# A question about Heizenberg uncertainty.

1. Feb 23, 2013

### ndung200790

In some QFT books they say:If we consider momentum p of particle being very great,then the physics is at short scale.Then how can we apply Heizenberg uncertainty principle when the momentum p of particle having a certain value?What do they imply when they say that?

2. Feb 23, 2013

### Staff: Mentor

p is not an exact value, but for large p (as distribution, if you like) this can be negligible.
Consider a particle, confined in a space of 1cm: It has a corresponding minimal momentum uncertainty of ~0.1 meV. If the particle has a momentum of 1 MeV (10 billion times more than this uncertainty), you just don't care.

3. Feb 23, 2013

### ndung200790

Is there any relation between great value p and great value of uncertainty in p?This(relation) explains why with the great p we have short scale physics as they say.

4. Feb 23, 2013

### Graniar

Great value of p is necessary for the great uncertainty in p.

Let's say, we have a particle with the well-known p, scuttering on the target (also well-known p).
Therefore there is a big uncertainty in x

But, after the scuttering, x may get well measured (xspace by affecting the lattice, xtime by energy dissipation), thus p should get big uncertainty.

In case of almost elastic scattering, xtime remain uncertain, and p uncertainty rely mostly on the angle uncertainty (ptime → E≈const ; px2+py2+pz2≈const)

Last edited: Feb 23, 2013
5. Feb 24, 2013

### ndung200790

By the way,are there any difference between particle and quantum of field?Do the value of field coincide with the wave function or not?

6. Feb 24, 2013

### Staff: Mentor

Particles are excitations of fields in quantum field theory, but I don't see the relation to the original question.

7. Feb 24, 2013

### ndung200790

Is that correct if I say c$^{+}$exp{p.x}/vacum> is the value of field of representation of a quantum of field.This quantum corresponds with a particle having the mean value of momentum equalling p.

8. Feb 24, 2013

### ndung200790

I mean a well defined momentum of a quantum of field corresponds with uncertainty of momentum of a particle having that momentum.

9. Feb 25, 2013

### ndung200790

I was wrong!Each ''quantum field value'' corresponds with a plane wave of particle!