutually exclusive worlds of experience after the measurement. It is in this sense that there are unambiguously more "worlds" after the measurement than before.

 

[Vanadium 50]

Does anyone know of discussions of this in the literature?

You might look to see if Sidney Coleman wrote anything on this. He's the one who explained it to me thus: in many-worlds, there are not many worlds. There is only the one world.

 

[atyy]

I agree with kith that it is semantic. In Many-Worlds, there is only one real world, and many experienced worlds, where each experienced world is the experience of a Copenhagen observer.

 

[bhobba]

I see this claim made fairly often, but it does not seem correct to me.

You are right.

It's an interpretive assumption that each of the possible outcomes in the mixed state after decoherence is a world. Nothing is created instantaneously - its just an interpretive assumption about mixed states from decoherence.

I have read Wallace:
https://www.amazon.com/dp/0198707541/?tag=pfamazon01-20

He has the advantage of having both a PhD in particle physics and philosophy. But I don't recall him discussing that one. It may be there - but I don't recall it. Then again once you understand in essence what MW is the answer it's pretty obvious.

MW can be viewed as Decoherent Histories with each history being a world and Decoherent Histories as MW without the many worlds. I once saw a you-tube video by Gell-Mann that looked at it that way - if anyone is interested I will try and dig it up - I think it was in the Q&A at the end of one of his lectures - but I am not sure. Interestingly towards the end of his life Feynman was converted to Decoherent Histories from a lecture on it by Gell-Mann,

Thanks
Bill

 

[bhobba]

You might look to see if Sidney Coleman wrote anything on this. He's the one who explained it to me thus: in many-worlds, there are not many worlds. There is only the one world.

Now why didn't I say that. That Sidney Coleman is one smart guy - but I think everyone knows that anyway.

Thanks
Bill

 

[bhobba]

But I think the more important question to ask is whether we should ascribe the property of "having a certain number of worlds" to the state alone.

Don't hold me to it, but I think that was Gell-Man's view - its just semantics. Personally I am attracted to that idea as wrll.

Thanks
Bill

 

[Demystifier]

Does anyone know of discussions of this in the literature?

This paper https://arxiv.org/abs/quant-ph/9709032 explains it in a similar way as you do.

 

[stevendaryl]

Another way of looking at many-worlds that doesn't require any splitting is this:

Define a "macroscopic state" to be some kind of coarse-grained description of the world. I'm not going to try to make this too precise, but the macroscopic state should fix the locations and velocities of all objects larger than say, a bacterium, and should fix the coarse-grained values of all long-range fields. I want it to be the case that every observation and measurement result can simply be "read off" from the macroscopic state. If a measurement of a particle's spin along some axis produces spin-up, then that means the world is in a different macroscopic state than if the measurement had produced spin-down.

Now, I'm assuming that this can be made precise using projection operators. The state of the universe, $|\psi\rangle$ is an element of some hilbert space, $\mathcal{H}$, and it evolves according to $|\psi(t)\rangle = e^{-iHt} |\psi(0)\rangle$ where $H$ is the hamiltonian of the universe. Each macroscopic state $j$ corresponds to a projection operator $\Pi_j$ on the hilbert space.

The meaning is that if the universe is definitely in macroscopic state $j$, then the state satisfies:

$\Pi_j |\psi\rangle = |\psi\rangle$

If the universe is definitely not in macroscopic state $j$, then the state satisfies:

$\Pi_j |\psi\rangle = 0$

If the universe starts off in state $|\psi\rangle$, then at a later time $t$, there will be a certain probability $P_j(t)$ of being in macroscopic state $j$ given by: $|\Pi_j e^{-iHt} |\psi\rangle|^2 = \langle \psi | e^{+iHt} \Pi_j e^{-iHt} | \psi \rangle \equiv \langle \psi | \Pi_j(t) |\psi \rangle$ where $\Pi_j(t) \equiv e^{+iHt} \Pi_j e^{-iHt}$

So in this view, it's not that the universe "splits". At all times, the universe already is split into (countably many?) macroscopic states $j$. The only thing that changes from moment to moment is the weight $P_j(t)$ given to each macroscopic state, and that increases or decreases smoothly with time.

 

[MathematicalPhysicist]

I agree with kith that it is semantic. In Many-Worlds, there is only one real world, and many experienced worlds, where each experienced world is the experience of a Copenhagen observer.

So in each world the wave function collapses, so it's a copenhagen interpretation after all!

 

[A. Neumaier]

From the frog's-eye view of an observer, however, there is one world of experience before the measurement and there are two mutually exclusive worlds of experience after the measurement.

No. Before the measurement there are one prior world of experience and two (or more) mutually exclusive potential posterior worlds of experience, and after the measurement again only one posterior world of experience. (How many potential posterior worlds there are depends on how far you want to see into the future - the number grows exponentially with the kinds of decision you consider - i.e., which variables you regard as measured. Theory does not guide you the least. If you measure a single position you have infinitely many potential worlds, one for each possible value, or for each pair of value and accuracy, or of only finitely many if you assume the measurement results to be discretized, or...)
Thus the concept of a world, and of a split, and what splits and when and how often and into what is completely subjective in MWI. There is objectively no dynamics of splitting, only the unitary dynamics, and subjectively no experience of splitting, only the one world of experience. The splitting is only in the words - a meaningless metaphysical hair splitting.

In Many-Worlds, there is only one real world, and many experienced worlds, where each experienced world is the experience of a Copenhagen observer.

There is only one experienced world, namely ours, and what we experience is not predicted at all by MWI. Any formally possible experience is predicted by MWI, and since only one is experienced, the probabilities assigned to it by a formal split is operationally meaningless. For the one world we live in, it is completely unpredictive, since it could be any of the predicted possible worlds. And we have no way to check beforehand in which of the worlds we are going to live - surely we live only in one of them, and the others are fictitious in an operational sense.

I'm not going to try to make this too precise,

That's the problem. MWI is an interpretation only if one makes nothing precise.

At all times, the universe already is split into (countably many?) macroscopic states j.

And how many depends on where you place the microscopic/macroscopic boundary - hence the number of worlds is completely subjective. Moreover in requiring that the macrostates are such that

every observation and measurement result can simply be "read off" from the macroscopic state

implies already that you require another interpretation of quantum mechanics that explains how measurement results appear from the uncollapsed microstate by assigning it to a macrostate in which the measurement problem is solved by uniqueness.

Thus MWI is a noninterpretation, if no recourse is taken to other interpretations.

 

[stevendaryl]

That's the problem. MWI is an interpretation only if one makes nothing precise.

I think that's true with every interpretation. None of them really tie things down.

 

[stevendaryl]

implies already that you require another interpretation of quantum mechanics that explains how measurement results appear from the uncollapsed microstate by assigning it to a macrostate in which the measurement problem is solved by uniqueness

I don't understand that statement at all. There is no additional interpretation involved. This view simply says that quantum mechanics is a way of predicting probabilities for macroscopic states. There is no additional assumption about measurements.

What I'm claiming is that the result of a measurement is always macroscopic. You produce a pointer pointing in one direction or another. You have a visible dot on a photographic plate. You have a click on a Geiger counter. These are all simply macroscopic facts about the world. There is no need to make a distinction between measurement results and other kinds of macroscopic facts.

 

[Derek P]

So in each world the wave function collapses, so it's a copenhagen interpretation after all!

No, just the appearence of collapse. No actual collapse.

 

[stevendaryl]

So in each world the wave function collapses, so it's a copenhagen interpretation after all!

There is no collapse in Many Worlds.

 

[rootone]

I'm not up with the relevant math, but ...
For MWI to be a logically consistent idea, then at least one more macroscopic dimension of space,
other than the three we know of, must be assumed.
Or not?

 

[Derek P]

Thus MWI is a noninterpretation, if no recourse is taken to other interpretations.

? @StevenDarryl was describing the smooth evolution of the emergent worlds. It was not even remotely a reformulation of MWI.

There is only one experienced world, namely ours,

You may believe so but MWI asserts exactly the opposite.
See this article - but only if you don't mind Vongher's provocative style.

 

[PeterDonis]

For MWI to be a logically consistent idea, then at least one more macroscopic dimension of space,
other than the three we know of, must be assumed.

What makes you think that?

 

[rootone]

What makes you think that?

Paui exclusion principle.

 

[PeterDonis]

Paui exclusion principle.

Elaborate, please. I don't see the connection.

 

[MathematicalPhysicist]

No, just the appearence of collapse. No actual collapse.

A copenhagen observer witnesses the collapse of the wave-function, doesn't he?

 

[PeterDonis]

A copenhagen observer witnesses the collapse of the wave-function, doesn't he?

That's a matter of definition. If you define "Copenhagen observer" as "an observer who observes wave function collapse", then there can be no such observer in the MWI, since there is no collapse in the MWI; everything is just unitary evolution.

So if you want to use the term "Copenhagen observer" in this discussion, you're going to need to come up with a different definition, one that applies if there is no wave function collapse. Which would of course raise the question of why you insist on using the term "Copenhagen observer" instead of something less confusing.

 

[PeterDonis]

each experienced world is the experience of a Copenhagen observer.

Given the issue I just addressed in my previous post, this is probably not the best choice of terminology.

 

[bhobba]

Thus MWI is a noninterpretation, if no recourse is taken to other interpretations.

I gave your post my like, and get your point, but I would not go that far. There is quite a bit of semantics involved - if it's meaningful - well that seems debatable - Gell-Mann for example seems to be of that view ie it isn't that meaningful being mostly decoherent histories in disguise with just some extra semantics about histories. But Wallace most certainly believes otherwise - but then again his strength - having both a PhD is physics and philosophy may be his undoing here. These days I am more with you and Gell-Mann even though I learned MW from Wallace.

Thanks
Bill

 

[A. Neumaier]

I don't understand that statement at all. There is no additional interpretation involved. This view simply says that quantum mechanics is a way of predicting probabilities for macroscopic states. There is no additional assumption about measurements.

What I'm claiming is that the result of a measurement is always macroscopic. You produce a pointer pointing in one direction or another. You have a visible dot on a photographic plate. You have a click on a Geiger counter. These are all simply macroscopic facts about the world. There is no need to make a distinction between measurement results and other kinds of macroscopic facts.

What you say here sounds just like my thermal interpretation: Each measurement result is macroscopic, hence a property of the state of the measurement device at the time of measurement.

But which property should it be if the measurement device is described by quantum mechanics (and hence, according to MWI, only by a wave function)? Clearly, this property must be a function of the wave functtion (the only thing that exists in MWI). But what to call measurement result is left unanswered by MWI and requires another interpretation.

You give no mechanism that makes the macroscopic state behave such that measurement is possible - i.e., that it correctly reflects in the measurement apparatus a property of the microscopic state of the measured system. You need to postulate (and this is the extra interpretive step) that the macroscopic state is a classical probabilistic state, and you need to justify why the observed (objective) frequencies, measured on individual systems with their individual states produce the correct probabilities. MWI doesn't do this. It gets (like shut-up-and-calculate) a probablility distribution by Born's rule, but...

It does not justify why this probability distribution is actually observable as relative frequency in the single world experimentally accessible to our culture. Splitting wor(l)ds does not help the least for that!

I think that's true with every interpretation. None of them really tie things down.

This current dilemma is called the measurement problem. Only tying things down can ever resolve it.

of the emergent worlds

No worlds ever emerge - otherwise there would have to be a dynamics specifying how they emerge. The emergence is only in the head of the believer.

 

[atyy]

Given the issue I just addressed in my previous post, this is probably not the best choice of terminology.

No, your previous post is not correct. If MWI does not have Copenhagen observers, then MWI is not a correct interpretation.

The only uncontroversial interpretation of quantum mechanics at present is the Copenhagen interpretation - which of course has the measurement problem. An interpretation of quantum mechanics that is a conceptually viable solution of the measurement problem must contain Copenhagen. It is the same as general relativity containing Newtonian gravity.

 

[A. Neumaier]

The only uncontroversial interpretation of quantum mechanics at present is the Copenhagen interpretation

It is just you who considers it uncontroversial. There wouldn't be the many alternative interpretations if Copenhagen were uncontroversial!

 

[atyy]

It is just you who considers it uncontroversial. There wouldn't be the many alternative interpretations if Copenhagen were uncontroversial!

Wrong. It is uncontroversial that Copenhagen has the measurement problem, which is why there are many attempts at interpretations that solve the problem. However, none of the other interpretations are uncontroversially solutions for all of quantum mechanics. Yet is uncontroversial that quantum mechanics is a very successful physics theory - that lack of controversy is based on the Copenhagen interpretation.

 

[A. Neumaier]

Yet is uncontroversial that quantum mechanics is a very successful physics theory - that lack of controversy is based on the Copenhagen interpretation.

No. That quantum mechanics is a very successful physics theory is based on shut-up-and calculate, which leaves the interpretation completely open, and hence adaptive to the situation at hand.

 

[atyy]

No. That quantum mechanics is a very successful physics theory is based on shut-up-and calculate, which leaves the interpretation completely open, and hence adaptive to the situation at hand.

Shut up and calculate is what is meant by Copenhagen.

 

[bhobba]

It is just you who considers it uncontroversial. There wouldn't be the many alternative interpretations if Copenhagen were uncontroversial!

Bohr and Einstein were not fools. Einstein did not come up with his own interpretation without reason. Dirac strangely I think had the best view of all, although not actually an interpretation:
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.485.9188&rep=rep1&type=pdf

I have written elsewhere I have read it a couple of times now and the more I read it the more I like it - I think Dirac is on the right track.

Thanks
Bill

 

[martinbn]

It is the same as general relativity containing Newtonian gravity.

Well, general relativity does not contain Newtonian gravity.

 

[bhobba]

Shut up and calculate is what is meant by Copenhagen.

Not quite - there is a bit more to it. It's something like the following 6 principles:

1. A system is completely described by a wave function ψ, representing an observer's subjective knowledge of the system. (Heisenberg)
2. The description of nature is essentially probabilistic, with the probability of an event related to the square of the amplitude of the wave function related to it. (The Born rule, after Max Born)
3. It s not possible to know the value of all the properties of the system at the same time; those properties that are not known with precision must be described by probabilities. (Heisenberg's uncertainty principle)
4. Matter exhibits a wave–particle duality. An experiment can show the particle-like properties of matter, or the wave-like properties; in some experiments both of these complementary viewpoints must be invoked to explain the results, according to the complementarity principle of Niels Bohr.
5. Measuring devices are essentially classical devices, and measure only classical properties such as position and momentum.
6. The quantum mechanical description of large systems will closely approximate the classical description. (The correspondence principle of Bohr and Heisenberg)

The link I gave shows Dirac had a more subtle view of 1 than Heisenberg, and some of the others are also open to debate.

Thanks
Bill

 

[Derek P]

No worlds ever emerge - otherwise there would have to be a dynamics specifying how they emerge.

That is palpably false.

The emergence is only in the head of the believer.

That's verging on being insulting. Please stick to analysing the physical theory before implying that its
proponents are delusional !