I like to tell students that negative numbers were invented to solve the equation:
1 + x = 0
There is a story line that goes with that introduction, I will spare you here from it.
What I write about here is one of the weird implications of some of these equations. Richard P. Feynman many years ago invited theoretical physicists to consider negative probabilities. Another application of these weird numbers are bank accounts. I own a big amount of negative money. Then you have negative temperatures hotter than positive infinity. Negative pressure that according to a friend of mine, solves several deep problems of modern physics. The particular negative numbers I consider here are the permeability and permittivity of metamaterials.
Professor Leonhardt and Dr. Philbin from the University of Saint Andrews in Scotland have recently written:
"Repulsive Casimir forces [16]-[22] have been predicted to occur between two different extended dielectric plates, in the extreme case [17] between one dielectric with infinite electric permittivity ε and another one with infinite magnetic permeability μ. They have not been practical yet and are subject to controversy [19, 20]. The closely related case of repulsive van der Waals forces has been studied as well [23]. Here we consider a different situation inspired by Casimir’s original idea [5]: imagine instead of two extended dielectric plates two perfect conductors with a metamaterial sandwiched in between for which ε = μ = −1 (Fig. 1A). Such materials can be made of nanofabricated metal structures [10]-[14]. One of the conducting plates may be very thin and movable, which gives a key advantage in observing repulsive vacuum forces."
With this proposal of negative electrical permittivity and magnetic permeability it may be possible to make levitating nanomachines. Somehow these machines may be pumping negative energy from vacuum fluctuations.
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I'll believe it when I see it, and I referred this link earlier in context with negative mass particles:
http://www.lns.cornell.edu/spr/2006-03/msg0073465.html
From Wikipedia:
http://www.answers.com/topic/exotic-matter
"Exotic matter is a hypothetical concept of particle physics. It covers any material which violates one or more classical conditions or is not made of known baryonic particles. Such materials would possess qualities like negative mass or being repelled rather than attracted by gravity.
***The closest known real representative of exotic matter is a region of pseudo-negative pressure density produced by the Casimir effect".***
In the case of there is a "Casimir pseudo-negative pressure density",
negative presssure causes the vacuum to mimic the effects of Dirac's interpretation of the negative mass states, where...
P=-u=-rho*c^2
You get this same effect in Einstein's finite static model when you generate matter from Einstein's vaccum energy.
You should listen to your friend... ;)
I wholly agree, I should listen to my friend. I hope you give me some slack. I have not read all the links you provided already.
Going back to Leonhardt, he does have very nice papers at the LANL archive. I understood what he is saying.
First of all, even if I did not understood all the details of the Casimir effect, it was clear to me that I had to pay attention, because the prediction was checked experimentally.
What these papers state is that if you introduce an active material, you can actually change the sign of the force from attractive (i.e. not that interesting) to repulsive (interesting). Now you can make a thin aluminum foil paper levitate. That will be neat, and we will learn more about these quantum fluctuations that have fascinated me almost since the first time I heard about them.
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