EPR said:
Is there a valid reference for the claim that there is just one world in the MWI?
No. I am simply pointing out that the term "world" in "many worlds" does not mean what you would ordinarily think it means. I am not claiming that all MWI proponents recognize or acknowledge this.
EPR said:
Did you assume the wavefunction(a mathematical tool) of the universe is the world?
Yes. That should be obvious from what I said.
EPR said:
I don't understand how you got from the statement that all the worlds were all there prior to measurement, to the latter claim that there is just one world.
By equivocating on the meaning of the term "world".
A better way of describing what I was referring to is to look at the math instead of trying to use ordinary language alone; my usual caution that ordinary language is the wrong tool to use for a precise description of physics applies even more to this particular topic.
Suppose we have an electron and we measure its spin in some particular direction. In the relevant basis, the wave function of electron plus measuring device starts out as this:
$$
| \psi \rangle_0 = \left( a | \uparrow \rangle + b | \downarrow \rangle \right) | \text{ready} \rangle
$$
where ##a## and ##b## are complex coefficients that satisfy ##|a|^2 + |b|^2 = 1##.
After measurement, the measuring device is now entangled with the electron and the wave function is:
$$
| \psi \rangle_1 = a | \uparrow \rangle | \text{up} \rangle + b | \downarrow \rangle | \text{down} \rangle
$$
Now, how would we describe this in ordinary language?
The usual MWI terminology would say that there is one "world" before measurement and two "worlds" after, and the process of measurement causes a "splitting" of one world into two. But the math above describes a unitary process; nothing is created or destroyed. All that happens is entanglement. The measuring device doesn't "split" into two devices; it just gets entangled with the electron. (This is true even if the "measuring device" is a human.)
An alternate terminology, the one I was implicitly using when I said all the worlds are present before measurement, says that there are multiple "worlds" any time we have multiple terms in the wave function. We have that both before and after measurement, as is clear from the math above. The issue with this, of course, is that whether or not the wave function contains multiple terms is basis dependent. There will be a basis in which the wave function before measurement has only one term (just rotate the electron part of the basis until the electron part of the state is one of the basis vectors). There will also be a basis in which the wave function
after measurement has only one term!
Yet another possible terminology would be to say that the overall wave function
is the "world", as I did in another part of what I posted. And on this view, of course, there is always just one "world".
My point is not really to advocate for anyone of these choices of terminology over the others. It is to make clear that there
are multiple possible choices of terminology, and that we should not rely on ordinary language terminology to give us a precise description of the physics. We should use math.
