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Has anyone ever modelled quantum measurement as a resonance effect, that is created by introducing a measuring device into the quantum system?

An analogy may explain what I mean: if you take the free air, this can oscillate at any frequency of sound, because the air has no constraints placed on it. However, if we introduce an organ pipe and encase the air, the air in that pipe will tend to oscillate at the resonance frequency of the pipe.

By constraining the air in the pipe, we reduce its freedom to oscillate at any frequency, and coerce it to oscillate at the pipe resonance frequency.

In this analogy, the air is the quantum wave, and the organ pipe the measuring device.

Before measurement, a quantum wave function is spread out spatially, and the particle it represents has lots of freedom regarding where it can locate. After measurement, the wave function collapses to a single point in space, which is the measured location of the particle.

Could introducing the measurement device into the quantum system cause this collapse of wave function via a resonance effect acting on the quantum wave? Before the measurement device is introduced, the system enjoys freedom. But inserting the measurement device into the system maybe constrains the quantum wave, restricting its positional freedom, via resonance effects produced in the combined system and measurement device.

In this resonance idea, what we view as a particle is merely a collapsed quantum wave, when the wave is constrained by resonance to a particular location.

Note that although I have a BSc degree in physics, my understanding of quantum mechanics is just at the level of the popular science books written by leading theoretical physicists. So if possible, please keep any answers roughtly at the popular science level.

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A measurement is an interaction that produces a record. As such a measurement is governed by the same laws of physics as other interactions and it can't break those laws. The equations of motion of quantum systems such as the Schrodinger equation are not compatible with collapse. They do not predict anything that resembles what you described here:

Before measurement, a quantum wave function is spread out spatially, and the particle it represents has lots of freedom regarding where it can locate. After measurement, the wave function collapses to a single point in space, which is the measured location of the particle.

To get anything resembling collapse you would have to modify the equations of motion of quantum theory, e.g - by explicitly introducing collapse terms as in spontaneous collapse theories:

https://arxiv.org/abs/2310.14969

This sort of theory is currently unable to reproduce the predictions of relativistic quantum theories and these constitute the bulk of predictions made using quantum theory:

https://arxiv.org/abs/2205.00568

If you want to understand measurement in quantum theory, as opposed to alternatives to quantum theory that feature collapse, then you have to treat the measurement device as a quantum system. The measurement device $M$ interacts with the system $S$ being measured and its environment $E$. So if you have a system in the state $\alpha|a\rangle_S+\beta|b\rangle_S$ and you do a non-destructive measurement you get: $$\alpha|a\rangle_S|a\rangle_M|a\rangle_E+\beta|b\rangle_S|b\rangle_M|b\rangle_E$$

This process supresses interference between the $|a\rangle_S,|b\rangle_S$ states and this effect is called decoherence:

https://arxiv.org/abs/1911.06282

Decoherence also arises in more general kinds of measurement process such as destructive measurements:

https://arxiv.org/abs/0712.0149

All that matters is that information about the measurement result spreads into the environment so that you can't undo the measurement.

What happens as a result of decoherence is that you effectively have multiple non-interacting versions of the same system and the relevant measurement results:

https://arxiv.org/abs/1111.2189

This is often called the many worlds interpretation of quantum theory but it is just an implication of quantum theory.

The set of states selected by decoherence is just the set of states copied into the environment and this isn't a resonance effect.

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  • $\begingroup$ I am not specifically disagreeing with this answer, but simply labeling it for what it is: A description following the Many Worlds Interpretation of QM (MWI). The arguments presented about collapse/decoherence are not generally agreed upon from one interpretation to another. $\endgroup$
    – DrChinese
    Commented Jun 23 at 15:35
  • $\begingroup$ @DrChinese Nature tells us exactly what the "collapse" represents. It's an irreversible energy transfer process. "Before the collapse" a quantum of energy was in the quantum system. "After the collapse" that energy is in the measurement system. One can find copper blocks near the LHC beamline where this energy transfer is, on average, so large that it heats solid chunks of metal by tens of degrees. I fail to understand why we are making such a big affair out of a process that is perfectly well defined in classical terms. $\endgroup$
    – FlatterMann
    Commented Jul 2 at 0:23
  • $\begingroup$ @FlatterMann Try reading arxiv.org/abs/quant-ph/0605249 $\endgroup$
    – alanf
    Commented Jul 2 at 7:37
  • $\begingroup$ @alanf Yes, the Hyperion thing is total intellectual nonsense. Just because some theorists don't understand the quantum-classical transition (because we are not teaching it at the university level), which is NOT an ensemble effect, doesn't mean that it's hard to understand. Mott solved the basic problem in 1929. It happens because of conditional probabilities on one copy of the system. One can never get a conditional probability out of an ensemble, which by definition is statistically independent. $\endgroup$
    – FlatterMann
    Commented Jul 2 at 17:30
  • $\begingroup$ @FlatterMann You can't have conditional probabilities if the square amplitudes don't obey the rules of probability as they don't in interference experiments. Talk of conditional probabilities puts the cart before the horse. The Mott analysis only describes a very limited subset of measurements arxiv.org/abs/0712.0149 $\endgroup$
    – alanf
    Commented Jul 3 at 8:33
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What you are describing ("a resonance effect created by the measuring device") is not possible... unless there are FTL (faster than light) influences (which is of course a possibility). If there were FTL influences, the measuring devices could conceivably be themselves in some kind of communication or mutual influence.

The reason is that far distant measurements on entangled particle pairs - measured on the same basis, say by Alice and Bob - always produce 100% certain results. A measurement by Alice will allow her to know the result of Bob's measurement on the same basis - regardless of distance. If the measurement apparatus itself was a variable, you would get a result less than 100% by an easily measurable amount. Out of thousands of experiments, such has never been observed.

Of course, there are a number of nonlocal formulations of quantum mechanics that are considered viable. Standard QM, in fact, features contextuality which does not respect locality. As @alanf correctly points out, there are viable local formulations too (such as the Many Worlds Interpretation, MWI, which he espouses).

Regardless, it is clear that the measurement device itself is not a statistically significant participant in the outcome through some yet-to-be discovered local (not FTL) mechanism.

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    $\begingroup$ This has nothing to do with quantum mechanics. One can do this classically with envelopes containing correlated messages as well. Knowing something about a physical state far away is, however, not a physical interaction. All known physical versions of quantum mechanics are indeed local. That wave functions are not separable is often being mistake for non-locality but since wave functions don't live in physical space that mistake is rather basic. One should probably ask how we should modify the teaching methods related to quantum mechanics to avoid such misunderstandings. $\endgroup$
    – FlatterMann
    Commented Jun 23 at 3:15
  • $\begingroup$ @FlatterMann Entanglement is not explainable in classical terms, and certainly not with envelopes. The purpose of my answer is not to debate whether there is nonlocality in QM; rather to demonstrate that the measurement apparati themselves do not play a starring role in the identical outcomes of measurements made independently at a distance from each other. Because if they did play such a role, then they would need to be in FTL communication with each other. Since most scientists reject that particular hypothetical FTL concept, we conclude the measurement devices did not dictate the outcomes. $\endgroup$
    – DrChinese
    Commented Jun 23 at 15:47
  • $\begingroup$ Entanglement is necessitated by relativity, which at least in my books is a classical property. The measurement systems do change the measurement outcomes, whether we like it or not. This follows immediately from the Born rule, if we want to stay at the level of the non-relativistic theory. It is only "how" they change these outcomes while still preserving the relativistic structure of the universe that upsets some people. I agree that there is a counterintuitive component there, but it can be broken down into pieces at the educational level that remove much of the "surprise". $\endgroup$
    – FlatterMann
    Commented Jun 23 at 17:00
  • $\begingroup$ @FlatterMann Relativity has nothing whatsoever to do with entanglement. Entanglement is fully explained by non-relativistic QM, and does not respect c - as has been confirmed by hundreds of experiments. The Born rule does not ascribe the measurement outcome as being "caused by" the measurement apparatus, and in fact does not define "measurement" - when/where it occurs or even what it consists of. Not sure why you would even mention the Born rule in this context. (Or mention relativity, for that matter.) $\endgroup$
    – DrChinese
    Commented Jun 23 at 17:55
  • $\begingroup$ Yes, "shut up and calculate" non-relativistic QM gives you the correct math, but it doesn't give you any intuitive reason why the math has to be that way and not some other. A relativistic approach gives the correct answer to "why" in two sentences flat. Even Bell recognized that, by the way. He mentions it in the last few sentences of his paper. The Born rule tells you that the spectral response of the measurement system determines the possible outcomes of a measurement. In experimental terms Born simply says that a spectrometer with a passband of 500-1000nm can't measure a 1500nm quantum. $\endgroup$
    – FlatterMann
    Commented Jun 23 at 21:52
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A measurement doesn't modify a wave function any more than throwing dice and recording the outcome modifies the probability distribution of dice. Wave functions are ensemble averages. They are abstract mathematical descriptions of the average behavior of an infinite number of copies of the same physical system. They can be indeed be derived from the same fundamental assumptions as probability distributions.

One of the problems with the way we talk about quantum mechanics comes from the very unfortunate choice of "particles" as the basis of quantum systems. There are no particles in Planck's theory of thermal radiation. Planck simply assumed that the energy that a hot body radiates into the vacuum is a multiple of a smallest unit. There are equally no particles in the photoelectric effect. There the metal absorbs a quantum of energy from the electromagnetic field. More generally there is no experimental evidence at all that these quanta of energy are bound to some form of corpuscular matter.

Instead, a quantum is the irreversible exchange of a small amount of energy, momentum, angular momentum and charges between two physical systems. When and where these exchanges are taking place can not be predicted and there is no theory that describes the dynamics of a single quantum exchange. Instead quantum mechanics is the ensemble theory of many such exchanges. We can predict the average frequencies of these quanta as a function of position, time, energy, momentum, angular momentum and charge.

What the measurement device therefor does is to absorb these quanta from the quantum system under measurement. Without the measurement device the energy will stay forever in the quantum system. With the coupling to the measurement device the quantum system will lose this energy forever. That's the physics behind "the collapse of the wave function". It's a trivial misnomer that should never have been introduced in the first place because it completely obfuscates the rather trivial physics that quantum mechanics describes.

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  • $\begingroup$ "...the rather trivial physics that quantum mechanics describes." Really? You are the only person I have ever heard describe QM as trivial. $\endgroup$
    – DrChinese
    Commented Jun 23 at 15:58
  • $\begingroup$ @DrChinese Quantum mechanics describes systems that behave similar to a Geiger-Mueller counter. They produce random looking time series of energy, momentum, angular momentum and charge transfers. That is, in my books, as simple as it comes in terms of physical systems. I would agree that we are obfuscating much of what the theory is about, though. I don't know why we are doing that, to be honest. It is not necessary and counterproductive for the learner of quantum mechanics. $\endgroup$
    – FlatterMann
    Commented Jun 23 at 16:53
  • $\begingroup$ "Quantum mechanics describes systems that behave similar to a Geiger-Mueller counter." Even more utter nonsense. I'm not sure where you have ever heard/read something like this, but I'd enjoy seeing a reference. From wiki: "Quantum mechanics is a fundamental theory in physics that describes the behavior of nature at and below the scale of atoms". The word "Geiger" is mentioned exactly... nowhere. Not mentioned in Plato either. Apparently, your analogy is what is counterproductive to learning QM. $\endgroup$
    – DrChinese
    Commented Jun 23 at 18:20
  • $\begingroup$ @DrChinese I got that "utter nonsense" from building single quantum detectors in high energy physics. That is the phenomenology of quantum systems at the single quantum level. No offense, but this isn't about philosophy. This is about telling students about the actual natural observations that are underlying the theory. $\endgroup$
    – FlatterMann
    Commented Jun 23 at 20:16
  • $\begingroup$ References for your strange statements would be welcome. QM describes systems like Geiger counters, really? QM is trivial, really? And why would you even mention the Born rule when discussing perfect 100% correlations of remote entangled systems (which proves definitively that a quantum measurement apparatus cannot individually affect outcomes)? See for example Fig. 3, values for zero & +/- .5 pi showing perfect correlations: arxiv.org/pdf/quant-ph/9810080 Born is not mentioned. Your ideas about energy exchange might be relevant for some basis types, but certainly not for spin tests. $\endgroup$
    – DrChinese
    Commented Jun 24 at 0:17

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