Today I want to talk about the many worlds interpretation of quantum mechanics and explain

why I do not think it is a complete theory.

But first, a brief summary of what the many worlds interpretation says.

In quantum mechanics, every system is described by a wave-function from which one calculates

the probability of obtaining a specific measurement outcome.

Physicists usually take the Greek letter Psi to refer to the wave-function.

From the wave-function you can calculate, for example, that a particle which enters

a beam-splitter has a 50% chance of going left and a 50% chance of going right.

But – and that’s the important point – once you have measured the particle, you know with

100% probability where it is.

This means that you have to update your probability and with it the wave-function.

This update is also called the wave-function collapse.

The wave-function collapse, I have to emphasize, is not optional.

It is an observational requirement.

We never observe a particle that is 50% here and 50% there.

It’s not a thing.

If we observe it at all, it’s either here or it isn’t.

Speaking of 50% probabilities really makes sense only as long as you are talking about

a prediction.

Now, this wave-function collapse is a problem for the following reason.

We have an equation that tells us what the wave-function does as long as you do not measure

it.

It’s called the Schrödinger equation.

The Schrödinger equation is a linear equation.

What does this mean?

It means that if you have two solutions to this equation, and you add them with arbitrary

prefactors, then this sum will also be a solution to the Schrödinger equation.

Such a sum, by the way, is also called a “superposition”.

I know that superposition sounds mysterious, but that’s really all it is, it’s a sum

with prefactors.

The problem is now that the wave-function collapse is not linear, and therefore it cannot

be described by the Schrödinger equation.

Here is easy way to understand this.

Suppose you have a wave-function for a particle that goes right with 100% probability.

Then you will measure it right with 100% probability.

No mystery here.

Likewise, if you have a particle that just goes left, you will measure it left with 100%

probability.

But here’s the thing.

If you take a superposition of these two states, you will not get a superposition of probabilities.

You will get 100% either on the one side, or on the other.

The measurement process therefore is not only an additional assumption that quantum mechanics

needs to reproduce what we observe.

It is actually incompatible with the Schrödinger equation.

Now, the most obvious way to deal with that is to say, well, the measurement process is

something complicated that we do not yet understand, and the wave-function collapse is a placeholder

that we use until we will figured out something better.

But that’s not how most physicists deal with it.

Most sign up for what is known as the Copenhagen interpretation, that basically says you’re

not supposed to ask what happens during measurement.

In this interpretation, quantum mechanics is merely a mathematical machinery that makes

predictions and that’s that.

The problem with Copenhagen – and with all similar interpretations – is that they require

you to give up the idea that what a macroscopic object, like a detector does should be derivable

from theory of its microscopic constituents.

If you believe in the Copenhagen interpretation you have to buy that what the detector does

just cannot be derived from the behavior of its microscopic constituents.

Because if that was so, you would not need a second equation besides the Schrödinger

equation.

That you need this second equation, then is incompatible with reductionism.

It is possible that this is correct, but then you have to explain just where reductionism

breaks down and why, which no one has done.

And without that, the Copenhagen interpretation and its cousins do not solve the measurement

problem, they simply refuse to acknowledge that the problem exists in the first place.

The many world interpretation, now, supposedly does away with the problem of the quantum

measurement and it does this by just saying there isn’t such a thing as wavefunction

collapse.

Instead, many worlds people say, every time you make a measurement, the universe splits

into several parallel words, one for each possible measurement outcome.

This universe splitting is also sometimes called branching.

Some people have a problem with the branching because it’s not clear just exactly when

or where it should take place, but I do not think this is a serious problem, it’s just

a matter of definition.

No, the real problem is that after throwing out the measurement postulate, the many worlds

interpretation needs another assumption, that brings the measurement problem back.

The reason is this.

In the many worlds interpretation, if you set up a detector for a measurement, then

the detector will also split into several universes.

Therefore, if you just ask “what will the detector measure”, then the answer is

"The detector will measure anything that’s possible with probability 1.”

This, of course, is not what we observe.

We observe only one measurement outcome.

The many worlds people explain this as follows.

Of course you are not supposed to calculate the probability for each branch of the detector.

Because when we say detector, we don’t mean all detector branches together.

You should only evaluate the probability relative to the detector in one specific branch at

a time.

That sounds reasonable.

Indeed, it is reasonable.

It is just as reasonable as the measurement postulate.

In fact, it is logically entirely equivalent to the measurement postulate.

The measurement postulate says: Update probability at measurement to 100%.

The detector definition in many worlds says: The “Detector” is by definition only the

thing in one branch.

Now evaluate probabilities relative to this, which gives you 100% in each branch.

Same thing.

And because it’s the same thing you already know that you cannot derive this detector

definition from the Schrödinger equation.

It’s not possible.

What the many worlds people are now trying instead is to derive this postulate from rational

choice theory.

But of course that brings back in macroscopic terms, like actors who make decisions and

so on.

In other words, this reference to knowledge is equally in conflict with reductionism as

is the Copenhagen interpretation.

And that’s why the many worlds interpretation does not solve the measurement problem and

therefore it is equally troubled as all other interpretations of quantum mechanics.

What’s the trouble with the other interpretations?

We will talk about this some other time.

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