Chance moves in mysterious ways.

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.

Looks like we are going to have to break this down further for you.A. A photon is fired at a film in the classic two slit scenario.B. A DOT appears on the film as a result.C. The film can be removed and the position of the DOT measured.(Note: no talk of "where the photon hit").What are you having difficulty understanding? Which point do you disagree with?Now, does there exist a deterministic model for the measured position of the DOT.i.e Given accurate enough instruments can we predict the position of the DOT to arbitrary accuracy.Actually, in case you screw that up, it means:If the same classic two slit experiment is repeated, does there exist a deterministic model for the measured position of the DOTEdited by sinequanon, : Spoon feeding.

quote:

---

Looks like we are going to have to break this down further for you.

​

A. A photon is fired at a film in the classic two slit scenario.

​

B. A DOT appears on the film as a result.

​

C. The film can be removed and the position of the DOT measured.

​

(Note: no talk of "where the photon hit").

---

Well you can leave that out but it's pointless to do so. Except, maybe if you want to leave out the fact that I was talking about it earlier. You do realise that the dot is a measurement ? And that the wave function of the photon collapses as a result ?

quote:

---

What are you having difficulty understanding? Which point do you disagree with?

---

The fact that when you introduced B it did NOT include the position of the dot.So B is the dot appearing AT A SPECIFIC LOCATION ? Right ? And you intend to stick with that definition, now, right ? No more games.

quote:

---

Now, does there exist a deterministic model for the measured position of the DOT.

---

If you bothered to go back to the discussion earlier you'd see that I already agree that the point at which the photon arrives is not-determistic - and that IS the location of the dot, whether you want to talk about it or not. Determinism only got introduced when you proposed a new example LEAVING OUT LOCATION. If you hadn't done that, we wouldn't have wasted all that time and posts on this diversion of yours. I told you it was irrelevant at the start, and you've just proved me right.

Well you seem to have sailed passed any mental obstacles PaulK is suffering from. Agreed. It is non-deterministic nontheless. A Hilbert space does afford rich structure and functionality, but simpler systems also have structure and functionality. I believe it is more a matter of degree.Quantum system are truly non-deterministic in the sense that something like the uncertainty principle would collapse if the system had an alternative deterministic model.It means there are certain thing we will NEVER be able predict. There is a predictable component, as you indicate, but is God hiding in the detail.

Trying to shift the question again by saying it pointless, and then changing it to something else? Later you will claim I shifted the point.Do you agree with A, B, and C. Answer the question even if you can't see the point.

quote:

---

Trying to shift the question again by saying it pointless, and then changing it to something else? Later you will claim I shifted the point.

---

No, trying to stop YOU shifting the question. Again.
And the fact that you did not confirm that you are going to stick with the definition of B you presented in your previous post rather suggests that you intend to do it, too.

quote:

---

Do you agree with A, B, and C. Answer the question even if you can't see the point.

---

I answered your questions. I've given you the benefit of the doubt too often. I won't repeat myself for the benefit of your silly games.

A. A photon is fired at a film in the classic two slit scenario.B. A DOT appears on the film as a result.C. The film can be removed and the position of the DOT measured.A clear answer would be in the form:"I agree with A, B AND C"OR"I disagree with B because..."Not this waffle...

Quit playing games. Your question has been answered.

I quite understand your fear and embarrassment of getting stuck again.We can continue once you've read up on the subject enough to answer the simple question.Do you agree with all three points, A, B, and C? If not which do you disagree with?

You've had your answer. Stop playing silly games.

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".

The impact locations on a wall of shot fired from a shotgun. I haven't read that particular book, but I have covered the standard mathematics university courses on QM and using Hilbert spaces and the Hermitian operator. We went up to the basics of string theory.Complex number algebra is sort of "by the way". It happened to come in handy as it does in many systems modelled using differential equations with second partial derivatives - a pendulum for example. If it were simply a case of "giving up" then we could not claim the system is random, just the model we use for it. However the theory is saying randomness is forced on us - no deterministic alternative. The theory is that randomness is responsible, which is what I mean by "randomness done it". Edited by sinequanon, : No reason given.

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.

Not sure what you are driving at here. Can you post an example of a unique characteristic? Can you also post an example demonstrating entanglement and strong superposition. The mathematical model is useful because it lets us get at deterministic properties. That does not imply that QM's non-deterministic component has been represented or has structure. It's almost a philosophical point about whether we can talk separately of deterministic and non-deterministic sub-structures.If you don't like the shotgun example take a 3D chaotic system. Plenty of structure there. Which part of the assertion, exactly?

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.