Quantum mechanics has made the right predictions

so far on every experiment we've thrown at it.

That's why many people are happy to accept

quantum mechanics or at least feel that they

don't have any choice.

But think about the situation with Newton's laws before

Einstein's theory of relativity came to the scene.

For two hundred years Newton's laws seemed hold

perfectly in every experiment done despite the fact

that they are actually wrong and relativity is

a better description of reality.

How can that be?

Because Newton's laws and relativity give almost

the same predictions on many experiments.

Newton's laws are only obviously wrong at

high speeds but people couldn't do those

experiments for a long time, so no one noticed that

Newton's laws don't always work.

Going back to quantum mechanics, it's possible

that there is al alternative theory that makes

all the same predictions, as quantum mechanics,

on experiments that have been done, but might

make different predictions on certain experiments

that haven't yet been done.

If an alternative theory exists, maybe it can

explain the stuff without resorting to all the

craziness quantum uses.

I should probably mention at this point that

if you haven't watched my last few videos

and you've heard that alternative explanations

to quantum are impossible, then you might want to

watch this video explaining Bell's theorem and

why that isn't the case.

Anyway, today's topic is a theory called

Bohmian mechanics or Pilot-Wave theory, which is

an alternative to the quantum mechanics.

It's a much more classical theory than quantum.

To start off with, there is none of this

"particles are in more than one state

at a time business".

A particle has only one position, one speed, etc.

at any given time.

This is regardless of whether they are being

measured or not. This means that it's

perfectly sensible to talk about the path the

particle took to get from "A" to "B",

Where is in quantum a particle has to take

all possible paths. One last thing I'd like to

point out about this theory is that

it's fully deterministic.

In other words - if I know a particle started out

in exactly this position with this speed

then I can use Bohmian mechanics to

calculate exactly where it would be

at any time in the future.

Just like with Newton's laws there is no

randomness in it.

But how can that work?

We know that there is randomness in the results

of the quantum experiments. You can do

the same experiment twice and get

different results.

How can Pilot-Wave theory explain this

if it's deterministic?

The answer is that randomness is not

true randomness. Think of a coin.

It seems like if you flip a coin

then the result is perfectly random.

There is no way you can figure out whether

it would be heads or tails.

But that's not actually true.

If you know which side the coin started on

and all the forces that affected it.

In theory you can use the Newton's Laws

to figure out exactly what you'll get.

So it only looks random because we don't

know all the forces.

I'm going to call this type of

randomness - "randomness because of ignorance".

Pilot-Wave theory proposes that the

randomness we see in these experiments

is of this type.

On the other hand notice how according to

quantum mechanics there is no extra information

that you can gather or calculations

that you can do, that would tell you

exactly what the result would be.

Quantum mechanics has true randomness.

Ok, how does the theory actually work?

Remember that Newton's laws tell us

that if you have a particle you can figure out

where it's going to go by knowing all

the forces pushing it?

Some of the forces that we are used to

are gravity and electromagnetism.

While Bohmian mechanics is just

Newton's Laws with slight adjustment - there

is an extra force.

We'll call this force - the quantum force.

And this is the really important bit.

We figure out what strength and direction

that force pulls the certain particle,

using the wavefunction.

You use the exact same wavefunction

for quantum mechanics, for that particle

to calculate the quantum force.

I won't explain how that calculation is done

but the point is that the wavefunction

still plays a central role in our new theory.

It's not just the same kind of role as in

quantum mechanics.

Here the wavefunction sort of guides the

particle on its path. That's why the theory

gets called Pilot-Wave theory.

Well now we have this extra force that pulls

and pushes the particle, so that the particle

will move in some kind of path.

How can we use this to explain all

about quantum experiments?

Let me illustrate with an impressive example.

The double slit experiment.

Hopefully you remember it. We shoot particle

and they get through if they go thourgh

either one or both of these holes

and then land on the screen where

they are detected.

They result of course is the interference pattern.

Let's try to get this result with Bohmian mechanics.

We assume each particle starts off

somewhere around here and they all

move forward and the few of them make it

to the slits. Say a particular particle got

to this point inside the slits.

We can use the wavefunction to calculate its path

and it looks pretty crazy.

Notice that if there was no quantum force

there wouldn't be any other forces on it at all.

So Newton's laws would tell us that it would

just keep going at a speed it's going.

Which would look more like this.

Now what if instead of starting at that point

we started very very nearby.

You see that the particle now goes on a completely

different path and if you start somewhere

different again - it goes somewhere else.

But when we originally shot our particles

we weren't a 100% sure exactly where they were

so you might shoot two particles from what

you think is the same spot but according

to Bohmian mechanics they could end up

in very different places.

Making the results look random but the theory

says that this randomness is just randomness

from ignorance. Ignorance in this case of the

starting positions and its no more mysterious

than a coin flip.

Now we can repeat the same calculations

for many particles getting through the slits.

As you can see an interference pattern

has emerged. How did this work out so perfectly?

It all comes back to that quantum force.

It's based on the wavefunction and designed

specifically so that of the particles moving

under it's influence, most will end up where the

wavefunction is big.

Basically that force is rigged to make give

the same answer as quantum mechanics.

This leads to some weird conclusion though.

Imagine we cover up one slit.

Now lets calculate where the particle should end up.

Here's one particle's path.

Now we might naively expect that if we

open up the second slit its path will still

look the same. That's not the case though.

What changed? The wavefunction.

The particle itself doesn't go through

both slits but the wavefuncion does, therefore

the force on the particle is now different.

So in a way this superposition and interference

business hasn't completely gone away,

it's just more hidden now.

Well, that's all I'm going to say about how

the theory works but I'll finish with some

quick thoughts. I think Pilot-Wave theory is

very impressive in a way that it gives the same

answer as quantum. But to me it's most impressive

in that it's showing two completely different

explanations about reality can both explain

the facts. Will we someday be able to test

which one is true?

If so, how?

And if not, what does that say about physics?

Are we really fifing out the truth?

Or we're just telling stories that work?