Explaining the Many-Worlds Interpretation

(c) 2010 Kim Øyhus

(With pretty pictures)

Quantum Mechanics is difficult and confusing, and one of its interpretations is "Many-Worlds", which says that there are lots of universes which divide into new universes on every quantum observation, and that this is what one gets if one take the mathematics of Quantum Mechanics as true.

I independently came to this conclusion in about 1990 when studying Quantum Mechanics at NTH, the Norwegian Institute of Technology, which sadly does not exist anymore. This is written in December 2009, so I waited a long time before writing this down.

This text is about how I came to this conclusion, hopefully explained in a good way, just like they did not explain it to me. Quantum Mechanics explanations usually have big dead zones that most explainers avoid, mainly because they do not understand it themselves, and are just copying others. So textbooks tend to copy each other, almost verbatim. The few exceptions to this I have studied myself, is Feynmans work, which admits the dead zones of understanding exists, but give understandable explanations on how to calculate and test, which is what is actually needed in science, and which can be used to find out stuff about the dead zones. And then there is "Understanding Quantum Mechanics, a User's Manual" by Michael A. Morrison, which is very good at explaining the fundamentals, but only for one-particle systems. One must have many-particle models to understand the many-worlds interpretation and its connection to Quantum Collapse.

What is this Quantum Collapse really?

To calculate the probability of an event, one squares the amplitude of the wave function.

Okay. Nice to know. But I thought events was something that could be modeled by wave functions, not something outside of it. And if this math is true, or at least consistent with all observations, how does it discern between events and other stuff?

After reading some more Q.M., some of which were mandatory in my study, some that I bought extra, and some popular science paper backs, of which I can only recommend "Q.E.D." by Richard Feynman, I got mostly mis-informed that this was about Observers, which somehow got probability waves to Collapse into events.

Again Okay, nice to know, but why do they not have any mathematical model of this collapsing stuff except the change of quantum wave into a probability function? How does one discern an observer from other stuff in the Universe? How does the universe do it? Is it doable at all? Does it even make sense?

After learning and using Q.M. for some years, I knew the calculations were done without any regard to any observer, except as some sort of process at the end of experimental quantum processes. It was really weird that physicists did not show any particular interest in this collapse process, but instead treated it as a sort of taboo. I finally got hold of articles about Bell, Aspect, and their experiments, which I did not understand at the time, because I had not learned many-particle Q.M., which unfortunately was rather badly taught, both in lectures and in books. But I got the point that one had to use many-particle models to understand this.

What is a Quantum Observer anyway?

All I got was that they were kind of magical, not described by math, avoided by physicists because of shame of unphysicality or something.

But fortunately, I knew computer science, which most physicists do not know, with the Church-Turing thesis, which roughly states that anything physical can be simulated by a computer. This means that observers can be simulated by a computer. So all I had to do to put observers into the math was to simulate a universal computer that observes quantum collapsing in its own little universe. To do this, I had to understand many-particle Q.M.

The difficult thing about many-particle quantum mechanics, in addition to understanding it, is that its wave function gets 3 dimensions for each particle, so it gets difficult to visualise and understand even for just 2 particles since they need 6 dimensions. To make the model comprehensible, and possible to visualise, I had to simplify it as much as possible, and I reduced it to just two dimensions, in addition to time, so the model can be visualised as a picture evolving in time, and shown here.

Pictures of this are further down in this article. You can also try a simulation in java.

A superposition

If we look at a superposition of a live and dead cat, why do we not see a sort of double exposure picture? According to many people, that is what we should see if quantum mechanics were right, and the collapse of the wave function is what stops that from happening.

But cats are far too big to model mathematically, so I went for the simplest superposition I could find: One particle moving along a line, and having a 50% chance of being reflected at a barrier on this line. This is in practice a half silvered mirror, except that it is only one dimensional, and the particle can be an electron, and the mirror a positive potential. After hitting the potential the particle will be in a superposition of being bounced back, and continuing forward.

This is similar to an electron in a thin wire with a small gap.

An observation

When the reflected electron passes by, what will it be like to observe it?

Which one of these claims is true according to the math?

So, to test this, the observer and math must be able to discern between at least these four possibilities. Humans can be observers, and we have eyes that do the observing part, and a brain that can be conscious of the observation. Many believe that this consciousness part is causing the collapse. If consciousness has a role, that role will happen after the eye does the observing, and the brain will not be in a superposition yet, so if it is sufficient to just model the eye, that should be apparent in the model, and it was so.

Instead of an eye, I use a much simpler device: just an electron that is in the path of the returning reflected electron. These 2 electrons will bounce when they hit each other, so the observing electron will move, and this movement can be further observed and amplified, thus doing its observing by bouncing into more observed observations.

So, what could happen in the model? How will the observing electron bounce? Here are the 4 scenarios from above:

Since everything happens in just 1 dimension, with 2 particles, this can be visualized as time slices of a 2 dimensional model, with full phase space. This is a complete Hilbert space model of this quantum mechanical system, modeled as a 2 particle Schrödinger equation, by me. The positions of the electrons are represented by the heights of the blobs:

Explanations 1D 2D probabilities 2D wave function
I start with 2 electrons:
The highest electron is moving upwards to a yellow half transparent mirror.
The lowest electron is the observer, and stands still.

Note that all 2D functions are symmetrical over the blue diagonal line, because electrons are identical. (fermions)

The upper electron is now being half reflected by the yellow mirror.
One can see the reflected part interfering with itself.

This is the splitting of the wavefunction into 2 worlds, even though only one electron is affected.

The upper electron is now in a superposition of
"Having gone through the mirror", and
"Been reflected downwards to hit the lower electron".

Note that the 2 probability blobs on the lower side of the diagonal are still on a horizontal line, meaning that just one electron is in a superposition.

The lower electron is now being hit by the reflected part of the upper electron, and is changing its positions and speeds to be in a superposition of "Being hit", and "Not being hit".

This is the observation itself, wherein the superposition gets to both electrons.

Both electrons are now in a clear superposition of
"Passing beyond the mirror while lowest electron stands still" and
"Reflected from the mirror into bouncing the lowest electron",
thus confirming the Many Worlds interpretation.
These heights are:
1. The mirror electron that passed through.
2. The observing electron standing still.
3. The mirror electron after hitting the observing electron.
4. The observing electron after being hit.

Both electrons are now in a superposition. That they are in 2 separate worlds can be seen by noting that the 2 probability blobs on the same side of the diagonal, have no coordinates in common. They are separated both horizontally and vertically. Before the observation, but after the mirror split, they had one coordinate in common. And before the mirror split, it was just one blob, which of course had both of its coordinates in common with itself.


Possiblity 3 is the correct one:
The observer got into a superposition of seeing the electron fully, or not at all, thus confirming the "Many Worlds" interpretation.

I did not do the actual simulation before now. When I studied, I just visualized it, but got the same answer.

To summarize what happens here:
First, one electron gets into a superposition of being in 2 places.
Then, the superposition gets to 2 electrons, being in 2 worlds, thus an observation.
If this second electron was in the retina of a human, then the superposition would split the surrounding atoms into 2 worlds, and then the neuron, and then the optic nerve, the brain, the entire observer, and then the entire universe around the observer, particle by particle, starting with the second electron. The superposition of the first electron is thus extremely contagious.


2010.01.04 First partial version.
2010.01.05 Proofread and a little rewritten.
2010.01.05 Some better explanations added on advice from friends.
2010.01.13 New pictures.
Any comment?