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Uncertainty Principle is related to quantum mechanics. |
This is a pure quantum effect it has no counterpart in classical physics. It was worked out by Werner Heisenberg and in symbols is represented as Delta p Delta x Less than or greater than h/2 Pi ,and in words says that the product of the uncertainty in momentum times the uncertainty in position can never be less than planck's constant divided by 2 Pi. Some examples try to explain it in terms of the error in measuring some quantity such as the position of an electron which is disturbed by the act of measuring it. Such an interpretation is wrong because it implies that with sufficient care perfect precision would be possible. What the uncertainty principle is saying is that there is built in to the universe an underlying doubt at it deepest level about what exactly can be specified. This arises directly from the wave-particle duality which is well established by experimental physics and confirms Planck's euation E = hf for photons and de Broglie's equation p = h/Lambda for material particles, such as electrons. If the momentum, p, of some entity is known precisely then so is its wavelength. This could be represented by a sine curve with this wavelength. But such a diagram would be as long as you like, a representation in a book or your notes would just be a little part of it. This means that the position of this entity could be anywhere where the wave extends, which is anywhere between + infinity and - Infinity. Instead of specifying the wavelength exactly imagine a second wave of slightly different wavelength being added to the original. An interference pattern would be produced, with maxima and minima localised in space. The entity, be it photon or electron or anything else, could not occur at a minimum, but could be near any maximum. Now imagine adding more and more different wavelengths. The interference pattern would become more and more complex, but also the maxima would be more and more sharply defined. This is just like the pattern produced by a diffraction grating compared with the pattern from a double slit. The grating's pattern is more sharply defined. The position of our test entity will be far more precisely defined than before. With an infinite sum of waves, all of different wavelengths, the interference pattern is a single infinitely thin peak. So now the position is defined exactly but nothing at all is known about the momentum as with all possible wavelengths all possible momenta occur as well. These two cases are extremes. If we pick a small range of wavelengths around a central wavelength and add them, a well defined wave pulse can be produced. This means that the position is reasonably well known as is the wavelength and hence the momentum. The detailed calculation produces the equation already quoted above. Squeezing the wave pulse to make it more precise needs a wider range of wavelengths; and using a smaller range of wavelengths gives a bigger range of positions. The two quantities are as if on opposite sides of a see-saw, so it is not possible to define both quantities together with total exactness. |
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