Chance moves in mysterious ways.

sinequanon are you basically saying that a "full" measurement of the photon would require complete knowledge of its wavefunction, (i.e. the actual amplitudes at each point), however a position measurement only samples (non-deterministically) the wavefunction over a small range of positions?I take from this: that you are, in general, making some point about measurement interactions not being entirely related to knowledge of the particle.Edited by Son Goku, : Clarity

I also assume that by eigenfunctions you are referring to the eigenfunctions of the position operator, postponing the technicality that they don't exist.(For people who don't know what I'm talking about an eigenfunction may be understand as being a state when a quantum mechanical object has a definite property. For instance an energy eigenfunction is when something has specific definite energy. If you are familiar with Schrdinger’s cat, then the cat being definitely alive after the measurement is an eigenfunction. Things like being "alive and dead simultaneously" are not eigenfunctions. There are no position eigenfunctions because a particle is never definitely exactly "here" or "there", there is always a bit of a spread.) Well first of all, let's take the example you and PaulK are talking about. The photon's wavefunction is spreading out from the emitter and propagating in the direction of the screen which will detect it. When it makes contact with the screen, we (the experimenters) will see the appearance of a white mark of finite radius on the screen. This white mark indicates where the photon's wavefunction is now concentrated. First of all it isn't an exact position because the mark is of finite size. Basically the wavefunction has been set to zero outside this mark.Now where on the screen this mark appears is random, although some places will be favoured by others. Your issue is that the lack of a causal structure for the selection of the marks position is no better than "god did it". I can understand your position in light of this simple example. However let's broaden the phenomena we are discussing.The randomness in QM is not the simple randomness that is commonly associated with that word. That is to say it is not simply a negation of determinism. For instance as we know from quantum computing it is capable of increasing computational capacity. We also know it possesses the structure of complex number multiplication. In fact in general this randomness possesses are very rich C*-algebra structure.(Again if I have lost anybody, C*-algebras are simply a type of mathematical structure, the point being they are very complex, with specific properties. An analogy would be a calendar. It is not merely a collection of numbers, it also possesses the extra structure of the numbers being ordered by date. Similarly randomness in QM is not just randomness, but possesses this extra mathematical structure.)"God did it" possesses none of this extra information. The randomness is also a phenomena with properties to be discovered, in a sense.

What simpler systems are you talking about? Maybe an example or two. Just to make sure I'm understanding you. To clear up something I was saying, the unpredictable component also has structure. There is a good book by Julian Schwinger where he analyses unpredictable results in QM and uses it derive complex number algebra. That is QM's randomness has an imprint of complex numbers. Very interesting stuff.However I understand your main point. All I can say is that Bell's Theorem seems to indicate that this is the way things are and from a purely physical perspective there is randomness. Basically randomness was forced on us rather than it being us giving up and saying "randomness did it".

I'm not sure that is true. It doesn't just come in handy in Quantum Mechanics it's literally responsible for nearly all of what is unique about QM. If QM was based entirely on real numbers there would be no entanglement and superposition wouldn't be as strong. If you use "higher" number systems, like the quaternions, you have difficulties with independant systems. It is true that this system has structure, like all physical systems. However I'm saying the nonpredictable component of QM itself has a structure, which instantly places it above simple assertions like "God did it". It's "Randomness with a C*-algebra structure on top". This structure is responsible for an incredible amount of physical phenomena. Would Bell's Inequalities and the Aspect experiments not provide evidential support to this assertion.

Well for instance if QM had any other norm higher than the square norm it would be physically trivial. If it had a first power norm, there would be no entanglement. If one had real numbers instead of complex numbers you couldn’t get three independent quantities like spin in the x,y and z directions to be equal superpositions of each other.If one had quaternions instead of complex numbers, interference wouldn’t work in the same way to give rise to effects such as lasers. It would be hard to stop the theory from being physically trivial. Complex numbers are at the core of what makes Quantum Mechanics the theory that it is. At least in my conception it is certainly not "by the way".(Again if I’m making no sense to people, if QM used a number system other than the complex number system, our world would be very boring.) Unless I’m very mistaken about QM, all this is specifically the structure of the non-deterministic component. The deterministic component is a Schrdinger-type equation. It’s the non-deterministic component that imposes the complex structure. Sure think about it, why isn’t the probability of QM standard statistics? Where does interference come from?
The indeterminate, measurement aspect of QM comes with its own mathematical structure. To give more detail, take quantum computers. They rarely take advantage of the deterministic aspects of QM, their power comes from the random part.In fact the most obvious things about QM is that it has a blatant divide between its deterministic parts and non-deterministic parts.However the main point is the probability of QM isn’t standard statistics, that’s more than enough to signal that there is something unusual about the randomness in QM. I don’t understand this. How does the fact that other systems have structure say anything about QM’s indeterminate aspects? Well Bell’s Inequalities give specific predictions of what the world would be like if it was actually random, as opposed to local hidden variables. The Aspect experiments tested this and the evidence came out in favour of underlying randomness. It therefore lends support to asserting that there is randomness.

Huh? What theory besides QM uses a 2-norm? How does it relate to energy? They are? How so? That certainly isn't what happened historically. The Schrodinger equation alone only gives unitary evolution. If you only had that, you'd think you were dealing with a standard physical PDE describing wave evolution. It's Born's 2-norm probability that then gives meanings to linear operators and their eigenvalues. It would make the post too turgid to go into. Any questions have their answer here:
http://www.scottaaronson.com/papers/island.pdf Yes, I understand that. Other things use complex numbers, why does it matter though? What are you saying? Fair enough. However if randomness has experimental tests such as the Aspect experiments which can directly falsify it then part of your original claim isn't true. The reason I'm bringing up this point about the mathematical structure in QM is because I'm trying to demonstrate that the random component has:
(a) Experimental support and the existence of experiments capable of falsifying it.
(b) We have found out properties of this randomness. Such as it having the 2-norm I describe above. This is a major insight. The existence of statistics other than the 1-norm humans had used up to then.This indicates that randomness is a feature of the world with properties scientists can study. This is a world away from

What about the last part of my post about the existence of a falsification test for randomness, which you claim does not exist? The fact that it does exist is a direct refutation of your position. Obviously there exist cases where one gets the length of things with a binary operation. The point is, the fact that QM uses 2-norm probability is something new and interesting. It was never seen before in standard statistics and gives rise to new physical effects. This is an important point, because you calim that "randomness did it" is as good as "God did it", which obviously can't be the case unless "God did it" somehow implies which normed statistics you should use.Eigenfunctions of energy. That's one single operator. And it doesn't even mean anything until you have the square modulus (2-norm) Born rule. Sure why weren't Hilbert Spaces used before in physics? You cannot be serious. That's like saying "All relativity says is that different things see different stuff, big deal".

Yes, to be fair work on this stuff does exist. There could be a deeper deterministic theory underneath QM*. I'm trying to show that QM's randomness isn't scientifically worthless.Think of it as being like somebody defending Newton's action-at-distance theories two hundred years ago. Some people might claim that the action happening at a distance is like saying "God magically did it instantly". You'd defend it by describing everything it has done, perhaps unfairly ignoring the work of "propagation" theorists who could turn out to have the right answer.*As a side note do you know of a deterministic model which can replicate QFT. Every deterministic model I've ever seen only matches QM's predictions not QFTs. For example Bohmian Mechanics.