A question about Heizenberg uncertainty.

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Discussion Overview

The discussion revolves around the Heisenberg uncertainty principle in the context of quantum field theory (QFT), particularly focusing on the implications of large momentum values and their relationship to uncertainties in momentum and position. Participants explore the conceptual and mathematical nuances of these relationships.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants question how the Heisenberg uncertainty principle applies when a particle's momentum is considered to be very large, seeking clarification on the implications of this scenario.
  • One participant suggests that while momentum can be treated as having a certain value, it is not exact, and for large momentum, the associated uncertainty may be negligible.
  • Another participant raises the question of whether there is a relationship between large momentum and large uncertainty in momentum, proposing that such a relationship could explain the short-scale physics associated with high momentum.
  • Further discussion includes the idea that a significant uncertainty in position may arise from scattering events, affecting the measurement of momentum uncertainty.
  • Participants also discuss the distinction between particles and quanta of fields, questioning whether field values coincide with wave functions and how this relates to the original topic.
  • One participant proposes a mathematical representation of a quantum field and its relation to particle momentum, while another reflects on the relationship between quantum field values and plane waves.

Areas of Agreement / Disagreement

The discussion features multiple competing views, particularly regarding the relationship between momentum and uncertainty, as well as the distinction between particles and quantum fields. No consensus is reached on these topics.

Contextual Notes

Participants express uncertainty regarding the definitions and implications of momentum and uncertainty in the context of quantum field theory. The discussion includes various assumptions about scattering processes and the nature of particles versus fields.

ndung200790
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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?
 
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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.
 
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.
 
ndung200790 said:
Is there any relation between great value p and great value of uncertainty in p?

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)
 
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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?
 
ndung200790 said:
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?
Particles are excitations of fields in quantum field theory, but I don't see the relation to the original question.
 
Is that correct if I say c[itex]^{+}[/itex]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.
 
I mean a well defined momentum of a quantum of field corresponds with uncertainty of momentum of a particle having that momentum.
 
I was wrong!Each ''quantum field value'' corresponds with a plane wave of particle!
 

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