Something about the theory of quantum measurement/collapse in the case of quantum fields... Suppose I have a field, either a scalar, vector or spinor, that I want to describe as a quantum object. For simplicity let's say that it's a scalar field ##\phi (\mathbf{x})##, where the ##\mathbf{x}## is a 3D position vector. The corresponding field operator is denoted ##\hat{\phi}(\mathbf{x})##.(adsbygoogle = window.adsbygoogle || []).push({});

If I do a measurement of the field strength ##\phi (\mathbf{x})## at some point ##\mathbf{x}##, does this also affect the field at points neighboring ##\mathbf{x}## ? If the field is required to be continuous, the "collapse" of the field strength to some value at point ##\mathbf{x}## is bound to limit the field strengths in some open 3-sphere containing ##\mathbf{x}## to an arbitrarily small neigborhood of the measured value.

The differential forms of Maxwell, Klein-Gordon, Schrödinger equations etc. obviously assume that the field is a continuous and differentiable function, but it's possible to circumvent this limitation by converting the eqs to integral form. Has the quantum theory of measurement even been developed to the point of being able to handle field strength measurements?

Edit: Clearly one can't have an arbitrarily small "test charge" for measuring the field without affecting it significantly at the same time, as electric charge is quantized.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A Field strength measurement and continuity

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**