Comment by jiggawatts | Hacker News Reader

Comment by jiggawatts | Hacker News Reader

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> MWI, like the Schrödinger equation, is fully deterministic; there is no randomness. The bits are not random in MWI. How to reconcile these?

There is a key concept in MWI that people (even Nobel laureate level physicists) are just unable to wrap their heads around:

    You're also a quantum object, 
    not just the experiment.

In MWI, the fundamental concept is that quantum objects expand into multiple dimensions. Hence by the rule above, so do you. This is the source of "randomness". From your in-universe perspective, you can't know apriori which "path" into the multiverse you take. You take all of them, but after some time, any observation you make is from the perspective of one of your copies, and each copy thinks of themselves as the unique, singular copy.

To summarise: You can talk meaningfully about the statistics that your future selves will experience, but you can't know ahead which one's perspective you'll have, because your current self will become all of them.

So from "God's point of view", outside the multiverse, the whole thing looks deterministic. From inside the universe it seems inherently random.

If you're a computer scientist by background, imagine this: You create a human-equivalent AI that you can converse with. Inside its memory you set up a 1-byte cell that it can observe. You then make 256 copies of the AI, one for each possible combination of bits set in the memory cell. If you ask one of the randomly selected copies what value it sees, it'll see whatever you've set, which will more than likely look some arbitrary -- random seeming -- combination of bits. If you repeat the procedure, each time with a randomly chosen AI, it'll report that the cell is changing "randomly". However, the overall system of all copies is entirely deterministic! The randomness is in your external selection.

From the outside, you can remove the randomness by asking every AI the same question to reveal the deterministic pattern. From in-universe, this is not an option. The AIs can't ask the other AIs what they see!

Right, in the universal view, it's just a huge wavefunction following the Schrodinger eq at all times. God can peek at it, and not have to collapse anything. If he decides to sample it, he's choosing 1 universe from all possibilities. It's a huge space, but it's linear from his dimension in which collapse doesn't appear.

[1] https://en.wikipedia.org/wiki/Universal_wavefunction

Ok, how does one derive the Born rule from that idea?

Could you ELI5 why the Born rule is incompatible with MWI?

(It being a problem with MWI is new to me, I am absolutely a physics amateur).

Say there's a quantum bowl with two identical red balls, and one blue ball. You take a ball with your eyes closed. Probably your ball is red, maybe it's blue. You open your eyes, see a color - what happened!

Here's three choices, none of them good:

1. Local Hidden Variables: When you open your eyes, you see which color your ball had all along! This is so obvious, but it's wrong for tricky reasons (Bell's Theorem) which I can't fit into the analogy; basically the ball cannot have "had a color all along."

2. Copenhagen: When you open your eyes, the ball just decides what color it is. The other balls will mysteriously agree, so there's not two blue or three red or whatever. How did they do that? Is that a real physical change, or just learning something new? (This is wavefunction collapse and it's very uncomfortable for obvious reasons.)

3. MWI: When you open your eyes, one version of you sees a red ball, and one version of you sees blue. Ok, but if there's red you and blue you, how can the red ball be "more probable?" Are there two separate "red ball" yous? Or maybe the red ball you is "more real?" (This is the relationship between the measure of the wavefunction and experimental probability, aka Born's Rule; MWI struggles to explain it, Copenhagen just postulates it).

> Are there two separate "red ball" yous?

You answered your own question!

Yes. There are multiple observers, they're cloned along with everything else.

All the "mystery" disappears as soon as you accept that.

It's like heliocentrism. Everything just "clicks" once you adjust you perspective.

It ought not to click, because it's a deep objection. In the ball example, the wavefunction is a sum of two components: there are two possible measurement outcomes. How do you get three worlds from two states?

Say you have an electron which is either up or down, a 2/3 percent chance to be up. The wavefunction looks like `2/3 * up + 1/3 * down`. In the MWI picture, when you measure the electron, you split into two worlds: how do you get 2/3 probability of "up" from two worlds?

You can say you split into three worlds, two of them identical. But that is not found in the Schrödinger equation (so now you have new postulates, which MWI hoped to avoid), and what if the probability were 1/pi, how many worlds would that be?

Your problem is in assuming that there is a finite number of universes created. Instead Think in terms of an infinite number of universes created, of which 2/3 of them are red, and 1/3 of them are blue.

(E.g. Imagine all the universes created map to the range 0 to 1, and the first 2/3's come up red, and the last blue (or reverse that, or shuffle it up). The mapping onto 0 to 1 is merely for visualization purposes, and is thus arbitrary.)

The hope and appeal of MWI is that the Schrödinger equation is sufficient. What you describe is way beyond what may be found in it.

"Many worlds" may arise naturally from the Schrödinger equation in this way: if you measure a system, the components of its wavefunction decohere, so that they no longer interfere. These components may be intuitively understood as "worlds."

We find ourselves in the world corresponding to the larger-measure component more often. But why? If your answer is "because more universes were created for larger measures," that is not found in the Schrödinger equation; it requires additional axioms, which is precisely what MWI hopes to avoid.

I see people asking, “but how do you get 3 realities from 2 possibilities?”

This is a misunderstanding. For simplicity’s sake, mwi people say that the universe “splits” into one child universe for each possibility- but that’s not what mwi actually says, just the pop science simplified layman version.

In actuality just as the quantum wave function is a continuous, analog wave there is a continuous analog sea of possible universes, and some have greater measure than others. And some are more correlated than others. The discorrelated ones appear to be separate from each other. But they’re all part of the same multiverse.

Think about it this way: we have no trouble conceiving of the universe having multiple possible futures, but only one past. That is not the case however. We also have multiple possible pasts, and in fact they’re not just possibilities but are real. Each future universe with this one as a past is real. Each past universe with this one as a future is equally real (that’s the mwi view of Schrödinger’s cat). Because of the arrow of entropy there will be more of the former than the latter.

Hope that helps..

I agree with that. But it still does not explain how probabilities arise.

What is the physical significance of "a universe with a greater measure than another?" What is the physical significance of the measure in MWI at all?

Traditional view: There is one experimenter, he picks a marble, it is either red or blue. If the experimenter repeats the measurement, he gets some red, some blue, with some percentage chance.

MWI view: There are many experimenters, in fact there is a continuum of them for each "run" of the experiment. The "setup" of each run that produces the mixed state in the bowl of marbles is splitting the whole universe (at the speed of light) and also splits the experimenters. Some of them are now in the "red" universe, and some of them are now in the "blue" universe and give matching answers. The percentage of them giving each answer is the same as in the situation above, but this percentage applies to even one run of the experiment.

However, the many experimenters and their percentages is not observable in a single experimental run from inside their universe. The experimenters cannot communicate, so after each run they only have 1 bit of information each (red or blue). They need to repeat the experiment to gain more than one bit of information.

However, now, their states are different. Some experimenters have a different history to the others. They aren't all the same any more! There's no "reset" button. This is the core of many of the "mysteries" and "apparent superluminal communication" in QM. There's no mystery. The state -- including the experimenters -- is splitting.

The classic "superluminal" communication isn't: Entangled opposite particles are simply saying that some universes have the (A,B) pair, others have the (B,A) pair. When you find out that you have the "A" particle, you instantly know that in your universe the other guy must have the "B" particle. There's no communication, instead the experiment is all about finding out one bit of information about "where you are" in the multiverse.

> Some of them are now in the "red" universe, and some of them are now in the "blue" universe and give matching answers. The percentage of them giving each answer is the same as in the situation above

The objection is: what fraction are in red universes, and why? Why is it 2/3rds and not, say, 3/5ths or zero?

In QM we can compute these fractions using the Born rule, which says that the probability of each outcome is proportional to its measure in the wavefunction. This is natural to postulate in Copenhagen, where we interpret the wavefunction as a probability density. If the measure of spin-up is twice that of spin-down, it means that spin-up is twice as likely.

But in MWI, the wavefunction is definitely NOT a probability density. Both spin-up and spin-down are physically realized. So why should it matter that spin-up has a higher measure?

Where does the Born rule come from in MWI? Can it be derived from the Schrödinger equation? If so, how? If not, what additional axioms are needed?

The Born rule is basically saying that the wave function and the measurements are related by a squaring relationship one way, or a square root the other way.

This squaring in QM is basically saying that there are two probability distributions, not one. There isn't just the particle, there is the particle and the experimenter. Similarly, there's the particle and itself in interference experiments. Or the particle and the detector. There's always (at least) two required for an interaction. Hence a squaring.

It's saying that the observed and the observer are part of the same system. We're not Gods viewing squiggly cartoons on a page, like we like to draw.

We are the drawing.

> Ok, but if there's red you and blue you, how can the red ball be "more probable?"

My understanding is that there are two "red yous" for every "blue you"

> In MWI, the fundamental concept is that quantum objects expand into multiple dimensions.

No it is not. The fundamental concept of MWI is that unitary evolution can explain all observations, without postulates like wavefunction collapse. "Quantum objects expand into multiple dimensions" is woo, not physics.

> This is the source of "randomness". From your in-universe perspective, you can't know apriori which "path" into the multiverse you take.

The objection to MWI is that it cannot derive observational facts like the Born rule. How does "you take all paths through the multiverse" help us derive that?

> If you're a computer scientist by background, imagine this

It's fun to imagine, but physics is an empirical science. The hope of MWI is to eliminate the postulate of wavefunction collapse, but you are talking about "256 copies of human-equivalent AI" which is not simplifying.

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