I Uncertainty Principle: Theorem or Principle?

[facenian]

Hello, It's been puzzling for me to try to understand this issue. To begin with it is clear that there are basically two principles, the Position-Momentum uncertainty and the Time-Energy uncertainty. It is also clear that there are at least two different interpretations attached to both. One is easy to interpret and according to this interpretation they are rather theorems derived from the formalism. These interpretations are statistical and are given for intance in the books by Griffiths "Intro.. to QM" and by Weinberg "Lectures on QM" and as I said before this is pretty clear and presents no interpretative dificulties.
There are however other interpretations which are not statistical(and are not thoerems and look like real principles) and they refer to individual measurements, which by the way seem the be the original ones used by Bohr, Heisenberg, etc. and there seem not to be agreement for the interpretation of Time-Energy uncertainty.
My question is about the relevance that the original interpretation given by the founding fathers of QM have today since the discussions about interpretation are very messy(for instance lots of papers)

 

[Nugatory]

My question is about the relevance that the original interpretation given by the founding fathers of QM have today since the discussions about interpretation are very messy(for instance lots of papers)

The original formulation of both the time-energy and position-momentum uncertainty principles is pretty much obsolete. The principles are still valid, of course, but they are now understood to be special cases of a more general principle that follows directly from the modern mathematical formulation of QM.

 

[vanhees71]

The energy-time uncertainty relation is special, because in QT time is not an observable but a parameter. For a very good discussion of this issue (also in relativistic context), see the first few pages of Landau&Lifshitz vol. IV.

 

[dextercioby]

Any physical principle or law is either a theorem or an axiom, when looked at from a mathematical point of view. The so-called „uncertainty principle” is a theorem when formulated in terms of the fundamental concepts of the theory of Quantum Mechanics, i.e. states and observables.