The Gamma-Ray Microscope

• A famous thought experiment to measure x and p for the electron:

• The resolution of a microscope is limited by the wavelength of light used, and by diffraction, so to measure position more accurately, use smaller g-ray wavelengths:

• Dx > l (l = g wavelength)

• However, Compton scattering changes electron’s momentum:

• Dp > h/l

• Therefore: Dx Dp > h

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In order to measure the momentum of the electron, you need to know it’s velocity, which means measuring its position accurately at two separate times. To measure it’s position once, you have to look at it with quantized photons, but when the photon bounces off, it changes the electron momentum in a random way, so that where it will be a short time later becomes more unpredictable.

To reduce the momentum uncertainty due to these random changes in momentum, you have to reduce the photon momentum, which means making the wavelength of the illuminating light longer, but this makes the position measurement more and more uncertain. In the end, you’re stuck with an inherent uncertainty in the product.