Now, at this point, you may be
feeling overwhelmed by all
these strange ideas and be about
to give up in despair.
How can anyone ever understand
such a bizarre theory?
And if you can't understand
it, how can you even think
about using it?
Here is the good news.
Whether we think we understand
quantum mechanics, and whether
there is yet more to discover
about how it works, quantum
mechanics is actually
surprisingly
straightforward to use.
The rules and the approaches for
using quantum mechanics in
a broad range of practical
problems and engineering
designs are relatively
straightforward.
We use the same mathematical
techniques that most
engineering and science students
will already have
mastered to deal with
the classical world.
And because of a particular
elegance in the mathematics of
quantum mechanics, namely, that
it is based entirely on
linear algebra, quantum
mechanical calculations can
actually be easier than those
in many other fields.
The main difficulty that the
beginning student has with
quantum mechanics lies in
knowing which of our classical
notions of the world have to
be discarded, and what new
notions we have to use
to replace them.
Indeed, it is this aspect that
makes it very difficult to
teach yourself quantum
mechanics.
Because such basic conceptual
shifts are required, you
simply can't pick up quantum
mechanics just from
encountering bits and
pieces of it as
techniques here and there.
You really need to take a course
that forces you through
a fairly complete development
of the subject's concepts.
As you do this, you should
expect to spend some time in
disbelief and conflict with what
is being asserted to you
in quantum mechanics.
That is entirely normal.
In fact, a good fight with those
propositions is probably
psychologically necessary
if you're ever get
on top of the subject.
Incidentally, I should say that
the associated teaching
technique of breaking down
the students' beliefs and
replacing them with the
professor's "correct" answers
has a lot in common
with brainwashing.
And, as we mentioned above,
there is a key point that
simplifies all the absurdities
and apparent contradictions.
Provided we only ask questions
about quantities that can be
measured, there are no remaining
physical problems
that need worry us--
philosophical problems.
At least, none that would
prevent us from calculating
anything we could measure.
As we use quantum mechanical
principles in tangible
everyday applications, such as
electronic or optical devices
and systems, the apparently
bizarre aspects of quantum
mechanics simply become
commonplace and routine.
You may soon stop worrying
about quantum mechanical
tunneling and Heisenberg's
uncertainty principle.
Perhaps in the foreseeable
future, such a routine
comprehension and acceptance
might also extend to concepts
such as non-locality and
entanglement as we start using
those more in practical
situations, for example, in
sending secure information.
For any of us, understanding
quantum mechanics marks a
qualitative change in
our view of how the
world actually works.
That understanding gives us the
opportunity to apply this
knowledge in ways that others
cannot begin to comprehend.
Whether your goal is basic
understanding or practical
exploitation, learning quantum
mechanics is, in my opinion,
at least, certainly one of the
most fascinating things you
can do with your brain.
