Arguably the scientific revolution began in 1514 with Copernicus who rejected the complexity
of ancient astronomy that insisted in placing the earth at the center of the universe.
He instead put it in its proper place, as revolving around the sun. This changed our
view of the universe as a kind of machine that followed precise laws, and that had order.
And if these laws were understood properly, motions and events could be predictable. This
was the foundation of scientific thought for centuries.
However, early in the 20th century, this idea of a predictable universe was turned on its
head. You might say this was the 2nd scientific revolution.
It is a revolution we are still coming to terms with. It is the idea that at its core,
the universe is a quantum universe, that it is made up of discreet bits of mass and energy,
that we call particles, that are interacting via quantized fields mediated by other particles.
The remarkable thing is that these bits of mass and energy are so small that we can’t directly
see them, only detect them using advanced instruments. And some like quarks are not
even directly detectable, so the question is how do we really know that they’re even
there? What makes us so sure? What led us to the
idea that the universe must be quantized? And what would happen if the universe was not
quantized? Join me as we try to answer those questions, coming up right now…
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Classical mechanics championed by Isaac Newton around 1665 had solved the problem of the
solar system, and reduced nearly all mechanical phenomena in the heavens and earth to a single
powerful equation: F=MA. Later, classical physics appeared to culminate
in the discovery by James Clerk Maxwell that a changing electric flux would produce a magnetic
field. So by the end of the 19th century, the combined theories of mechanics by Newton
and electromagnetism by Maxwell, seemed to explain so many phenomena, that some were
even ready to declare that pretty much anything that we could ever learn from physics had
more or less already been learned. This was a classical world. Classical physics
is continuous. This means you can always keep dividing things into smaller pieces.
Pour yourself a glass of water. Then pour half of that into two smaller cups. Now split
the water of these two cups into 4 cups. And continue. You can keep doing this in the classical
picture. There is no limit. The concept of continuity might seem obviously
wrong today, but back then this was thought to be how things worked. The concepts of particles
like photons existed, but these particles could have any continuous amount of energy.
Today we of course know that water is made from molecules, and eventually you will end
up with just one molecule which you can’t split any further without changing its essential
properties. Scientists soon realized that classical physics
had some major flaws because certain phenomena could not be explained.
For example, the color of a hot glowing body had to be explained. Why you ask?
As we know, every object emits some radiation. If you go into a room and turn off the light
it will be completely dark. But if I had an infrared camera, I could still see you in
the camera, as your body will be emitting infrared light, or heat according to your
temperature. Objects that are much hotter start emitting the more energetic visible
light. A good example would be if you heat up a piece of metal up to a really high temperature.
First it will become red, then yellow and eventually white as it can send out any color
of visible light. In 1900 two scientist, Lord Rayleigh and
James Jeans had used experimental data to come up with a law for how black bodies emit
electromagnetic radiation. The problem was that according to their theory
a black body will send out energy in any frequency range allowed by the temperature. And the
hotter the object, the more frequencies become available, and the more energy would be emitted.
This classical theory works fine for black body radiation at frequencies below the UV
range, but for more energetic black body radiation in the UV range and beyond, the theory completely
collapses, because according to this theory, very hot objects should instantaneously radiate
away all their energy until they reache their minimum energy - around absolute zero. This
is clearly not what happens! This is why it is called the ultra-violet
catastrophe. If you have a black body and sum the total
amount of radiated energy, according to their formula, you find that the black body can release and arbitrary amount
of energy. This would in principle cause matter to radiate away all its energy.
The solution to this problem marked the end of the classical world and the beginning of
the quantum world. This solution was actually already there when this ultraviolet catastrophe
was coming to light because around the same time in 1900, Max Planck had come up with
an equation to explain black body radiation. He had made the assumption, which seemed strange
at the time, to treat electromagnetic radiation as being quantized.
Thus, it was not continuous energy that matter released, but discrete quanta of energy, and
thus the emission of radiation was limited to quanta of energy, proportional to a constant.
This idea materialized as Planck’s famous equation E=hf, where the quanta of energy,
E, is equal to the frequency f times Planck’s constant. The introduction of this constant
introduced a minimal discreet increment of energy. So energy couldn’t be just any value,
it had to be an integer multiple of Planck’s constant. In the classical case, there would
be a lot more energy radiated because the energies could be any value, not bound by
integer multiples of Planck’s constant. This dispatched physics straight from the
classical world to the quantum world. And in this world only specific discrete values
of things like energy, momentum, spin etc. were allowed. And consequently you will find
Planck’s constant in about all quantum equations today. His constant, h, is the symbol of this
quantization. Another phenomenon that only quantum mechanics
could explain was why an electron does not lose all its energy when orbiting a nucleus.
In 1911, when Ernest Rutherford came up with the model of an atom as being electrons orbiting
around a central nucleus, there was a big problem. If electrons orbit around the nucleus,
then their circular motion means that they are constantly accelerating, since acceleration
is any change in either speed or direction. An orbiting electron would be constantly changing
direction, and so accelerating. The problem with an accelerating electron
is that according the Maxwell’s laws, the changing electric field means that it must
be emitting photons. And if it emits photons, it must be losing energy. This would mean
that the electron would continuously lose its orbital energy, and eventually hit the
nucleus. But that’s not what happens because atoms
exist. And they are usually stable. So what’s going on? Niels Bohr came up with part of
the answer. Only special orbits are allowed around the nucleus where the angular momentum
of the electron is a whole number multiple of Planck’s constant over two pi. So electrons
are in fixed orbits according to their energy states. Light is only emitted or absorbed
when electrons jump from one orbit to another. This is significant because it means that
atoms as we understand them cannot form in classical physics. The orbits of electrons
have to be quantized or they will not exist. Similarly, matter beyond a certain temperature
would radiate away all its energy due to the ultraviolet catastrophe.
Now to fully grasp our quantized world, it isn’t actually enough just to consider objects
as being quantized. This was what we initially did, and this is the basis of the famous Schrodinger
equation. The problem is that around the same time as
Max Planck and the other pioneers of quantum mechanics were rewriting the physics books,
a certain scientist by the name of Albert Einstein also decided to join in the destruction
of the classical world. His theory of special relativity and later
general relativity also completely changed the way we think of the world, but in a slightly
different way. You can watch my videos on Special and general relativity, but for this
discussion, the problem related to quantum mechanics comes down to the fact that Einstein’s
brilliant new theory contained a statement along the lines of “The laws of physics
are the same for any speed at which you are moving.” Thus, no matter if you move a 10,
100 or one million km/h the physics you experience should be the same.
The problem here is, that the first formulation of quantum mechanics does not take into account
the speed of movement. Now, this becomes a problem if you work with things moving close
to the speed of light, because then things start to get inaccurate. So, we have to do
the quantization of our world a bit better to fix this issue.
The problem can be understood simply by looking at the Schrödinger equation. Einstein’s
theory of special relativity tells us that we must treat space and time equally to form
a theory compatible with the spacetime of relativity.
If we look at the Schrödinger equation, we see that the space component is second order,
the squared part, but the time component is first order. This equation explicitly doesn’t
treat space and time equally! It was only a few years later that Paul Dirac
managed to fix this issue, and in his equation both the space part and time part are first
order, so they satisfy relativity. The equation he came up with was the famous Dirac equation,
which was the first quantum field theory equation of motion.
Note that it wasn’t the first quantum mechanical equation to satisfy relativity, but It is
arguably the most important. This led to the so called second quantization.
In practice what these equations do is instead of quantizing objects, they quantize fields.
And this gave rise to quantum field theory, or QFT. And It was a new quantum theory that
incorporated the idea of quantization while respecting Einstein’s requirements from
relativity. In QFT, particles are treated as quantizations of fields. This allows us to
treat space and time equally. And it is still today the best understanding of physics. I
have a video on QFT, if you want to learn more about it.
Note that quantum mechanics including the Schrodinger equation is still highly useful.
It just has limits to its area of application at high velocities. It’s just like we still
use Newtonian physics to calculate many things. It only has limits close to the speed of light
or under high gravitational influence. Another big departure from classical mechanics
is the idea of probabilities. The Schrodinger equation has something called a wave function.
The wave function of a particle is related to the probability of finding the particle
in a given location if you were to measure it. Prior to measurement, we cannot know in
advance where it will be. So the outcome is not deterministic, only
the probabilities of the alternative possible outcomes are. This lack of determinism is
a complete departure from classical physics, where if you know all the forces acting on
a particle, you could predict its path. You might say well this is the same thing
as statistical thermodynamics where statistics are used to describe the motions of molecules
in a gas. But in that field it was just from convenience. Theoretically, the path of every
molecule could be determined. It was just not practical. But quantum mechanics is fundamentally
different. The positions of particles cannot be determined precisely or predicted in advance.
In this sense, the future of the universe is not predetermined in quantum mechanics.
The world and the universe would be very different if it was not quantized. It would be a deterministic
world where, theoretically the future would be predictable. But the world would not exist
as we know it because, atoms could not form. And if that’s the case, then we would have
nothing but quantum particles. But if quantum mechanics doesn’t exist,
then what would we really have? There would be nothing. Since general relativity is not
quantum mechanical, you could in principle have a spacetime where quantum mechanics doesn’t
exist. But this spacetime would be completely empty. There would be no matter, no radiation,
and no energy. So there may be a universe where quantum mechanics doesn’t exist. But
that universe would consist of nothing. And if you have a question, leave it in the
comments because I try to look at all of them. I will see you in the next video my friend.