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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?