Originally posted by jcsd
You just have to take into account that energy obeys an uncertainty relationship and it's only conserved within the limits allowed by this uncertanity relationship.
I guess I just don't understand
that uncertainty relationship. Can you explain it to us?
Another thing I just realized. This so called uncertainty relationship seems to suggest that there is no problem with an infinite uncertainty in energy. So, I think that just about puts us where we are now. How certain are we of the amount of energy there is in the universe? I am personally just about infinitely uncertain. But according to the uncertainty relationship provided, that's OK. Because I've lived for some number of years, and my uncertainty of the total energy of the universe is huge, so these two factors are in agreement with this uncertainty relationship. Am I misinterpretting?
I do not at all see what this has to do with energy conservation.
Originally posted by jcsd
For example you can think of quantum mechanical tunelling as a particle borrowing energy within the limits of uncertainty, ...
Why would I think of it that way? The QM wavefunction extends to regions of space where classical particles have zero probablity to exist. I don't understand "borrowing energy within the limits of uncertainty." Can you elaborate this borrowing process?
Originally posted by jcsd
Simlairly if you were to perform a measuremnt on a superposed state your results would never violate the conservation of energy.
I agree, but I didn't mean that there would be a violation of energy conseration. I meant that energy conservation just doesn't make sense to me in the case of a superposition of energy eigenstates.
For simplicity, let's say that a system is in a superposition of 2 energy eigenstates, ψ
a and ψ
b, with nondegenerate eigenvalues, E
a and E
b, respectively. Let's say that the superposition is:
ψ = (ψ
a + ψ
b)/√2.
If I measure the energies of some number of these identical systems, then half of the time I will find that the energy is E
a and half of the time I will find that the energy is E
b. It's not that this amount of energy was conserved or something. We can't really say anything about the particular amount of energy of the system until we make the measurement. So, that's why I'm saying it doesn't really make sense to me to speak of energy conservation in this case.
Originally posted by jcsd
The convential interpretaion is the Copenhagen interpretaion suitably adjusted to allow new concepts in quantum measurment such as decoherence.
It is my experience, as well, that the Copenhagen interpretation is the conventional one. I don't know anything about decoherence (I don't even know what it means), though, so I guess that disqualifies me from much of the discussion.