Hello and welcome to the IFT channel
You have asked us to explain the Casimir effect
The Casimir effects is a real physical effect
proposed theoretically in 1948, and which goes as follows:
Take two parallel metallic plates in vacuum;
take them uncharged, carrying no electric charge whatsoever;
there's nothing here, it's complete vacuum, there is no particle at all between the plates,
and nonetheless, the two plates attract each other.
They attract with a force given by this expression,
where "A" is the area of the plates, "L" is the distance between them,
"h" is Planck's constant, and "c" is the speed of light in the vacuum.
We can ask what's the explanation of the Casimir effect.
By the way, the Casimir effect was observed experimentally in 1997, and so
it's an absolutely real effect, which occurs in Nature, and which can be observed with experiments.
What's the explanation of the Casimir effect?
You may wonder if the force among the plates is of electromagnetic nature.
The answer is "no".
It's "no", because the plates are electrically neutral, there is no electric charge on the plates.
Could the attractive force among the plates be of gravitational nature?
The answers is again "NO",
because, although there is a gravitational attraction between the two objects,
it is negligibly small as compared with the experimentally measured forces.
So the explanation of the Casimir effect must be of a different kind.
In fact, the Casimir effect can be explained through Quantum Field Theory (QFT)
The key idea in Quantum Field Theory
is that, for any elementary particle, like the electron, the photon, the muon, the Higgs boson,...
there exists a field. This field permeates all the space
and local excitations of these fields are what we interpret as particles.
Now, the excitations of the field (in this case, we have drawn the photon field, as example)
can be of two different kinds:
excitations that we interpret as real particles,
the physical particles we observe experimentally,
and other excitations, which we described as due to virtual particles.
These virtual particles, at an intuitive level,
can be described as particles that exist
only for an extremely short time interval.
For instance, we can start with an initial state of vacuum,
from which there come out photons
which exist for an extremely short interval of time
after which they disappear back into the vacuum.
These virtual particles are thus a concrete excitation of the fields
and we can compute the energy due to these virtual particles.
The explanation of the Casimir effect is that the vacuum between the two plates
is a vacuum with no real particles,
but in which the fields continue to exist, and so do their virtual particles.
We call this vacuum the quantum vacuum.
We can compute the total energy due to the virtual particles between the two plates,
and the force which we measure experimentally is given by
the derivative of the energy with respect to the distance between the plates.
This is the explanation of the Casimir effect, at the intuitive level.
Now I'd like to talk about other topic, also possibly related to the Casimir effect.
It's the question of the cosmological constant.
We now know that the Universe is expanding at an accelerated rate.
This is an observational fact,
we can see experimentally in astrophysical and cosmological observations
that the Universe expansion is accelerated.
The accelerated expansion of the Universe
can be described using Einstein's General Relativity equations, which I wrote here.
This equation can describe the way the Universe is expanding throughout its history.
In this equation, we see on the left hand side,
several terms describing how the gravitational force behaves,
and in the right hand side we have terms corresponding to sources of the gravitational force,
the mass and energy of particles, stars, galaxies... everything in the Universe.
In particular, there is a term containing explicit sources, and a term called the cosmological constant.
This cosmological constant is a contribution to the expansion of the Universe
which is present even if the Universe would be completely void of matter of any kind.
Imagine a though experiment, taking the Universe and removing
galaxies, stars, the mass of all galaxies... we are left with nothing
so this term vanishes.
However, there remain the fundamental fields.
The fundamental fields can have their excitations due to virtual particles.
So we may wonder if we can interpret this cosmological constant term
as the total energy due to virtual particles,
similar to what we did in the Casimir effects.
We can measure experimentally the value of the cosmological constant,
its around 10^{-3} electronvolts, to the fourth power.
That's a fact, an experimental value.
Now we can compute it, in analogy with the Casimir effect,
by using the virtual particles of all the fields in the Standard Model of Elementary Particles,
and get the theoretical value for this cosmological constant.
The result is... a disaster!
This is described as the worst theoretical prediction in the History of Science.
The theoretical value found from this computation
is 10^{120} times larger than the observed value.
So we need to think about other theoretical explanation
for the small observational value of the cosmological constant.
The explanation can be of two kinds.
It may simply be that the cosmological constant cannot be interpreted
as the energy due to virtual particles in the vacuum,
and there's another explanation which we still don't know;
or it may be that we just don't know all the particles that exist:
we're doing this computation with the particles we know in the Standard Model,
but there could be other fields, other virtual particles contributing to this quantity.
This is the so-called cosmological constant problem,
one of the biggest open problems in Cosmology and Physics of fundamental interactions today,
and one of great research activity here at the IFT in Madrid
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