Is the cat alive? Is it dead? I bet you know what we are talking about:
it’s probably one of the most famous cats in the world! Indeed, we are talking about Schrödinger’s
cat. This is a famous paradox that tries to illustrate how weird the microscopic world is, by
applying concepts of quantum mechanics to everyday life… and the consequences are very bizarre!
Do you want to know more about this? Watch this video and I will tell you!
Before talking about Schrödinger’s cat, let’s introduce briefly its ‘owner’ first. Erwin
Schrödinger was an Austrian physicist born in 1887. He provided several important contributions
in many fields of physics, such as statistical mechanics, cosmology, and thermodynamics. However,
his most notable results were probably those related to quantum mechanics.
Quantum mechanics is a branch of physics that tries to explain the behaviour of particles
at microscopic level. We may think that atoms and elementary particles act by following laws
similar to those that we observe in the macroscopic world. Well… not even close!
In fact, the microscopic world is quite bizarre: atoms and particles do not behave as we would
expect. There are, indeed, several weird phenomena that characterize the quantum world.
To show how strange these phenomena can be, Schrödinger ideated his famous paradox of the cat.
Let’s see what this is about. Here is the paradox.
Let’s imagine to have a cat and to put is inside a steel chamber. In the same chamber,
there is also a tiny amount of a radioactive substance. In a radioactive substance, each atom
has a certain probability of decaying: this means a certain atom may decay, but may also do not.
The amount of substance in the chamber is tuned such that there is a 50 % probability that one
atom will decay over a time interval of one hour, and a 50 % of probability that no atom will decay.
Furthermore, there is also a Geiger-Muller counter inside the chamber. A Geiger-Muller counter
(also known as GM tube) is an instrument used to detect particles emitted by a radioactive decay.
In this case, if the atom in the substance decays, a particle will be detected by this
Geiger-Muller counter. But it’s not over. This detector is also connected to a small hammer:
if the Geiger-Muller counter detects a particle emitted as a result of a radioactive decay,
the hammer will be released and will shatter a flask containing
hydrocyanic acid: a deadly poison that, eventually, will kill the cat.
To summarize: if an atom in the radioactive substance decays, the acid in the flask will
be released, and the poor cat will die. If no atom in the radioactive substance decay, the acid will
remain inside the flask, and the cat will survive. So far, nothing strange. However,
a weird situation occurs if we try to apply the laws of quantum mechanics to this situation.
In fact, according to quantum mechanics, the atom in the radioactive substance is
at the same time in two different states: decayed and non-decayed (we will see this
in more detail later). What are the implications of this fact? It may sound totally non-sense,
but this means that the cat is also in two different states: dead and alive at the same time!
And what is even more weird is, this is true only until the chamber is sealed and nobody is
“observing” the cat. The moment somebody opens the chamber and looks inside… the
cat will be instantly either dead or alive! Ok, all of this probably sounds non-sense,
I agree. But in order to understand this paradox and why it leads to these weird conclusions,
we need to explain a bit more how the quantum world works. Let’s take a step back.
The first thing we need to understand is the concept of “wave function”.
In the macroscopic world, any physical quantity of a certain object is well-defined.
For example, if I throw a ball to you, we can use kinematic equations to describe exactly the
position of the ball is at any instant of time. And we can also use equations to calculate the
velocity of the ball. Thus, in the macroscopic world, physical quantities of a certain object
are perfectly defined and can be calculated, provided that we know the initial conditions.
In the quantum world, things are different. The reason for this is that a particle
has a dual behaviour in the microscopic world: it behaves both as a particle and… as a wave.
Let’s take, for instance, an electron moving inside a box. In classical physics, the electron
would have a well-defined trajectory inside the box. But this picture does not represent reality.
In reality, the electron behaves as a wave, so it doesn’t have a well-defined position.
On the contrary, it is “spread” over a certain portion of space: we can imagine, somehow,
that the electron is simultaneously present in all the positions inside that region.
This may sound quite disturbing, but it’s something real in the quantum world.
Mathematically, the position of the electron (or of any particle) is describe by the so-called
“wave function”. The form of this function can be quite complicate; however, what we actually
care about here is its meaning. The wave function allows to calculate the “probability of finding
the electron at a certain point in space”. This probability is a number between 0 and 1:
so there will be regions inside the box where this number is, for instance, 0.5 (which means
50% of probability of finding the electron there), or other regions where is 0.1 (which means, 10% of
chances to find the electron there), and so on. Another concept we have to understand is the
following. Before any interaction with the surroundings occurs, the electron has no clear
position, because all the positions where the wave function has a probability greater than zero are
possible. The particle doesn’t have a definite position yet: it’s like it exists simultaneously
in every point of the allowed region of space. However, the moment we “observe” it,
we force the system (in this case, the electron in the box) to interact with the surroundings.
As a result, the electron will instantly assume a well-defined position (within the “region
of possibility”), according to the probability described by the wave function. This phenomenon
is known as “wave function collapse”: at the moment of the observation, the wave function
instantly takes a value of 1 (which means 100 % probability) at a certain location, and a value
of zero everywhere else. It’s like the electron instantly “appears” at a well-definite location.
But how is all of this connected to the Schrödinger’s cat?
So, we have seen how particles behave in the microscopic world: they behave like a wave,
and therefore they don’t have a clear position in space, until they interact with the external
world (for example, when we “observe” them). At that moment, their wave function collapses,
and they take a well-define position. This behaviour is valid not only for
the position of a particle, but for other physical quantities as well. Another example is the spin of
an electron. It is not easy to explain what is the spin of a particle according to quantum mechanics,
but we can think it as a quantity describing the direction of rotation.
Imagine every particle is rotating around its axis: in this simplified model,
the spin of an electron can only have two possible values, clockwise and anticlockwise.
When the electron is “free” and is not interacting with the external world,
its spin is in reality a superposition of these two different states (clockwise and
anticlockwise) existing simultaneously, both with 50% probability. But the
moment we “observe” the electron, we make it interacting with the external world, and so
its wave function collapses into one of the two possible states.
As a result, its spin will now be either clockwise or anticlockwise, not both of them!
Something similar occurs with Schrödinger’s cat, if we use this interpretation. In fact,
the wave function of the atom in the radioactive substance has two possible states: one state
in which the atom has decayed, and one state in which it is not. These states are equally likely,
so when the box is closed, it’s like the atom is simultaneously decayed (with 50% probability)
and not-decayed (with 50% probability as well). As a result, the cat can also be described as a
superposition of two different states, equally likely: a “cat is alive” state and a “cat is
dead” state! It sounds very bizarre, but this is what we get when we try to apply the principles
of the quantum world to macroscopic objects. However, when we open the box, we actually
“observe” the cat: so we cause an interaction between the system and the external world.
As a result, its wave function will collapse into one of the two possible states: the cat
will “become” either alive, or dead, not both. Of course, this explanation sounds totally
ridiculous to our mind… we know that the cat must be already alive or dead well before we
open the box. It can’t be “dead and alive” at the same time! So, where’s the catch?
The issue is, the rules of the quantum world cannot be applied to macroscopic objects. This
is because macroscopic objects contain billions of atoms. Each of them, if taken individually,
behaves as we described before: it has a wave function that describes all the possible states
of the atom, and when the atom interacts with the surroundings, its state collapses instantaneously
into one of the several possible states. However, when we consider billions of atoms altogether,
this effect is “mediated” and we are no longer able to observe this effect. Why is that?
The reason is, particles in the quantum world behave as waves. When
two or more waves interact with each other, a phenomenon known as “interference” occurs:
when the waves are in phase, they “add up” and we observe a wave with larger intensity;
but when the waves are not in phase, they “disrupt” each other, and we no longer see
the wave. This is exactly what happens, for instance, if you throw two small stones into
a pond. A circular wave is originated from each of the points where the stones entered the water;
these two waves expand and reach each other. Then, they will interfere: you will see regions
of water where the two waves add and produce a larger wave, and regions where the two
waves cancel each other, producing no wave. So, in order to observe the quantum effects
in the macroscopic world, the wave functions of all atoms in the objects must be “aligned”
correctly in order to interfere in the right way. However, this is impossible, given the fact that
there are billion atoms: so, it’s like the wave functions of the atoms interfere with each other
in a destructive way, making impossible for us to see a macroscopic object behaving as a wave.
And for this reason, the cat in the box cannot be both alive and dead at the same time:
because the rules of the quantum world cannot be applied to it. We know that even if we don’t
open the chamber and we don’t observe the cat, it will be for sure either alive or dead, not both!
Of course, Schrödinger didn’t believe that the cat in the box was “alive and dead” at the same time.
His only purpose was to show to the general public how weird the laws of quantum mechanics are,
by ideating this hypothetical system in which quantum properties are “transferred” from a
microscopic object (the atom in the radioactive substance) to a macroscopic one (the cat). Indeed,
Schrödinger himself started his original article about this paradox by writing “One can set up
a ridiculous experiment…”. Nonetheless, this interesting argument started a debate between
scientists about questions such as “when does a quantum system stop existing as a superposition
of states?”, or “how small should be a system in order to observe these quantum weird effects?”.
These questions are very interesting and not easy to address, given the bizarre nature of the
quantum world. Even Albert Einstein participated to this debate, formulating a modified version of
the paradox in which he replaced the poison in the chamber with explosive gunpowder…
In any case, we are quite sure there is somebody that doesn’t like this debate to
continue that long… the poor cat in the chamber! "This video ends here! Thanks for watching
everyone! Did you find the paradox of Schrödinger’s cat interesting?
Do you find the quantum universe bizarre? Are you curious to know more about it? Let me know
in the comments below, be sure to subscribe, and I'll see you next time on the channel!"