Chris Spencer edited untitled.tex  about 9 years ago

Commit id: 98be5f004417d23316ffc271e82871321cdc9eee

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For sake of brevity, the result is given for a force per cm^2   \[F=\frac{\hbar c \pi^2}{240 a^4} \]   Casimir concluded that there exists a force between the two plates which is independent of material and interpreted as a zero point pressure of electromagnetic waves, this result is now known as the Casimir effect. \\  This result is hard to understand without a knowledge of quantum field theory or quantum electrodynamics. A brief anecdote on QFT will be given to try to understand the Casimir effect. effect and the vacuum field. Quantum Field Theory states that all the fundamental fields are quantized at each and every point in space. A field can be seen as space being filled with interconnected vibrating balls and springs. Vibrations in a field then propagate and are governed by the appropriate wave equation for the field in question. The second quantization of quantum field theory or canonical quantization requires that each ball and spring combination be quantized. The field at each point in space is a simple harmonic oscillator and its quantization puts a quantum harmonic oscillator at each point. The vacuum we assume to be empty is not so empty after all. As it would be, the vacuum has all the properties a particle may have such as spin, energy but on average these cancel out. If these properties cancel shouldn't the vacuum be empty? The exception is the vacuum energy. Since the vacuum field's quantization is a quantum oscillator, we know that the ground state of a quantum harmonic oscillator is $E_0=\frac{1}{2} \hbar \omega$