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Nov 3 at 8:50 comment added mathemania I think what you mean is $\delta \phi = \phi'(x) - \phi(x)$ compares the transformed field to the original field at the same point $x$. The transformed field $\phi'(x)$ is moved. Suppose $\phi(x)$ is a sine wave, let $x = \pi/2$. Let $\phi'(x)$ be the transformed field by moving it to the right by some amount (assuming the new sine wave does not align with the old sine wave), clearly $\phi'(x)$ at $x = \pi/2$ will have a different value compared to $\phi(x)$ at $x = \pi/2$.
Mar 14, 2017 at 21:12 vote accept StarBucK
Mar 14, 2017 at 16:51 history answered CAF CC BY-SA 3.0