Why can we believe the value of field is fluctuated?

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Discussion Overview

The discussion revolves around the fluctuations of fields at the micro-level, particularly in the context of quantum field theory and the behavior of electromagnetic fields. Participants explore concepts related to quantization, the nature of particles and fields, and the implications of these ideas in quantum mechanics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants question the basis for believing that field values fluctuate at the micro-level, suggesting that the existence of photons may necessitate expressing fields in terms of operators and deducing fluctuations through Heisenberg commutators.
  • There is a query about whether it is necessary or possible to quantize statistical electric fields.
  • One participant discusses the computation of variance for measurable quantities, noting that while the expected value of the electric field in vacuum is zero, the expected value of its square is not obviously zero and may yield infinite results under naive calculations.
  • Another participant raises the issue of quantizing fields in the presence of charges, contrasting classical Coulomb fields with their quantum counterparts.
  • Concerns are expressed regarding the nature of unpolarized light and its relation to fluctuating fields.
  • One participant presents three ideas about the relationship between particles and fields, questioning which, if any, of these ideas is correct.
  • There is a discussion about the global character of photons and the implications for the position representation of zero mass particles in quantum mechanics.

Areas of Agreement / Disagreement

Participants express various viewpoints and questions regarding the nature of fields and particles, with no clear consensus reached on the correctness of the ideas presented. Multiple competing views remain, particularly concerning the quantization of fields and the interpretation of particles.

Contextual Notes

Some discussions involve unresolved mathematical steps, such as the computation of expected values and variances, and the implications of these computations are not fully clarified. Additionally, the definitions and interpretations of terms like "excitations" and "point particles" are not universally agreed upon.

fxdung
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What is the basis for the believe that the value of field is fluctuated at micro-level?Does the existence of photons demontrate the need of express field in form of operators then deducing the fluctuation of quantum field through Heizenberg commutators?
 
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Does we not need or we can not quantize the statistic electric fields?
 
Well, for any measurable quantity [itex]A[/itex], we can get an estimate of how much it varies by computing the variance: [itex]var(A) = \langle A^2 \rangle - \langle A \rangle^2[/itex], where [itex]\langle \rangle[/itex] means taking the expected, or average, value. In vacuum, in the absence of any charges, we can compute [itex]\langle \vec{E}\rangle[/itex], the expected value of the electric field, and we find it's zero. But the computation for [itex]\langle E^2 \rangle[/itex] is not zero, or at least, is not obviously zero. (I believe the naive way of computing it results in an infinite value, which of course, makes no sense. I'm not sure what a more careful analysis yields.)
 
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In the present of charges,existing the longitudinal electric field(statistic field).Why we do not consider the quantization of the fields?Classically the field is Coulomb field,but how is it if we consider ''the corresponding quantum fields''?
 
fxdung said:
What is the basis for the believe that the value of field is fluctuated at micro-level?
The notion of unpolarized light cannot even be expressed in terms of non-fluctuating fields.
 
fxdung said:
In the present of charges,existing the longitudinal electric field(statistic field).Why we do not consider the quantization of the fields?
In QED, the whole electromagnetic field is quantized. But what one sees when starting from the Fock space is only the noninteracting (asymptotic) piece, where the longitudinal part of the field vanishes. The remaining part is created by the interaction, which modifies all field operators.
 
I am confused between three following ideas:
-Particles is product of exciting state of field.But what is the exciting states?
-Field is a huge cluster of many particles between them have exchange interaction and that the number of particles can be fluctuated.Electromagnetic field is a ''set''of photons.
-Particle is a packet of field.But why the particle is a point particle?
Which idea is correct or the all are correct?
 
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I have heard that there is not concept about probability of photon at a position.So photon concept has global character.Then I think that the packet of field of a quantum field(photon) carries the point particle(or point photon) and then having not the Heizenberg relation between position and momentum when the mass of particle is zero.
Quantum mechanics for zero mass particle has not position representaion.It is the answer for my question above.Is it correct?
 
fxdung said:
Quantum mechanics for zero mass particle has no position representation. It is the answer for my question above. Is it correct?
Yes.
 

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