Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: PAOLO137 on 23/03/2012 14:23:09
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Let's figure out a so called "conceptual experiment".
Arrange two parallel metal plates where d=distance between plates << D=dimensions (suppose rectangular) of the plates. Apply a DC voltage difference to the plates, obtaining a sufficiently constant electrical field in the volume between the plates. Let an electron be thrown horizontally between the plates. Classical physics tells us that the electron will follow a parabolic path bent towards the positive plate, since obeying a constant transverse force.
How will be seen the same event using QED? Sorry to be so trivial. Thanks to anyone who will answer anything. Paolo
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There are several things that have to be answered or set before you consider the answer to this question. The most notable one and root of the need to question is "how are you going to observe the motion of the electron" This question is also true of the classical case because your description of the classical conceptual experiment is a theoretical prediction of the motion of an electron based on its predicted behaviour in a uniform electrical field.
Let us set this question aside for the moment and assume that we have a method of observing the electron that does not disturb its motion significantly and produces results of a reasonable accuracy to see how it has moved.
The quantum mechanical vacuum contains a vast number of particle antiparticle pairs continually popping into and out of existence for brief periods. For the sake of simplicity let us keep this activity at a reasonably low energy and only consider electrons. The static electrical field will cause these electrons and positrons to move slightly differently between their creation and destruction. Our electron will be interacting with all of these and exchanging photons all the time and moving around in a zig zag path the close you look at it the more violent the zig zag path will be. This is a bit like the "brownian motion" (QV) of pollen grains in water. However there will be a slight difference between the interactions due to the electrical field causing the electrons and positrons to move differently. The net result will be that our "electron" will move in the the path defined by the classical process. Please note it os quite possible that "our" original electron could have been annihilated by one of the positrons it interacted with leaving it pair electron to travel on in place of our electron. But as individual electrons are totally indistinguishable we could never know.
Quantum field theory is just a mathematical process that in effect takes all these processes into account because it is possible to in effect average or integrate out the violent zigzags to define a simple path.
The simplest way of doing this experiment is not to use one electron but use loads of them asnd assume that they all behave in a similar manner on the average and sacrifice some of them along the route into a detector to show the path they have followed.
Here is a picture of this classic "Crookes tube" deflection experiment.