1.1.2. Vacuum Energy


Quantum fields without interaction in flat spacetime are an infinite set of independent linear harmonic quantum oscillators for their time variation -- one oscillator for each mode of the field. The spatial mode is determined by the boundary conditions on the field and its first partial derivatives. This part of the quantum problem is the same as in classical electrodynamics. The equally spaced energy levels correspond to independent quanta of the field that we associate with real particles. The virtual particles correspond to the finite "zero point" energy of hf/2 per mode in the lowest energy state or "vacuum" state of each mode of the field.

Consider the space between two closely spaced flat conducting parallel plates. The boundary conditions give a maximum wavelength that can fit between the two plates along the normal direction. The maximum normal wavelength between the plates is twice the plate separation. This restriction is not found outside the plates. Therefore, there are more field modes outside the plates than inside. This implies that the vacuum zero point energy density due to the virtual particles outside the plates is bigger than it is inside the plates. The result is a measurable Casimir attractive force between the plates found by experiment. These zero point energy forces can be used in the operation of delicate nanodevices.


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