The Casimir effect is a physical force that arises from a gradient in the expectation value of energy from the presence of an underlying quantum field. It was predicted by Dutch physicist Hendrik Casimir in 1948. Quantum field theory states that there is an underlying quantum field for every particle. These fields must be quantized at every point in space, which results in a non-zero vacuum energy even in empty space. The Casimir effect occurs when two conducting plates affect the virtual photon field between them, limiting the possible photon modes and resulting in a slight excess of energy outside the plates. This creates a pressure gradient pushing the plates together.

1. Casimir Effect
Erich Wanzek

2. The Casimir effect
• The Casimir effect is an effect that is understood through quantum
field theory
• The Casimir effect is a physical force that arises from a gradient in the
expectation value of energy from the presence of an underlying
quantum field.
• The Dutch physicist Hendrik Casimir predicted the force in 1948

3. The Casimir effect
• Quantum field theory states that
there is a underlining quantum field
for every particle
• These fields must be quantized at
every point in space
• Can picture this as a set of HOs at
every point in space
• Collective excitations, represent
particles
• The quantum field have a non-zero
energy. There is a zero point have a
vacuum energy

4. The Quantum Vacuum
True vacuum
Non-zero Vacuum Energy
• The is a non zero vacuum energy expectation value. This
is because the is always a lowest energy ground state for
the field. Random excitation means virtual particles.
• The quantum electro dynamical field, or the photon field,
constantly has virtual particle photons popping in and out
of existence.

5. The Casimir effect
• Two conducting plates affect the virtual
photons which constitute the field, and generate
a net force. Why?
• The plate limit the photonic modes of the
quantum field in between the plates to a discrete
spectrum of energy eigenvalues that photon can
have. Where as the free vacuum can pretty
much take on a continuous spectrum of energy.
• The overwhelming more energy modes outside
the plates creases a pressure gradient which
pushes the plated together.
• the radiation pressure of the field outside the plates
will tend to be slightly greater than that between the
plates, which will therefore be attracted to one
another.

6. Deriving the value of the Casimir force

7. Measuring the Casimir Effect
• The strength of the force falls off rapidly with distance.
• It is measurable only when the distance between the objects is extremely small.
• As it is so tiny, the Casimir force proved extremely difficult to measure.
• One of the first experimental tests was conducted by Marcus Sparnaay at Philips
in Eindhoven (Netherlands), in 1958, in a delicate and difficult experiment with
parallel plates, obtaining results not in contradiction with the Casimir theory, but
with large experimental errors
• Not until 1997 that Steve Lamoreaux, at University of Washington, provided the
first firm experimental confirmation of Casimir's theory. He Measured the force
to within 15% of the value predicted by the theory
• indirect validation of the predicted Casimir energy had been made by measuring
the thickness of liquid helium films. Subsequent experiments approach an
accuracy of a few percent.

8. Dynamical Casimir effect