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The Casimir Effect
HobbySpacer writes "A recent article in Physics World provides a lucid description of the the Casimir effect, which is an attractive force between two surfaces caused by electromagnetic fluctuations in the vacuum. The article discusses some practical application such as the nanotech machines mentioned here earlier."
isn't the force two objects excert on eachother called gravity? seriously though, I wonder how these forces are effected by non-vacumes - i.e. a virtual vacume with one lonely hydrogen moluecule. Is the H2 excerting forces on the two mirrors? are these forces the same magnitude as that the mirrors excert on eachother in pure vacume? more? less? 1/distance squared?
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There's this other thing called a Casimir, when you have a Hamiltonian on an odd-dimensional space, you're guaranteed (by anti-symmetry) to have a null direction for the flow at any point, and this is called the "Casimir" for the flow. Does anyone know if this is the same thing?
Come on, give it up, that's
The forces between two plates in a non-vacuum are difficult to predict, at best. At that scale, the laws of thermodynamics begin to become inapplicable.
However, you can use the ideal gas equation to get an idea of what is happening:
PV = nRT
P is the Pressure, V is the Volume, n the number of molecules of gas, R the Rhydberg constant, and T the temperature. If you hold the temperature and the number of molecules constant and then decrease the volume (the case you mentioned above, where a single hydrogen atom has gotten in between the plates), the pressure will begin to grow linearly.
Because you are moving the plates together, the volume reduces in proportion to the distance between the plates. This means the pressure rises in proportion to the distance between the plates. I'll also make an assumption (a dangerous thing) that the temperature will remain constant because we'll give it time to cool off, and the number of particles remain the same. The last assumption is due to the plates being much larger than the distance between them, so only a very few number of particles on the edges will ever get to escape.
The force on the plates due to pressure is only the area of the plates times the pressure. As the pressure rises, the force rises proportionally.
Because the plates are attracted by the Casimir effect, and the casimir force grows quadratically as the plates draw nearer, eventually, even the pressure will be insignificant compared to the Casimir force. I think that's a pretty good conclusion using rough estimates.
In reality, you can't control the number of particles in the system unless you build some sort of box to hold stuff in between the plates. Also, the laws of thermodynamics depend on there being a large number (millions) of particles, so you can't use them with nay degree of reliability in these kind of situations. My conclusion is suspect, because it is really only an educational guess.
It is much easier to make a vacuum, thus making the problem a lot easier.
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