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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)?

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The device that shoots the photon has a finite size, and that is the source of uncertainty of photon's position. – C.R. Aug 21 '12 at 17:02

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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 $\frac{\hbar}{2}$.

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But one may say that momentum is measured when you shoot the photon, since the ideally perfect gun allows you to impose energy and direction, so if you don't change this settings the measure is always the same with 0 standard deviation. – luciano Aug 22 '12 at 7:38
Your ideally perfect gun only exists in your head though. Think about how you are going to create the photon at the fundamental level. For example, you could have an atom that drops from a higher to a lower energy level and emits a photon. The model that governs this process is a quantum mechanical one, so it won't create classical particles, it will create quantum states that have some spread in p and x. – DJBunk Aug 22 '12 at 13:37
Furthermore momentum and direction aren't complimentary observables. When you create something with well-defined momentum along the x axis, and well defined position along the y and z axis you might say it 'has direction' in the x direction but it will have very ill defined position along on the x axis and ill defined momentum along the y and z axis. – DJBunk Aug 22 '12 at 13:41
I perfectly know that momentum along x does commute with position along y and z, indeed in the expansion of my question I have already mentioned explicitly position in the direction of momentum. The perfect single-photon gun exists only in my head, as many devices in many thought experiments that can (and must) have an explanation. – luciano Aug 22 '12 at 20:31
I don't get the feeling you we agree yet. My point is that all you have said so far is that you have some 'ideal photon source' but you haven't said how it works. If you tell me how it would work we can discuss it, but otherwise you are just asserting that something like it exists, but not how it would create a photon with no uncertainty. I have given an example of how you would actually create a single photon state. – DJBunk Aug 23 '12 at 1:51

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