I am also confused in energy in QT

[wangyi]

Is it really conserved or not?
In one hand, from the Heisenberg principle, \delta E \delta t ~h, then energy is not strictly conserved.

While in the other hand, from the Feynman diagrams we are drawing, the four-vector of momentum is conserved in every vertex, so energy is conserved everywhere.

I think some of the examples raised in the post before can not well illustrate the broken of energy conservation rule in quantum level, because they can be explained as the energy-0(or nearly 0) state creats a pair of particles, one carries positive energy and the other carries negative energy.

regards
wangyi

 

[marlon]

https://www.physicsforums.com/journal.php?s=&action=view&journalid=13790&perpage=10&page=3

Scroll down to the what are virtual particles entry.

Energy is conserved between the initial and final state but not during the transition between these states

marlon

 

[dextercioby]

Incidentally,when computing Green functions (closely linked to S-matrix elements) u'll end up with a $\delta^{4}\left(\mbox{incoming momenta-outgoing momenta}\right)$ which should say it all.

Daniel.

 

[marlon]

Incidentally,when computing Green functions (closely linked to S-matrix elements) u'll end up with a $\delta^{4}\left(\mbox{incoming momenta-outgoing momenta}\right)$ which should say it all.

Daniel.

Hence, energy conservation is respected between final and initial state. When it comes to virtual particles, momentum-conservation is respected AT ALL TIMES because of the above formula. Each vertex has such relations and besides they determin which exact momentum the virtual particles will have to 'carry over'

marlon

 

[wangyi]

Do you mean this:
Energy conservation is always respected.

But how is the superposition of state having different energy?
When we measure it, it fall into each energy with posibility.
Does it mean when we measure it, we must pass energy to it?

In the same way, if a state is a superposition of positive charge and negative charge(can this be made? I think it can, but not sure), when we measure the charge, it falls into either positive or negative. But it is not likely true that we pass any charge to it.

 

[wangyi]

I now think it is like this, do you agree with me?
Energy conservation is always respected.
the deltaE deltaT relation only tells us that the particle can go off the mass-shell by amount deltaE during time order deltaT?

 

[marlon]

I now think it is like this, do you agree with me?
Energy conservation is always respected.
the deltaE deltaT relation only tells us that the particle can go off the mass-shell by amount deltaE during time order deltaT?

correct

marlon