This video answers the homework questions
I set in my previous video called understanding
quantum mechanics. If you’re new to my channel,
you probably think it’s extremely naive
of me to set homework questions nobody is
obliged to do, on youtube videos that noboby
is obliged to watch. And it probably is naive,
but I just don’t believe learning is a passive
process. Even if you never do answer the homework
questions, I hope that me asking them prompts
you to think, and I hope this video will be
useful to you because it’ll cover the common
misconceptions from the original video and
I’ll also answer the most frequently asked
questions.
Ok, so the first homework question was:
Can you do the double slit experiment with
large objects and still get an interference
pattern?
Remember that in the video I said, that objects
only act strangely when they’re not being
measured, but this doesn’t happen for a
big object because it’s constantly being
measured. So the straight forward answer to
this question is to just stop things from
measuring it. But is that possible? People
pointed out that if an object is made up of
lots of particles wouldn’t the different
particles interact with each other? And what
about gravity? Every object is interacting
with other objects via gravity, so doesn’t
that mean that nothing can escape being measured?
There were lots of great questions along these
lines, and somehow they all boil down to this
bigger question: what is a measurement? This
is easily the million dollar question of quantum
mechanics and it’s still unsolved, so we’re
going to go talk about it in lots of detail
in the series. But for now, I want to address
a misconception that I can debunk, that I
saw in the comments a lot. People thought
that when I said measurement, what I really
meant was interaction. In other words, they
thought that if a particle interacts with
another object, it has necessarily measured
it. And I can see why you’d think this since
my examples of measurements were about particles
hitting other particles. But this is not necessarily
the case. Actually, a measurement is when
you get information about what the particle
is doing leaking out. Let me explain.
In one example I showed, the object is hit
with a air molecule. But the point is, the
air molecule will change it’s own path depending
on where the object is. If it’s here, it'll
bounce off like this, but it’s here, then
the air bounces off like this. So since us
seeing the final state of the air molecule
is enough to decide where the object is, we
say the air molecule is carrying away information
about the objects position. That’s what
makes this a measurement, not the fact that
the air is interacting with the object, but
that it is leaking information about the object
to the outside world. Let me explain with
this point a bit further with another example.
Suppose that you some weird hypothetical thing
that changes colour when it comes into contact
our object, but it goes straight through it.
This is clearly some weird interaction. Now
say that the object can be here or here again,
and the thing comes in like this. In either
case, the final state of the thing is this.
The thing clearly interacted with the object,
but it hasn’t measured it, since it gives
you no information about where our object
is.
That’s an important point so I hope it's
a bit clearer. Now let me get back to the
question about when our object is made of
different interacting parts. For simplicity
imagine our object is just made of two bits
stuck together. If one of the bits is in this
position, then you know that the other bit
has to be here too, and similarly, if you
saw one part over here, then the other bit
would be here too. So clearly, the one bit
does contain information about the other.
The reason this doesn’t count as a measurement
though is that this information isn’t being
leaked out into the wider world. For it to
count as a measurement in QM it is really
important that the information be carried
away, and you can no longer interact the particles
together. There’s a reason for this, and
it’s something I’ll cover in detail in
the main series. But for now, let me convince
you for now by appealing to experiment. The
double slit experiment has been done with
many things made up of composite parts. Many
of you mentioned they've done it with Buckyballs,
which are molecules with 60 carbon atoms and
still saw the interference pattern. But apparently
it’s been done with molecules with over
800 atoms as well and it still works. So composite
systems can still have interference.
Another great question I got a lot was, what
about gravity? Does that count as a measurement?
To answer this I’d need to assume just slightly
more quantum mechanics than I’ve taught
you. So I’m going to set this as a homework
question in the third main video of this series
and you guys can give it a go for yourselves
then, and I’ll give you my solution in another
one of these.
But, getting back to the actual homework questions
now, the second question was, imagine if you
had some measuring device that could actually
measure which door an electron went through.
What would happen?
Remember, I’d said that the electrons act
strangely when they’re not being measured,
but right now, it is being measured- and so
it has to act as normal again. For an electron,
that means it has to be in just one place.
You won’t see go through both slits, just
the one. But -doesn’t this contradict what
I said previously, since now we know each
electron is going through just one door? No,
because see that the pattern on the wall is
no longer the interference pattern. Instead
it’s exactly what you’d expect in the
case each electron goes through one door,
which is what’s happening in this case.
Quantum mechanics is sneaky.
Question 3. This one’s about Bohmian Mechanics,
and I’ll keep it short because I have talked
myself hoarse about this theory before. The
question said, in Bohmian mechanics, aka pilot
wave theory, the electron does in fact go
through just one door in the double slit experiment.
But in my last video, I seemed to rule out
that possibility- so what incorrect assumption
did I make?
Well, when we looked at the single slit experiment,
we saw electrons going vaguely here. So we
assumed that if electrons were really going
through one door each, an electron going through
door 1 wouldn’t mind whether the other door
happens to be open. It would just do what
it was going to anyway, and end up vaguely
here in any case. That’s how we got a contradiction.
But that’s not the case in Bohmian mechanics
though. The electron does go through this
one door, but it cares a lot whether the other
door is open. That’s because it has this
thing called a guiding wave that spreads through
all of space, and tells the electron which
way to go. So when both doors are open, the
wave goes through both doors and then tells
the electron to go somewhere else.
Ok, so those were the main homework questions,
let’s have a lightening round of responses
to other common comments.
People asked 'doesn’t the single slit pattern
actually look like this, with one main band,
and a few much fainter bands on either side?',
where as I always draw it as this. The answer
is yes, I just draw the main chunk because
it’s easier and clearer, but I could have
done it properly and nothing would have changed
in any of my arguments.
Next. There were lots of people who tried
to answer homework question 1 by using this
equation, called the de broglie wavelength.
I made a video about the uses and abuses of
that equation, but basically, that equation
is only valid in a very very specific circumstance,
and one that almost certainly doesn’t apply
to a complicated real object.
-Also, I got lots of comments saying that
I was wrong about waves, because of Quantum
Field theory, or that I should talk about
quantum field theory instead because all the
paradoxes clear up when you look at it. Actually,
I think the paradoxes of quantum mechanics
just get compounded in QFT. But that’s something
to talk about much much much later.
And that’s all for this video. Thank you
so much to everyone who did leave a comment
on my last video and I really encourage all
of you give the homework questions a go in
the future. But, unfortunately, while I love
reading and replying to all the comments,
soon it’ll be too much for me to reply to
each personally. I’ll kept reading them
all, and I’ll reply to as many as I can
in the future, but that’s where I’d love
for you all to help me and comment on each
others work. As I saw in the comments last
time, that leads to way more interesting discussions
anyway- I try to ask questions that can be
answered in multiple ways, so that you guys
can learn from each other. And this works
when we all treat each other with respect
and remember we’re all here to learn. Thanks
guys. See you for the second proper video
in the series.
