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Electron and Positron beams collide at SLAC and CERN for high energy experiments. Electron beam is produced by thermionic emission from tungsten filament and then launched in the Electric field to gain desired energy. So up to the point before the collision this beam is classical as we are using classical mechanics to control its position and momentum (hence energy). At the point of collision, however, the beam becomes a Quantum Field, as it is participating in the Feynman Diagram. Essentially we are accelerating a quantized Field in the classical lab using classical apparatus. We are using PURE classical mechanics to do calculations before the collision and PURE quantum calculation during and after the collision.

My question is how is that possible??

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    $\begingroup$ Because in this case it can work out that way. A fast-moving electron isn't interacting with anything (although you will need the appropriate relativistic calculations to make and keep the beam in the machine). In the electron's frame of reference it is just sitting there. When it interacts you (likely) are going to use the center of mass frame, and you need to treat the interaction appropriately. That means using quantum theory. $\endgroup$ – Jon Custer Jun 1 '18 at 13:34
  • $\begingroup$ @JonCuster That looks like an answer in a comment. ;) $\endgroup$ – PM 2Ring Jun 1 '18 at 14:39
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    $\begingroup$ "Classical" and "quantum" are not two different states of an electron or electron beam, they are two different ways of describing the electron or the beam. Which one you choose depends on what problem you are trying to solve. $\endgroup$ – Solomon Slow Jun 1 '18 at 16:59
  • $\begingroup$ Electron would have infinite uncertainty in x if there is precise value of its p, according to the uncertainty principle meaning it could be at any place along the trajectory if treated as Quantum. This situation arises at least during collision when the electron is pure quantum. So are we negating the Principle at that point and somehow bringing the electron forcefully to make a collision??? Even a free electron is described by a plane wave with a wave length given be de Broglie equation. My real concern is when the character of electron transitions from being classical to quantum. $\endgroup$ – Majid Malik Jun 3 '18 at 3:53

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