Understanding Uncertainty Principle

mananvpanchal

Hello All,

I want to understand uncertainty principle.

I understand that when we measure x accurately we cannot measure p with that accuracy.
The process of measuring x accurately might like this: some detector fires high energy photon to that small particle, and we can know x accurately. But the high energy photon can change momentum of the particle.
But, when we fires low energy photon to that particle we get fuzzy region of probability for that particle.

Now, I want to understand how can we get accurate momentum by getting fuzzy region of the particle? What might be the process to get it?

mananvpanchal

Hello, All

Why my question is unanswered? Please, tell me what is wrong in my understanding. Please, correct me if some thing I misunderstood.

Thanks.

phinds

I can't help you with methodology for measurements, but I will point out that the UP is NOT a measurement phenomenon. That is, it is NOT a problem that we just don't have the right kind of measurement equipment, it is that it is impossible, regardless of measurement technique, to get arbitrarily precise measurements of BOTH position and momentum at the same time.

There are many threads on this forum that discuss this. I suggest a forum search.

mananvpanchal

I have searched forum, but I don't get exactly what I want.
I am not talking about measurement phenomenon, or measurement equipment.

My question is: We can determine precise position of a particle, but in this act we change its momentum.
Now, I want to measure momentum precisely, I don't care about preciseness of position now. How can I do that?

IttyBittyBit

If your particle is a photon, for example, you can measure its momentum precisely by measuring its energy and/or frequency precisely. There are many ways of doing this (for example, pure gases only absorb light of very specific frequencies; you could use this fact to build frequency-sensitive photodetectors).

With things like conventional photodetectors, though, they are already well-localized in space so you can't measure a precise frequency for a single photon. A way to get around this is to use an ensemble of photons, all with the same momentum (e.g. a laser beam) to get a precise frequency. A laser beam is 'smeared' out in one dimension, so a precise frequency can be calculated for it.

Frequency measurements on laser beams are done a variety of ways. One way is to pass the beam through a prism and record the deflection angle. There are more precise ways, of course, but they are a little technical.

mananvpanchal

Thanks IttyBittyBit.