We have a mathematical model of physics, which includes things like superpositions of wave-functions. We don't know how or even if they map on to reality, we but do have a habit of talking equating "states" with wave-functions. Then when describing superpositions, we end up with paradoxes like your first sentence.
This goes beyond Einsteinian "the physical world is not what you thought it was" thinking, and starts challenging logic itself. If QM really did challenge logic like that, then we would have to start rebuilding every other field of thought, including even mathematics.
I think it is more reasonable to see if some lateral thinking in QM can make the seeming paradoxes go away.
That whole thinking - that states are well defined, and can be only either one or the other - that's the classic world approximation, it's not reality. You firmly believe in it because your crucial early years, when you were crawling on the floor at your parents' house, were spent in a classic-world-approximation universe. That's why it's so hard for you (and pretty much everyone else) to let go of it.
The quantum phenomena are the more fundamental reality. This classic universe that you think you understand is just an epiphenomenon. Just foam floating on the ocean.
The fundamental reality of the electron is the wave function. States, and everything else, emerge from it. It's not a corpuscle. It's not a wave. It does not behave like ping-pong balls, or like waves in a pond, although it shares a few characteristics. Fundamentally, it's something different. The only way to know that entirely different thing is via the mathematics of quantum mechanics - and whatever intuition you can derive from it after you do the math.
There is no equivalent for that stuff at the human scale of things.
Very much this. This should be prologue to any introduction QM book/class/whatever.
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Building on this idea, "an electron can be both states at the same time" isn't necessarily the right way to think about it.
I mean, it's sort of right, but relies on an intuitive understand of what the heck that even means. And QM reality is grounded not in our human intuition, but in the math of wave functions. If we associate "state up" with a wave function concentrated one way and "state down" concentrated the other way and "both states" as a mixture, then okay. We give foreign concepts familiar descriptions all the time. (Like, maybe, telling someone that a byte is a letter...it's kind of true, for some concept of letter.)
But the true fundamentals of QM are not particles or waves or discrete states, but wave functions and Hilbert space.
This is a very simplified colloquial way of stating a concept that also makes it seem mysterious. The state of an electron is described by a vector 'v' in a 2D complex vector space. Now, to actually talk about the vector concretely you should choose a basis. Suppose your basis is one in which the vector 'v' is not parallel to any of the basis vectors. Then you can say the vector v is "somewhere in between basis vectors e1 and e2". No magic in the way I have stated it. There is a little bit of fake magic when you start thinking about the random measurement results you get when you measure the electron in state 'v'. But these effects can be simulated in a classical deterministic universe.
The real magic of quantum mechanics is in entanglement which can't be simulated in a classical deterministic universe. But that is a much longer story.
Now to answer your question, yes there is lots of physical evidence that this non-deterministic description of systems is a good model of reality. This comment box is too small to state it. People are currently in the process of determining if this probabilistic description is a good one outside of the mathematical framework of QM. See http://www.nature.com/news/quantum-physics-what-is-really-re...
Personally, I think "simultaneously points both up and down" is a terrible way to describe superpositions. So let me avoid that phrase, and see if I can rephrase your question. Would it be fair to say that you're asking this question?
> Is there any real physical evidence that an electron can be in a superposition of two states, that can only be explained using quantum mechanics?
Surprisingly, the answer to this question is yes. The evidence is the Bell experiment[1].
As I understand it, Bell's test only shows indeterminism or non-locality. Since we believe non-locality for other reasons, how does it support indeterminism?
What are the other reasons for believing non-locality?
(I'm a fan, since the main objection I see to non-locality is that observations can't be fully explained in terms of local factors, and to me that still seems preferable to the Copenhagen interpretation that observations have a completely inexplicable component. But I don't know of any hard evidence for non-locality.)
The main use of non-locality I've seen is in relation to (fused) anyons carrying quantum numbers held non-locally over their constituent parts. I expect we see other non-local effects in things like very low temperature condensates and probably stuff like superconductors and superfluids (since the math of the vortex structure is similar to anyons).
Of course, entanglement can be interpreted as non-locality, where what happens to one particle inside of a bounded area depends on the fate of its entangled partner, outside of the box.
The real reason to use non-locality in place of indeterminism is that it provides a clear research avenue to combine the QM effects (based on information locality) with GR (which is about the causal relations between things). QM would really just be telling us that the actual causal net doesn't look like it does from macro scale. It transitions both frameworks to be about causal nets, instead of a weird mishmash that's hard to combine.
Of course, that's if we can do QM as pure non-locality, rather than indeterminism. I just think it's strange that it seemingly hasn't been investigated.
Ed: I guess it has been investigated some by say, Bohm, but I feel like science (the institution) gives undue weight to the interpretation they were taught in school, even when it's both arbitrary and constraining. It's like everyone screaming that of course there's exactly one parallel line, that's what you're taught in school and have been since the Greeks, right? Well, maybe non-Euclidean geometry models some things better.
Similarly, I think scientists baked some arbitrary design and philosophy choices in early, then never bothered to explore other approaches, because they were able to compute decent results.
Isn't there some serious issues with the original Bell's tests - such as performing a post-selection of events (from the data-set) to remove all events that did not match the expectations of the experiment (...95% of the data was thrown out)?
I did, and it states that electrons can hold one of two spin values. But within the mathematical framework of QM, that value is unknown before measurement - so it is ambiguous - which is interpreted (by QM) as a possible superposition of both values.
The physical experiment itself only detected spin up or spin down.
And that is the main question, how can we know this [electron superposition state] is not just a product of the framework being used, with no real counterpart in reality?
The real evidence of this is from the last experiment under "Sequential Experiments". Essentially, you only select particles with spin-up in the z direction, then you select particles with spin-up in the x direction. So the resulting particles should be up in both the z and x direction. But if you measure in the z direction again, you find an equal distribution in up and down, indicating that you can't simply treat the spin as both pointed in the x and z direction, and that measuring in the x direction has scrambled the previously well-defined z direction.
This experiment shows that measuring the spin direction in different axes does not commute. Measuring in one direction scrambles the other, which is equivalent to saying measuring in x then z is not the same as measuring in z then x. This fact is inherently related to the notion of a superposition. If a particle's spin direction is well-defined in one measurement basis, it is not well-defined in another - meaning it is in a superposition state in that measurement basis.
You might ask - why can't I describe the system after measuring in the x-direction as just a random mixture of up and down in the z-direction? Physicists use something called a density matrix to describe systems that have both some degree of quantum superposition and classical randomness. One way to measure the degree to which some stream of particles is a random mixture or not is to interfere particles in that stream with each other.
In the Stern-Gerlach experiment, after measuring in the x-direction, if the information in the z-direction was actually simply randomly scrambled, the probability that any two particles from the stream are truly identical is 1/2. If the particles are all identically in a superposition state, then any two particles will always be identical.
You can actually test the indistinguishability of two particles by doing an interference experiment. One very nice example of this is this experiment:
https://arxiv.org/pdf/1312.7182.pdf
Two atoms were trapped next to each other using lasers. If these atoms have the same spin, they're indistinguishable. If they have different spin, then they are distinguishable, and won't interfere with each other. In fig. 3, you can see varying levels of interference depending on how well-aligned the spins are.
I am not quite sure what you mean. There is tons of experimental evidence for quantum mechanics.
Specifically for electron spin, you seem to agree that it has spin 1/2 (because you say that it can be spin up or spin down). But that already concedes that there are superpositions of up and down. Spin left, spin right, spin straight forward, spin backward are all equal superpositions of spin up and spin down; and all these states are trivially constructed.
Bound electrons (in an orbital) can only have 1 of 2 quantum "spin" states - which is in relation to the nucleus and/or the magnetic field. Up or down. With the spin-up electron having a slightly higher or lower energy level then the spin-down electron (depending on other factors).
I think the question is how you unambiguously measure spin-right or spin-left as existing. Most experiments report only a stream on spin-up and spin-down measurements, inferring the original superposition.
Mathematical frameworks that assume Quantum Systems are deterministic (only being in state A or B) during unobserved periods have never been validated by experiment. It is great if you have a model, but if that model fails to agree with experimental results.
But as I understand it, this is because of technical lock-in: physicists had to choose between non-locality and indeterminism, chose indeterminism, got forced in to non-locality for other reasons, and never went back to re-examine the model, because it was getting decent computational results, and it would be a lot of work to rebuild.
I've never seen a solid argument for indeterminism being anything but an extraneous assumption in QM. Entanglement (and other behaviors at low temperature) necessitates non-locality, which means the most parsimonious model would also use that, rather than indeterminism, to resolve Bell's inequality.
So is there any reason besides "it predicts good enough" and "technical lockin" to keep using models with indeterminism?
(Physics actually seems a hodgepodge of random philosophical assumptions no one bothered to ever review because they're deep in the model. Not unlike code suffering from code rot.)
1. The philosophical basis of our physical theories is a very well studied problem. The reason you don't see it in common parlance is that most of us, even most professional physicists, are not qualified to talk about these issues in detail. For stuff you have not seen, you need to dig deeper into literature. Its all there - I am not qualified to point to a good resource.
2. Physicists are always happy to consider all sorts of theories. Problem is that any new theory must also retrodict all known experimental results as well as make new predictions. The reason you don't see better theories than QM is that we physicists have failed to be creative enough to think of a theory that is better than QM at prediciting experimental results. When we do, or when you tell us a precisely defined mathematical model of reality that is better than QM at predicting reality, we will throw away QM like a burning brand and hop onto the philosophical bandwagon of the new theory.
I think one of the factors for that is the fact that most high-level scientists learn to be cautious about the claims they make. You're much more likely so hear a layman make strong claims about X or Y than you are to hear the same from a PhD physicst, on average.
What a lot of people who didn't go through the grinder of Academia seem not to understand, is that when one says "I don't know", it doesn't mean "I know nothing about this". If I say "I don't know", chances are I could discuss the subject at length, but my comprehension is not satisfactory to answer the question on a deep level, or I don't really grok the subject enough to feel confident to give my opinion. This is less present in laymen and can lead to some friction in discussions.
(Physics actually seems a hodgepodge of random philosophical assumptions no one bothered to ever review because they're deep in the model. Not unlike code suffering from code rot.)
(Sorry for replying so late, I hope you'll still see this.)
Well, the situation of entanglement is not really* different from the following one:
Imagine you have two pairs of socks, a red pair and a blue pair. Now, certainly you only wear a red (blue) sock on your left foot iff you wear one of the same color on your right foot, right?
So, consider the measurement of your left sock's color by pulling up the leg of your pants and looking at your sock. If it is red, you can be 100% sure you will measure your right sock to be "red" as well, and, similarly, if it is blue you will measure blue on the right, too. Now, in order to explain this phenomenon, do you need faster-than-light travel of your left sock's color to your right sock at any point? No. The results of the color measurements on both sides are just correlated with each other because both subsystems (both socks) were prepared that way earlier.
* Granted, the issue of entanglement is actually slightly more complicated since a sock being either red or blue is not quite the same as the sock being in a superposition of both colors, i.e. being red and blue at the same time. But this difference just boils down to the fact that, in (the Copenhagen interpretation of) quantum mechanics there are measurements whose outcome is non-deterministic and superpositions just encode this very fact (together with complementary observables that allow us to distinguish between pure eigenstates and superpositions in the first place. Without complementary variables we would never see a difference between the two.) So, for instance, in entanglement experiments one often prepares two particles in a superposition of eigenstates of the spin-z operator and then proceeds to measure the particles' spin with respect to another axis. It turns out that the results of both measurements will be random but correlated. Will you able to explain the results using the sock analogy? No, because the socks are entirely classical, in particular deterministic, and there are no complementary variables such as spin x and spin z (e.g. the color of the socks has nothing to do with it being made from cotton or wool and both properties are defined independently). Will you now need non-locality, though? Still no, you just needed to add non-determinism in the form of complementary variables to your theory.
So, put differently, if your theory of quantum mechanics is non-deterministic, then it can very well be local. Only if it is deterministic, it must be non-local (see, for instance, Bohmian mechanics). So, while you could have both, indeterminism and non-locality, at the same time, you certainly don't need both and, in fact, in the standard (Copenhagen) interpretation of quantum mechanics we don't have both. I think the missunderstanding that the Copenhagen interpretation is both non-deterministic and non-local originates from the idea that we imagine the wave function to collapse upon measurement and this collapse to propagate faster-than-light from one entangled particle to the other. But the collapse of the wave function is not just not compatible with special relativity but it is also not compatible with the unitary time evolution of quantum mechanics, so we should consider it merely a tool for us instead of something that is actually happening. What matters at the end of the day are expectation values of measurements and for that you don't need the collapse of the wave function or non-locality at any point.
Your example has the problem of having a 'hidden' variable; the assignment of sock to foot. When you put on your socks, you assign a sock to a foot. So, when you later look, this determines the outcome, in this case the color of your socks.
This is not the case with the classical Copenhagen interpretation of QM - there are no hidden variables. I.e., the assignment of sock to foot happens at the moment when you look at them. In the meanwhile, you've been - metaphorically speaking - in a superposition of all possible states of wearing socks.
Now, in order to explain this phenomenon, do you need faster-than-light travel of your left sock's color to your right sock at any point?
Yes. More specifically you need non-locality, because you expect both feet to have socks of the same color. Now either this is a hidden variable, or the two socks have to coordinate their color at some point in time.
Hidden variable theories have been proven not to be applicable. That leaves some way of coordination. Which requires non-locality.
1) "Hidden variable theories have been proven not to be applicable." This is flat out wrong. Bohmian mechanics is a deterministic hidden-variable theory of quantum mechanics which can do without a probabilistic interpretation of quantum mechanics by giving up locality. The choice is really between giving up locality or determinism. But you don't have to give up both and the Copenhagen interpretation certainly does not give up both.
2) There is no hidden variable in my example. A hidden variable, by definition, is a variable that is inaccessible to measurements. Moreover, my example doesn't depend on the "feet" at all and would work perfectly well without them. That being said, I think what you're actually referring to is that you already choose a certain color when you put your socks on, i.e. the socks' color is not uncertain even if you decide to not look at them until later. True but this is why half of my comment is discussing exactly this point. I admit, though, that I'm being a bit vague there, so here goes another example: Let's say a friend of yours blindfolds you and flips a coin to determine whether to give you a pair of blue socks or a pair of red socks. He subsequently hands you a pair of the respective color and you put them on and decide not to look at them until later. From your point of view, the chances of your left sock being red/blue is 50% each. However, no matter the outcome of your measurement of looking at your left sock, you can be sure that if you look at the color of your right sock afterwards, its color will always be the same as your left sock's one. The two results are correlated. Now, I hope you won't argue that this is still not quantum mechanics because in QM a sock can be multiple colors at the same time whereas classically/in my example they cannot and will always have a certain color, no matter our (lack of) knowledge. This is exactly the point. If I could explain away quantum mechanics through a classical example like this we wouldn't need a non-local or non-deterministic model of our world. But Bell's inequality tells us otherwise. Anyway, what my example does demonstrate is that even for measurements whose outcome is probabilistic, correlations between the results (or "coordination" as you call it) can perfectly well be explained through prior arrangement, i.e. an arrangement at a point in space and time that lies in the past light-cone of both measuring events. So no faster-than-light traveling is needed.
Now, of course this is not the most rigorous argument one can make. For a more rigorous one please refer to the C* algebras approach to quantum mechanics where "locality" can be defined a bit more precisely and regular quantum mechanics indeed turns out to be a theory respecting locality.
If you imagine Im at 0 on the x-axis, and I create an entangled pair, then send one to L and one to -L, then measure both: can't I, at x=0, verify they (don't) match at time L/c rather than 3L/c?
If it were locally probabilistic, then it should accidentally (not) match some of the time between t=L/c and t=3L/c: it cant be both non-deterministic and local if they never match during that time window.
Seperately: fused anyons in electron gases seem to exhibit non-local qunatum numbers. That's why MS wants to use them for quantum computing. Im not sure your sock example is sufficient to explain the stability of topological-regime quantum values against thermal noise and decoherence.
Thanks for your remarks! Unfortunately, I'm pretty busy this weeek, so I just came here to tell you that I will think about your comment a bit and respond as soon as possible!
> Is there any real physical evidence that an electron can be both states at the same time, outside the mathematical framework of QM?
Another way to respond to your question is to consider that the transistors inside the machine you used to post your comment were designed based on QM models of the electron that essentially follow from the Schrodinger Equation (e.g. via Fermi-Dirac statistics [0]).
As far as has been known since 1947, without QM it is extremely unlikely humans would ever have discovered how to build solid state semiconductor devices like the transistor. A key intrinsic feature of QM is superposition.
The double-slit experiment is a famous experiment that provides "tangible" evidence for superposition. [1]
You can't think of an electron as a little ball whose behavior is described by a weird quantum mathematical formula. The universe is really made of quantum mechanics. The electron is actually an excitation in the wave function, a fundamentally quantum object, of which "tiny ball" happens to be a lossy and flawed, but not altogether terrible description.
there are certain experimental results in quantum mechanics that only make sense if you accept things like superposition and entanglement. for example: https://www.youtube.com/watch?v=v657Ylwh-_k
Electron diffraction implies wave behaviour, and wave behaviour implies the superposition principle. Is that good enough evidence or are you looking at experiments measuring entanglement in electrons?
Why does it mean electrons "exist" in any sense instead of being a model that could explain the data? And if such objects did exist, why could they not follow classical mechanics?
Meh, I could also ask you to provide evidence that you're not a p-zombie... There's an undivisible thing (particle) that has undivisible charge (electron) which exhibits properties and behaviour that could not be explained clasically. How do you explain classically (i.e. Newton's laws and no limits on observables uncertainty) electron diffraction and discretized spin?
> How do you explain classically (i.e. Newton's laws and no limits on observables uncertainty) electron diffraction and discretized spin
Now you're changing the question :)
My original point in this was that hacker news poster "powertower" asked for evidence about an electron's properties outside of QM, and I objected to this question because once you leave QM you're in a different kind of universe.
We have a mathematical model of physics, which includes things like superpositions of wave-functions. We don't know how or even if they map on to reality, we but do have a habit of talking equating "states" with wave-functions. Then when describing superpositions, we end up with paradoxes like your first sentence.
This goes beyond Einsteinian "the physical world is not what you thought it was" thinking, and starts challenging logic itself. If QM really did challenge logic like that, then we would have to start rebuilding every other field of thought, including even mathematics.
I think it is more reasonable to see if some lateral thinking in QM can make the seeming paradoxes go away.