Question on number of generated worlds in many world interpretation

[mitochan]

TL;DR Summary

In collapse of state 3/5 |0>+ 4/5 |1> to |0> or |1> how many worlds are generated in many world interpretation ?

Hello. I am curious to learn many world interpretation.
In collapse of state 3/5 |0>+ 4/5 |1> to |0> or |1>, it jumps to |0> with probability 9/25 or to |1> with probability 16/25.
In many world interpretation I assume 9 worlds of |0> and 16 worlds of |1> so total 25 (or its multiple) worlds, one of which we are in, are generated. Is it right?
I will appreciate your confirmation/teachings.

 

[PeterDonis]

I am curious to learn many world interpretation.

What references have you read?

In many world interpretation I assume 9 worlds of |0> and 16 worlds of |1> so total 25 (or its multiple) worlds, one of which we are in, are generated.

Why are you assuming this?

 

[mitochan]

Hello @PeterDonis
I read https://en.wikipedia.org/wiki/Many-worlds_interpretation. I do not understand how many worlds are generated in collapse or quantum jump of states. So I assumed an idea that in many worlds theory probabilities for states after quantum jump, I said 9/25 for |0> and 16/25 for |1> in OP, could be interpreted as statistics of generated worlds, e.g. generated nine |0> worlds / generated nine |0> worlds + generated sixteen |1> worlds, etc. Your teaching will be highly appreciated.

 

[PeterDonis]

I read https://en.wikipedia.org/wiki/Many-worlds_interpretation.

The usual caution that Wikipedia is not a valid source for learning actual physics applies even more to this particular topic. You really, really need to learn this from textbooks and peer-reviewed papers.

I do not understand how many worlds are generated in collapse or quantum jump of states. So I assumed

If you do not understand, you should not assume. Why would you expect your assumption to be valid?

In fact, the term "many worlds" is really a misnomer, because the whole point of the MWI is that everything is unitary evolution, all the time, even during measurements; and unitary evolution preserves information, so it can't "create" any "worlds" that weren't already there. There is only one wave function in the MWI--the wave function for the entire universe--and in that sense there is always just one "world".

In the case of a measurement with a discrete set of possible outcomes, like the one in your scenario, roughly speaking, there will be one "branch" of the wave function after measurement corresponding to each outcome. These "branches" are what the term "worlds" refers to, but, as noted, that term is really a misnomer.

The role that the coefficients in the wave function before measurement play (the 3/5 and 4/5 in your example) is to determine the relative "weight" of the branches after measurement. So, in your example, there would be two branches after measurement--one for each possible outcome--with the "0" outcome branch having a weight of 3/5 and the "1" outcome branch having a weight of 4/5. In ordinary language, we would call the squares of these weights, 9/25 and 16/25, the "probability" of the corresponding outcome occurring, but in the MWI there are no probabilities--both outcomes happen, and each outcome has its own branch. Figuring out what the "weights" actually mean in the MWI is one of the most salient open issues with this interpretation.

 

[mitochan]

Figuring out what the "weights" actually mean in the MWI is one of the most salient open issues with this interpretation.

I misunderstood that MWI ,as its main advantage to Copenhagen interpretation, explains "weights" as statistics in sets of different kind of worlds. Now I know "weights" is the key issue and it is still open. Thanks @PeterDonis.

 

[PeterDonis]

Thanks @PeterDonis.

You're welcome!

 

[EPR]

unitary evolution preserves information, so it can't "create" any "worlds" that weren't already there. There is only one wave function in the MWI--the wave function for the entire universe--and in that sense there is always just one "world".

Is there a valid reference for the claim that there is just one world in the MWI? Did you assume the wavefunction(a mathematical tool) of the universe is the world?

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.

 

[PeterDonis]

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.

Did you assume the wavefunction(a mathematical tool) of the universe is the world?

Yes. That should be obvious from what I 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.

 

[EPR]

The point is the math doesn't say there is one world. Or that there isn't.

It says there is an abstract useful mathematical entity known as wavefunction. We can assume many things about this statistical tool, but in general, it's not believed to be a world as it lives in its own space - Hilbert space. Which is not a world to most physicists.

 

[PeterDonis]

the math doesn't say there is one world. Or that there isn't.

The math doesn't say what the ordinary language term "world" means, no.

 

[EPR]

But we can agree that the term 'world' doesn't mean math. There are no textbooks or peer reviewed papers that make the claim the world is math.

 

[PeterDonis]

we can agree that the term 'world' doesn't mean math.

Who said it did?

 

[PeterDonis]

It says there is an abstract useful mathematical entity known as wavefunction.

According to the MWI, the wave function is not "an abstract mathematical entity". It is real.

 

[EPR]

The claim that a global wavefunction(math) of the universe is a world is confusing the map for the territory.

 

[PeterDonis]

The claim that a global wavefunction(math) of the universe is a world is confusing the map for the territory.

Not for MWI proponents. See my post #13.

 

[akvadrako]

I would say in the splitting version of MWI there is just one quantum universe but there any many semi-classical worlds, probably an infinite number.

Saying there is just one world does seem confusing since people don't normally call the quantum universe a world.

 

[physika]

of terminology over the others. It is to give us a precise description of the physics. We should use math.

Math is terminology too.

.

 

[PeterDonis]

Math is terminology too.

Perhaps, but it is a different kind of terminology from ordinary language; it is precise where ordinary language is vague, and it is quantitative where ordinary language is qualitative.