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marcus

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## Main Question or Discussion Point

How do you imagine the Casimir force working? By what mechanism does it arise, as you picture it?

If you had two square plates each 1.6 meters (5 feet) on a side and you could position them side by side almost touching but with say 1/60 of a millimeter gap, by what force would they attract each other?

I ask because there seems to be some misunderstanding at PF or at least a difference of opinion as to the mechanism causing the force. Someone was telling me that vacuum energy exerts a positive pressure and that is what pushes the plates together (!) because the vacuum energy is thinner between the plates than on the outside.

Probably the negative pressure associated with the vacuum energy density is irrelevant here---though suspected to play a vital role in cosmology. Instead what matters is the fourth power dependence of the energy density between the plates. The fact that the energy density is so much less when they are closer together! That's my take---what do you think and how do you explain the force?

I'll calculate the force in natural units. If the separation distance is L and the area is A, then the formula for the force is simply

(pi

the constant in front is about 1/24, since pi-square is about ten.

it is just some fairly harmless numerical constant

the main thing you have to do is divide the area of one of the plates by the fourth power of the separation.

In natural units (hbar=c=G=1) the side of the square is E35

and the area is E70

The separation of 1/60 of a millimeter is E30

so the fourth power is E120

So the force is E70 divided by E120, or E-50 (and dont forget the numerical constant)

the natural unit of force (plays a central role in the Einstein eqn of GR and in the friedmann equations, discussed in other PF threads) in metric equivalent is 12E43 newtons.

So when you say the attraction Casimir force is (1/24)E-50

then it works out in metric terms to (1/24) x 12E-7 newtons

or 1/20 of a micronewton. But the metric equivalent is a side issue. the answer might just as well be left in natural units as (1/24)E-50.

E-50 is sort of like a micronewton, so what difference does it make whether you say (1/24)E-50 or (1/20) micronewton.

Damgo told me a while back in another thread that he didnt

find it prohibitively difficult to adapt to natural units---those used

in his QFT text---and I have been trying this out and in fact it

is not difficult at all. The calculations are all much easier too.

As a comparison test, try calculating the same Casimir force in

metric units. It will be a bit messy but you should get the same answer of 1/20 micronewton.

If you had two square plates each 1.6 meters (5 feet) on a side and you could position them side by side almost touching but with say 1/60 of a millimeter gap, by what force would they attract each other?

I ask because there seems to be some misunderstanding at PF or at least a difference of opinion as to the mechanism causing the force. Someone was telling me that vacuum energy exerts a positive pressure and that is what pushes the plates together (!) because the vacuum energy is thinner between the plates than on the outside.

Probably the negative pressure associated with the vacuum energy density is irrelevant here---though suspected to play a vital role in cosmology. Instead what matters is the fourth power dependence of the energy density between the plates. The fact that the energy density is so much less when they are closer together! That's my take---what do you think and how do you explain the force?

I'll calculate the force in natural units. If the separation distance is L and the area is A, then the formula for the force is simply

(pi

^{2}/240) A/L^{4}the constant in front is about 1/24, since pi-square is about ten.

it is just some fairly harmless numerical constant

the main thing you have to do is divide the area of one of the plates by the fourth power of the separation.

In natural units (hbar=c=G=1) the side of the square is E35

and the area is E70

The separation of 1/60 of a millimeter is E30

so the fourth power is E120

So the force is E70 divided by E120, or E-50 (and dont forget the numerical constant)

the natural unit of force (plays a central role in the Einstein eqn of GR and in the friedmann equations, discussed in other PF threads) in metric equivalent is 12E43 newtons.

So when you say the attraction Casimir force is (1/24)E-50

then it works out in metric terms to (1/24) x 12E-7 newtons

or 1/20 of a micronewton. But the metric equivalent is a side issue. the answer might just as well be left in natural units as (1/24)E-50.

E-50 is sort of like a micronewton, so what difference does it make whether you say (1/24)E-50 or (1/20) micronewton.

Damgo told me a while back in another thread that he didnt

find it prohibitively difficult to adapt to natural units---those used

in his QFT text---and I have been trying this out and in fact it

is not difficult at all. The calculations are all much easier too.

As a comparison test, try calculating the same Casimir force in

metric units. It will be a bit messy but you should get the same answer of 1/20 micronewton.

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