# What limits causality in the many-worlds interpretation (MWI)?

It's widely held that it's either very difficult or impossible to affect the outcomes of experiments in other branches of the many-worlds.

The reason given is usually something along the lines that the "worlds" are orthogonal, and each world obeys the SchrÃ¶dinger equation on its own as if the other worlds didn't exist.

But there is still a state vector for the whole system in a higher dimensional Hilbert space. We don't need to worry about the whole universe here-- we can start with a single quantum coin flip in a sealed laboratory and take it from there.

The state vector evolves and its evolution can be influenced-- one of the mes in this lab after the first coin flip can switch magnets on and off etc, do what he likes. He could even set off a hydrogen bomb in the middle of the lab.

What stops him making changes that the other "him" can perceive? It seems that whatever he does he can only affect the lab's relative state relative to him, and not the other guy's. He can cause the state vector to move, but only in a subspace the other him is unaware of.

The MWI is usually expressed in terms of information and observations. But it seems like the same rules must apply in the other direction-- i.e. causality has to be restricted as well. Somehow causality, as well as observation, is also a kind of entanglement.

(Later update) OK I think I might have figured this out.

Our system starts in the state |lab>. After I flip the coin, it evolves into a |lab>|H> + b |lab>|T> where |x>|y> is the tensor product of |x> and |y> and a and b are complex coefficients, each with the value 1/sqrt(2) in this case.

Now, any action that the me who got heads now performs must be observable by me. All observations must obey the normal probability rules. This means that however the left-hand component of that expression evolves, its overall coefficient of 'a' in the combined system cannot change.

Suppose I flip another coin, for example. The state evolves to:

a (c |lab>|H>|H> + d |lab>|H>|T>) + b |lab>|T>

c and d have to be normalized on their own, or my second coin flip would not be empirically faithful. The whole expression (representing the state of the branched universe) also has to remain normalized. It follows from this that c and d can only divide up the contribution made to the total by a, and cannot affect anything else in the whole expression. Unless there are interference effects. If there are, then I can alter things in the a * b and a b * terms which would be observable by the other me.

The fact that the initial coin flip states |H> and |T> are orthogonal kills any interference terms and is therefore said to "decohere" the system into two non-interfering components. But this leaves room in theory for communication between the worlds so long as decoherence can be prevented (which is what the Plaga experiment for example is proposing).

Or so people say. It seems to me that the mathematical description of Alice communicating with herself across universes is mathematically identical to EPR-like setups where Alice tries to communicate with Bob remotely with an entangled pair of particles. In the latter case we have two correlated coins in a single universe, and in the former case two correlated coins in two universes.

The more correlated Alice's coin is with Bob's, the less she knows about her coin on its own. So she can only send Bob random "messages". The same exact problem applies to Alice trying to talk to the other Alice.

• If the outcome of one experiment in the MWI changes the outcome of another experiment in another branch, then you are not dealing with an interpretation any longer but with a modification of QM. This should be experimentally testable. If it is, it may mean that the MWI is true, but it may also mean that there are other, equivalent interpretations for the same effect that do not require many-worlds, which would put the MWI back in the same place where it is now: that of a complicated explanation for a simple phenomenon. – CuriousOne Sep 8 '15 at 12:56

In principle there is nothing in the MWI which prevents communication between the different branches of the wavefunction. Indeed a (fairly controversial) paper was published in Foundations of Physics in 1997 with a proposal for an experiment to test this very possibility arXiv link.

There are other proposals including several David Deutch which exploit the possibility of interference effects between the wavefunction branches to test the MWI against Copenhagen and other competing interpretations.

The problem is that all of these tests are (so far) either utterly beyond our experimental capability or sufficiently expensive / difficult to perform that (as far as I know) no one has tried to perform them. Hopefully one day we'll be sufficiently advanced to remedy this situation but I don't think it'll be very soon.

The main issue is that once you've let decoherence happen the overlap between the two states is incredibly small which makes communication incredibly difficult. Tests of this nature generally involve putting macroscopic objects in superposition something which is currently a long way outside our capabilities as a species.

• Thanks for your answer. I have heard about the Plaga and Deutsch experiments and the point about decoherence. What I'm struggling to understand is just how to explain how an agent's causal influence is restricted to the branch he's in, assuming for the sake of argument that everything has decohered. The MWI shows how my memory states are correlated with the events I've observed, but it doesn't immediately say how my memory affects what I can do and limits what I can influence. – user68014 Sep 8 '15 at 11:06
• @user68014. I don't really understand. Are you asking why a person in one branch can't affect / communicate information to another branch? It seems that they can in fact do this but it is difficult because it requires quantum level control over the entire system after the interaction and the entire system includes the (macroscopic) experimenter, all of their equipment etc. – or1426 Sep 8 '15 at 15:32
• The problem is that whatever I do, even set off a bomb, I can't affect the other branch. There must be some formal way of showing why not. – user68014 Sep 8 '15 at 15:51
• @user68014 If you choose to set off a bomb then your brain is different. So the worlds are still distinct. – Timaeus Sep 8 '15 at 18:10

It's my opinion that the reason is as follows. Time evolution is just an illusion, the future versions of you just exist out there. What we refer to as the time evolution according to the SchrÃ¶dinger equation is not really a time evolution in the sense that things change. Nothing changes, we only ever have the same static eternal multiverse. All you are doing is performing a change of basis to extract the information about your other so-called "time evolved" copies in the multiverse. In the generic case there are multiple observers who have the same information about what they perceive to be "the past".

In this picture the notion that one observer could influence another observer who shares the same past makes no sense, as they exist a priori in a static multiverse. Every moment that you experience is a different you who lives in a different sector of the same static multiverse.

• Unless you're arguing that the Block Universe picture implies that causality doesn't exist at all, the fact remains that I can influence things in one half of the Hilbert space but not the other. This is the thing I'm trying to understand better. – user68014 Sep 8 '15 at 19:02

We don't need to worry about the whole universe here-- we can start with a single quantum coin flip in a sealed laboratory and take it from there.

If you think you can consider a single particle in isolation then you fail to grasp the entire method by which separate worlds form in the MWI. It would be like it you tried to use the Copenhagen interpretation without having a classical apparatus or any kind of measurement device at all.

The state vector evolves and its evolution can be influenced-- one of the mes in this lab after the first coin flip can switch magnets on and off etc, do what he likes. He could even set off a hydrogen bomb in the middle of the lab.

The fact that the coin flip landed on different sides means the configuration space has a heads up coin in one option and a heads down coin in the other. Which means the configurations are non overlapping.

The wave assigns a complex number (and a spin state) to every configuration of all the particles. If there are $n$ particles there are $3n$ coordinates and a complex number is assigned to every configuration. If the coin is heads then you have a nonzero configuration with a certain number of particles a certain distance above the center of mass. If it is tails you have a different number a certain distance above the center of mass. They are different configurations. Wherever the other particles are , the configuration is of the particles in the coin somewhere and if the coin is different the total configuration is different. If the total configuration is different they don't interfere and they are orthogonal.

That is exactly how different worlds form in the first place. Lots of other particles move differently based on how the original particles change their individual configuration and so the total configuration wanders off into regions of configuration space and it becomes impossible either in practice or on accident to overlap again.

What stops him making changes that the other "him" can perceive?

The coin being in a different position is enough.

It seems that whatever he does he can only affect the lab's relative state relative to him, and not the other guy's.

Yes, if the coin is in a different positron then they can't interfere. And if you looked at the coin, and oticed it, now you brain is different. So the same problem exists. And it doesn't matter even if you could forget, different air molecules have bounced off it and it is too hard to remove all trace of the effects of the two different coin tosses.

He can cause the state vector to move, but only in a subspace the other him is unaware of.

Correct.

The MWI is usually expressed in terms of information and observations.

I thought bit was common to express it in terms of the SchrÃ¶dinger equation and what its solutions look like.

But it seems like the same rules must apply in the other direction-- i.e. causality has to be restricted as well. Somehow causality, as well as observation, is also a kind of entanglement.

There isn't a separate causality, there is the evolution according to the SchrÃ¶dinger equation. Causality can be considered a blame game. Things end up a certain way because they were a certain way. Your brain state plus the environment it interacted with determine the future evolution. Therefore it is easy to assign blame, different brains would evolve differently, evolve to do different things.

The fact that the brain has to change itself to react to different situations limits its ability to remerge different worlds.

I can tell you how hard it is to remerge different worlds but then you might go too far and not realize how any quantum effects happen at all. How, for instance, can an electron interfere at all.

Here, the dBB theory is helpful. It has configurations evolve in time in a way guided by the wavefunction. The particular path isn't important for MWI but at least it allows you to imagine a path in configuration space where the change in each particle's coordinates depends on 1) its momentum (determined by how the phase of the wave changes in the directions in configuration space corresponding to that particle) and 2) the forces on the particle which are determined by a) the classical forces you would expect from that configuration and b) the quantum potential determined by the wave.

So what happens is you can imagine a density of configurations and the density variation exerts forces on each configuration which combined with the velocity of that configuration (determined by the phase) makes the configurations change.

When you reach, say, a barrier the configurations with the particle closer to the barrier slow down which means the ones behind push against it and so the ones behind slow down and the leading one gets pushed farther into the barrier. Eventually the very most leading ones get pushed through and the ones in the most trailing end got pushed away before even getting close to the barrier itself.

But as long as there were many configurations corresponding to many ways the barrier itself was configured then they all can shuffle around so when the beam partly tunnels and reflects through many barriers in many places it is possible for them to cross in configuration space. And having two configurations that approach is exactly the condition you need for a quantum potential to exert a force and make the configuration change in a state dependent way rather than a configuration dependent way. Though the quantum potential.

So quantum effects can happen. But once enough things have changed that barely any configurations allow the beams to travel into a common region of configuration space then the small overlap has an effect that is lost amongst the individual beams affecting themselves and becomes unnoticeable.

• "The wave assigns a complex number (and a spin state) to every configuration of all the particles. If there are particles there ate coordinates and the complex number is assigned to every configuration. " In the Hilbert space there are 3n dimensions for every possible value of position. You might have meant this. Anyway I think this may be the clue to the answer. A single entanglement like one coin flip adds a new discrete dimension to the Hilbert space and partitions it into two, with enough space for two whole laboratories to evolve separately. – user68014 Sep 8 '15 at 18:49

Whether the MWI allows communication depends on what definition of communication you want to use.

Communication in everyday life is something like this. I have information I want to send to you. I can arrange for you to have access to one copy while I have access to another. For example, you will be able to see this answer to your question on your computer screen, while I will be able to see this answer on a different computer screen somewhere else, so there are at least two copies of it and possibly many more. In this sense, communication between branches is impossible in the MWI. Suppose that in one one Everett branch I find out that X, so my state is $|X\rangle_{me}$ and in another branch I find out something else $|Y\rangle_{me}$. I then make a copy of the information I have in each branch so that the state is $|X\rangle_{me}|X\rangle_{copy},|Y\rangle_{me}|Y\rangle_{copy}$. In that case, interference between two different versions of you is prevented unless all of the copies of the information are undone.

If you undo all of the copies and undergo interference, then the final state may depend on both $X$ and $Y$. This is how quantum algorithms work. However, it will not be the case that each version of you has a copy of $X$ or $Y$.

So unless by communication you just mean "information processing involving both $X$ and $Y$", then communication involving people in two different branches is possible in principle. (In practise not so much since copies of the information you hold cannot be erased in practise.) If by communication, you mean communication in the ordinary sense explained above, then communication involving two Everett branches is impossible.