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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
> 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.
It certainly knows.
It knows, but you don't. You don't because you haven't measured it yet. And until you measure it, the answer is not the simplified version of the cat being dead and alive at the same time, but that there's a probability it's dead, and a probability it's alive, but it'll never be more than probability until you actually confirm it. Once you confirm it by measurement, the probability of one state goes to one, and the probability of the other state goes to zero.
This goes back to the age-old question: If a tree falls in a forest and no one is around to hear it, does it make a sound? It certainly makes a noise, but does it make a sound?
If there's nothing to observe reality, does it still exist? That's the essence of Schrodinger's cat.
"If a nation expects to be ignorant and free in a state of civilization, it expects what never was and never will be."
No. Well, maybe for the cat, we're not able to do the experiment to tell.
But in the equivalent test using a photon in place of a cat and orthogonal polarization states in place of dead or alive, the photon most certainly does not "know" what state it is in.
This is the essence of Bell's inequality and the fact that there is no local hidden variable theorem compatible with the results of QM.
Tim.
God said, "div D = rho, div B = 0, curl E = -@B/@t, curl H = J + @D/@t," and there was light.
http://arxiv.org/abs/1111.3328v2
http://arxiv.org/pdf/1111.3328v2.pdf
http://stephan.sugarmotor.org
I've never understood how some people can be so dogmatically sure about the existence of an objective reality. Not to say there isn't one. but I've actually heard some people claim that 100% of their own experience supports an objective reality external to themselves. That would imply that a persons dreams, hallucinations, emotions, being fooled by optical illusions, and other such things were all proof of something about the nature of that reality. A little bit of introspection here soon shows that, however convinced you are of there being an objective reality or however certain you are that your experiences support it, you simply can't, in reason, claim that every single experience you have proves something about the nature of that reality.
Hell, most people don't learn that their 'self' is running on a physical substrate normally called a brain, until they are at least eight to ten years old. All those other experiences up until then certainly didn't reveal much about the underlying nature of any objective external reality until then, did they? That's a pretty damned important fact about the supposed objective external reality, considreing that brain will have litterally trillions of sensory experiences before it ever even possibly gets to a state where it can become aware of its true nature, and then only if it grows up in a society that has learned modern medicine.
It amazes me still that so many people can think kicking a stone really refutes Bishop Berkeley.
The evidence that QM is more than a mathematical trick mounts. It's worth noting that, at the beginning of the 20th century, most scientists weren't at all sure atoms were real and not just a mathematical convenience. It took Einstein's paper on Brownian motion to convert many scientists to the viewpoint that atoms were more than a convenient simplifying model. If this work holds up as well as Einstein's, it may be equally respected in the judgment of history.
Who is John Cabal?
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...
The argument used to be whether the wave function was "real" or whether it was a mathematical artifact, in other words is a particle actually smeared out or does it exist at one point and we're just limited in our observations of it (aka a "hidden variable"). These days the argument is whether the (Copenhagen interpretation) wave function actually exists or whether it's a mathematical artifact of a different theory, such as Everett's "Many Worlds" interpretation. Personally I go with Everett, but for philosophical/anthropic arguments rather than anything testable at the moment.
Please consider this account deleted, I just can't be bothered with the spam anymore.
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.
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.
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)
I am not convinced that the particles regarded as fundamental actually are. I'm not even completely convinced that "particles" at that level even exist in the normal sense, since we know interference patterns exist when the gap is in time rather than in space. That makes no logical sense when using a corpuscular model.
It is my suspicion (IANAQMPBTIBO) that in precisely the same way that matter is merely energy that has "condensed" and entangled, particles are merely waves that have "condensed" and entangled. This is based on the fact that fundamental particles of the same type are totally interchangeable and no two particles of the same type are in the same state. To me, that does not appear distinguishable from saying that a single wave appears to be every particle of that type, since that would give you what is observed without having to have any new or excessively complex physics to explain it.
If that is correct, then neither space nor time are particularly important in QM. Which has been theorized by better minds than mine. You would be able to map everything into waveforms and not need spacetime for them to exist in. Rather, spacetime would be one way an observer could interpret those waveforms - it would be subjective, not objective. The waves themselves would be the only "reality". Again, there's a branch of QM based on just such a notion.
To answer your question as to what is "vibrating", in this line of thought there wouldn't be anything TO vibrate, per-se, no time for it to be vibrate in and no space in which the vibrations could take place. You'd simply have a multidimensional waveform where if you made some axis space and another one time, you could treat it as though something was vibrating. In practice, though, it would be a static n-dimensional waveform whose existence was logical rather than physical.
I like this particular branch of QM, as it means physics is a branch of mathematics, a specific group with specific properties and specific operations, and that the universe is a specific set of functions that wholly reside in that group. It makes maths the "ultimate" reality, which means these sorts of philosophical musings about the world can be answered through mathematical analysis (although maths permits that answer to be rigorously undefined).
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)
Not if it's running on the 'cloud'. Come on man, get with the times.
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
Given that I've spent the majority of my life working with computers, I've come to accept reality as just another theory. Does the OS know it's inside a virtual machine ? (without the hypervisor intentionally making itself known) How can any person know, with absolute certainty, that they're not a brain in a jar, being fed simulated input ? How can we even know we're a brain at all ? For all I know, my entire existence could be a work of fiction, the Internet could be a fabrication of my mind, along with all its inhabitants.
The only thing we can reasonably assume, is that thought exists.
(and yes, I think the best psych/philosophy profs were the ones who dropped acid on a regular basis :)
-Billco, Fnarg.com
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
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.