User:Martin Hogbin/MP

Some thoughts on the Measurement Problem in Quantum Mechanics

Is there a definition of measurement that does not require human or other conscious intervention?

Consider a measurement to measure which slit a particle went through in a double slit experiment. The aim of the measurement is to turn the small uncertainty in the position of the particle into a much larger uncertainty, say in the position of an indicator orthe flow of current in an indicator lamp.

Suppose however that incertainty, according to some measure is conserved. In other words, it is not possible to turn a same uncertainty into a large one. Whenever this would happen, either through an intentional experiment or by chance, a measurement is deemed to have been made and the wave function collapses.

If uncertainty is a conserved quantity then there should be a related symmetry according to Noether's theorem or its quantum form, the Ward-Takahashi identity.