Slashdot Mirror
A Boost For Quantum Reality
Eponymous Hero sends this excerpt from Nature:
"The philosophical status of the wavefunction — the entity that determines the probability of different outcomes of measurements on quantum-mechanical particles — would seem to be an unlikely subject for emotional debate. Yet online discussion of a paper claiming to show mathematically that the wavefunction is real has ranged from ardently star-struck to downright vitriolic since the article was first released as a preprint in November 2011. ... [The authors] say that the mathematics leaves no doubt that the wavefunction is not just a statistical tool, but rather, a real, objective state of a quantum system."
it is, and it isn't.
the mathematics leaves no doubt that the wavefunction is not just a statistical tool, but rather, a real, objective state of a quantum system.
If that's the case, I would suppose that wavefunctions have wavefunctions.
Sheesh, evil *and* a jerk. -- Jade
In practice applying the pop version of quantum theory to everyday life does result in a more cohesive and intuitive reality than trying to go with previous thoughts. It certainly does a better job of handling times when you have to reinterpret events when new information comes into play.
> The philosophical status of the wavefunction [..] would seem to be an unlikely subject for emotional debate
Well not to me. I guess any subject a given amount of people put lots of effort in can arise emotional debates. *Especially* if the subject in question is discussed philosophically.
Maybe. No. Yes. No. Yes.
I can see how people could get so passionate over the topic. I myself passionately don't know what the hell they're talking about.
Reality is not a wave function. It's a useful model, but it's absurd to think of it as real and physical.
The cat isn't really both alive and dead. It's either still alive or it died. It certainly knows.
Reality is reality and models are models.
http://arxiv.org/abs/1111.3328v2
http://arxiv.org/pdf/1111.3328v2.pdf
http://stephan.sugarmotor.org
Most people think of matter as a solid when in fact there is no fundamental solid but matter is in it's base form a vibration which is roughly the same as a wavefunction. In some ways a wavefunction is no different a vibrating string so it's not as crazy as it sounds.
this needs an insightful mod at least.
I don't get why people get so hung up on these aspects of QM... QM is NOT a complete theory anyway, and treating a particle as a localized field configuration (quantum field theory) neatly fixes many of the seemingly inconsistent aspects of non-relativistic QM (albeit while creating a thousand other problems/questions). It's ultimately irrelevant in some sense...
The paper is related to Einsten-Podolsky-Rozen (EPR) paradox and the related "hidden variables" hypothesis which AFAIU states that there are some hidden variables apart from wave function that we can not observe directly. However, under some assumptions it can be proven that their existence affects some statistical properties of a particular type of measurements and therefore can be experimentally tested. One of such theorem was Bell inequalities published in 1964. In the Nature paper in question authors prove similar "no-go" theorem but under different assumptions. To quote:
The result is in the same spirit as Bell’s theorem[13], which
states that no local theory can reproduce the predictions
of quantum theory. Both theorems need to assume that
a system has a objective physical state such that prob-
abilities for measurement outcomes depend only on .
But our theorem only assumes this for systems prepared
in isolation from the rest of the universe in a quantum
pure state. This is unlike Bell’s theorem, which needs
to assume the same thing for entangled systems. Fur-
thermore, our result does not assume locality in general.
Instead we assume only that systems can be prepared
so that their physical states are independent. Neither
theorem assumes underlying determinism.
There is, however, another theorem by Kochen and Specker that is not cited in this paper but also does not assume locality. From wikipedia
The essential difference from Bell's approach is that
the possibility of underpinning quantum mechanics
by a hidden variable theory is dealt with independently
of any reference to locality or nonlocality, but instead
a stronger restriction than locality is made, namely
that hidden variables are exclusively associated with
the quantum system being measured; none are associated
with the measurement apparatus. This is called the
assumption of non-contextuality.
It would be interesting to know what would be the relation of results from the paper to that theorem...
If the wave function has an effect then it what way is it not real? Maybe its the mathematician in me but if reality can only be understood mathematically then I have no problem with that, thats just a problem with our imagination. I have always thought the divided universes interpretation of quantum physics multiple states was reading too much into things, a bit like during the steam age everybody wanted to interpreted things in terms of steam engines, thats useful, but the model implies things which the pure maths itself doesn't.
Think of probability distributions. If you throw a die and don't look at the result, you don't know which of the possible results happened. However you know that if you throw that die often enough, you know that each result happens approximately the same number of time. Therefore you can assign the same probability to each result, i.e. 1/6 each. But the probability distribution does not describe the current state of the die; the current state of the die is that it shows one of the numbers 1 to 6. It just tells you about your knowledge of that state; the equal probability just means "I have no idea which result happened, and there's no reason to favour either one."
Now assume that a trusted friend looks at the cube and tells you that it is not a 6. Now suddenly the probability distribution you assign to the cube changes: You'll assign probability 0 to the 6, and probability 1/5 to all other results. However the physical state of the cube does not change at all. Only your knowledge about it changes.
Finally you look at the die, and find e.g. it shows the 3. At that point the probability distribution "collapses" to the distribution which assigns 1 to the result 3, and 0 to all other results.
Now the idea of non-real wave functions is exactly like that. For those interpretations the wave function doesn't tell you what state of the system is, but only which results you get how often when you measure certain properties. When you measure, your knowledge changes, and therefore the wave function "collapses" just the same way the probability distribution "collapses" when you look at the die.
The Tao of math: The numbers you can count are not the real numbers.
Its that there's no such thing as an unlikely subject for emotional debate.
The problem with that analogy is that it can't explain the double slit experiment. How can you explain a single photon producing an interference pattern unless it goes through both slits simultaneously?
You're a temporary arrangement of matter sliding towards oblivion in a cold, uncaring universe
Here is thought I had the other day: assume mathematical "function" that defines our universe and underlying physics (function that "theory of everything" is trying to find), works in _reverse_ direction of time. So that every particle (or whatever) at t is calculated from local state at (t+1). We usually thinks of laws of physics going in "natural" direction of time. Now, after the inevitable final end of intelligent civilizations in this universe, surely there will be some artifacts made by durable nanomaterials, that persists long after stars and even black holes evaporate into 'nothing". Universe calculated from backwards will therefore have such "intelligently designed" artifact at the _beginning_, as sort of input parameter, so it have to find a mathematically plausible way going forward (which is backwards in time for us) how these artifacts were created. Intelligent life and physical laws supporting intelligent life might be _result_ of something strange at the function input. That means if you have function where random "state" is input and set of equations ("laws of physics") is output, as soon as you put something looking improbable at input, say set of large prime numbers, function might find it is easier to create universe with intelligent civilization, which created this prime numbers, then to create universe where laws of physics created such improbable outcome by chance.
839*929
The 19th century mechanists that seem to dominate Slashdot can't explain it. Like creationists, they can't handle any science which doesn't conform to their preconceptions.
Required reading for internet skeptics
Maybe you understand it, maybe the GP does too, but are you saying the photon doesn't go through both slits simultaneously? It's fairly well accepted that a particle evaluates every possible path and the resultant path comes down to the derived probability for each possible end result.
How does this work?
Short Answer: Read up on QED.
Long (and probably incorrect because it's my understanding) Answer:
The way I get my head around this is to say consider everything as a field. The electron field, the photon field, the proton field (actually a composite quark field) etc.
However "things" only exist in discrete units. A photon on the double slit experiment starts as a quantum unit of energy emitted from an electron, propagates through the photon (em) field before finishing up as another interaction with an electron on the detector. As per QED the photon evaluates every possible path to the end point(easy to conceive if it is a field, but energy exists in quantum units). Where there are two holes there are paths that the wavefunctions can interact with each other and provide the interference pattern. Where there is one path the straightforward case applies where the photon (also consider it as a disturbance in the em-field) only interacts with itself so the rotation of the vector that you consider as you evaluate each possible path only evaluates to a minimum at the straight line case; whereas for two slits the photon rotation vectors have many probabilities about how the disturbances in the em field again interact with the electron in the detector.
Actually that's a rubbish explanation but I'm not Richard Feynman,,,
"The weirdest thing about a mind, is that every answer that you find, is the basis of a brand new cliche" -
The article confused me greatly so I read some of the arxiv preprint linked above. Here's the idea and context as I understand it. I've included some basic quantum background since most people here don't have it.
* Intro to wavefunctions via an example. Electrons have a property called "spin" which has two states, "up" or "down". These can be measured in, for instance, the Stern-Gerlach experiment where those electrons with spin up are deflected up by a magnetic field and those with spin down go down. The wavefunction corresponds to a list of the probability of each outcome occurring. The probabilities evolve through time via the Schrodinger equation which allows predictions to be made. One might prepare an electron where its spin wavefunction corresponds to the list [1/3, 2/3], so 1/3 of the particles go up and 2/3rds go down. [I've oversimplified; wavefunctions are actually elements of an abstract Hilbert space and complex-number amplitudes are used instead of real-number probabilities. I love Hilbert space but it's too much to explain here.]
* Spin is not a classical property. One can measure spin "left" and "right" in addition to "up" and "down" by rotating the Stern-Gerlach (SG) device mentioned above and measuring left/right deflection. Suppose you run a stream of electrons through an up/down SG device which gives 80% of them "up". You then run those "up" electrons through a left/right SG device--it will always come out with 50% "left" and 50% "right". Even more strangely, if you then run the "left" electrons through another up/down SG device, the probabilities will now be 50%/50%, even though you selected only spin up electrons at the first stage so you'd expect 100%/0%. The act of going through the left/right device altered the spin up/down state somehow.
* Hidden variables. Perhaps the electrons above have definite "spin vertical" and "spin horizontal" properties before the experiment starts. The act of going through a device must change the other property, though everything might be deterministic if there is some further hidden property controlling which electrons have their spin up/down states altered in which ways by passing through the "left" SG device. The alternative is that there are no definite properties which determine the wavefunction; the wavefunction is all there is, reality is somehow fundamentally probabilistic, and the wavefunction is "real" instead of a statistical construct.
* Bell's theorem. Suppose spin up/down and spin left/right are definite properties and some hidden variables explain the above results. Using entanglement (which I'll leave undefined) and the assumption that information cannot travel faster than light, one can measure both the spin left/right and spin up/down values of a particle before the hidden variables have a chance to act (note: they might act in a very bizarre, perhaps even non-deterministic, manner, but we get to measure things before they have that chance). This gives a testable prediction which differs from quantum mechanics. If the experiment is performed, the "definite property" theory does not predict reality while the use of wavefunctions does predict reality. This is strong evidence for the reality of wavefunctions, though it's not completely conclusive.
* The paper. It derives Bell's fundamental contradiction from fewer assumptions. In its own words,
The result is in the same spirit as Bell's theorem, which states that no local theory [i.e. one without faster-than-light communication] can reproduce the predictions of quantum theory. Both theorems need to assume that a system has a objective physical state L such that probabilities for measurement outcomes depend only on L. But our theorem only assumes this for systems prepared in isolation from the rest of the universe in a quantum pure state [e.g. a particle measured as spin "up" right after the SG experiment above]. This is unlike
I think you've misinterpreted my comment. I'm saying that the photon goes through both slits (and all other possible paths). I was trying to point out that the gp's explanation of a rolled dice doesn't explain what is actually happening.
You're a temporary arrangement of matter sliding towards oblivion in a cold, uncaring universe
I can't remeber the finer details of Berkeley's argument, but I really don't see his point.
Most likely the world exists as we perceive it. In this case he is just wrong.
In case that the world does not exist, but is just an illusion of some sort, then what? If noone else exists, theres no point in telling them? Let alone spend time on writing a book about it?
You might as well entertain the idea that the world just is. Maybe the illusion will be removed from your eyes and you will see the real reality later on, but discussing it here makes no sense at all to me.
Of course it's real. There isn't an imaginary term in the wavefunction equation.
It's about physicists got serious about quantum-wave physics. Thanks to the Copenhagen interpretation, quantum-wave physics have been avoided by almost everyone. It's time for physicists to give up their religious beliefs and get on with it.
Don't stop where the ink does.
The Link in the comment of the article was quite interesting.
http://freespace.virgin.net/ch.thompson1/People/CarverMead.htm
Basically stating that there is nothing statistical about quantum phenomenon and that Bohr got it wrong after all (to my limited understanding).
"we are all atheists about most of the gods that societies have ever believed in. Some of us just go one god further."
not is is not is not
I intend to patent the direct manipulation of the quantum wave function, which will, among other outcomes, be the basis for my infinite improbability drive.
The wavefunction tells you exactly what state a system is in.
Consider a quantum dice. You can perform a roll-operation on it which sets it to a rolled-dice state. You can also perform a result-operation, that also sets the state, each characteristic state of the roll-operation has a value associated with it (1, 2, 3, 4, 5 or 6). You can look at the result without altering the state after the first result is found (it's a projection operator in other words). The first difference with your explanation is that you can roll as many times as you like without altering the state after the first roll. That is, when you roll a quantum dice, it is in a unique state. Rolling it again will not alter its state!
These two operations do not commute. The rolled-state can be written as a superposition of the six result-states - and it keeps that state no matter how many times you re-roll. When you use the result operation, that rolled-state collapses to one of six result-states. Which state it collapses too is random.
The maths of Quantum Mechanics is mostly linear algebra. If it was just practical statistics there wouldn't be so many disagreements about its meaning. Nevertheless, it's QM that agrees with reality.
Who ordered that?
As I said I love Hilbert space, so your comment is enough motivation for me to write up a brief explanation.
The n-dimensional Hilbert space is the collection of length-n lists of complex numbers. One can add these lists and scale them, so for instance [1, i] + [2, 1] = [3, i+1] and 2*[i, -1] = [2i, -2]. Physically, each component of the list corresponds to a possible experimental outcome. More specifically, the probability of the outcome corresponding to the ith component is the square of the magnitude of the ith component. For the electron spin up/down experiment I talked about the wavefunction [1, 0] gives a |1|^2 = 100% chance of measuring spin up (and 0% chance of measuring spin down; this is called a pure state). [sqrt(1/3), sqrt(2/3)] corresponds to a 1/3 chance to measure spin up and 2/3rds to measure spin down. You may wonder why the magnitude-squared business is used at all (why not just keep track of the probabilities?) which is where the complex numbers come in to play. The state [sqrt(1/3), i * sqrt(2/3)] has the same experimental outcomes given this single measurement as the previous state, [sqrt(1/3), sqrt(2/3)] but it is fundamentally different from it since the two components are "out of phase". More elaborate experiments can detect the difference. In this case it turns out the result of the spin left/right experiment is encoded in the phase difference between the two components.
Hilbert space comes with an important operation called an inner product, which I'll denote by the term "dot". It can "single out" the entry at a particular position in a list. For instance, by definition [1, i] dot [0, 1] = i, singling out the second component. The operation is extended to more general lists on the right-hand-side by rules I won't discuss, and it has a physical interpretation in terms of probabilities--the magnitude of (A dot B) squared is the probability of measuring a particle with wavefunction A in the state described by wavefunction B, which fits what I said above in light of the computation |[sqrt(1/3), sqrt(2/3)] dot [1, 0]|^2 = |sqrt(1/3)|^2 = 1/3. Note that the sum of the squares of the magnitudes of the entries in the list must be 1 since the experiment will have some outcome with 100% certainty.
One can have infinite dimensional Hilbert space where the lists are allowed to have infinite length. Sequence space is a popular example: it contains [1/1, i/2, 1/3, i/4, 1/5, ...] and [0, 1, 0, 0, 0, ...]. We often restrict ourselves to lists where the sum of the magnitudes squared are 1 since these are the only physically meaningful wavefunctions, giving the so-called projective Hilbert space. [1, 1, 1, ...] is certainly not in that space since it has infinite sum-of-squares. Actually, [1/1, i/2, 1/3, i/4, 1/5, ...] doesn't work here either, but sqrt(6)/pi * [1/1, i/2, 1/3, i/4, 1/5, ...] does work. (There's a beautiful proof using Parseval's theorem.) [1, 1, 1, ...] fails particularly badly since it cannot be scaled to an element of projective Hilbert space as we were able to do with the other list, so we don't allow it in regular Hilbert space at all. Any other lists that have infinite sum-of-squares are similarly excluded. The inner product is extended in a natural way to infinite lists. That's all the structure one requires.
I should note that Hilbert space is more often defined as an abstract vector space over the complex numbers equipped with a positive-definite sesquilinear inner product which is moreover Cauchy complete with respect to the induced norm. Projective Hilbert space is usually defined as projective equivalence classes over a Hilbert space with semi-canonical norm-1 representatives. My definitions are equivalent, assuming the axiom of choice (everybody does), and they're obviously more accessible (though it's much less pretty IMO). I should also mention that wavefunctions and elements of Hilbert space are usually written with the bra-ket notation and as sums of pure states (as the paper does); my notation is from Python and was chosen considering the audience.
Stephan Wolfram says it's cellular automata, all the way down.
He also says that Philip Taylor Kramer is stealing his thoughts.
the preceding comment is my own and in no way reflects the opinion of the Joint Chiefs of Staff
The only real loser is religion, whic presupposes just the one timeline. But then, religion has a long history of losing out to science and changing its teachings accordingly (like cockroaches, the memes don't die, they just adapt), so even that is unlikely to change if or when the multi-world hypothesis is proven.
Not sure why you believe that religion pre-supposes one timeline. Certainly, there are adherents of religions that take that viewpoint, but all religions usually do is say: there's this god over here and he or she or they say "Hi, I'm God or some really powerful entity. I have some stuff to say and you probably should listen." Sometimes there is an "or else" clause. That or I missed where the Prophet Elijiah discussed wavefunctions or timelines in the Bible.
Most of the major monotheistic religions these days posit an all powerful, all knowing deity. I don't think you could state that such a being requires only one timeline. In fact, I don't think you could legitimately place your bounds on their power or even guess their extent. Presumably, such a being could do whatever science shows is happening and it would be "Just as planned." Certainly, that sounds like feeble reasoning to the mind that limits itself to the empirical, but we know full well that that while science is very useful, even science has not even had a chance to have the last word on many important things yet.
Point being, some of the religionists were or are certainly making faulty assumptions on what their religion requires from science. Those assumptions don't mean that the religion actually requires that. However, now you are making assumptions on what religion requires, and you're equally wrong. Maybe if a deity actually said "The world is exactly 4000 years old, and you will never find dinosaur bones, you cannot break the sound barrier, and natural family planning will never fail", then you could probably discount that deity. Most religions are not that specific about such things.
The question is, which universe do you inhabit?
Ugh. Why people think this is somehow better than collapse interpretations I'll never know. I have a very hard time accepting that my coffee mug, while just sitting on my desk, is (as many worlds interpretations insist) spawning zillions of universes near continuously is positively ridiculous.
Required reading for internet skeptics
The question is, which universe do you inhabit?
Ugh. Why people think this is somehow better than collapse interpretations I'll never know. I have a very hard time accepting that my coffee mug, while just sitting on my desk, is (as many worlds interpretations insist) spawning zillions of universes near continuously is positively ridiculous.
I think it might be easier to just have a single quantum reality. That coffee mug is a quantum object, though we only know its quantum state very roughly, so roughly that it looks like a classically-described object. There is no decoherence, no picking of universes. There are just quantum interactions: in the case of a "decoherence event", you've just got a quantum interaction between one relatively-well determined quantum entity (the experiment) and a much larger undetermined quantum entity (the rest of the universe).
Of course, this does mean that reality is not at all what we thought it was...
"Little does he know, but there is no 'I' in 'Idiot'!"
Perhaps
Why do people feel it necessary to answer this question? What good would a resolution do anyone? Outcomes are still the same regardless of what you believe. Even if the "wavefunction" was "real" whatever that means there is still no guarantee we are aware of everything there is to know about it. What good is the label?
I'm somewhat confused about the timing of this article here on the site. The initial response to the PBR paper a couple of months ago was pretty varied, and mostly confused -- both from the lay public as well as from physicists. And so far this discussion also seems to suffer from misunderstandings and misinterpretations of what is the issue here. Frankly, this kind of confusion is unavoidable with an issue as subtle as this, within the constraints of a forum discussion (which is why I won't try to argue my point in detail here), although even some physicist blogs have made a mess of it. Anyway...
The reason I say that the timing is odd is that Slashdot decides to write about the PBR article, coincidental with the appearance of another paper to similar effect (but making different assumptions) on arxiv:
http://arxiv.org/abs/1205.1439 (by Lucien Hardy at Perimeter)
About a month ago, there was another publication by Roger Colbeck and Renato Renner (at PI and Zurich respectively, although Roger Colbeck has just moved to Switherland too, I think):
http://arxiv.org/abs/1111.6597
The upshot of all of these is, crudely speaking, that reality is at least as "complex" as the quantum state (there have been hints of this also from earlier work by Montina, which I think is referenced in Hardy's paper). It does not say that the quantum state as we describe it mathematically is literally a real thing. The background of a lot of these papers is a recent (last 20 years) trend towards statistical/subjective/operationalist interpretations of the quantum state, mostly brought about (in my opinion, anyway) by people working in quantum information/computing.
The abstract isn't saying the wave-function is real, if says if the wave-function isn't real than quantum theory is wrong. Since general theory of relativity and quantum theory are incompatible in some aspects we *know* quantum-theory is partially wrong (like Newtonian physics). So, while mathematically interesting, it's old news.
I should note that Hilbert space is more often defined as an abstract vector space over the complex numbers equipped with a positive-definite sesquilinear inner product which is moreover Cauchy complete with respect to the induced norm.
I'm glad you noted that, because I was really going to give you some grief if you skipped that part.
Don't disappoint your bird dog. Go to the range.
That's not an exact analogy. However to see that, you have to look at the details of quantum mechanics. The post I answered to however questioned the concept, and therefore I explained the concept on the case which everyone can understand immediately, which is classical probabilities.
Now with quantum mechanics, there's no "die" beyond the probabilities, however the basic idea of the interpretation as state of knowledge is the same. Except that in this case it's not knowledge about a hidden reality (the "die") but about the measurement results themselves (the numbers observed).
The Tao of math: The numbers you can count are not the real numbers.
But you didn't understand that the explanation wasn't meant as an explanation of what is really happening. It was meant as an explanation how something that is not real can apparently "have an effect" (the point the OP had a problem with) by using classical probability as example.
The Tao of math: The numbers you can count are not the real numbers.
Why, oh why, do so many people insist in reading things into texts which simply are not in the text. Be assured that I know very well that quantum mechanics is not just classical statistics. After all, I'm working in the fields. However the concept of explaining one point with a different, but simpler example sharing just that single property seems to be lost to most people :-(
The Tao of math: The numbers you can count are not the real numbers.
Hello: The paper in question can be found here: http://arxiv.org/pdf/1111.3328.pdf Apologies if this has been posted already.
Wow, that gave me a nosebleed! All kidding aside, I just wanted to say thanks. Your first post made the rest of this thread make a lot more sense - kudos!
It gripped her hand gently. 'Regret is for humans,' it said.
Try this as a thought experiment. Imagine your brain and your DNA scanned into a computer. This is used to generate a simulated you. This simulated you is placed in a simulated room in which all the known laws of physics are simulated to a high degree of precision.
You are placed in an identical, but real, room. The two rooms are connected via a terminal (or, in the copy's case, a simulated terminal).
You and the simulated you can ask for any scientific equipment that can fit into the room. Both of you can conduct whatever experiments you like. The only requirement is a unanimous agreement between you, your copy and those running the experiment as to which of you is physical and which is virtual.
If no observation, experiment, or set of experiments, exists that can prove which is real, then you cannot prove what is "real" - there'd be nothing so unique to reality that would allow you to unquestionably establish that something belongs to reality and not to something else. If, however, you CAN through experimentation reach a unanimous verdict, then an objective reality is provable.
It is my opinion that it is the first case that would turn out to be true.
No such completely open ended experiment is possible. If it were, any new scientific observation of a previously unknown phenomenon could not be properly modeled on the simulated side and produce the same result as on the real side. In fact, if the results do differ, you have proof of objective reality, or at least that both sides are simulated differently. The simulation cannot have universal knowledge beyond that of its creators. Call that a reasonable postulate.
These arguments are in the same vain as the arguments for Bell's hypothesis.