# Worlds in a cup of water

1. Dec 24, 2013

### kye

1. In a hydrogen atom, how do you compute the total numbers of positions possible (possible Psi^2) for the electron? Does each position signify one world?

2. Or do worlds only came about if there are quantum choices to be made? For example, as each hydrogen and oxygen dissolve and reform the hydrogen bonds. Do this create worlds?

3. If so, how many worlds possible or can exist in a cup of water? Does each world as big as the universe or solar system or only as big as the cup of water?

4. How does this "relative state" relate to it? How about the idea of the universal wavefunction, where all possible states already exist in the cup of water. If so, is this synonym to worlds splitting? How many kinds of MW are there? Please differentiate it by means of the example of the cup of water (assuming it is 250 ml).

Thank you.

2. Dec 24, 2013

### michael879

Many "worlds" interpretation is an interpretation, not a formal theory so these types of questions are usually impossible to answer, or completely a matter of opinion/guess. The usual interpretation is that for a continuous variable like position there are uncountably many worlds, each one corresponding to a different position. Before measurement these worlds all overlap. After measurement the observer entangles with the particle and gets split up into the different worlds, quickly followed by the rest of the planet (since any macroscopic effect will propagate at near light speed).

3. Dec 24, 2013

### Simon Bridge

1a. You don't ... $|\psi(x)|^2$ is not the total numbers of positions possible - it is the probability distribution of possible positions. There are infinite possible positions in this model. 1b. No.

See "many worlds interpretation" of quantum mechanics - you appear to be taking a pop-science description a bit too literally.

3a. one: the World of the cup, 3b. No. The Universe and Solar System exists around the cup of water.
It is easy to get sidetracked by artistic imagery - realise that the "words in a cup" thing is a metaphore. To understand the physics you need to be more precise in your language.

What do you mean by "World" and how can such a world be said to be "in" a cup of water?
What do you mean by "cup" for that matter?

You are talking about extremely complicated objects as if they are simple.

What "relative state" is "this"?

Sounds like nonsense to me.

No. By definition of "universal wave function": all possible worlds (under a "many worlds" interpretation) would already be represented.

The "world splitting off" usually refers to a measurement - there is only one world available at a time.

What do you mean by "MW"?

Meaningless request.

4. Dec 24, 2013

### bhobba

You are confusing things atrociously. The number of positions is infinite - assuming of course in QM one can speak of position independent of measurement context.

If you are thinking of MW that spitting into worlds only occurs at decoherence.

I think it would be wise for you to study a good book on QM such as Ballentine, then study Schlosshauer's text.

Thanks
Bill

5. Dec 24, 2013

### kye

But the possible positions of the moon is finite for the volume of diameter that includes moon. As illustration, if you will plot all possible positions of the moon in the sky. It is not infinite. In QM, I know electrons positions are probabilistic and understood QM, so the possible positions of the electrons is not infinite because the volume of the atom is known.

Do you not know that in H20. The hydrogen bonds dissolve and form at millions of times a second. How each molecule attract is probabilistic.. this is the context of of I meant if worlds split whenever there are quantum choices, then a cup of water can form many worlds.

Note Everett original paper is about relative state and later upgraded to Many worlds. I just want to know how they differ in the cup of water where probabilistic occurences occur in the hydrogen and oxygen interactions. If you are not familiar with chemistry. You may not know what I'm talking about.

6. Dec 24, 2013

### bhobba

Errrr. You do understand that position is a real number, and the reals are infinite?

Thanks
Bill

7. Dec 24, 2013

### kye

Are you saying that real numbers are infinite up to a certain number (like there are infinite numbers between the number 3 and 4.. like 3.0000001, 3.00000000002, and so on? But even if each position varies by the planck scale distance. It is still finite. So the numbers of possible position of the moon is finite. Prove it is infinite.

8. Dec 24, 2013

### kye

I think you are familiar with chemistry.

Take the oxygen and hydrogen molecules in H20. The electrons in them don't have position before measurement. When different H20 molecules finally touch and hydrogen bond form. The electrons suddenly have positions (to form the hydrogen bonds). This is when branches or worlds split. Unless you are saying that when hydrogen bonds form, there is not instance when the electrons suddenly appear? It's as if hydrogen bonding is in pure state? I understood it that when hydrogen bond forms, it constitutes measurement from the point of view of them, no??

9. Dec 24, 2013

### bhobba

A bond is not a position - that's a silly confusion of terms.

When a bond is formed the position of the electron, if it was to be measured, can only be in certain places. They don't have positions independent of measurement context.

Thanks
Bill

10. Dec 24, 2013

### bhobba

11. Dec 24, 2013

### kye

What I was saying was that the atom can measure each other. Let's take the case of a single oxygen and hydrogen. Isolated, their electron has no position. When the oxygen and hydrogen go near, the electrons suddenly appear because they are measuring each other, and hence form the covalend bond. So here no worlds split? But there are many quantum choices of what part of the atoms the electrons would appear for the covalent bond. Won't be form branches? This is the context of what I meant by worlds in a cup of water, because the difference positions of the covalent bond may constitute branches.

12. Dec 24, 2013

### kye

Let me give more details of what I'm saying. Isn't it charge is related to the position of the electron. Psi^2 is the probability of knowing where the charge of the electron is. But since the charge of the electron is at the position of the electron, that's just the same as knowing the position.

How do you define Psi^2 exactly as far as charge is concern. Don't you consider Psi^2 as the instantaneous charge density?

13. Dec 24, 2013

### kye

It is said that any stochastic quantum events is what form Everett branches. Are you guys saying there is no stochastic events in the h20 molecular dynamics in a glass of water? What objects then can form unprepared stochastic quantum events aside from carefully prepared double slit experiment?

14. Dec 24, 2013