How Many Parallel Worlds Are There?

[Dragonfall]

If we accept the many-worlds interpretation, how many parallel worlds are there? Finite? Countable? Uncountable? Even bigger? Do we need to bring the continuum hypothesis into it?

 

[Dmitry67]

Well, in MWI there is only one world...Just different branches which don't interact. So let's call them 'worlds'

Based on the Quantum Decoherence ideas, any system with finite energy has finite number of states, and it has finite maximum entropy. So the number of 'worlds' is also finite (for the given isolated subsystem).

Our observable universe at any moment is finite in size and energy, hence, the number of branches in it is also finite (and we can not be decoherenced with any events outside our observable part of the universe)

 

[Dragonfall]

Nothing in quantum physics is described by an infinite dimensional state vector?

 

[MathematicalPhysicist]

Unaccountable.
2^null_aleph

The explanation is rather simple, if every bit of infomartion is decoded to 0 or 1 (nay or yay) then the number of world is the number of sequences of 0 and 1, which we know from set theory what it is.

 

[Tac-Tics]

different branches which don't interact.

If they never interact, with what experiment would you be able to test for their existence?

 

[Dragonfall]

Unaccountable.
2^null_aleph

The explanation is rather simple, if every bit of infomartion is decoded to 0 or 1 (nay or yay) then the number of world is the number of sequences of 0 and 1, which we know from set theory what it is.

I don't see how this is related to quantum physics, or the many-worlds interpretation.

 

[Dmitry67]

http://space.mit.edu/home/tegmark/multiverse.html

The answer is that there are only a finite number of possible states that a Hubble volume can have, according to quantum theory
...
Although classical physics allows an infinite number of possible states that a Hubble volume can be in, it's a profound and important fact that quantum physics allows only a finite number.
...
Let's first ignore the important complication of past history and ask how many physically distinct states N there are in a volume V. In classical physics, N is infinite (indeed uncountably infinite) as you say, since even specifying the position of a single particle requires infinitely many decimals. In quantum mechanics, however, N is finite: if the temperature never exceeds T, we of course have N < ln S, where S is the entropy of the thermal state with temperature T (I'm taking Bolzmann's constant k=1). Interestingly, the number of states appears to be finite even when taking general relativity into account, which is closely related to the holographic principle: the entropy is maximized if all the matter in V is in a single black hole, in which case, as you know, the Bekenstein-Hawking formula says that N is of order the surface area measured in Planck units. So yes, I see your reasoning, and find it quite striking that quantum mechanics, uncertainty principle and all, contrary to what one might expect, gives fewer states than classical physics. In the limit V->oo, quantum mechanics therefore gives a countable rather than uncountable infinity of states

 

[MathematicalPhysicist]

I don't see how this is related to quantum physics, or the many-worlds interpretation.

Quantum physics tells you that before experimenting you have a probability for certain outcomes.
Now the many world interpratation tells you that all of the possibilities for the other outcomes which haven't happened do happen in other worlds, and because every outcome can be represented as a string of 0 or 1 as happening in our world, each world can be represented as a string of 0s and 1s of occurrences in our world, the set of all these worlds is unaccountable as a set of sequences of 0s and 1s.

I look at the large scale, quantum cosmology, and not in a certain finite volume.

 

[yossell]

Interesting question, but the replies leave me more confused than I was before.

I suppose there are different versions of the MWI - some say that there is division on measurement (which reintroduces a version of the measurement problem), others that there's splitting whenever there's superposition (which introduces the preferred basis problem).

On the second view, I would have guessed that there are uncountably many - the reason being that a quantum system can be treated as an integral of position eigenstates and that there are uncountably many of these, each corresponding to a branch. And, I suppose, even if we think splitting happens only after measurement, and there's a branch for each possible result, because any value of position is possible, there would be uncountably many branches.

MathematicalPhysicist: I didn't understand your reply. How are these strings of 0s and 1s being generated? Why does every outcome correspond to an infinite string of 0 and 1, and why does every infinite string of 0 and 1 correspond to an outcome? You need a 1-1 correspondence between the two to get the result.

Dmitry: interesting link, but I don't understand Max Tegmark's argument.

 

[Dmitry67]

Classical mechanics: How many possible orbits can you imgine for Earth rotating around Sun? Infinitely many. Any system of 2 gravity-bound objects can be in infinite number of state.
QM: How many states can you imagine for the Hydrogen? 2 (on the ground state) - ortho- and para-

 

[JukuJohannes]

I didn't understand your reply. How are these strings of 0s and 1s being generated? Why does every outcome correspond to an infinite string of 0 and 1, and why does every infinite string of 0 and 1 correspond to an outcome? You need a 1-1 correspondence between the two to get the result.

I think he means that all the information in the universe can be coded into bites, 0 & 1, based on this information, one can calculate the number of times universe splits, because one could predict all the events that occur in the universe.
In this interpretation according to quantum theory- in any event, what happens, all the possible outcomes that are possible, do happen, even if the probability is very small. Just every outcome that is possible, happens in different universe or parallel world, that means universe splits. And it is speculated that the most probable one happens in our universe, that's why we do not see really bizarre things here ;)

For example, if we collapse electrons´ state to spin +45 or -45, we see only one of these spins in OUR world, but actually the other possibility too happens, only in other universe

 

[Dragonfall]

I'm still confused about the answers. Our observable world might be at any time finite in size and energy, but what if the "splitting" happens infinitely often during a finite time period?

 

[confinement]

In standard quantum mechanics, there are uncountable many positions at which you could observe a particle, the set has cardinality of the continuum of real numbers C. This would imply that each event has C outcomes. The number of splittings can be put into correspondence with the moments of time which are another uncountable set of size C. It seems that C times C = C so there are C world in the that interpretation.