Degrees of freedom

dev70

i have read it, starting from Energy-time uncertainty principle to quantum fluctuation. And i dont find any exact interpretation of the energy-time uncertainty principle. Some say it means energy conservation can be violated for some time some say its not possible. I am stuck at that point. Whats the reality?

andrien

energy is conserved at all moment,it is just that particles can have different momenta which does not satisfy on-shell condition.

Jano L.

Depends on what you mean by energy. In quantum theory, there are states which are not eigenstates of the Hamiltonian and there are people who refuse to assume it has a meaning for such states. Then the question is dissolved, energy does not exist, hence no question about its conservation.

Of course, this is not very satisfactory, because from thermodynamics we have good reasons to believe that energy has meaning all the time and is conserved all the time.

The proposals for temporary violations of such conservation are not very credible, because that would require special equations of motion (for example, not reversible) and I think there are none in the most basic theory. Also, if there was temporary non-conservation, one would expect that the energy would fluctuate away (random walk) or perform some run-away. The fact that these things do not happen (it seems) are best evidence that the energy is conserved all the time.

dev70

thank you everyone for your help..