A Closer Look at the Randomness of Quantum Measurements in QED

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SUMMARY

The discussion centers on the inherent randomness of measurement results in Quantum Electrodynamics (QED), specifically regarding position observables. It highlights that in the Schrödinger picture of non-relativistic quantum mechanics, nature randomly selects eigenvalues during measurement events. The Path Integral Formulation is noted for computing averages, which are deterministic and do not exhibit randomness. The conversation concludes that while individual measurement outcomes are random, the overall probability distribution can be determined through moments and cumulants.

PREREQUISITES
  • Understanding of Quantum Electrodynamics (QED)
  • Familiarity with the Schrödinger picture of non-relativistic quantum mechanics
  • Knowledge of the Path Integral Formulation in quantum mechanics
  • Concept of probability distributions and statistical moments in quantum theory
NEXT STEPS
  • Explore the implications of randomness in Quantum Electrodynamics
  • Study the differences between the Schrödinger picture and the Path Integral Formulation
  • Investigate the role of statistical moments and cumulants in quantum measurements
  • Learn about probability amplitudes and their significance in quantum transitions
USEFUL FOR

Quantum physicists, researchers in quantum mechanics, and students studying the principles of Quantum Electrodynamics will benefit from this discussion.

LarryS
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In all Quantum Physics experiments, the sequence of measurement results is inherently random.

Consider just the position observable.

In the Schrödinger picture of non-relativistic QM, in each measurement-event, nature steps in and randomly selects one of the observable's eigenvalues/vectors to be the measurement result.

In the non-relativistic version of the Path Integral Formulation, what exactly is nature randomizing when a position measurement occurs? The space-time end point of a path? The entire path (beginning point and ending point)?

Thanks in advance.
 
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The things that are not random in quantum theory are the averages (and generalizations of the average such as the higher order moments or cumulants).

The path integral computes the averages. So in one sense, there is no randomness in the path integral.

The full probability distribution can be recovered from all moments or all the cumulants. Thus these deterministic quantities fully specify the randomness,
 
atyy said:
The path integral computes the averages.

By "averages" do you mean the single probability amplitude of the particle transitioning from one space-time point to a future space-time point?
 

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