Let's assume we have a perfect single-photon source: a device emitting exactly one photon at a time, with defined energy and direction. Let's shoot a photon: we know exactly the position of the photon (starting point and time, velocity) and it's momentum (energy and velocity). Would such a device violate uncertainty principle? Where is the trap?
Just to clarify things, my question essentially is: a particle (e.g., a photon) prepared in an eigenstate of momentum can be found everywhere (at least along the direction of momentum)?
Best Answer
In your post when you say you 'know' the position and momentum of a single photon you really don't know anything, you are just making a prediction, not making a measurement. In your head you are basically assuming classical physics and using the initial parameters of the system to calculate the final parameters. In order to actually know any properties about a system you will have to perform a measurement, and to really say anything conclusive you will have to do this many times. Take your single photon source and measure the momentum and position of the outgoing photons numerous times - the product of the standard deviation in momentum and position will be greater than $\frac{\hbar}{2}$.