Does the many worlds interpretation of quantum mechanics mean in some worlds dice always land on the numbers you guessed?

Question

I suspect this is a common misconception of the Many Worlds interpretation of quantum mechanics.

I'd like to preface this by paraphrasing Hawking's book A Briefer History of Time: He refers to theories that predict infinites (black holes with infinite density as one example) as inevitably being wrong.

I noticed on the topic of "many worlds" people often interpret the theory as meaning there would be versions of the universe where everything that they could imagine within the realm of physics does happen.

Let's look at an extreme where one person talks about rolling dice and always guessing correctly:

In one of the many worlds dice always roll the number I predicted beforehand. This seems to suggest that in some worlds magic appears to be real.

Another agreed, adding:

In some [of the] many worlds the particles that make me up happen to fly apart while at the exact same time somewhere else radom particles reform a perfect copy of me.

I replied:

You guys are misinterpreting the concept. There are finite outcomes for any wave function. Let's say in this world in your room you're rolling a die. There are finite ways quantum probability can affect that roll, and it's a very very tiny effect. There could be a world where you get a disease causing tremors that might shake your hand affecting the roll but that doesn't mean the universal wave function where that happens will have you sitting in your room rolling dice right now. Quatum randomness create finite future branches and the real world variation might be incredibly small, except for unusual scenarios, like schrodinger's cat where a tiny quantum wave function has a major real world effect.

Another countered my argument saying under the many worlds interpretation there would be countless previously divergent timelines starting from the big bang. Yet another replied:

Even extremely small probabilities will occur, given infinite tries.

But I think they're wrong about this. My final argument against the idea was this:

Infinite time and space is a mathematical anomaly. Even hawking says something to this effect in his book A Briefer History of Time referring to black holes and any other theoretical concept that predicts infinites. Not that time or space have some fundamental limit, but rather each universe's timeline is limited, the matter within it is limited, and the number of possible particle interactions in feynman diagrams is limited too. If anything the planck length might create a limit on the smallest meaningful positional difference an entity can end up at in a wave function.

But alas, I'm not sure that any one of us in that discussion were anything more than physics enthusiasts. I'd like to know the correct answer from those of you here who can actually speak intelligently on the topic.

Answer 1

I agree that it’s nonsense to think of one scenario as tracing way back in time to alternate world branches and saying the long duration means there is someone similar enough to me to call him me, except from a branch from years ago, and he is rolling dice in the same time and place, and they come up as I guessed. I’m with you on that one.

It is not correct to say all possible quantum effects are very very tiny and couldn’t change the result of a single roll. There is the result that both dice will entirely quantum-tunnel through the desk. There is the result that one will. There is the result that every atom in the dot on one of the die will find itself a whole centimeter from the center of its wave-function. These are unlikely enough to consider them impossible, but there they are. And quantum effects that change the bouncing and dynamics of the dice would not have to be anywhere near that unlikely, although still unlikely.

The very reason macroscopic quantum effects are tiny is due to averaging and probability. Even if it would take 10^200 rolls (re-simulations is one way to imagine it) to get the result we need (way more than the number of plank times since the big bang), that is one of the worlds. The number of worlds is not infinite, but the number of them is stupid large. Every tick forward in time creates so many.

Because we are allowed to impose incredibly unlikely quantum events, I’m guessing that there are some outcomes where “what I guessed, was rolled” would be a reasonable interpretation, especially if we start the clock at the time just after the guess when we became committed to roll, which we should be allowed to do: a couple seconds of shaking the dice and then throwing them - because anything that then happened would be a world where “I guessed and threw dice”. Considering it this way, we have quantum effects in the brain and arm of the roller, plus the dice and table. More than enough for there to be the outcome we need. If we go back just a bit earlier we can “quantum-alter” the guess, where quantum alter means determine there is some result allowable by the quantum state evolving through time, however unlikely, that includes the desired outcome. And as we’ve just seen talking about the dice, they can be huge, and hence will be huge in one of the worlds. I think it might be true that there is some quantum branch that includes “what I guessed was rolled”, for any parity rolling of the dice that occurred. But note that this is different than saying there is one of those worlds where every roll Ive ever done came out as I guessed, and still include a person like me. And it seems almost impossible that there could be a world with a me and the exact same rolling events as in this world, especially if Im always guessing right. It’s not entirely clear which of these is meant by “theres a world where “I” always guess right”. Taken just as that, it is very unclear whether it’s true: The rolls could happen in different times and places than this world, but there must be “I” (close enough to that). I don’t have a strong belief on that one, but given the number of extreme things that can happen and the sheer number, far beyond imagination, it doesn’t seem ridiculous. But I will reaffirm my belief (all these are just beliefs or even opinions as no one is calculating anything) that any single roll has a world where I guessed correctly.

And finally, if there are not many worlds, then the claim:

If many worlds, then one where I always guess right

technically does not have a truth value as the premise is always false. We consider hypotheticals a lot, but they don’t have a rigorous truth value in set-theoretical logic. Nor do or can they in science, as they are not falsifiable.