In this video I’ll be talking about a remarkable alternative theory or interpretation of Quantum
mechanics; Pilot wave theory.
aka de Broglie Bohm theory, aka Bohmian mechanics.
There are people who think that this theory has been disproved or discredited, but more
recently, there are people who think that Bohmian mechanics explains everything quantum
mechanics does without any quantum weirdness.
Both these positions are wrong, so I thought it was time to make a new video clarifying
all this, since my old videos on this are 3 years old now.
So what is Bohmian mechanics?
To answer that, I better quickly explain what Quantum mechanics is.
100 or more years ago, physicists were finally able to do experiments on really small things
like atoms, and though that was cool, they weren’t really expecting to be surprised.
Newton’s laws and the rest of physics as they knew it should apply just as well to
galaxies as electrons.
But that’s not what they found.
Take for example, the double slit experiment.
When you shoot things one at a time toward two doors, you expect that if it makes it
throw, it will go through one of those doors and end up somewhere behind it, so that you
eventually get two clumps.
They decided to try this simple experiment with really small things like atoms.
You shot them out one at a time but you can’t actually see them going in their path and
so you can’t see which door they went through, but you’d expect them to do the same thing
essentially as before and end up in the same two clumps.
Only they didn’t.
They ended up in these weird patterns like this.
Physicists scratched their heads.
Then they tried the same thing again, but this time they closed one of the doors randomly.
Now the particle had to be going through just one door, so it had to just land somewhere
behind that door.
And they were right; the final pattern was just what they expected in the first place.
But then they tried it again with both doors open at once and... it was the same strange
pattern.
So they scratched their collective heads again- and came up with an idea!
They proposed Newton was wrong after all.
Actually, what really happens is, when an object has more than one option available
to it, and no one is checking which is does, it kind of does all of them at once.
This is called a quantum superposition- they gave it this fancy name because they didn’t
really know what they meant by doing all possible things at once.
This sounds totally crazy, but ‘look!’
they said.
It can explain the double slit experiment.
See, the atom doesn’t just go through one door or the other, it goes through both.
Then, it’s able to interfere with itself!
And that gives the strange pattern.
When there’s only one door open, it isn’t in a superposition, so it can’t interfere
with itself and it just does the usual thing- and so you get back the normal pattern.
This quantum superposition thing got applied to many many many more experiments, and it
always made the right prediction.
And so, even though Quantum mechanics is crazy, we’re all forced to accept it by experimental
facts.
At least, that’s the convention wisdom.
Then came Bohmian mechanics.
The aim of this theory is to explain all the same experiments as quantum mechanics can,
but without superposition.
In fact, you can prove that Bohmian mechanics produces exactly the same results as quantum
mechanics for all possible experiments, but the objects in this theory are always in one
place, and have one speed.
How is this possible?
Let’s look at the double slit experiment to understand.
In Bohmian mechanics, the particle must have a path from it’s start, through one of the
slits to the back wall since the particle is in just one spot at each time.
In contrast, in quantum mechanics, the particle takes every possible path.
The first thing the theory needs to explain is, if your particles all start in one place
and they follow a predetermined path, why don’t they all end up in exactly the same
spot.
Bohmian mechanics explains this by saying, you don’t actually know exactly where the
particles started out.
This first particle might have been just left of that one, which meant they end up going
to different places.
It’s just because you don’t know exactly where it started that you don’t know where
it will end up.
This is the exact same as in the non-quantum case.
So that sounds reasonable.
But a fancy way to put this is that the initial position is a ‘hidden variable’- since
it’s a variable you don’t know, it’s hidden, making Bohmian mechanics a hidden
variable theory.
You’ll hear the term hidden variable uses disparagingly all the time by people so I
thought I’d introduce it to you so you see it’s not necessarily a bad thing for a theory
to have hidden.
Anyway.
This is the important part; so to check you’re paying attention, let me ask you a question.
Suppose that in the situation that one door was closed, this is the path that this particle
would take according to Bohmian mechanics.
If I opened the other door, will that path change or not?
Seriously, pause the video now and think about the answer.
Well let’s see what’d happen if the path didn’t change.
Then all objects that went through this door would end up here, and similarly for objects
going through the other door.
You end up with the wrong prediction.
But I told you Bohmian mechanics always gets it right.
So what really happens is, the particle does change path when the other door is open- even
though it’s not going through it.
So if that door is open, it feels a force pushing it into some weird wonky path like
this.
In fact, here’s a simulation of a bunch of paths that particles starting in slightly
different positions take.
And you can see that where they end up really does exactly reproduce the interference pattern.
So here is the key take away point from that: there still is quantum weirdness in Bohmian
mechanics, it’s just a bit hidden.
In standard quantum mechanics, a particle is in a superposition of all possible places,
but in Bohmian mechanics the particle is in one place, but it’s aware of and affected
by all the other possible places it could be.
Just to be clear; This is not a typical feature of a classical theory of physics.
Bohmian mechanics has one really awesome advantage over standard quantum mechanics; it doesn’t
have the measurement problem.
The measurement problem is arguably the biggest conceptual difficulty of quantum mechanics.
Let me explain that.
In the double slit experiment, imagine if you put little detectors on the doors that
flash every time a particle goes through it.
Then you could find out which door the particle went through!
But then you look at the pattern and you see that it’s not the interference one.
This is explained in ordinary quantum mechanics by saying that, when you measure a particle
that’s in a superposition, the superposition collapses to just doing one thing.
But why?
Why do quantum particles get shy like that?
Bohm proposed a solution to this inside of Bohmian mechanics called decoherence.
It’s basically the idea that when you measure something, what you’re really doing is getting
your measurement device to interact with it, and that interaction makes it look like there’s
this collapse.
I won’t go into this much here because decoherence deserves it’s own video- not just on how
it relates to Bohmian mechanics, but also how it relates to other interpretations like
many worlds.
But now let’s look at a common criticism of Bohmian mechanics.
You will hear people harp on about how Bell’s theorem proves that no hidden variable theory
can give the same results as quantum mechanics.
This is clearly rubbish because Bohmian mechanics exists and predicts everything quantum mechanics
does and is a hidden variable theory.
You know who also used to get frustrated by people misinterpreting Bell’s theorem?
John Bell.
He was a huge fan of Bohmian mechanics and wrote lots about it, for example this quote
about the Bohm’s explanation of the double slit experiment.
He didn’t misunderstand his own theorem.
What Bell’s theorem actually says is any theory that reproduces the results of quantum
mechanics, so for example, quantum mechanics itself and Bohmian mechanics, has to be nonlocal.
Something is nonlocal when you have one thing over here affect another thing over there
instantly.
Quantum mechanics and Bohmian mechanics are nonlocal and the situations they’re nonlocal
in are the same, basically EPR experiment like set ups, where there’s a person on
each of two different sides of the universe, and what one of them does to their particle
instantly effects the others particle -because their is entanglement in Bohmian mechanics,
it’s have a difference interpretation.
but it’s still there and certainly not classical.
This is a point I think people have gotten confused about.
You might have seen Veritasium’s beautiful video about how you can reproduce the effect
of pilot wave theory by using a water phenomenon called walking droplets.
If you haven’t watched that, then do, it’s mesmerising.
These walking droplets are completely classical; in fact in the video Derek makes them at home,
so you might be tempted to conclude that pilot wave theory is totally classical since it
can be mimicked classically.
But can all of Pilot wave be mimicked by these water experiments?
Actually, it’s only experiments where there is isn’t entangled particles that can be
mimicked this way, because when there are entangled particles in Pilot wave theory they
affect each others movements no matter how far they are from each other.
But classical systems can’t have these nonlocal effects, so they can’t produce the right
results.
That’s why these water experiments can reproduce all kinds of quantum phenomena like the double
slit experiment, or tunneling, or harmonic potentials, but it could never reproduce a
Bell experiment.
It’s impressive how much Bohmian mechanics can explain classically, but it still has
very nonclassical parts, and that’s important to remember.
To wrap up, there are plenty of big pros but also a fair number of cons for anyone considering
taking Bohmian mechanics as their interpretation of quantum mechanics.
But enough being impartial.
You might be wondering, do I believe in Bohmian mechanics.
No, I don’t, but I don’t believe any interpretations since there a several that are consistent
with the facts at the moment.
But do I like Bohmian mechanics?
Yes and no.
No, because of that relativity criticism, and also because I worry about how natural
the maths of this theory is.
But Yes, because on some levels it’s much more intuitive, and it answers the measurement
problem.
But putting aside how plausible I find the theory itself, the thing I love the most about
Bohmian mechanics, aka Pilot wave theory, is that it shows us there’s still plenty
of room for debate on what quantum mechanics actually means.
That even something as seemingly fundament as quantum superposition can be questioned.
We need to keep critically investigating the interpretation of quantum mechanics.
As John Bell put it “Bohm has shown us the way.”