Undergrad Conservation of energy and measurement problem

[entropy1]

If we have a two dimensional measurementbasis, then we have two possible outcomes of the measurement. Now I figured: considering the law of conservation of energy, if one particle goes in, one and only one can come out. So outcome "both results simultaneously" cannot happen, for that would violate the law of conservation of energy. So would "neither outcome". So, that leaves us with one outcome or the other.

So I am wondering if the law of conservation of energy could account for measuring only single outcomes? (Measurement problem)

 

[PeterDonis]

I am wondering if the law of conservation of energy could account for measuring only single outcomes?

No, it can't. In the many worlds interpretation, the measured system becomes entangled with the measuring device, and the whole entangled state is still an eigenstate of total energy with the same eigenvalue. In the case of measuring a single particle, each "branch" of the entangled wave function only has one particle in it, so one particle goes in and one particle comes out. But because there are multiple branches, you can't attribute the total energy to each branch separately; you can only attribute it to the entire entangled wave function as a whole. Neither branch has a well-defined energy by itself, because neither branch is a well-defined state by itself; only the full entangled wave function is a well-defined state.

 

[A. Neumaier]

If we have a two dimensional measurementbasis, then we have two possible outcomes of the measurement. Now I figured: considering the law of conservation of energy, if one particle goes in, one and only one can come out. So outcome "both results simultaneously" cannot happen, for that would violate the law of conservation of energy. So would "neither outcome". So, that leaves us with one outcome or the other.

So I am wondering if the law of conservation of energy could account for measuring only single outcomes? (Measurement problem)

In the statistical interpretation of QM, only the expectations of the energy is conserved.

 

[entropy1]

Thanks. I have to study that some.

I vaguely recall that I have asked this very question before. The search function is inadequate for searching threads.