Quantum mechanics formalisms and conservation of energy

[KleinMoretti]

TL;DR Summary

conservation of energy after measurement in different formalism of qm

in a recent thread @PeterDonis said that in standard quantum mechanics a system being measured must be considered open and you need to include the measurement device if you want to talk about conservation of energy, my question is if the formalism of qm used changes anything here?

 

[PeterDonis]

the formalism of qm used

What do you mean by this?

 

[KleinMoretti]

What do you mean by this?

so for example if you used the Heisenberg picture as oppose to the Schrödinger

 

[PeterDonis]

so for example if you used the Heisenberg picture as oppose to the Schrödinger

Why would that make a difference? Both pictures are mathematically equivalent and make the same predictions.

 

[KleinMoretti]

so what you said in that thread I mentioned,
"However, it should be noted that, in basic QM (i.e., without adopting any particular interpretation--discussion of how particular QM interpretations deal with collapse belongs in the interpretations subforum), "collapse" is not claimed to be an actual physical process; it's just an update you make in your mathematical model when you know the result of a measurement. Since making a measurement on a quantum system requires the system to be open, i.e., it has to interact with other systems, one would not expect conservation laws to hold for the measured system alone, since conserved quantities can be exchanged through the interaction. For example, the measured system could gain or lose energy from the interaction that takes place during meaurement, so its energy taken in isolation would not be conserved. Only the energy of the whole larger system, including the measuring device and anything else the measuring device interacted with, would be conserved."

is true regardless of the picture of qm you use right?

 

[PeterDonis]

is true regardless of the picture of qm you use right?

It's true in both the Heisenberg and Schrodinger pictures, yes.

 

[KleinMoretti]

It's true in both the Heisenberg and Schrodinger pictures, yes.

so just for further clarification when someone says something is true or holds in standard or basic qm, the formulation (e.g Heisenberg, Schrödinger, interaction, etc) is not relevant?

 

[PeterDonis]

when someone says something is true or holds in standard or basic qm, the formulation (e.g Heisenberg, Schrödinger, interaction, etc) is not relevant?

Yes.

 

[KleinMoretti]

Yes.

The reason I asked is because I came across a thread in physics stack that mentions that there are ways to make the Heisenberg and Schrödinger formulations non-equivalent and then I remember your comment from that previous thread here and got me wondering if the formulation one uses changes anything regarding conservation of energy after measurement.

 

[PeterDonis]

I came across a thread in physics stack that mentions that there are ways to make the Heisenberg and Schrödinger formulations non-equivalent

Two of the papers referenced in that response are talking about quantum field theory, which is different from non-relativistic QM. In QFT it's not even clear at the outset what the "pictures" mean, since their definition requires a notion of "time evolution" (the difference in "pictures" in NRQM is in how much of the time evolution you put in the states vs. the operators), and in QFT there is no such notion, at least not in the basic formulation, because any such notion would be frame-dependent.

The other paper talks about methods of quantization other than the Born-Jordan prescription. That paper appears to be talking about NRQM, but AFAIK nobody actually uses any other methods in NQRM. I don't think that paper's analysis would even apply to QFT, since in QFT the whole question of "methods of quantization" is different.

 

[KleinMoretti]

Two of the papers referenced in that response are talking about quantum field theory, which is different from non-relativistic QM. In QFT it's not even clear at the outset what the "pictures" mean, since their definition requires a notion of "time evolution" (the difference in "pictures" in NRQM is in how much of the time evolution you put in the states vs. the operators), and in QFT there is no such notion, at least not in the basic formulation, because any such notion would be frame-dependent.

The other paper talks about methods of quantization other than the Born-Jordan prescription. That paper appears to be talking about NRQM, but AFAIK nobody actually uses any other methods in NQRM. I don't think that paper's analysis would even apply to QFT, since in QFT the whole question of "methods of quantization" is different.

another reason I was curious is because whenever I look through discussions or questions regarding QM (for example my question about conservation of energy in QM in that previous thread) most answers are with respect to quantum mechanics in general without mention of a formulation/picture which is why I wonder if that simply meant the answer is true regardless of the formulation/picture.

 

[PeterDonis]

I wonder if that simply meant the answer is true regardless of the formulation/picture.

As has been stated, it does.

At this point the OP question has been answered and this thread is closed.