Uncertainty Principle: How Does Position Depend on Photon Wavelength?

[zodas]

I have a quite simple doubt.

One of the practical applications of Heisenberg's uncertainty principle is given by Heisenberg's microscope. In this thought expt. Heisenberg imagines of a hypothetical microscope in which an observer attempts to measure the position and momentum of an electron simultaneously by shooting a photon at it.

If the photon has short wavelength and high momentum, the position will be measured accurately but the momentum will be uncertain, if not, the converse will happen.

How does the uncertainty of position depends on the wavelength of photon ?

 

[arkajad]

Check http://en.wikipedia.org/wiki/Angular_resolution"
On the other hand, nothing prevents you from using at the same time both short and long wavelength light. Usually this possibility is not being discussed - for reasons that are not being given.

 

[Dr Lots-o'watts]

zodas: Heisenberg's microscope is an elementary way of skimming the principle, it gives insight, the only application is pedagogical. The actual derivation is much more rigorous.

arkajad: Having two photons hitting the same electron simultaneously is quite an obstacle. No current technology can resolve less than a 10e-16s time delay, which is all that is need to make the system a succession of 2 collisions, each involving 1 photon and 1 electron.

 

[arkajad]

arkajad: Having two photons hitting the same electron simultaneously is quite an obstacle.

It does not matter. You are not able to control the time of hitting the electron even with one photon. It hits when it hits.

 

[Dr Lots-o'watts]

Exactly. That can also be said to be a consequence of HUP.

 

[arkajad]

Nevertheless I would venture to predict that when one day we will be able to monitor continuously two non-commuting observables, we will see a particular chaotic pattern in the experimental data, this pattern is not predicted by an ordinary quantum theory, but can be predicted by the theories somewhat more predictive than QM in its textbooks' version that has answers ready only for joint probability distributions of mutually commuting observables. But that's just my guess based on reading many papers on continuous monitoring of quantum systems.