As you understand the answer is very complicated and I do not think anybody can answer it in full extend. What we can assume is that ψ(X) = ψ(ψ1, ψ2, ...,ψi, ... X, ...). Where ψi is wave function of universe belonging to the set of the multiverse. At this point we do not have any evidence that universes interact with each other (black holes are under question). That means ∫ψi(X)ψj(X)*dσ=0 for i not equal to j and 1 when i=j. And it means that universes are isolated from each other.

If somebody proves that ∫ψi(X)ψj(X)*dσ=a where a is not equal to zero then conservation laws would have to be extended to the level of multiverse. But can be applied to single universe when correlations constants are small enough.

Normalization conditions are not enough to make conclusions about kinetics of processes. Also it does not provide any information on size of the system but rather on number of elements.

Thanks Dmytro, very interesting answer

You're absolutely right that any extant universes could be fully separate, in which case no multiverse wavefunction would exist (by the way, under certain string theory scenarios, as you are aware, gravity would actually 'seep through' between universes, and some have speculated that this is actually the source of dark matter. That remains however highly speculative.)

One way to approach the gist of the problem is to scale down to one universe - i.e. consider only the wave function of one universe only and ask the same question.

The reason why the answer would very likely be no is that we would then have an implicit ψ function - whose domain of solvability is restricted. However, within that lone Universe there would constantly exist unpredictable, random evolutions of ψ in time caused by Heisenberg-type events, and there is no reason why these random events should always keep ψ within its domain of solvability. Hence, the implicit equation for ψ would no longer be satisfied. This would lead to the wave function of "all there is" not encompassing ψ, leading to a contradiction (it would not be the wave function of all there is since it would not contain ψ ) and hence the universe would be open;

Another approach - which I like - is to say, with the likes of Max Tegmark and many other contemporary theoretical physicists - that math constitutes the ultimate reality and that the physical world is a manifest expression of underlying mathematical reality (that is another discussion, but there is a strong case to support this view) . In that case the universe (or multiverse) is a manifestation of all of math, and physical laws reflect mathematical laws.

To cut a long story short, under that latter view, the wave function of a whole universe being an expression of all there is within an all-there-is, total, self-contained isolated universe's physical manifestation - it therefore must reflect the whole of mathematics.

As such, it inescapably becomes subject to Gödel's proof - i.e., the math system is open, and hence therefore the Universe is open as well.

What do you think?

Intuitively I say NO,

a multiverse is a different concept than that of a universe.

So a multiverse cannot contain itself.

Of course you can rebate this, by saying that a set of 1 unit is the unit and the set simultaneously.

Or you can argue with the sand corn paradox (sorties paradox),

A heap of sand minus one grain is still a heap...

well you construct it actually the other way round,

a universe + a universe form TOGETHER a multiverse.

So you need this multiplicity to have a multiverse, and a multiverse is a set of units ("unitary universes", note the redundancy)

So I insist: NO

I am not sure about part that math the ground and physics expresses it. Unless by math you mean Math that can describe everything and it is the one we do not know yet.

I really hope that universes correlate within multiverse, that would make things (physical laws) a little bit more complicated but in the same time more cohesive.

Another question would be about number of multiverses. Yes, multiverse is set of unuverses but it is possible that set of multiverses create some kind of cluster that represents all possible futures and pasts. And I am not sure it would be limited system. Just thinking out loudly.

Chris

I want to argue this purely from a geometrical point of view. In three dimensions you can't contain a box inside another box of the same size. However, “Size” may not be a reliable measure when you start transcending dimensions. For example, you can draw a straight line infinitely long but its area (a 2D measure) will always equal zero. Similarly, you can draw a 2D square infinitely large but its volume (a 3D measure) will always equal zero. So, when you move between dimensions, size is not a valid measurement. In say, 11 dimensions it may be possible that a universe can contain itself inside itself. I have no proof of this however.

Monsieur Uphoff,

Vos contributions étaient drôles au début, maintenant elles deviennent pathétiques