About the Uncertainty Principle

[tonyxon22]

If I understand correctly, this very important principle in quantum theory says that the more precise you know the position of a particle, the less precise its momentum can be known. So this raises several questions to my mind:

1) Does this principle applies to photons? Isn’t a photon source, and a photomultiplier (which I understand are able to detect individual photons) a completely defined system? If light travels in straight lines, we can emit one single photon and also detect it, so I think that indirectly we know everything about the photon, including its position and of course speed (because it’s fixed) at all times. I mean, is seems logical that we can predict that the photomultiplier is going to detect a photon when you shoot light into it, so I don’t see where the uncertainties are in this system.

2) Regarding the other particles, how is it possible to manipulate them without know exactly where they are and how they’re moving? In old TVs for example where you had a shooter of electrons manipulated by magnetic fields to make them crash in a particular way against a sensitive screen to create an image. Don’t you need to know where the electrons are in the first place, and what your magnetic flied is doing to them (how they are moving)? I have the same doubt with the Large Hadron Collider. In order to cause a frontal collision between to protons at 99,999% the speed of light(!) don’t you need to know exactly where they are and how they are moving?
Thanks and best regards,

 

[vanhees71]

First you should tell us, which uncertainty principle you mean. It applies to any pair of observables,
$$\Delta A \Delta B \geq \frac{1}{2} |\langle [\hat{A},\hat{B}] \rangle|.$$
If you have the position-momentum uncertainty relation in mind, it's a bit tricky for photons since photons do not have a position observable in the usual sense.

Concerning 2) You don't need to know that accurately to deal with particles. E.g., in an accelerator like the LHC you accelerate clouds of protons (or heavy ions), called bunches, in an electromagnetic field. Classical relativistic mechanics and electrodynamics is sufficient to construct the accelerators. Sometimes also statistics is of great help (e.g., in the famous techique of stochastic cooling, which was the key invention by van der Meer to enable the discovery of the W and Z bosons at CERN).

 

[Khashishi]

1. Light doesn't travel in straight lines. It diffracts. Also, in order to localize the position of a photon, you need to create an electromagnetic wave packet. If you are familiar with Fourier transforms and signal processing, you will know that a wave packet contains many different frequencies (and hence, different momenta). A smaller wave packet will contain a larger spread of frequencies. Consider the difference between a continuous laser and a short pulse laser. You can more exactly identify the position of a photon in a short pulse laser pulse, but not the frequency. For a continuous laser, a single photon could be anywhere along the beam between the source and target. And if you try to cheat by putting the target very close to the source, you will get cavity resonator effects, and these will resonate over a spread of frequencies. The smaller the resonator, the larger the spread of frequencies.

2. Your TV pixels are very large so you don't notice the quantum effects which occur at small scales. If you look closely, you will see that there is some fuzziness around where the electron beam strikes. It's not a point but a small Gaussian blob. The size of the blob is much larger than the quantum limit, which is probably on the order of angstroms.