What is quantum mechanics explained
You are currently facing one of the most important equations of all time.
It is called the Schrödinger wave equation. Let me explain why it is so beautiful.
First of all, as you can see, it is really simple.
Usually, in the Physics world, simple and elegant
formulas are the most important ones. Even Einstein had this strong belief:
that the world and the universe could have been described by means of some...cute
formulas. A well-built theory is usually visually good in terms of equations.
As Einstein himself said: “It can scarcely be denied
that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as
possible without having to surrender the adequate representation of a single datum of experience.”
Just think about it. It's like when you want to express your emotions.
Sometimes you don't think too much about them, your words come out of your mouth and you produce
a messy cascade of words. Your interlocutor can still understand what you are saying, but it
is kinda difficult to follow your thoughts. But if you write your thoughts on paper, you
will probably find a better way to express them. A more efficient and concise way. This also holds
for physics theories. We could have good ones, but some of them are just more elegant than others.
Of course, this is a hard job, and our scientific inability to simplify
is something we should always accept.
But besides its formal beauty, the Schrödinger equation tells us something more.
It is the starting point for the understanding of quantum mechanics. What is it?
Follow me in this video: I will explain it to you, keeping it simple.
I could start and end this video by saying that quantum mechanics is the study of very small
things, but you would be very disappointed then. So I will try to tell you something more.
First of all, for “very small things” we mean we are interested in stuff that exists in the
real world, but has atomic-scale dimensions. We are talking about atoms and subatomic particles.
So we can say quantum mechanics deals with the atomic and subatomic world.
And if you take a lot of particles, you have the macroscopic world.
The macroscopic one, is the world you, me, we are used to.
In everyday life, we have to deal with macroscopic objects.
Your Moka is a macroscopic object. However, it is made of atomic and subatomic particles.
Now. The macroscopic
world is well described by Classical Physics, for example, Newton gave us some laws that fit well
what we observe in the everyday life. Classical physics can help us understand
why the Earth orbits around the sun, why do we have seasons, how planes fly and much more.
So it is really useful. But at a certain point,
at the end of the 19th and the beginning of the 20th century,
scientists realized that something was missing. When they decided to study the atomic and
subatomic world, they found classical physics didn't work anymore.
They needed another approach. This was a huge issue, a problem that needed to
be solved. In fact, Physics is no more physics if it can't describe reality.
The desire to resolve inconsistencies between observed phenomena and classical theory
led to two major revolutions in physics that created a shift in the original
scientific paradigm: the theory of relativity and the development of quantum mechanics.
The most important result is that light behaves in some aspects like particles,
and in others like waves. I know what you're thinking: no way!
And that's pretty the same thing physicians were
thinking when they first approached the undiscovered world of quantum mechanics.
Let me explain it better. Matter, the “stuff” of the universe,
consists of particles such as electrons and atoms. But it also exhibits wavelike behaviour.
This phenomenon has been verified not only for elementary particles but
also for compound particles like atoms and even molecules. For macroscopic particles,
because of their extremely short wavelengths, wave properties usually cannot be detected.
Although the use of wave-particle duality has worked well in physics,
the meaning or interpretation has not been satisfactorily resolved. Bohr called it the
"duality paradox" and regarded it as a fundamental or metaphysical fact of nature. A given kind
of quantum object will exhibit sometimes wave, sometimes a particle, character, in respectively
different physical settings. He saw such duality as one aspect of the concept of complementarity.
Talking about this wave-particle duality, Einstein said:
“It seems as though we must use sometimes the one theory and sometimes the other, while at times we
may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of
reality; separately neither of them fully explains the phenomena of light, but together they do.”
One of the most famous experiments that allowed scientists to understand the dual
nature of matter was the double-slit experiment. It demonstrates, with unparalleled strangeness,
that little particles of matter have something of a wave about them,
and suggests that the very act of observing a particle has a dramatic effect on its behaviour.
To start off, imagine a wall with two slits in it. Imagine throwing tennis balls at the wall. Some
will bounce off the wall, but some will travel through the slits. If there's another wall behind
the first, the tennis balls that have travelled through the slits will hit it. If you mark all the
spots where a ball has hit the second wall, what do you expect to see? That's right. Two strips
of marks roughly the same shape as the slits. In the image below, the first wall is shown
from the top, and the second wall is shown from the front.
Now imagine a light at a wall with two slits. As the wave passes through both
slits, it essentially splits into two new waves, each spreading out from the slits.
These two waves interact with each other, and they are said to interfere with each other.
The interference could be disruptive or constructive, and in the first case,
they will cancel each other out. I the second case, they will reinforce each other,
giving spots with the brightest lights. So when the light meets a second wall placed
behind the first, you will see a stripy pattern, called an interference pattern.
Now, if you do the same thing with a beam of electrons, you would expect to see
two rectangular strips on the second wall, as with the tennis balls,
because they are particles. But what you actually see is that
the spots where electrons hit replicate the interference pattern from a wave.
As you can see, this experiment suggests that what we call "particles", such as electrons,
somehow combine characteristics of particles and characteristics of waves.
And this is the real essence of the quantum world.
Basically, everything can be described or associated with a so-called wave function.
In physics, we usually indicate a wave function by means of the Greek letter “psi”:
ψ
And if you remember, the psi function appears in Schrödinger's equation.
In quantum mechanics, the Schrödinger equation is a fundamental equation that determines the
temporal evolution of the state of a system, for example of a particle, an atom or a molecule.
When it comes to quantum mechanics, intuition is no more present.
For example, if you hold a ball you will notice it has some mass because of its weight.
You can feel its weight, and if you take something heavier you will notice. It is just something
very intuitive, and the Classical Physics world is built upon this kind of intuition.
However, when it comes to quantum physics, things get more complex, and we soon realize
we can't predict exactly what is going to happen to the motion of a ball, for example.
Or we can't really tell, for example, if a cat is black or white. One has to imagine reality as a
set of possible configurations, and you don't know a priori which configuration is going to
be chosen. We can tell that there is a certain probability associated with each configuration.
Only when we make measurements, we can see the chosen configuration,
which we call state. Let's go back to the cat. Let's suppose you want to pet him.
We have a cat, but we don't know if it is black or white or whatever colour.
Quantum mechanics essentially states that the only way for us to know which colour the cat is,
is to “measure” it, and we do so by applying some mathematical objects to the “state” of the cat,
which is called “operators”: you have a wave function, a state (which in this case is the
colour of the cat), you apply an operator, you get the result: black, white or whatever.
If you repeat the experiment a high number of times, you will end up with a
distribution probability of colours, and this distribution will have a peak on one colour,
and that will indeed be the colour of the cat you are want to pet.
One of the requirements of quantum mechanics is of course the description of macroscopic reality.
In the “big number of atoms” limit, quantum mechanics should reproduce the macroscopic world.
That is, putting in the crassest possible terms, if you see the cat is white, quantum
operators applied to the colour configuration should mainly give the “white” result.
Many aspects of quantum mechanics are counterintuitive and can seem paradoxical
because they describe behaviour quite different from that seen at larger scales.
Do you know what quantum physicists Richard Feynman said about quantum physics?
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Feynman said quantum physics deals with "nature as she is – absurd".
For example, the uncertainty principle of quantum mechanics means that the more closely one pins
down one measurement (such as the position of a particle), the less accurate another
complementary measurement pertaining to the same particle (such as its speed) must become.
If you know very well the position of a particle,
you will lose a lot of information about its speed.
And vice-versa, you know very well the velocity of a particle, you will keep losing track of it.
Another example is entanglement, in which a measurement of any two-valued state of a particle
(such as light polarized up or down) made on either of two "entangled" particles
that are very far apart causes a subsequent measurement on the other particle to always
be the other of the two values (such as polarized in the opposite direction).
Quantum mechanics teaches us an important thing about nature:
its description is essentially probabilistic. Before quantum mechanics, we were used to thinking
that the world is governed by some given laws that give precise results. You act, you get
precise results, and every action is followed by a reaction that seems to be predictable.
Instead, nature doesn't work like that. The probability of an event—for example,
where on the screen a particle shows up in the double-slit experiment—is
related to the square of the absolute value of the amplitude of its wave function.
We can just say, for example, that we have an 80% of chance that we'll find the particle in
a given position interval, but we will know where it is only when we will measure it.
Another important thing quantum mechanics tells us is that is not
possible to know the values of all of the properties of a system at the same time.
This is of course due to the uncertainty principle we discussed before.
Last but not least, we know that quantum mechanics is a good theory because,
even if it studies the “very small things”,
it closely approximates the classical description of nature in the case of large systems.
Well, I guess that's all for today.
"This video ends here! Thanks for watching everyone! Do you like quantum mechanics?
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