# Interpreting Casimir Effect along with Hawking's Radiation

I currently watched a video on youtube about Casimir effect

and here's the link

The professor in the video talks about Casimir effect and Hawking's blackhole radiation

While talking about blackhole radiation, he says that mass of blackhole decreases if some particle or antiparticle loses its pair when only one of it(either the particle or the antiparticle) gets sucked into the blackhole

Because a particle is created from nowhere, a mass, energy is created from nowhere, and because it unsatisfies energy conservation, he says that 'the mass of blackhole shrinks to pay the energy debt'

Here's my point.
If blackhole reduce their mass to satisfy energy conservation, why not in Casimir effect.
I mean, Casimir effect is about force applied on metal plates toward each other
Since force*distance is work (energy), Casimir effect tells us that energy can be created from nowhere and we don't talk about the energy debt
However, about Hawking's theory, he tells us that in order to pay the energy debt, mass of blackhole should reduce.
But why not on Casimir effect?

## Answers and Replies

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mfb
Mentor
Why not what with the Casimir effect?

Hawking radiation can be summed up as "massive black hole emits a photon with some energy, black hole loses some energy". Nothing mysterious, energy is conserved in the same way a flashlight conserves energy. I don't see where you see anything analogous related to the Casimir effect.

Why not what with the Casimir effect?

Hawking radiation can be summed up as "massive black hole emits a photon with some energy, black hole loses some energy". Nothing mysterious, energy is conserved in the same way a flashlight conserves energy. I don't see where you see anything analogous related to the Casimir effect.
Sorry, you didn't get my point. My bad, poor english. Hawking radiation conserves energy, right?
The process is this.
1.blackhole in a total vacuum
2.creation of virtual particle
3.only one sucked into blackhole
4.unsucked virtual particle loses its partner and becomes real
1.->4. : vacuum -> real particle made : I know how the video explains this.
Mass of blackhole is reduced in order to conserve energy (energy to make a particle = energy loss of blackhole)

However, let's talk about Casimir effect
1.vacuum with two plates
2.two plates attracted to each other (force is exerted)
3.due to the force, they move closer to each other
4. F * s = W (work, which is energy)
1. -> 4. : vacuum -> energy is made due to Casimir effect attraction

Here's the point.
Energy of vacuum is 0
Casimir effect tells us that work is done, and therefore, energy nonzero.
Energy came out of vacuum, and this doesn't obey the conservation of energy.

Does this mean that we can acquire energy from the vacuum?
Hawking's theory says that 'energy is conserved : loss of blackhole mass = creation of particle'
Casimir effect says that 'energy is created : no energy in vacuum -> work is done on plates'

mfb
Mentor
Hawking radiation conserves energy, right?
Yes, as every other process does.
The process is this.
No, this is a description for non-experts because the equations are too complicated.
1. -> 4. : vacuum -> energy is made due to Casimir effect attraction
No, the energy was there before - as potential energy of the plates.

So Casimir effect tells us that
there was energy in the vacuum before the push, and this vacuum energy was used to push the metal plates.

Therefore, "Vacuum contains energy"?

Thanks

"Vacuum contains energy"?
Knowing that Casimir force is experimentally confirmed , why the question mark?

timmdeeg
Gold Member
Note that according to Jaffe the casimir force can be interpreted without taking reference to the quantum vacuum (s. Wikipedia), but instead to van der Waals forces, simply said the sum of forces between molecules and Atoms respectively.
Of course regardless the interpretation energy conservation holds for both.

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Note that according to Jaffe the casimir force can be interpreted without taking reference to the quantum vacuum (s. Wikipedia), but instead to van der Waals forces, simply said the sum of forces between molecules and Atoms respectively.
Of course regardless the interpretation energy conservation holds for both.
Quote from http://arxiv.org/pdf/hep-th/0503158v1.pdf :

"Despite the simplicity of Casimir’s derivation based on zero point energies, it is nevertheless possible to derive his result without any reference to zero point fluctuations or even to the vacuum. Such a derivation was first given by Schwinger[24] for a scalar field, and then generalized to the electromagnetic case by Schwinger, DeRaad, and Milton[25]. Reviewing their derivation, one can see why the zero point fluctuation approach won out. It is far simpler"

Normally, one should be careful when it comes to interpretations of existance and reality questions in quantum physics. I give advantage to simplicity. This doesn't affect reality of the observed effect.

timmdeeg
Gold Member
Right, it doesn't. However I'm not sure anymore as to wether the wording 'interpretation' is the correct one. If I remember correctly, Jaffe's calculation predicts the measurement with high accuracy.

Staff Emeritus