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Hedrick Casimir first introduced the idea of the vacuum field in 1948. Interest started when Casimir and Polder earlier in 1948 described the interaction between q perfectly conducting plate and an atom by using the Van Der Waals-London forces, then correcting it for retardation effects in the limit of large distances. Then the next issue was to show the effects between the interaction between two perfectly conducting plates using this Van Der Waals retarded interaction. It is useful to understand the properties of the paper that lead to the Casimir effect. Casimir considers a cubic cavity of a volume $L^3$ bounded by perfectly conducting square plate with side L be parallel to the XY face and investigates the situation where plate is at a small distance from XY face and situation where the distance between is a distance $\frac{L}{2}$ [1]. Looking at the resonant frequencies of this system, $ \frac{1}{2} \sum \hbar \omega $, the sum being over all the resonant frequencies, notice the problem that this goes to infinity and is not physical. The differences between the frequencies is well defined for the two situations. Labeling the situations of small interaction and long interaction, differences are \[\frac{1}{2}(\sum \hbar \omega )_I -\frac{1}{2}(\sum \hbar \omega)_{II}\] and the value given is the interaction between the plate and the XY face. Cavity will have dimensions \[0 \leq X \leq L, 0 \leq Y \leq L,0 \leq Z \leq a \] with the wavenumbers given by \[ k_i=\frac{ \pi n_i}{L}, k_z=\frac{ \pi n_z}{a} \] where i=x,y and $a$ is the small distance to be used between plate and XY face. The total K is given by $K=\sqrt{k_x^2+k_y^2+k_z^2}=\sqrt{x^2+k_z^2}$.\\  For every $k_x,k_y,k_z$, there is two be two standing waves unless $n_i$ is zero, which case there is one standing wave. $k_x,k_y$ can be regarded as continuous variables for very large L, then in polar coordinates \[ \frac{1}{2} \sum \hbar \omega = \frac{ \hbar c L^2 \pi}{\pi^2 2} \sum_{(0)1}^{\infty}\int_{0}^{\infty}\sqrt{\frac{n^2\pi^2}{a^2}+x^2} x dx\] where the notation of $(0)1$ means the n=0 term is to be multiplied by $\frac{1}{2}$. When $a$ becomes large, the summation can be turned into an integral. Now the interaction energy between plates for the situations above is \[\frac{1}{2} \sum \hbar \omega = \frac{ \hbar c L^2 \pi}{\pi^2 2} \sum_{(0)1}^{\infty}\int_{0}^{\infty}\sqrt{\frac{n^2\pi^2}{a^2}+x^2} x dx-\int_{0}^{\infty} \int_{0}^{\infty} \sqrt{k_z^2+x^2} x dx(\frac{a dk_z}{\pi} dk_z}{\pi})  \] 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. \\