This discussion focuses on the behavior of photons and electrons emitted from a stationary thermal source, modeled as a 2-level system using a 2-dimensional Hilbert space. The density matrix for both particle types is defined as ##\rho=\frac{1}{2} \mathbb{1}_2##, indicating an unpolarized state. The conversation explores the implications of filtering these beams through perfect filters, which results in a completely polarized state. Participants discuss various interpretations of quantum mechanics, particularly regarding the states and observables of individual particles before and after measurement.
PREREQUISITESQuantum physicists, researchers in statistical mechanics, and students exploring the foundations of quantum mechanics will benefit from this discussion.
Demystifier said:Let me try to make an analogy from biology.
(A) To make sense of animals, one also needs plants. (Otherwise animals would have nothing to eat.)
(B) But in a certain limit animals themselves behave like plants, e.g. in a vegetative state.
That's called second quantization in cooked-matter community.vanhees71 said:I'm a 2nd-order vegetarian
Quantum mechanics in the Copenhagen interpretation, with a quantum treatment of the small system and a classical treatment of the detector, is as good an approximation as quantum mechanics of quantum chemists who treat a single molecule by considering the nuclear motion as classical and the electronic motion as quantum. In both cases it is an approximation fully justified under known conditions by a more detailed theory.vanhees71 said:But the derivation contradicts the statement by the Copenhagen doctrine that there are two realms in dynamics, the quantum and the classical. The mentioned derivation proves the opposite: Classical behavior can be explained from quantum dynamics by an appropriate course-graining procedure!
I've not found the time to read these papers. Could you point me to a specific one, where the outcome of the experiment contradicts the minimal interpretation? If this is true then Copenhagen in your definition is a different theory than quantum theory in the minimal interpretation, i.e., then there must be a result that cannot be described by the standard kinematical and dynamical postulates + Born's rule. I can't find any hint to that in the papers you cited!A. Neumaier said:Moreover, quantum mechanics in the Copenhagen interpretation has the strong advantage that it can be applied to single systems. See the six papers mentioned in post #28, where the ensemble interpretation apparently has to pass.
The minimal interpretation makes no assertions about single systems. But the experimental papers (distinguished by their titles) claim that individual quantum jumps of single systems can be observed. They don't need to explain their findings, only ensure that their experiments are done with the proper care. This is why I cited very different papers over a very long time span so that you can see that it is not a fluke.vanhees71 said:I've not found the time to read these papers. Could you point me to a specific one, where the outcome of the experiment contradicts the minimal interpretation? If this is true then Copenhagen in your definition is a different theory than quantum theory in the minimal interpretation, i.e., then there must be a result that cannot be described by the standard kinematical and dynamical postulates + Born's rule. I can't find any hint to that in the papers you cited!
It is your claim, so it is your task to bring the experimental evidence I provided into agreement with your claims.vanhees71 said:In my opinion, there is not the slightest evidence for the reality of any collapse-like dynamics whatsoever!
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.vanhees71 said:if you define shot noise as "quantum jumps", then "quantum jumps" are of course measurable and observed,
Well, I find LL confusing. At page 21 they say that apparatus is classical but attribute a wave function ##\Phi## to the apparatus. Of course, they explain what they mean by "classical" in Eq. (7.3), but it may be misleading to call it classical. The transition from (7.2) to (7.3) is really a "collapse", except that they don't call it so (which is probably what @vanhees71 likes about LL).atyy said:Yes, I am happy if you subscribe to quantum mechanics as given in Landau and Lifshitz. It is wrong but not misleading, ie. it is correct FAPP :)
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 said: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.
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 said: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!
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.vanhees71 said: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.
Demystifier said: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.
Right! What I meant to say is that you cannot calculate deterministic Bohmian trajectories if you only know the mixed state.stevendaryl said: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?
A. Neumaier said: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.
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).Dilatino said: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?
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.Dilatino said:Also, how can one observe the measurement process itself, as observing something means measuring it ...?
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.vanhees71 said:I've not found the time to read these papers.
Not quite. I answered this a moment ago in a new thread.vanhees71 said: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?