Back Correcting the Uncertaininty Principle?

[bstacey]

I'm sort of new to quantum mechanics and was wondering that when we use a photon (light) to measure a particle for its velocity (momentum) with varying wavelenghts depending on the accuracy we want, why can't we back correct to take into consideration the wavelength of the photon when finding out the probability of the position? Hence making it's position more accurate or even exact?

 

[lightarrow]

I'm sort of new to quantum mechanics and was wondering that when we use a photon (light) to measure a particle for its velocity (momentum) with varying wavelenghts depending on the accuracy we want, why can't we back correct to take into consideration the wavelength of the photon when finding out the probability of the position? Hence making it's position more accurate or even exact?

Because you can't. Using a longer wavelenght means having a not very focused image of a point: you see a disk instead of a point and the disk diameter increases with wavelenght.

 

[bstacey]

Well what if a shorter wavelegh was used to measure the position? Would this effect the momentum? And can't this be taken into account when predicting it and then back corecting?

 

[HallsofIvy]

What do you mean by "taking into consideration the wavelength". All you can do with wave length is say "the particle is within one wavelength of the measured position". The smaller the wavelength, the more accurate the measure of position, but knowing the wavelength doesn't allow us to say more than that.

And every time you "hit" a particle with a photon to measure its position, you change its momentum and so its speed. The lower the wavelength, in order to get a more accurate position, the greater the energy of the photon so the greater change in momentum.