Infinities and the Many Worlds theory

[Gordon Imroth]

Can anyone help me understand a feature of the Many Worlds interpretation of quantum theory, please?

Many people (on this forum and elsewhere) say that the Many World's theory implies infinity parallel universes. I can understand why people think so. For example:

Suppose a photon is sent through a slit to hit a screen at any point. There are infinity points (of the power of the continuum) where the photon can hit the screen, so the Many Worlds theory implies the continuum number of universes, in each of which the photon hits at only one place.

Alternatively, we might say that the number of choices for a photon at any quantum event is always finite, however large. There may be infinity mathematical points on a screen where the photon can hit, but there are not infinity real physical points in space. This implies that space and time are atomic, however, and the problem with that idea is that, in the Many World's theory, classical physics is true in each parallel universe, and classical physics allows the infinite divisibility of space and time.

So my question is: does the Many Worlds theory imply infinity parallel universes, or is it an entirely finite theory? And if Many Worlds is entirely finite, then what happens to classical physics in each universe?

Thanks for your help.

Gordon.

P.s. Suppose we could design an experiment so the trajectory of the photon can follow every possible curve from source to target. As the infinity of curves is greater than the infinity of points on a surface, the Many Worlds theory implies an infinity of greater power than the continuum number.

And as for curves, so for surfaces (perhaps employing multiple photons); and the infinity of surfaces is even bigger than the infinity of curves.

If the Many Worlds theory implies a physical infinity, then what size infinity does it imply, or all of them?

 

[Ken G]

So my question is: does the Many Worlds theory imply infinity parallel universes, or is it an entirely finite theory? And if Many Worlds is entirely finite, then what happens to classical physics in each universe?

I would say the MWI approach is an interpretation of some other theory, so if the other theory is discrete, then MWI is discrete, and if the other theory is continuous, then so is its MWI. None of that means that there really are an infinity of worlds in MWI-- it seems unlikely that any continuous theory is an exact representation of actual reality. (I feel the same could be said of MWI, but that's a matter of opinion.)

P.s. Suppose we could design an experiment so the trajectory of the photon can follow every possible curve from source to target. As the infinity of curves is greater than the infinity of points on a surface, the Many Worlds theory implies an infinity of greater power than the continuum number.

I don't think there is any meaningful physical way to think about an "infinity of points" on a surface. We can treat the surface mathematically that way, but any actual experiment we use to test our theory is not going to be able to distinguish an infinity of different locations on the screen. "Infinity" doesn't mean anything in physics beyond "a number so large that making it any larger wouldn't have any important consequences." The same can be said about the continuity of classical physics.

 

[Gordon Imroth]

Ken G,

Thanks very much for your reply, and so quickly. I need to go away and think about what you said.

For now, I can say I understand your point that MWI is an interpretation and whether it is discrete or continuous depends on the underlying theory; in which case, what basis do people have for saying MWI implies infinity parallel universes, or (I presume) others say it does not?

What I am looking for is an objection to MWI, which I thought might be that MWI implies infinity parallel universes of many different powers all at the same time.

Thanks again,

Gordon.