How do we know superposition exists?

Question

How do we know superposition exists? Has it been observed, or has it been deduced, and how certain are we?

The Copenhagen Interpretation seems to imply that superposition collapses into one state once measurement has occurred, so I don't understand how we can observe it.

The reason I ask is I'm totally bewildered by the mainstream interpretations of Quantum Mechanics. I understand its probabilistic; I'm very accepting of the idea of there existing fundamentally stochastic scenarios where the initial state does not entirely determine the next state. What I don't understand is why superposition is so necessary to the theory. The two mainstream explanations are the Copenhagen Interpretation and the Many Worlds Theory, which both seem so incredibly farfetched and counterintuitive.

Thanks for any help or insight.

Answer 1

The Copenhagen Interpretation seems to imply that superposition collapses into one state once measurement has occurred, so I don't understand how we can observe it.

In general, you should not expect interpretations of quantum mechanics to tell you anything about what you can observe. They're not physical theories. What makes them fall short of being physical theories is that they don't make predictions about observations.

Superposition, however, is a feature of quantum mechanics that is independent of any specific interpretation, and that does make definite predictions about observations. For example, we can do double-slit diffraction with particles. For an example with photons, see the photo at the beginning of section 34.4 here http://www.lightandmatter.com/html_books/lm/ch34/ch34.html#Section34.3 . For an example with neutrons, see Zeilinger et al., Rev Mod Phys 60 (1988), 1067.

Without superposition, it's hard to imagine how we could get areas of high probility and areas of low probability. We can observe these effects even under conditions in which it's only possible for a single particle to have been present at any given time.

Either the Copenhagen interpretation or the many-worlds interpretation can tell a satisfying psychological fable about why we observe these things. If the interpretations seem farfetched to you, then you're free to dispense with the interpretations, which are philosophy, not science; you will then find youself initiated into the "shut up and calculate" school. But I don't think that suffices to render the observed phenomena less counterintuitive.

I'm very accepting of the idea of there existing fundamentally stochastic scenarios where the initial state does not entirely determine the next state.

I'm not so sure you should accept that. Whether this is true or false probably depends on your definition of "state."

Answer 2

Your question is an excellent one, though I am late to the party by 10 years, maybe you have a chance to read it.

Let's first look at classical mechanics. It was widely successful because it made predictions, and those predictions turned out to be true. I include Einstein into the classical side, as I view it as an extension. Have a look at the moon landings. This was based on classical mechanics, and it predicted the future by almost a week. “Landing a man on the moon and returning him safely to earth”. This is impressive, no doubt, and alongside a plethora of other impressive things, classical mechanics did establish the reputation of physics. To put this short: The models make predictions and the observations match.

But then, when scales got smaller, suddenly the predictions failed. The Stern-Gerlach experiment is one, the double-slit experiment another, there were more. The observations were simply consistently different from the predictions.

Now you have a situation where you have a starting state and observations leading to an end state. You can do mathematical calculations on the system that leads from one state to another. Physicists did exactly this, and this leads to superposition (as part of the whole system) as the only possibility that we currently know that makes reliable predictions.

These predictions are just as powerful as the classical mechanics in their realm. Numerous technical inventions have been made from it, including (the list is not exhaustive) the tunnel diode, the laser, and the CD.

But it is a mathematical model that transforms one state over time into another, and that fits the observations. As for now, superposition does the job, so nobody bothers to seek alternatives. But you can not fully exclude a mathematical model that does the same job but does not need superposition.

However, there is one point that will never go away: It is the difference to the predictions of classical mechanics that triggered the search for other models at small scales. In other words, there is no quantum mechanical model without a valid classical model. For example, if you make calculations on flying to Alpha Centauri in 2 seconds (which you can easily do, paper doesn't blush) and then observe that there is a difference to the prediction. This will not allow you to conclude flying to Alpha Centauri above the speed of light must be a quantum mechanical effect.

Answer 3

How do we know superposition exists?

If there's no superposition,- How do we get interference pattern on the screen in the double-slit experiment ?

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You bump a pair of stones into the water and you see that there are zones with maximum and minimum heights of water ripples traveling across. So you conclude that a pair of bump targets generates superimposed waves.

Similarly,- you bump electron stream into region of closely cut slits and you see maximum and minimum hit regions on the screen. Now you know that in electron case there's no physical wave, contrary to water ripple case. So what interferes here ? Answer is- probability waves. Electron falling into single slit, has some probability distribution of hitting screen at particular point along screen height (usually Gaussian), let's name it $P_1(y)$. When you cut two slits and let electron through,- you notice that hit probability pattern along $y$ changes into something like $P = P_1(y) \circledast P_2(y)$, where $\circledast$ denotes unspecified convolution of probability waves.

Now in general in quantum mechanics many of probabilistic states can convolve between themselves, because there's nothing special in electron travel path probability. $P$ can mean photon polarization state superimposed probability when it goes through a set of polarizing $\lambda / 2~$ plates, it can mean electron spin state superposition, it can mean superposition of qubit on/off states in quantum computer and so on.

Answer 4

We observe quantum superposition the same way we observe most things: by gathering evidence of it. The evidence is always indirect. That should not bother you. The evidence you have of almost everything is indirect. I ever never seen Mount Everest, for example, but the evidence available to me that that mountain is a genuine feature of planet Earth is strong enough that I would consider it a waste of my time and energy to doubt it. I can say the same about small things such as atoms and molecules.

Coming to quantum superposition, the evidence is in the fact that this aspect of quantum theory is built into the very foundations and it as an aspect of almost every application of quantum theory you can think of. It is part of the structure of atoms for example. The success of quantum theory in predicting emission spectra of atoms is very strong evidence of quantum superposition in electron wavefunctions in atoms. You can say the same for the prediction of chemical valence and the periodic table.

The interference experiments, such as interferometers (Young's slits, Mach Zehnder, etc.) give somewhat more direct evidence of quantum interference, but it is still indirect. The point now is that in order to calculate correctly the probability of a photon or other entity to end up in one output path or another, it is necessary to include the contribution of all available paths through the interferometer. The contribution of more than path is another way of referring to the presence of more than one wave in a superposition.

Finally, a brief word on interpretations of quantum theory. These raise other issues, and much more subtle ones, than merely quantum superposition. You can treat quantum superposition as simply an agreed thing when it comes to single particles or small numbers of particles. What is harder to agree is whether highly complicated systems such as photographic film, video cameras, cats and humans can be accurately described by a superposition of very different states. An important aspect, often omitted from hasty descriptions, is that it is questionable whether the approximation of the isolated system ever holds for such objects, which have significant amounts of mass and chaotic internal dynamics.