|Gloria's collapse model.|
Spontaneous localization models for quantum mechanics are, if you ask me, a particularly ugly modification. In these models, one replaces the collapse upon observation in the Copenhagen interpretation by a large number of little localizations that have the purpose of producing eigenstates upon observation. These localizations that essentially focus the spread of the wave-function are built into the dynamics by some stochastic process, and the rate of collapse depends on the mass of the particles (the higher the mass, the higher the localization rate). The purpose of these models is to explain why we measure the effects of superposition, but never a superposition itself, and never experience macroscopic objects in superpositions.
Unfortunately, I have no reason to believe that nature gives a damn what I find ugly or not, and quite possibly you don’t care either. And so, as a phenomenologist, the relevant question that remains is whether spontaneous localization models are a description of nature that agrees with observation.
And, to be fair, on that account spontaneous localization models are actually quite appealing. That is because their effects, or the parameters of the model respectively, can be bounded both from above and below. The reason is that the collapse processes have to be efficient enough to produce eigenstates upon observation, but not so efficient as to wash out the effects of quantum superpositions that we observe.
The former bound on the efficient production of observable eigenstates becomes ambiguous however if you allow for a many worlds interpretation because then you don’t have to be bothered by macroscopic superpositions. Alas, the intersection of the groups of many worlds believers and spontaneous localization believers is an empty set. Therefore, the spontaneous localization approach has a range of parameters with macroscopic superpositions that is “philosophically unsatisfactory,” as Feldman and Tumulka put it in their (very readable) paper (arXiv:1109.6579). In other words, if you allow for a many worlds situation whose main feature is the absence of collapse, then there really is no point to add stochastic localization on top of that. So it’s either-or, and thus requiring absence of macroscopic superpositions bounds possible parameters.
Still, the notion of what constitutes “macroscopic reality” is quite fuzzy. Just to give you an idea of the problem, the estimates by Feldman and Tumulka go along such lines:
“To obtain quantitative estimates for the values [of the model parameters] that define the boundary of the [philosophically unsatisfactory region], we ask under which conditions measurement outcomes can be read off unambiguously... For definiteness, we think of the outcome as a number printed on a sheet of paper; we estimate that a single digit, printed (say) in 11-point font size, consists of 3 x 1017 carbon atoms or N = 4 x 1018 nucleons. Footnote 1: Here is how this estimate was obtained: We counted that a typical page (from the Physical Review) without figures or formulas contains 6,000 characters and measured that a toner cartridge for a Hewlett Packard laser printer weighs 2.34 kg when full and 1.54 kg when empty. According to the manufacturer, a cartridge suffices for printing 2 x 104 pages...”And so on. They also discuss the question whether chairs exist:
“One could argue that the theory actually becomes empirically refuted, as it predicts the nonexistence of chairs while we are sure that chairs exist in our world. However, this empirical refutation can never be conclusively demonstrated because the theory would still make reasonable predictions for the outcomes of all experiments...”Meanwhile on planet earth, particle physicists calculate next-to-next-to-next-to leading order corrections to the Higgs cross-section.
Sarcasm aside, my main problem with this, and with most interpretations and modifications of quantum mechanics, is that we already know that quantum mechanics is not fundamentally the correct description of nature. That’s why we teach 2nd quantization to students. To make matters worse, most of such modifications of quantum mechanics deal with the non-relativistic limit only. I thus have a hard time getting excited about collapse models. But I’m digressing - we were discussing their phenomenological viability.
In fact, Feldman and Tumulka’s summary of experimental (ie non-philosophic) constraints isn’t quite as mind-enhancing as the nonexistent chair I’m sitting on. (Hard science, my ass.) Some experimental constraints they are discussing: The stochastic process of these models contributes to global warming by injecting energy with each collapse and since there’s some cave in Germany which doesn’t noticeably warm up in July, this gives a constraint. And since we have not heard any “spontaneous bangs” around us that would accompany the collapses in certain parameter ranges, we get another constraint. Then there’s atom interferometry. And then there’s this very interesting recent paper
- Are collapse models testable with quantum oscillating systems? The case of neutrinos, kaons, chiral molecules
M. Bahrami, S. Donadi, L. Ferialdi, A. Bassi, C. Curceanu, A. Di Domenico, B. C. Hiesmayr
Nature: Scientific Reports 3, 1952 (2013)
In this paper the authors calculate how spontaneous localization affects quantum mechanical oscillation between two eigenstates. If you recall, we previously discussed how the observation of such oscillations allows to put bounds on decoherence induced by coupling to space-time foam. For the space-time foam, neutral Kaons make a good system for experimental test. Decoherence from space-time foam should decrease the ability of the Kaons to oscillate into each other. The bounds on parameters are meanwhile getting close to the Planck scale.
For spontaneous localization the effect scales differently with the mass though, and is thus not testable in neutral Kaon oscillation. Since the localization effects get larger with large masses, the authors recommend to instead look for the effects of collapse models in chiral molecules.
Chiral molecules are pairs of molecules with the same atomic composition but with a different spatial arrangement. And some of these molecules can exist in superpositions of such spatial arrangements that can transform into each other. In the small temperature limit, this leads to an observable level splitting in the molecular spectrum. The best known example may be ammonia.
Now if collapse models were correct, then these spatial superpositions of chiral molecules should localize and the level splitting, which is a consequence of superpositions of two eigenstates, become unobservable. The authors estimate that with current measurement precision the bound from molecular level splitting is about comparable to that of atom interferometry (where interference should become unobservable if spontaneous localization is too efficient, thus leading to a bound). Molecular spectroscopy is a presently very active research area and with better resolution and larger molecules, this bound could be improved.
In summary, this nice paper gives me hope that in the soon future we can put the ugly idea of spontaneous localization to rest.