# Uncertainity Principle , particles and antiparticles

1. Nov 19, 2009

### bpm_vns19

Is Uncertainity Principle is applied during particle antiparticle generation and is it a deterministic principle related to their positions and momentum in space ?

2. Nov 19, 2009

### jambaugh

The uncertainty principle always applies but it may not be relevant to the question at hand.

One thing to note. A pair of particles may have very sharply defined relative position (i.e. you can know they are almost exactly a distance x apart) but still not have a well defined absolute position but rather have a well defined total momentum.

I don't know if that is relevant to what you're thinking about. Why do you ask?

3. Nov 19, 2009

### Neo_Anderson

You've heard of particle/wave duality, right? Well, when trying to measure these two properties on a particle, then where's the particle? Where's it's wave?
We don't know for sure. We are uncertain. We are uncertain of the particle's momentum if we try to measure its position. Likewise, if we try the obverse--try to measure where the particle is at (its position), then we don't know the particle's momentum. Hence, Heisenberg's Uncertainty principle.

Heisenberg's Uncertainty principle tries to answer the question, "How do we go about measuring a particle if it's a wave, also?" HUP was borne out of attempts at answering this question.

4. Nov 20, 2009

### jambaugh

Heisenberg's UP is the statement about uncertainty it isn't "trying to answer the question 'How..."

Also the HUP isn't just about position and momentum but rather any two non-commuting observables such as x-component and z-component of angular momentum.

Again how are you trying to connect this to pair creation?

5. Nov 20, 2009

### Fra

Just to point out one important thing, the uncertainty principle properly refers to statistical measures, so in a sense it's a statistical principle. The uncertainties(delta X) in the HUP are standard deviations relating to means, not "absolute errors" relating to single samples of arbitrary confidence.

$$\sigma_x \sigma_p \geq \frac{\hbar}{2\pi}$$

As you may know standard deviation is defined as an error window that is valid to a certain confidence level. (+/-$$\sigma$$ around mean covers ~68% of the samples.)

/Fredrik

6. Nov 20, 2009

### Neo_Anderson

If you actually read my post, you would have noted that I said that the HUP "was bourne out of [problems measuring momentum and position simultaneously]"; I made no assertion that the HUP is restricted to the momentum/position measurement problem only.

Furthermore, the HUP did try to answer how! Heisenberg used it to describe how we are to go about measuring momentum and position of a particle simultaneously, and his answer was that we can't; hence, there is uncertainty in either the momentum or the position and he developed the HUP relation as a consequence.

To the OP, I think Fra answered your question adequately; HUP is strictly statistical in nature, as is most of QM.
HUP is not needed to determine the time at which the pair is created, since the created pair can be determined by the effect of the reaction that created the pair (eg, we know precisely when a correlated photon pair is created when we excite a calcium atom by an external lasing source). After particle creation, however, HUP must be applied to either particle--the reaction itself tells us nothing about the state of the correlated pair after they leave the apparatus they were created in.

7. Mar 14, 2010

### bpm_vns19

When you say that "when trying to measure these two properties on a particle, then where's the particle? Where's it's wave?" .How it is applicable in pair particle production ?There the particle is not alone . It is with its antiparticle .

How can be uncertainty principle then applied during pair particle production ?Can you give me a clear picture of that ??