Yeah, that’s what I was afraid you’d say.
Yeah but an oxygen molecule reacts with iron and many other materials in the absence of any measurement being made by anyone or anything.
If one oxgen can be considered collapsed from the standpoint of the other, which is which? That is, for this to be true don’t the probability functions for both of them have to have collapsed into physical oxygen atoms having a mass, a velocity, etc.?
Here’s the crux; you don’t know anything about the state of the system before you’ve observed it (and it’s worth noting again that the act of observing means that you’ve interacted with the system, 'cause you can’t just stand back and look at it), and by observing it, you cause it to collapse. The oxidation reaction mentioned above is, like all other potential states, in superposition until you interact with the system.
Now, from any rational viewpoint, this is all bunk. Of course you didn’t have to come along and look at the atoms to make them do their thing, nor is one atom more privileged than the other. Or is it? Perhaps they’re both simultaneously “observing” each others states, and when you come along you see the resolution of that, which happened long before you interacted with it. Or maybe it knew you were coming and resolved itself just before you got there. (I call this the Little Blue Men interpretation.) It could be that all possibilities exist simultaneously in relative states (many worlds) to one another. Or perhaps, as Chronos suggests, there is no collapse, and what you observe is only one possible state which corresponds to your own state; maybe Wigner’s friend is simulataneously happy and sad at the cat’s survival and demise, and when you inquire as to the cat’s state of health, he tells you (both states of you) that it’s alive and dead. I’d like to think that they do, in fact, exist outside of your involvement and acknowledgement, but there’s no way to check that, at least insofar as we know.
Now, you can ask the Dancing Wu Li Masters to come and explain it to you, or maybe you can get Winnie the Pooh to give you his opinion on the topic. (I don’t recommend having Wiley Coyote give you his take on it, but hey, it’s your dime.) Conventional quantum mechanics, however, has nothing useful to say about these interpretations, other than that they’re all possible and equally absurd, and most importantly, all come to the same observable result, predictable by calculated probabilities. Hell, we don’t even know what “waveform collapse” really means, or if it’s even a strictly necessary concept except to give an arbitrary starting point for the calculation.
Most people might think that physicists studing quantum mechanics are real big brain know-it-alls, but in fact, they know absolutely nothing, or rather, they know that they know nothing. And now, so do you.
Stranger
I think Quantum Theory and Quantum Mechanics are great. By means of it, the arrangement of electron shells in attoms, the emission of light, the photoelectric effect and much else have been explained.
However, I think the molecule of iron oxide is real and exists whether or not anyone observes it. And so is that cat. 
Think of a water wave impinging on the two slits. Qm is a wave theory.
No, there is no chance that both detectors will register a hit. But there is a chance that either detector will. When the probability wave collapses at one of the detectors, that’s it.
But it’s also a particle theory. It’s two…two…two theories in one. 
The whole wave/particle business isn’t as paradoxical (or stupid) as it sounds. Fundamentally, whatever is going on at the quantum level just isn’t like anything you experience in normal life. That alternately modeling it as a wave and a particle works just means that we lack an accurate analog to represent it conceptually. However, the dual formulation works mathematically, which at least according to Heisenberg and friends, is all that is required.
If it helps, you can think of it as a three dimensional blob in space that acts like it has a wave moving in it (making some parts more or less dense) as the probability wavefunction, but only interacting with other blobs at common tangents, where they can join up together and effect each other’s shapes, but always remain distinct…well, unless the big is made of up of smaller blobs which suddenly bust appart, or accepts/exchanges a blob from anther blob in order to keep the blobs together. Actually, I don’t know if that helps at all; it sounds more like a bad horror movie, but anyway that’s sort of the way I visualize it. It’s not necessarily a better conception than any other, but it makes me stop worrying about it, so it’s at least useful in that regard. Then again, I also tend to think of electromagnetic fields as big arrays of corkscrews, so what do I know?
Stranger
Helpful.
Confusion reasserts itself.
I am going with the wave idea so then my concept of a wave has it arcing out to my detectors and should arrive at both simultaneously. But wait! Actually one detector registers it first and then all the rest of it instantly disappears!
Not making fun of you…more myself really at the confusion this all engenders.
Then we have Stranger on a Train with some wonderfully written and detailed explanations that while fascinating still leave me confused.
Perhaps there is no understanding this outside of the mathematics but I just can’t help but think that the “right” answer ought to be elegant and understandable to my mere mortal mind. Of course there is no reason the Universe should oblige my opinions but there it is anyway.
We have analogies which help me understand what the word “wave” means in the real world, and analogies which help me understand what the word “particle” means in the real world. But I am still befuddled by the use of the word “collapse” in these contexts.
To me, a wave “collapses” when it has spread out so far that the amplitude of each crest has become negligible. I’m pretty certain that’s not what is meant here. I suspect that “collapsing a wave” might be similar to “solving an equation”, but I’m not sure. Anyone know what I’m talking about? (because I don’t)
It gets a lot worse. Let’s say we do the calculations and it turns out there is a 50% propability for the particle to be found at either detector. This means that for a single photon it will be completely random as to which detector registers it. But if you run a large number of identical experiments .5 will register at D1 and .5 will register at D2.
And here’s a little fact to make things more interesting. The probability wave doesn’t carry any energy so it can’t be real in any sense of the word. I’ve studied this stuff for many years and really all that happens is you gain a familiarity with the equations. Actual understanding isn’t possible. Pick an analogy you like and stick with it.
“Collapse” is what happens when you "measure’ (i.e. interact) with it, giving it a definite locus of action i.e. the position and momentum (or time and energy, or vectors of the angular momentum, or whatever) of it, which can be known only to the precision that the product of their standard deviations from a Gaussian distribution are greater than or equal to h/4π. In other words, by observing the particle, you reduce it from being a big smear of probability all over the place to knowing where it is and where it is going to a much smaller–but never smaller than a specified amount–degree of probability.
The business of collapse can be viewed as a mathematical formalism; going from a very general knowledge of where the particle is at to a more precise understanding. But there is–at least in the view of the Copenhagen interpretations–no known physicality in collapse, and in fact the whole system is viewed as being nonreal[sup]*[/sup] in any material sense until the collapse event occurs. In other words, (as stated by many a physics professor) “shut up and calculate,” i.e. do the math and stop worrying about things we can’t measure. That this is a dissatisfying explanation is part of the whole underlying unreal strangeness of QM. I can’t help you there, other than to say that there’s nothing “real” about collapse any more than there’s anything real about Road Runner cartoons.
Stranger
[sup]*[/sup]I’m using the terms “real” and “nonreal” in the materially observable sense; i.e. if you can’t demonstrate that it exists before you look at it, it’s “nonreal”. Personally, I don’t buy that; I think objects actually exist regardless of whether you’re looking at them or not, but there’s no way to prove that they’re not being constructed by Little Blue Men (as a friend of mine posits it) right before you enter the room.
And people call religion mystical.
Tsk, tsk. There’s nothing mystical about it. There is a well defined set of rules and procedures to follow in QM. Anyone at all who follows those rules and procedures gets an answer that can be confirmed by experience and everyone gets the same results. That those results are often stated as probabilities is meaningless. So are the results of games played in a gambling casino, but nobody compares their methods to mysticism.
Oh, so now suddenly it’s all precise and thoroughly understood, with only one interpretation. Why didn’t someone say so up-front, and spare people from reading through three tandem-linked threads about how mysterious it all is?
In fact, the interpretations are pretty much on the level of mysticism, hence why most physicists ignore them in practice. But the overall mechanics are testable and work to extraordinary precision at matching the predicted probabilities.
There are multiple interpretations, but just one theory. The theory works; the intepretations are, in a functional sense, irrelevent and perhaps fundamentally untestable.
Stranger
The mechanics of using QM are precise and well understood as **Stranger **said. If you get into the whys and wherefores then things get hazy.
Of course nobody knows what is behind gravity either, so that’s also mysticism. And let’s not get started on what underlies electricity.
OK. So - try this.
I take a ball and pitch it into a dark room. I watch the ball go away until it enters the darkness. At the point where I can no longer see it, is it now a wave function and not collapsed? Has it moved from the realm of “reality” to “probability”?
What happens when I hear it strike the back wall?
This is a really negative statement and I should be ashamed of myself.
If a person really puts the time and effort into studying this stuff he will develop a profound understanding of why he can’t understand it.
In fact the longer and more diligently one studies QM his knowledge of his ability to not understand becomes exponentially more insightful and deeply satisfying.
Whack-a-Mole I hate to say this but my ability to not understand QM is much greater than your ability to not understand it. (He quietly chortles at his superiority)
Let me take a crack at this. I noticed in your OP you said,
This is your problem, right here. The photon is not in any one location before the measurement. It does not have a location. Its location is a function of the interaction between photon and detector. That is the weirdness of quantum mechanics: All the photon “is” is a set of probabilities that determine the likelihood of the interaction having this or that outcome.
The same goes for any of these quantum attributes (known as “quantum numbers” in physics parlance). The particle simply does not have a definite value of location, or spin, or whatever, until a measurement is made. Some of the ancient Greeks had this idea about potential which is suitable here. The particle exists, but it exists as potentiality. It exists as probabilities governed by the Schrodinger equation.
The key concept for me when I was learning this was that classical physics is a theory of objects, and quantum theory is a theory of interactions. Quantum mechanics tells us that this interaction will have these possible outcomes, each with an associated probability. Repeated measurements of that interaction, whatever it is, will reproduce those outcomes with exactly those probabilities.
I hope this helps.
Belrix, that’s an excellent thought experiment. When you lose sight of the ball, it does enter a superposition of possible trajectories. When you hear it strike the back wall, you’re observing it again, so the wavefunction collapses. If you had the echolocation of a bat (or an equivalent piece of equipment), you could use that sound to locate exactly where on the wall the ball hit, and thus you would know exactly which trajectory (out of all the possibilities) the ball followed.
It’s all Little Green Men, right? (Not to be confused with the Little Blue Men of quantum mechanics, of course.)
There is, again, no physical substantiation to waveform collapse, so we can’t say when it happens or indeed how it happens. In the case of a ball thrown into a room at non-relativistic speeds we can essentially say that it is all “local” (causally linked without any funny business or worries about transformations) and that it never really disappears; maybe you can’t see it, but someone with an infrared camera could, and of course when it strikes the back wall, the energy (and thus information) of the impact is transferred back via sound waves in the air.
There are no real world boundaries between quantum systems (save for–presumably–event horizons like those found around a “black hole”, and even that’s questionable) and thus no way to establish where probability ends and reality begins, other than that we know when we interact with a particle we’re seeing a discrete state, not a superposition of waveforms. The business about the cat in the box is just a hypothetical experiment, an analogy intended to make a macro-sized system behave in a quantitized fasion.
Stranger
IMO, most popular descriptions of QM make a fatal, early mistake: They do not force the reader to clearly and carefully examine his/her most fundamental notions of physical reality. The apparently-paradoxical behavior of physical particles operating in QM stems in large part from unstated assumptions held by the reader.
The particle-wave duality is an excellent example. Most folks have underlying beliefs about the properties of particles and waves that are inherently contradictory, e.g. a particle has a definite material component and a specific position in space (i.e. if it’s at point A, it can’t also be at a separate point B), waves are really a form of energy (they have no material component) and can, theortically, occupy all relevant space. So when it’s glibly explained that a photon is “both a particle and a wave”, it sounds like nonsense. It’s closer to the truth to say “we have no macroscopic analog for what a photon is, but we can say that under certain circumstances it exhibits certain properties like a particle, in other cases certain properties like a wave.”
Tearing out and re-examining one’s common-sense notions of the universe it not at all a simple task; when most folks (myself included) ask questions about QM, we expect the answers to build on something we’ve already learned and accepted. But I’ve come to the conclusion that it’s necessary to get the really fundamental points of QM, to gain a personal acceptance of the data, not just a glib, superficial understanding. It’s still frustrating though, like asking someone a question like “Who is the president of France?” and getting in response “Well, to really understand you’ve first got to learn this unfamiliar language, then read a lengthy history of France and spend two years living in Paris; but in the meantime, I can tell you it’s someone who is highly intelligent yet wouldn’t understand a single word you said and will become a different person in the next two months.” (with apologies to Jacques Chirac and his soon-to-be sucessor in the May election, who I think all speak fluent English)