We mentioned previously
one of the bizarre
aspects of quantum mechanics.
The process of tunneling allows
particles to penetrate
barriers that are simply
classically too high for them
to overcome.
This process is, however,
actually nothing like the idea
of digging a tunnel.
There's no spade here.
There's no hole that we dig.
It's just not what's going on.
We're confronting here the
common difficulty in quantum
mechanics of finding words and
analogies from everyday
experience to describe quantum
mechanical ideas.
And we will often fail to come
up with good words or good
descriptions from what we see
around us in our classical
world as we try to explain
quantum mechanics.
It's not that we don't
understand it.
We just don't have the words
to describe the things that
we're talking about.
There are many other surprising
aspects of quantum mechanics.
And as we start to learn quantum
mechanics, we are
confused when told, as we
often will be, that some
questions simply does
not have an answer.
For example, we might think it
perfectly reasonable to ask
the question, as scientists did
for several centuries, of
whether light is composed
of particles or waves.
It would seem, according to
our common sense, that it
would have to be one
or the other.
But in fact, if we insist on
this either/or answer, that is
that light must be definitely
either a particle or a wave,
than there actually is no
answer to that question.
The only answer we can give to
it is that both of these,
which is the idea of
wave-particle duality, are
simultaneously true.
Another example is we might
think it perfectly reasonable
to ask, what are the position
and the momentum, or more
loosely the speed, of some
particle, such as an electron.
Quantum mechanics will
enigmatically reply to us that
there is actually no answer
to that question.
We can know one or the
other precisely,
but not both at once.
This particular enigma is an
example of Heisenberg's
uncertainty principle.
Indeed, though it may seem
bizarre, in the cases of both
wave-particle duality and
Heisenberg's uncertainty
principle, in the quantum
mechanical view of the world,
there is no contradiction
involved in
either of these concepts.
They are natural phenomena that
lead to no confusions in
quantum mechanics, at least if
we separate them off from
another and much more genuine
difficulty called the
measurement problem, to which
we will return later.
One of our natural human desires
is to find causes and
meanings in the things that
we see round about us.
These are part of the way that
we construct models of reality
that enable us to function
efficiently as human beings.
So as you learn quantum
mechanics, you are likely to
keep wanting to know the meaning
of various terms and
concepts as you work to
construct your revised models
of how things work.
It's common and natural,
therefore, for the student to
ask what something means.
However, I can warn you know
that this is going to be quite
frustrating at first.
These interactions often take
the following form.
The student asks about the
meaning of something in
quantum mechanics, such as the
uncertainty principle or the
wave function or some
other topic.
The professor or instructor
replies with the question,
well, what was it you
wanted to measure?
If you can tell me what you
wanted to measure, we can
figure out how to calculate that
with quantum mechanics.
And the student waits in vain
for the professor to answer
the question about what
something means.
This is also--
and this is quite serious,
incidentally--
called the shut up and
calculate approach.
Despite this, it is a rather
important as a student to at
least try to frame
these questions.
Without to some extent fighting
quantum mechanics and
its ideas, you will
never actually
understand them properly.
The more serious philosophical
version of this approach is to
assert that things that don't
have meaning in science are
the things you can't measure.
Or if you can't measure them,
you don't have meaning.
This philosophical approach of
dealing only with questions
that can be answered by
measurement or that are purely
logical questions within some
formal system of logic, that
approach is what is called
logical positivism.
We regard everything else
as meaningless.
If you can't measure it in the
real physical world, it's
meaningless.
And it is the most common
approach taken in dealing with
quantum mechanics, at least
at the elementary
philosophical level.
And by allowing university
professors to dismiss most
student questions themselves as
meaningless, it saves a lot
of time in teaching
the subject.
Now one very substantial
difficulty with this
philosophical approach is that
it is not clear in quantum
mechanics what measurement
actually is.
Indeed, it can even be proved in
at least one interpretation
of quantum mechanics that you
can't actually make a
measurement in quantum
mechanics.
This whole issue is referred to
as the measurement problem
in quantum mechanics.
And it is important to
understand that the
measurement problem is, in some
people's opinion, really
not satisfactorily resolved.
You need to know that, because
otherwise you may just think
that somehow it is just that
you are not smart enough to
understand it.
And that might cause
you to give up.
Actually, it is not clear if
anyone is smart enough to
understand it, so
join the club.
At least don't worry
that somehow the
problem is with you.
The problem is not with you.
This is a real and arguably
unresolved
problem in quantum mechanics.
If, at this point, you're
raising an objection that
there's an inconsistency in
saying that quantum mechanics
will only answer questions about
things we can measure
but quantum mechanics cannot
actually explain the process
of measurement, you're
quite justified in
raising that objection.
Now what was it you
wanted to measure?
