Particles from a thermal source

[vanhees71]

If I remember correctly, the quantum jumps are jumps of the state of a single atom, measured through a continuous measurement that produces shot noise in the excited stated but none in the ground state. Thus by observing the presence or absence of shot noise one can see or hear when the atom is in the ground state or in the excited state. And one finds that the atom jumps in both directions (one stimulated, the other spontaneous) and then stays some time before it jumps again, and part of it is controllable externally.

It "jumps" on a macroscopic scale. Shot noise is of course only measurable on an ensemble. Here you use a single atom and excite it with lasers, i.e., you prepare it with a time-dependent external em. field. The shot noise comes from very many excitation-relaxation processes. So it's no contradiction to the ensemble interpretation at all. I still don't know, how to make sense of the probabilistic content of QT according to Born's rule if not by measuring an ensemble, be it the preparation of many identical atoms or, as in this case, a single atom in a trap, a quantum dot and other fascinating ways the AMO physicists can handle nowadays!

 

[A. Neumaier]

It "jumps" on a macroscopic scale. Shot noise is of course only measurable on an ensemble. Here you use a single atom and excite it with lasers, i.e., you prepare it with a time-dependent external em. field. The shot noise comes from very many excitation-relaxation processes. So it's no contradiction to the ensemble interpretation at all. I still don't know, how to make sense of the probabilistic content of QT according to Born's rule if not by measuring an ensemble, be it the preparation of many identical atoms or, as in this case, a single atom in a trap, a quantum dot and other fascinating ways the AMO physicists can handle nowadays!

Whatever the origin of the shot noise, its presence indicates an excited state of the single atom, and its absence indicates the ground state. Thus by observing the statistics of the shot noise you can observe how the atom changes states. And the observed fact is that the atom remains in the ground state until excited by an external stimulus. Then it jumps at a random time (predictable in the mean) into the excited state and stays there again until at another random time (predictable in the mean) it jumps back to the ground state. Thus one can predict only the fraction of time the atom is in one eigenstate of H or the other, consistent with the ensemble interpretation. However, in addition, one can see from the experiment the temporal behavior of the single atom, and it jumps! There is only one atom, so there is no question that it is the single system that jumps. This is an observable fact as much as anything that can be observed in the quantum domain.

 

[vanhees71]

I only object against "jump". It sounds like a discontinuous process of some quantity, but there's no such thing in quantum theory. The transition from one to the other state is a continuous process. It takes time to get from one state of definite energy to another. This is the content of the time-energy uncertainty relation.

 

[A. Neumaier]

The transition from one to the other state is a continuous process. It takes time to get from one state of definite energy to another. This is the content of the time-energy uncertainty relation.

Just as a measurement (or a jump of a swimmer into the water) takes time. The Copenhagen interpretation idealizes the measurement to be instantaneous, and hence works with an instantaneous jump. As these experiments show, this is a quite reasonable approximation, unless you highly resolve the time. It was certainly fully adequate for the measurements done at the time the Copenhagen interpretation was formed.

It is the same kind of idealization physicists use when they say (in derivations of linear response theory, say) that they switch on the interaction at time $t=0$. Switching also takes time but is treated as instantaneous, since the difference doesn't matter for the purpose at hand.

 

[stevendaryl]

Bohmian mechanics always takes a view that the full closed system is in a pure state, even if an open subsystem is in a mixed state.

That isn't clear to me. Surely you can use Bohmian mechanics to reason about mixed states? A mixed state for the full system can be interpreted as ignorance about the true wave function. You could do the same thing in Bohmian mechanics, right?

 

[Demystifier]

That isn't clear to me. Surely you can use Bohmian mechanics to reason about mixed states? A mixed state for the full system can be interpreted as ignorance about the true wave function. You could do the same thing in Bohmian mechanics, right?

Right! What I meant to say is that you cannot calculate deterministic Bohmian trajectories if you only know the mixed state.

 

[Dilatino]

Just as a measurement (or a jump of a swimmer into the water) takes time. The Copenhagen interpretation idealizes the measurement to be instantaneous, and hence works with an instantaneous jump. As these experiments show, this is a quite reasonable approximation, unless you highly resolve the time. It was certainly fully adequate for the measurements done at the time the Copenhagen interpretation was formed.

It is the same kind of idealization physicists use when they say (in derivations of linear response theory, say) that they switch on the interaction at time $t=0$. Switching also takes time but is treated as instantaneous, since the difference doesn't matter for the purpose at hand.

But is there not, due to the time/energy uncertainty, an upper limit to how much you could increase the time resolution to observe a quantum process without distroying the system?
Also, how can one observe the measurement process itself, as observing something means measuring it ...?

 

[A. Neumaier]

But is there not, due to the time/energy uncertainty, an upper limit to how much you could increase the time resolution to observe a quantum process without destroying the system?

Yes, there is, as in any idealized description. Modeling the jump of the swimmer with a camera resolution (24 pictures per second) one clearly sees a continuous movement. In the quantum case, it is similar but slifghtly different: One cannot say between two shot noise events whether the atom observed is now undergoing a jump, but one can say it in retrospect after sufficient time has passed. And one can deduce estimates for the time needed to complete a jump (as in the case of a swimmer).

Also, how can one observe the measurement process itself, as observing something means measuring it ...?

As always in quantum mechanics, from the outside. Thus if you model the detector for measuring the small system in quantum terms then you need another external observer to observe the detector. One needs to end this after finitely meany steps, not to run into the paradox of Wigner's friend.

 

[A. Neumaier]

I've not found the time to read these papers.

Maybe reading Section 7 of http://arxiv.org/abs/1511.01069 is enough to understand how the state of single atoms can be continuously monitored and shows jump of diffusion properties depending on the kind of measurement it is subjected to.

This justifies the collapse as an instantaneous approximation on the system-only level to what happens in an interaction with an appropriate measurement device on the system+detector level.

 

[vanhees71]

Are you saying that quantum dynamics cannot discribe this "jump", but that it necessarily have to be described by classical physics or something outside of any model/theory? That's what "collapse" means as I understand it. It may of course be that there are other definitions of collapse than this. I'll have a look at the paper.

 

[vanhees71]

Ok, Sect. 7 of the above paper answers my question satisfactorily! It's NOT a collapse but good old Wigner-Weisskopf. There are no jumps but rapid exponential decays (which are of course an approximation as is well known for decades, because strictly exponential decay is imcompatible with quantum theory; see Sakurai, Modern quantum Mechanics, but in many cases a very good approximation) with the usual probabilistic meaning of transition matrix elements. It's all very well compatible with the minimal interpretation!

 

[A. Neumaier]

Are you saying that quantum dynamics cannot discribe this "jump", but that it necessarily have to be described by classical physics or something outside of any model/theory?

Not quite. I answered this a moment ago in a new thread.