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Before I give you summary of all quantum mechanics, I’m going to give you a 90
second history of it, so you can get a little background on how quantum mechanics came to be.
So here we go!
Classical mechanics failed to describe how an electron could orbit an atom. An accelerating
charge like that of an electron around a nucleus always creates electromagnetic radiation according to
Maxwell's classical equations. This
means the electron would constantly lose energy and eventually crash into the nucleus.
Niels Bohr solved this problem by hypothesizing that electrons could exist without radiating
energy if they rotated in quantized orbits proportional to Planck’s constant. Louis
de Broglie later showed that if such quantized orbits exist, then electrons must be waves.
Astonishingly, experiments showed that not only electrons but all quantum particles
like photons and even atoms exhibit interference, with no exceptions,
implying everything else must be waves too. Erwin Schrodinger developed an equation to
explain this wavelike behavior. His equation describes how a wave evolves over time.
But the problem is that whenever we detect these quantum objects, we detect them as particles, not
as waves. This presents a conundrum. Experiments like the double slit experiment suggest waves,
but detection appears to indicate particles. So Max Born came up with the idea that we should
interpret the wave determined by the Schrodinger equation as a kind of probability. This allows a
single quantum object to be described as a wave. So we've adopted a wave interpretation of a
particle, which evolves through time according to the Schrödinger equation. And analogous to
a classical wave, it does not have a distinct location. It has only a probability of being found
at any particular location. This location can only be determined once we measure it, not in advance.
That’s your 90 second history. Now if you are intrigued by this and want to
understand this better, and particularly ponder about what it all means, then stay tuned
because that’s coming up right now.
So now that you know a little bit about
the history of quantum mechanics, let me explain what the big deal is.
It would be nice if we could just scale down everything, we know about
our macro world to the quantum world. For example, if the Newtonian mechanics
of a basketball applied to electrons and atoms, there would be no problem.
Everything would be intuitive, and we could relate everything to our everyday experience.
But the universe did not make things so simple for us. Quantum objects such as electrons,
photons and atoms, are not like little basketballs or tiny piece of dust. They are like waves because
they create interference patterns like we see in the double slit experiment.
The Schrodinger Equation was developed to explain how these waves evolve. And it’s quite accurate.
So if we have a rigorous mathematical model to describe these waves,
what’s the big deal, since we know how it works?
The problem is that we only observe particles, or at least particle-like
behavior whenever we detect these quantum objects. This phenomenon can be seen in places like a cloud
chamber and particle accelerators. The subatomic objects seem to behave like particles, not waves.
So to incorporate this into our quantum mechanics theory, the concept of measurement was introduced.
So, you’ll hear physicists say, at least in the most common interpretation of quantum mechanics,
that whenever a measurement is made, the wave collapses and becomes a very localized wave,
which effectively makes it look and behave like a particle.
Measurement means an interaction, and interaction of the quantum object with some kind of measuring
device, more specifically an irreversible exchange of energy somewhere in the measurement process.
This seems nice and clean. But there is a huge problem.
No one can explain how or why this so called “wave collapse” occurs through measurement.
This is called the “measurement problem” in quantum mechanics.
And since all our information comes from a measurement of some kind,
we can never directly see or touch this quantum world.
Everything we observe must go through this measuring process that seems to result in
the conversion of quantum objects into particles like the classical world we are familiar with.
So how this wave evolves according the Schrodinger equation,
while highly accurate in making predictions, is never actually seen.
Like I showed two videos ago, ultimately quantum theory boils down to a theory
of interacting harmonic oscillators combined with a measurement postulate.
But no one can explain how the interactions of the harmonic oscillators are different than the
interaction of the measurement device. If we really want to understand reality, this is a
fundamental problem that we need to resolve. Now, having said all this, let me add,
that not resolving the measurement problem, has not prevented us from predicting and
measuring outcomes from these equations. There is a philosophy called, “just shut
up and calculate” – meaning, don’t worry about what’s really going on. If the bottom line is
that all our equations work, and are highly accurate, that’s all we should care about.
I don’t subscribe to this kind of thinking myself because I think that the purpose of scientists,
particularly physicists is to explain the inner workings of the universe,
not simply create equation that make predictions without a deep understanding.
In classical mechanics, things are concrete, objects have distinct positions and velocities.
In Quantum mechanics, objects have wave-like behavior. They are more specifically described
by wave functions, which are abstract mathematical solutions to the Schrodinger equation.
These waves aren't localized but instead take up all of space.
It isn't until you look for a particle that it becomes what appears to be a particle;
before that, the particle is a collection of probability waves that theoretically
extend out to the entire universe. Now, this has some pretty profound consequences.
One is called the Uncertainty Principle,
which states that you can never simultaneously know exactly where something is, and how fast
it is going. More precisely we cannot know the position and momentum at the same time.
This has to do with the probabilistic nature of quantum mechanics. Let’s do
an example to understand why this is the case.
When we say we can’t know where an electron is because it’s a wave,
what we mean by wave is the wavefunction from the Schrodinger equation.
And this related to the probability of finding the electron at any point
in space. But a perfect sinewave for the electron spreads that probability
throughout all of space, so the "position" of the electron is completely uncertain.
But a perfect sine wave means we know the wavelength, so we would know its
momentum quite precisely because of the deBroglie relation where momentum equals
Planck’s constant over the wavelength. p = h/ lambda. So in this case we have an
infinite uncertainty in position, but no uncertainty in momentum.
On the other hand, if we want to know the position of the electron precisely,
we would need to add many waves of different wavelengths so that we
can get an interference pattern, such that we can get a more localized wave.
This localized wave would give us a more precise location, but now we have no idea what the
momentum is. This is because all the waves that are needed to create the localization, being that
they are of different wavelenths have different momentums using the same deBroglie relation.
So either we know the position very precisely or the momentum precisely, but not both.
What’s important to understand is that this not a limit of our measuring equipment. it’s
that exact answers to both the momentum and position of a quantum object do
not exist in the universe at the same time. The universe itself doesn’t know the answer.
This is hard to accept and goes completely against our everyday experience.
So you have to ask, why don’t we see this wave behavior in macro objects like a basketball,
or tennis ball, or even a tiny particle of dust? Well, I’ll let you in on a little secret,
dust particles, tennis balls and basketballs do propagate as waves,
just like electrons. In fact, everything does!
And their wavelengths can be calculated just like a photon or electron’s using de Broglie’s
formula, wavelength equals Planck’s constant divided by momentum. But for large objects,
the momentum is so much bigger than the Planck's constant, that their wavelengths
are an undetectable fraction
of their physical size — so we can never notice their quantum mechanical properties.
For example, the wavelength of something the size of a tennis ball moving 10 meters/second,
is 10^-33 m. This is less than the width of a proton. So we would never notice it.
A second consequence of wave-like behavior
is nonlocality. A wave exists over multiple regions of space.
This nonlocality explains interference, but it
also means that Waves can add together to give complex interference patterns.
So waves of multiple particles can add together to give a single
wavefunction corresponding to multiple particles. This gives rise to a strange
correlations between such particles, in a phenomenon called “Entanglement.”
Einstein called this, “Spooky action at a distance” because it appears to
indicate instant communication between distant objects at faster than the speed of light,
which is forbidden by Relativity theory.
But while two or more objects are correlated, no communication is actually happening. Correlation
does not mean communication. The wave behavior of electrons also means that the concept of
circular orbits of electrons around the nucleus of atoms, that you commonly
see everywhere when an atom is depicted, is wrong.
A better picture is that they exist in a well-defined probability cloud
around the nucleus that might look more like this.
The main point is that the Universe is quantized. Familiar quantities such as energy,
momentum, electric charge, mass and possibly even
time and space – are not continuous. They occur in discrete quantum units.
So for example, the state of an electron is quantized. By state,
I mean its energy, angular momentum and other properties.
So an electron in a state of 3.4 eV of energy that moves to 13.6 eV of energy, does not pass through
any intervening energy values. It just disappears from the old state and reappears in the new one.
It never exists between these two states. This is how an electron
moves from a lower energy shell of an atom to a higher energy shell.
This quantization is not directly observable in our daily experience
because the intervals between the units are too small for us to notice. It isn’t
that quantum mechanics only exists at small scales. Quantum mechanics is all there is.
It is everything. Newtonian mechanics or the physics of our macro scales just happens to
be a good approximation of the underlying more fundamental quantum mechanical universe.
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