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There was a time when everything that happened was seen as random, or a seeming miracle,
sometimes attributed to the unseen hand of a divine being.
Then Greek and other ancient civilizations began to explore rationality and logic to
explain how the universe works.
A paradigm shift came through the likes of Galileo and Newton and the introduction of
classical mechanics.
The universe was then viewed as a kind of cosmic clock ticking with mathematical precision,
where almost every movement and phenomenon could be explained and predicted through observations
and equations.
In the early 20th century, this view of a mechanical, deterministic, and predictable
universe was shattered with the advent of Relativity and quantum mechanics.
Time was no longer set in stone, and the precise location of particles was no longer measurable.
Einstein, Planck, Bohr and Schrodinger led this new paradigm shift.
This might seem like the end of the story, but there has been one additional more recent
paradigm-shifting development in physics that perhaps did not receive as much fanfare.
But it is undoubtedly equally profound.
And that is how quantum mechanics was supplemented, and made more complete by quantum field theory,
or QFT.
It is the basis of the best theory we have in physics today to explain nearly everything,
called the Standard Model of particle physics.
What is Quantum Field theory?
Why is it necessary?
How is it different than quantum mechanics?
That’s coming up right now…
Classical mechanics has been, and continues to be used to explain many phenomena that
we can observe.
Consider a planet orbiting a star.
We can use Newton’s laws to model it fairly accurately.
If the planet were to somehow lose its kinetic energy or slow down, it would spiral into
the star and collide.
Now consider something conceptually similar, an electron orbiting the proton of a hydrogen
atom.
In this case, we could again try to use Newton's laws to model it.
Instead of the attractive force of gravity for the star and planet, the two objects’
electrical charges keep it bound together.
This is where classical mechanics fails because, as we know from Maxwell’s laws, an accelerating
charge creates electromagnetic radiation.
And the constantly changing direction of the electron creates an acceleration.
This means the electron would constantly give off photons, losing energy in the process.
It would thus spiral towards the nucleus and collide.
But we know that no such thing actually happens in reality.
Atoms are stable.
An electron does not crash into the nucleus.
Why?
...because we were using the wrong tool to describe the model of an atom - Classical
mechanics.
We have to use a new tool – quantum mechanics.
Niels Bohr proposed that the electron maintains a stable orbit because its energy is quantized.
It can only be in an orbit that is an integer multiple of a minimal quanta.
And its lowest energy state is the lowest orbit that the electron can have.
It cannot be lower.
This minimal quanta, by the way, is proportional to Planck’s constant.
In Newtonian physics we think of objects as discrete particles having very specific and
measurable properties, such as a mass x, momentum y, and position z.
In quantum mechanics, our objects are wavefunctions described by some completely different mathematics.
This is as shown by the Schrodinger equation, which is perhaps the most important equation
in quantum mechanics.
Here, the location of a particle is unknown until the moment of measurement.
We cannot know where it is beforehand.
We can only know the probability of finding it at any specific location.
Prior to measurement, the wave function depicts a kind of smearing out of its location.
Thus, in the quantum mechanical model of the hydrogen atom, the electron is not spinning
around the nucleus like a planet around a star.
It’s in some unknown location at some unknown distance from the nucleus.
All we know is that the chance of finding the electron at any specific location or distance
from the nucleus has a probability associated with it.
And we cannot determine the location in advance of measuring it.
So the better model of the atom is like a cloud around a fuzzy nucleus.
The white cloud represents the probability cloud of the location of the electron.
Note that the nucleus too would be fuzzy as well, since it is also a quantum object.
But its cloud would be more localized than the electron’s.
Now, you might think this is a great model.
I know everything now.
We can stop here.
But we can’t because quantum mechanics has some problems too.
There are some things it also cannot explain, and we get the wrong results,
just like when we tried to explain the electron’s orbit with the classical formulation.
First of all, quantum mechanics is not relativistic.
That is, it will give you wrong results if the quantum object is moving close the
speed of light.
Schrödinger’s equation simply doesn’t obey Einstein’s theory of special relativity.
The practical result of this is that as it doesn’t incorporate a speed limit, the speed
of light, needed to make causality work.
For example, it allows for two measurements to influence each other faster than light.
This would mean that there would be some reference frame in which the future could influence
the past, breaking causality.
A second problem with quantum mechanics is that it only tells you how a particle evolves
over time, this is, how it goes about its business.
It does not tell you how it is created or annihilated.
So it can’t account for things like beta decay, due to the weak nuclear force, where
a neutron transforms into a proton, an electron and an antineutrino.
In this case quantum mechanics breaks down because it doesn’t work if we change the
number of particles.
In the case of the Beta decay I just described, the down quark of a neutron decays to an up
quark changing the neutron to a proton, and at the same time, emits an electron and an
antineutrino via a mediating W boson.
This change to other particles can’t be described by quantum mechanics.
This is where quantum field theory explains things that quantum mechanics cannot explain
on its own.
So what is quantum field theory?
Well, it’s a mathematical framework that combines classical field theory (a classical
field would be like a magnetic field as described by James Clerk Maxwell), special relativity,
and quantum mechanics.
There is a field for every particle of the standard model.
So in our beta decay example, there would be field for the down quark, the W boson,
the up quark, the electron, and the antineutrino.
All of these fields extend out in all of spacetime.
In other words, the fields are always there and exist everywhere including inside your
body.
Although they exist everywhere and you can’t see them, they are not nothing.
They are teeming with virtual particles.
These are particle-antiparticle pairs that get created and destroyed.
So for example, the down quark field will always have some spontaneous creation of down
quarks and anti-down quarks, which get created an annihilated almost instantly.
They come in and out of existence constantly.
These virtual particles can’t be measured but nature allows the creation of these virtual
particles by letting them borrow energy from the vacuum, as long as the energy is put right
back into the vacuum.
This happens so quickly that it’s as if nature doesn’t register them as real measurable
particles.
We can visualize these fields as a kind of ocean.
Just like the ocean always has some turbulence, the fields always have a kind of turbulence
even in their ground state of minimal energy.
This turbulence is due to virtual particle creation and annihilation I just described.
In these turbulent seas, if there is enough energy, a larger wave can be created which
CAN be measured.
These are the real particles.
So in the up quark field for example, an up quark will be created if there is energy of
2.3 Mega electron volts (or MeV), which is the mass of one Up quark.
Two Up quarks will be created if there is energy of 4.6 MeV.
So a particle is nothing more than an excitation in this field.
These excitations are quantized not continuous.
So the fields can only create particles in integer increments.
They cannot for example have one and a half up quarks, only two quarks or three quarks etc.
Energy can be transferred between two fields via a mediating boson field.
This is considered an interaction or a force.
Matter particles can’t interact on their own without a mediating boson.
So while in quantum mechanics there is no way for the neutron to split its energy into 3
different particles – a proton, electron and an antineutrino, in quantum field theory
this can be done via energy exchange between the fields.
You start with the fields of all the different particles, which are always there, and you
finish with the fields of the same particles.
Some of them just have more or less energy, after the exchanges of the energies, depending on the interaction.
So in our beta decay example, you start with the down quark field.
This field transfers its energy to the up quark field and the W boson field.
The W boson field then transfers its energy, almost immediately to the electron field and the neutrino field.
So we started with one particle in the down quark field and we ended up with three particles
simply by the fields exchanging energy.
Note that although the number of particles changed, the total energy is always conserved.
If you add up all the masses and kinetic energies at the beginning, they will equal all the
masses and kinetic energy at the end.
In other words, the energy of the fields is the same before and after the energy exchange.
So by having quantum fields we can mathematically account for and model creation and annihilation
of particles, as well as the mechanism of force exchange.
The icing on the cake is that the theory is fully relativistic, and free of causality
violations.
But even this modification of quantum mechanics is not perfect.
For example, it is still missing gravity.
We do not have a quantum field theory for gravity.
If we did, it would mean that we could model a field for the theoretical graviton particles,
and gravity would be mediated between matter particles by the exchange of this graviton
boson.
So even QFT which is extremely accurate for the forces and particles we do know about
in the standard model, remains as yet incomplete.
The fact that we don’t have this tells us something.
It reminds me of the saying that when you have a hammer as your tool, everything looks
like a nail.
Our tool is QFT.
So far everything we know has been a nail.
Either gravity is not a nail, or maybe we just don’t really know how to use the hammer.
But still in my view, QFT is probably the most beautiful theory in science.
And here’s why: because it tells us is that the universe and
everything in it, including us and all living things, the whole planet, every star, every
galaxy, and even things outside the visible universe are all connected.
Everything, even our thoughts, dreams and ideas are composed of excitations in the same
quantum fields.
And these fields extend to not only all of space, but all of time.
The universe is made of the same basic stuff, and we are all simply a series of excitations
in it.
So when someone says we are all one, or that we are all connected to the universe, this
is not just a fanciful idea, but has a real physical meaning.
I find this to be beautiful.
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I will see you in the next video my friend.