Two deeply unrelated quotes that I find apply here. The first is from a segment on a Christmas special of the British radio comedy panel show, The Unbelievable Truth, and the second is Einstein's.
"Schrodinger, philosophic science whiz
popped a kitty in his
a pretty kitty and says
‘If you open the box, the 'lectric shocks.’
'Don’t touch the box… the cat is now a paradox.’
'Both dead and alive is the feline situation’
'But its status will be changed by the act of observation’
The main thing that we learn from that: Schrodinger did not like cats." -Rufus Hound
“[I advocate] that one conceives of the psi-function [i.e., wavefunction] only as an incomplete description of a real state of affairs, where the incompleteness of the description is forced by the fact that observation of the state is only able to grasp part of the real factual situation. Then one can at least escape the singular conception that observation (conceived as an act of consciousness) influences the real physical state of things; the change in the psi-function through observation then does not correspond essentially to the change in a real matter of fact but rather to the alteration in our knowledge of this matter of fact.” -Albert Einstein
I would strongly advise people who do not have extensive tuition in Quantum Mechanics to refrain from speculating about the consequences of QM. I have been taking QM classes for several years now, and the most valuable thing I've learned is that almost everyone's understanding of QM is based on bad ad-hoc analogies, and it takes years of study to progress to gradually less ad-hoc analogies. Different mathematical models inform different "interpretations" of QM. If you can't tell the difference between a rigged and non-rigged Hilbert space, you certainly don't have enough background to speculate on classical QM, and I'm not at the point where I could even tell you the background required to speculate on modern QFT.
Local hidden variable theories are not possible, but any local theory is not possible, assuming definite outcomes of experiments (many worlds might be considered local, but there is no definite outcome).
Non-local hidden variable theories are quite possible, do quite well in explaining a number of facets of QM, and, in fact, inspired Bell's work.
Nevertheless, Einstein certainly was no fan of the non-locality though he did not know of Bell's argument, of course.
Non-locality can't be right though, since locality is defined by the speed of light, and nobody will tell you that sending information faster than the speed of light is possible.
The tension is not with FTL, but rather with the tension of a seeming need in QM for "now" and that in relativity of "not now". There are a number of ways to work in a "now" in a way compatible with the mathematics of relativity. For a full exploration of these ideas, one can see https://arxiv.org/pdf/1307.1714.pdf which explores ways that the wave function itself possesses multiple possibilities of extracting a "now".
To what extent those "now"s are acceptable is certainly open to much debate.
Non-locality doesn't imply that you can transmit information FTL, in fact you can't without classical channels. You can send random bits with entangled particles, but that is the precise opposite of information.
Many worlds isn't the only alternative. The "cleanest" (i.e. least magical) proposed solution I know of is einselection, which gives us emergent behavior of the schroedinger equation that looks kind of like many worlds and kind of like "ideal" non-unitary collapse, but doesn't posit any "unobservable" or "magical" processes unlike many worlds or Copenhagen.
You have to be clear about what is real in the theory. Many worlds presentations often suffer from this as they often talk about splitting universes, whatever that would mean.
A nice version which might coincide with what is in mind for einselection is to take the wave function and integrate it out to get a mass density on three space. This mass density will the various different "worlds" present in it by means of the evolution; any given time will not tell us what belongs to which world, but as time evolves, we can see which pictures correspond to which ones, like fuzzy tv sets. See https://arxiv.org/pdf/0903.2211.pdf
There isn't much to recommend any of the many 'Interpretations' of QM, and if you deal with people involved in using it for their jobs, they tend to adhere to a "shut up and calculate" interpretation.
After all, why construct an ontology based on what is clearly not complete at all energy scales? Still, where there are gaps, people will "theorize".
It is all a matter of what you want out of science. Some people, such as myself, enjoy having a narrative about how the universe works consistent with experiments. This is both satisfying and useful in finding new directions to push or ways to solve problems (such as a recent attempt to solve the divergences in QFT by using boundary conditions appropriate for particle flows: https://arxiv.org/pdf/1506.00497.pdf). If you have just quantities to compute, but have no idea what those quantities represent in reality, it is hard to see how one can think of that as understanding how the universe works.
It is not clear why having a "complete" theory would change one's position on ontology. It is either important or it is not to a person, just as some people love playing with big machinery and only care about models in as far as it enables them to do that. Others really do not care about big machinery except as it produces potential data to suggest new models or discard the old. Why should one make a judgement about that?
It certainly has a basis in reality. The story needs to be consistent with what we know, at least in the realm that it claims to give sense to. Science is not about getting the absolute truth, it is about getting information and a story consistent with what we know to be true, often with caveats about where the story applies.
And, of course, you can deny ontology all you like, but everyone operates with one in their mind. It is impossible to do interact with reality and to use equations without some internal assumption of an ontology, however vague and unexamined it might be. It is just that the "shut up and calculate" crowd does not want to discuss it, much like how "very religious" people often do not want to talk about their religion. They are simply not interested in examining stuff that may challenge their world views. But it doesn't mean they don't have an underlying belief.
It is similar to, paraphrasing Bell, how solipists buy life insurance.
The real point of science is to question our assumptions and obtain a better understanding, often contradicting what we thought was true. In order to do that, one has to look at what one believes is true. This is what the investigation of different ontologies is doing. But, as I said, many are not interested in pursuing that line of thinking and that's fine.
But it is not fine to say it should not be pursued at all or to imply it is less important or noble. Different aspects of understanding should be pursued by those who find those aspects enjoyable to pursue.
I think your comment is a bit inappropriately arrogant. I follow discussions in recent papers and on physicsforums.com from researchers and professors who have been studying QM for more than several years, yet they constantly disagree on even basic points, so I don't think even a lifetime of education in QM means you have a more intuitive understanding of it's consequences than a reasonably informed layman.
The only thing they can agree on is how to calculate the expected results of experiments.†
Also, hidden variable theories are not disproven by Bell - just local ones.
Parent comment is interesting in that it shows the disconnect between the way people get trained in quantum mechanics (or any hard science, for that matter) and what it takes in order to achieve a real understanding of the ways of Nature. Quantum mechanics is a highly mathematized and highly technical subject, and all this math and all these technicalities could be seen as merely a scuffolding; it is still hard to learn about the building by spending years studying the scuffolding. To me, it seems that the arguments about the basics will continue until the final unification with gravity has been found, because this may result in discovery of important constraints on the ways we should be thinking of these things. In the meantime, I think it maybe only people who apply quantum methods in their daily practice - quantum chemists, specialists in solid state physics etc. - will be the ones to have a better understanding of such matters as whether wave functions are real or not. Books about applied aspects of quantum theory could prove tremendously useful in that regard to everybody. One of the best for beginners, I believe, is Quanta by Atkins.
You could replace QM with "magic" and it could be a dialogue by one of those fancy mages in any fantasy story.
Do you see a way to "sell" QM to the public in a way that would reflect the diversity of the ideas and the concepts in a better way? Something that could replace what we have now? Does it make any sense at this point to do this at all?
How about this intuition? Photons are massless and travel at light speed. But that is our perspective. From the photons perspective time is standing still. It is "touches" all space/time points on its path at once, and passes its quanta to only one point, depending on some chance function.
Entanglement is the same, from our perspective it is spooky action at a distance, or over time. But from the two photons (and thus the qm phenomenon that created them) perspective it is the same instance.
That is a consequence of time is relative. As mind bending as that might be. Or is this totally off?
It's wrong, but it's hard to explain precisely why without reference to group theory.
Imprecisely why, the issue is that you can't find a global frame in which a massless particle is at rest. In General Relativity that's because there are no global frames at all; in Special Relativity, it's because global frames are Lorentz-invariant; a common tool in General Relativity, the Local Inertial Frame, is also Lorentz-invariant.
The spacetime of Special Relativity is Minkowski spacetime (AKA Minkowski space AKA flat space) and at every point in that spacetime the Poincaré group (developed by Minkowski) is the isometry group. The Poincaré group has several subgroups, and here we can focus on the Lorentz group.
The Lorentz group has three rotation generators J_[x,y,z] (Cartesian coordinates) or J_[\rho,\theta,\phi] (Spherical coordinates) etc, or in general coordinates, J_[1,2,3] or just J_i. It also has three boost generators along the same axes, K_i. There is a commutation relationship which is satisfied between these generators.
(The Poincaré group also has translations. In Cartesian coordinates: P_[x,y,z,t]).
For a massive spin-1 particle at rest at a single point in the Lorentz frame, the particle's angular momentum is invariant under rotations on any set of axes, but the direction of the angular momentum is changed.
However, the photon is a _massless_ spin-1 particle, by definition under most theories and with excellent experimental support. As noted above, we can't find a Lorentz frame in which such a particle is at rest. However, by careful choice of coordinates, we can pick a single axis along which the whole of the massless spin-1 particle's momentum is found. The four-momentum ends up being invariant under the subgroup generated by [J_1, K_2-J_3, K_3+J_2], which produces a transformation matrix giving the rules for rotations around the particle's momentum [given in detail in Wigner, 1939].
Because this sets up a gauge in which _locally_ the momentum is contained, we can rule out the possibility that a photon is smeared out globally, even when considering a very very low-momentum photon (remembering the Einstein relationship for a massless particle, E = pc = \hbar\omega = hc / \lambda; so we're talking a wavelength comparable to the size of the universe).
Intuitively, this is because you can always find (nearby, Lorentz) observers for which the photon's momentum is always contained within a single axis, and those observers are no less privileged than any other.
Now, to consider your '"touches" all space/time points on its path at once', we need to do a bit of defining. The worldline is the entire path through the whole block universe spacetime Special Relativity. [http://backreaction.blogspot.co.uk/2008/05/block-universe.ht...] Every fundamental object has its own worldline. So you're verging on a tautology; the photon is at all its (own) spacetime points along the worldline.
However, we can apply some 3+1 formalisms to foliate the block universe of Special Relativity by taking 3d spacelike hypersurfaces along surfaces at a constant _coordinate_ time. In each of these hypersurfaces, there is at each point a probability of interaction between the photon and anything that feels electromagnetism. Because of Lorentz invariance, the exact probability distribution is observer independent. However, as noted above, it is possible to choose observers who will see probabilities extremely close to zero except near a small 3-volume. Conversely, this rules out observers who see identical probabilities everywhere.
So in that sense, at any given point, a photon does not "touch" all space at each point in time along its worldline.
From this we can address your second last paragraph. A pair of correlated (entangled) photons whose worldlines develop a spacelike separation after entanglement are not in non-Lorentz-invariance-violating contact. A discovery of _any_ (local) Lorentz-invariance violation would be extremely exciting new physics, but there is a mountain of evidence suggesting that doesn't happen in our observable universe. [https://www.wikiwand.com/en/Modern_searches_for_Lorentz_viol...]
That is, if we do a 3+1 formalism and do a foliation on a timelike coordinate across the region(s) where the partial worldlines are spacelike separated, we can find no hypersurface on which the nonzero parts of the probability distributions of the pair of photons overlap.
Maybe my intuition is: the world is round. And your reply is: no, there are mountains, rotation flattens the poles, the moon causes bulges (the tides) due the the earth's constant falling to the center of the earth/moon system. An intuition is an extremely zoomed out/abstract version of the real thing.
Not saying that this is the case. Perhaps in the above analogy the world is actually square, or donut shaped, and so my intuition is way off. But I am out of my depth to judge. So I am hoping you can. If a high schooler had my kind of intuition, or no intuition at all, with which situation would you be happier?
I can say that "Conversely, this rules out observers who see identical probabilities everywhere." is a good point, but also what I meant by "chance function", as apposed to an equal chance for all the points.
In the quantum eraser experiment, even if you erase (or not) on a much longer path, the result is the same. But it is no ftl comm, because the other observer needs the eraser data to filter the photons and find the signal. But what causes that randomness, knowing that we can rule out hidden state? In my intuition, because it is all evaluated at once. But what is the birds eye view of that answer if it is better not to have that intuition?
Regarding the quote by Einstein: This turned out to be (partly) wrong. While the wave function can hardly be an object of reality (since its collapse depends on the observer, i.e. is not Lorentz invariant) and is thus rather a descriptive means for us, uncertainty in the quantum sense has nothing to do with a lack of knowledge. Put differently, there is a difference between a physical system being in a superposition of states A and B or being either in state A or state B (but not both of them at the same time). There're various experiments that can distinguish between both.
Just for the sake of anybody reading, your claims about the reality of the wave function are not settled science.
Published in 2012, the PBR theorem[1] suggests with some caveats that 𝛹 must be interpreted physically or modified to make new predictions of which there is no evidence of.
Thanks for the link![1] I should have been more precise.
What is settled science is that the collapse of the wave function happens due to different causes for different observers. Example: Take two detectors A and B and place an apparatus in the middle that emits two entangled photons in opposite directions. In the lab frame, both particles will reach the detectors at the same time, so that both detectors cause the collapse of psi simultaneously. In contrast to that, two observers moving to the left and right respectively will see one of the photons reach its respective detector before the other photon reaches his. Thus, for one observer it's detector A causing the collapse (and B then only receives a disentangled photon) and for the second observer it's the other way around. Hence the causal chain of events is reversed (which is forbidden by special relativity).
Now, the problem here is obviously the collapse of the wave function itself (and the faster-than-light propagation of the disentanglement which, however, is widely accepted). Since we still don't know how the collapse actually works[2], it's likely (and I think assumed by most physicists nowadays) that the non-unitary(!) collapse should be replaced with a different mechanism. (Such as decoherence[3] but there are still a lot of questions remaining.)
So it is in this sense that I say that the wave function (in our formalism today) cannot be an actual part of reality because it only works until a collapse occurs. That doesn't mean, though, that the quantum states themselves (given by the wave function in intermediate times) can't correspond to reality. In fact, as I said myself, quantum uncertainty doesn't have anything to do with a lack of knowledge. That is, the view that quantum states merely represent statistical properties of an underlying state (which a priori might be part of a hidden variable theory) is wrong. While I think this was known before 2012, the PBR theorem gives a very general proof of that.
Let me start with a rather mathematical definition: Unitary operators[1] are invertible operators that preserve the inner product of the Hilbert space they live on. They are used in quantum mechanics to describe the evolution of the state of a physical system. The preservation of the inner product in this context (roughly) translates to the statement that probabilities of measurement outcomes don't change, i.e. that probability is conserved. Invertibility, in turn, means that even though we can only talk about probabilities in quantum mechanics, we do so in a deterministic way. Put differently, if you know the state (= the wave function = the set of probabilities) of a system at a time t1, the state at other times t0 < t1 or t2 > t1 is uniquely determined. That is, using the unitary evolution operator, you can basically go back and forth in time, thus determine what the state of the system will be in the future or what it was in the past. In this sense, quantum mechanics is still a deterministic theory, even though we can't predict measurement outcomes with 100% certainty anymore. (Namely, what we can do is deterministically predict probabilities.)
Now, the problem with the collapse of the wave function (or the measurement process in general) is that it breaks this, i.e. the collapse is non-unitary. Probabilities are changed and the process is neither reversible nor predictable, i.e. entirely non-deterministic. If you have a system in a superposition of states A and B (say with a chance of 50% of measuring A or B, respectively) and you then measure A, then – due to the collapse of the wave function – the state of the system will be A with a probability of 100% directly afterwards. The probability changes and you have no way of knowing anymore what the state was before the measurement. (Nor did you have any idea that you would measure A and not B before actually carrying out the measurement.)
On the one hand, this shouldn't come as a surprise because the fact that "god plays dice", i.e. that systems might be in superpositions of states until they are observed and have to decide, is at the heart of our interpretation of quantum mechanics. On the other hand, this is weird because all the equations governing quantum mechanics are unitary evolution equations, so actually shouldn't allow non-unitarity. The crucial point seems to be that we still haven't nailed down what a measurement actually is and that we use classical terminology to describe it (i.e. we distinguish between the quantum systems and our classical measurement devices). But if our world is entirely quantum, then our instruments should be quantum, too, in particular they should not be able to bring about a non-unitary time evolution. Hence, the question is how the unitary interaction of a small quantum system and a large quantum system (like a measurement device) can lead to an apparent break of unitarity – even though it is actually not. A related question is how classical behavior emerges from quantum behavior for large objects (that is, why is our world entirely classical when the microscopic world actually is not).
Concluding, my reference to the non-unitarity of the collapse of the wave function served to remind the reader that the collapse is not compatible with unitary time evolution and thus explain why, as a concept, it likely (hopefully) won't survive the next revolution in physics.
Sorry for getting back to this so late, but yeah this was great! Again thanks for taking the time to write this. I had no clue it got this weird in quantumland, and it's awfully fascinating.
I've known about schrödingers cat for years, though my physics background is just high school + the odd popular science book.
It wasn't until a few months ago that I learned on reddit that it isn't an explanation of quantum physics, but a critique.
This explains why the cat isn't an observer that causes the wave function to collapse or why the cat isn't dead or alive, but we as outsiders can't know and thus simply think of it as both until we open the box.
I first came across the story when reading Douglas Adams' "Dirk Gently's Holistic Detective Agency" many decades ago. It spurred me to learn a bit more about philosophic science.
Now it appears that every man and his cat spouts on about Mr. Schrodinger and his hapless kitty at the drop of a decayed subatomic particle... Verschränkung has become pop culture...
Has anyone written code that can do quantum decoherence of radiation in an OpenGL fragment shader?
Edit: I'm imagining some kind of subset of QuTiP that could calculate photon (electron?) states from a wave function, ported to GLSL.
Edit 2: Maybe a Born probability that would draw the interference pattern from the double slit experiment? Or a reduced density matrix or something? The word "matrix" makes me think it might be amenable to a GPU, but I don't really know GLSL or quantum physics.
"Schrodinger, philosophic science whiz popped a kitty in his a pretty kitty and says ‘If you open the box, the 'lectric shocks.’ 'Don’t touch the box… the cat is now a paradox.’ 'Both dead and alive is the feline situation’ 'But its status will be changed by the act of observation’ The main thing that we learn from that: Schrodinger did not like cats." -Rufus Hound
“[I advocate] that one conceives of the psi-function [i.e., wavefunction] only as an incomplete description of a real state of affairs, where the incompleteness of the description is forced by the fact that observation of the state is only able to grasp part of the real factual situation. Then one can at least escape the singular conception that observation (conceived as an act of consciousness) influences the real physical state of things; the change in the psi-function through observation then does not correspond essentially to the change in a real matter of fact but rather to the alteration in our knowledge of this matter of fact.” -Albert Einstein