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Heisenberg uncertainty principle and quantum physics

comes from: quantum mechanics uncertainty principle Heisenberg

devised a thought experiment to explain the uncertainty principle. We want to see through an electron microscope Gamma rays. This radiation has a wavelength of about 10 -12 meters.

The gamma ray detector of a particular size, covering a viewing angle 2α . The resolution of such a system determines the minimum size or that can be distinguished, and is related to the wavelength and the angle of detection

This resolution we determine the uncertainty in the position. If we place an electron in a particular position, radiation does not distinguish it from another that is at a distance less than D x .

When the gamma ray photon strikes the electron angular momentum tells _and P, as in the Compton effect . The Gamma ray meanwhile bounced out to the detector, may fall between two limiting cases, marked in the drawing as ₁ p and p 2

Both give the same signal photons in the detector, even under an exchange angular momentum than the electron. In both cases, the total angular momentum in the x-axis (electron + photon) is equal to the photon momentum p before the crash:

may seem that this result is due to limitations of the experiment . But not, it is the experiment that is limited by nature. Let's try the case wholly ideal in which the spatial resolution of the microscope is perfect , ie Dx = 0, because we use a Gamma-ray radiation does not, but cosmic rays, or others a wavelength as close to zero as we like .

The result is that the indeterminacy of the moment is growing up to be infinite: it is impossible to determine the angular momentum. The shorter the wavelength of the photon, the greater its angular momentum, and the greater the amount that can pass the electron after the collision.

Now suppose we decrease the size of the detector to make it as small as we want. This means that the detection angle is zero, and consequently, the uncertainty of the angular momentum is zero, we have determined with perfect accuracy the angular momentum, Dp = 0 .

However, spatial resolution, the uncertainty in the position Dx is the shooting at infinity: it is impossible to determine the position of the electron.