The discussion revolves around whether Heisenberg's Energy-Time uncertainty inequality implies a violation of energy conservation in quantum mechanics. Participants explore the implications of the uncertainty principle on the concept of energy conservation, particularly in the context of quantum states and measurements.
Participants do not reach a consensus on whether the uncertainty principle implies non-conservation of energy. Multiple competing views are presented, with some asserting that conservation is maintained while others express skepticism about the implications of the uncertainty principle.
Limitations in the discussion include varying interpretations of the energy-time uncertainty relation, the dependence on definitions of observables, and unresolved questions regarding the implications of measurement duration on energy values.
reilly said:First, energy conservation, when valid, applies to a system throughout it's lifetime, not just for beginning and final states. (See, for example, Noether's Thrm.)
Well, obviously this is your opinion on this matter and i respect it. I just do not agree with what you are saying but there is no point in starting a debate on this.With my very cynical hat on, I'll say, once again, 'virtual' particles are a convenient conceptual fiction -- a perusal of the history of QFT will flesh-out this notion. They are useful to the theoretician, as long as she does not take them too seriously.
I am still hoping that you will pick a specific Feynman diagram (a weak interaction at tree level with a virtual W boson in the intermediate state if you want, or anything else) so that we can write down the expression and show that the total energy is conserved even in the intermediate state.marlon said:Yep that is true. I don't think anybody tries to counter that. The question is ofcourse about the "when valid"-part.
Well, obviously this is your opinion on this matter and i respect it. I just do not agree with what you are saying but there is no point in starting a debate on this.
regards
marlon
nrqed said:I am still hoping that you will pick a specific Feynman diagram (a weak interaction at tree level with a virtual W boson in the intermediate state if you want, or anything else) so that we can write down the expression and show that the total energy is conserved even in the intermediate state.
Yes that is true. I do see your point and i hope that i have made my point more clear. Again, i think most of the confusion/discussion was actually caused by the fact that i did not state my point clear enough. I hope that's solved now.Let me consider the electron-positron scattering diagram in the s channel at tree level. The photon in the intermediate state is off-shell of course. But the energy (as well as the three-momentum) of the off-shell photon is euqal to the energy (and three-momentum) of the initial electron and positron, q_{\gamma}= P_{electron} + P_{positron} (where the P's are the physical four-momenta of the electron and positron). Therefore energy is conserved. QED (no pun intended)
Regards
Patrick
It still seems to me that we are not saying the same thing. Well, it seems like some statements agree with me and then other statements are in disagreement. I agree that the energy is conserved throughout the entire diagram thanks to the W being off-shell, but then you seem to say the opposite in the next sentences so I am a bit confused.marlon said:Ok. How about we look at the Feynman diagram of the neutron beta decay. This is the example that i have used several times to illustrate my point. The W boson NEEDS to be off mass shell because a real W boson is far to heavy. As we have agreed before, energyconservation is defined for initial and final states, for real particles, etc etc... For energyconservation to be respected, the W boson should be real yet this is impossible. Hence the apparent violation. Now ofcourse, in the beta decay energy is indeed conserved throughout the entire diagram (thanks to the W boson being virtual, not real). I know that that is exactly what you want to say and it has been my fault not to agree with you on that directly. I should have been more clear on that.
The article I quoted shows, not that you can measure energy in an instant, but that dE*dT > h can be violated.vanesch said:Yes, this is exactly the paper that koantum talked about and which I commented. It is apparently true that the interaction between the measurement apparatus and the system can be arbitrary short, I didn't realize this. But this was not the claim. The claim was that it takes time dT to have the result available.
In the Bohm example, in a very short time, the px momentum (and eventually, the py momentum) energy equivalent has been transferred to the condenser state...
But now we must still measure the energy of the condenser !
While it is true (and I ignored this) that you can now consider the condensers as independent from the system under measurement, you will now have a new energy measurement to perform, so the problem starts all over again.
If you accept to talk about the quantum states of the condensers, after the interaction with the particle, they are now entangled with the particle states, but their own states are not yet sufficiently separated for them to be "pointer states". They will need to evolve during at least a time dT, before they are "grossly orthogonal" for different energy input states which are of the order of dE.
Nevertheless (and that's what I learned), the advantage of this is that you can have rapidly successing energy measurements on a same system.
However, for instance, you do not have the result available in very short time (so that you could take a decision based upon that to act on the system, for instance).
Do they violate energy conservation?
We are really using the quantum-mechanical approximation method known as perturbation theory. In perturbation theory, systems can go through intermediate "virtual states" that normally have energies different from that of the initial and final states. This is because of another uncertainty principle, which relates time and energy.
In the pictured example, we consider an intermediate state with a virtual photon in it. It isn't classically possible for a charged particle to just emit a photon and remain unchanged (except for recoil) itself. The state with the photon in it has too much energy, assuming conservation of momentum. However, since the intermediate state lasts only a short time, the state's energy becomes uncertain, and it can actually have the same energy as the initial and final states. This allows the system to pass through this state with some probability without violating energy conservation.
Some descriptions of this phenomenon instead say that the energy of the system becomes uncertain for a short period of time, that energy is somehow "borrowed" for a brief interval. This is just another way of talking about the same mathematics. However, it obscures the fact that all this talk of virtual states is just an approximation to quantum mechanics, in which energy is conserved at all times. The way I've described it also corresponds to the usual way of talking about Feynman diagrams, in which energy is conserved, but virtual particles can carry amounts of energy not normally allowed by the laws of motion.