Measurement

The vast majority of experimental evidence for the success of Quantum Field Theory in describing the elementary particles of nature comes from the comparison of particle collisions with calculations of scattering "amplitudes". These amplitudes are numbers which describe the relative importance of various elementary field interactions in contributing to the total process of one particle colliding with (scattering off of) another. The amplitudes are added together and the dependence of their total magnitude on various physical variables, such as scattering angle, is compared with that actually observed. The total amplitude which describes the transition from an initial set of states (the incoming particles) to a final set of states (the outgoing particles) is equivalent to the statistical correlation of the incoming and outgoing states weighted by the exponent of the classical action associated with the fields. Hence we actually compute the dependence of field correlations on physical parameters. It is interesting to note that the total amplitude must be the sum of contributions from every topologically distinct elementary process which obeys the relevant conservation laws.

It is important to understand what the numerical outcomes of measurements depend on:

The measurement of the electromagnetic field of a particle depends on the spacetime frame of reference of the measuring apparatus (which may be another particle). For instance, by moving with the particle, the relative velocity between the particle and the apparatus is zero and hence so is the magnetic field.
The helicity of a particle depends on the spacetime frame of reference, since a Lorentz Transformation may change the sign of the momentum but not that of the spin.
In the coordinate/momentum representation of the field, the magnitudes of various energy modes depend on the spacetime frame of reference of the measuring apparatus. In an accelerating reference frame, a measuring device "sees" a thermal bath of particles which are not there in a (relatively) inertial frame of reference, since there is not a consistent choice of representation between the frames.
Similarly, the only measurable force in a curved spacetime is the "tidal" force, which measures the "spread" between adjacent geodesic paths.
The commutation relations between field operators imply that measurements always disturb the field: the measurement of two different physical properties in two different orders are different measurements.
Uncertainty relationships define which physical properties can coexist. For example, a photon cannot have both a definite angular momentum and a definite polarization, because angular momentum implies a rotating polarization.

Quantum Gravity Concept Map Index:

References

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