I’m looking for the opinions of those better-versed in physics than I am on this article:
http://www.csicop.org/si/2006-04/quantum-mechanics.html
It seems to clear up a lot of confusion I’ve had on the subjects, but in that, it makes me wonder if it actually stands up to current scientific speculation?
The sum-over-histories school of thought described in the article is actually a pretty well-established way of thinking about quantum mechanics, and has been since Feynman popularized it in the '50s (or so.) The disadvantage of it is that for anything but the simplest systems, it becomes very very mathematically complicated to make any predicitions using this formalism alone, and it’s usually easier to revert to the old-fashioned Schrodinger or Heisenberg way of thinking of things.
I don’t find anything particularly glaringly wrong with the article, but don’t find it very helpful, either. Basically, instead of understanding weird quantum mechanics, you’re supposed to understand a weird version of classical mechanics, and then see how QM is kind of like that. Except for all the strange things about QM (like, predictions are for probabilities, waveforms collapse, particles can be entangled ), which the article pretty much ignores or glosses over. So if you have to understand a weird, non-intuitive mechanics, why not just go right to QM?
s/complicated/nonsensical/
Modern physics (or more precisely its ramifications) becomes a little easier to grasp philosophically if you let go the firm hold on the concept of existence that you culturally grew up with. It’s a linguistic construct and it really is not nearly as natural as it seems.
Your consciousness is only able to deal with itself - all your sensory input, all your feedback, all your biology is already thoughts and ideas in your consciousness by the time YOU get to deal with it - pretty much by definition. You have to decide for yourself what existence means to you but in the purest sense it’s the idea that some other idea did not entirely originate within your mind and is somehow connected as cause or effect with something that is purely outside of the scope of your consciousness.
For me, this perspective makes things like definite existence (in the material sense), absolute truth, etc complete nonsense and makes things like Heisenberg Uncertainty Principle completely natural. In fact, for the more common pairs of concepts such as position and momentum it flows from the definition. Since you have no way of gauging the probability (other than it’s not 1 and not 0) that there is more to position and momentum than the ideas of what they are in your head - examine that before moving on to observation. Position is an abstract idea of some sort of quantifiable value of just how much do two things not occupy the same space - it’s kind of an awkward way of phrasing it but it’ll do. Momentum, or to simplify assuming we know what mass is, velocity, is some sort of a quantifiable value of just how much position changes over time. Now, the ideas itself of absolute position and absolute change in position are incompatible for obvious reasons. If it’s absolute it’s not changing and if it’s changing it’s definitely not absolute. Now armed with that you can go ahead and try to measure planck’s constant (although this philosophical approach does not necessitate the existence of a constant it pretty much necessitates the existence of some, possibly non-deterministic or immesurable, limiting function).
Using same type of philosophical reasoning things like relativity, wave-particle duality, wave function collapse etc. also fall into place (Although I’m still trying to grasp entanglement), and a lot of Newtonian mechanics becomes simply absurd.
The reason I went on this spiel (and mods, if you feel it’s grossly incompatible with GD, you can delete it but drop me a line) is because the article was very grating for me. It tries to explain something very natural using a very weird concept of a fixed definite. If you simply consider the fact that the only fixed definite you have is self-contained valid logic, and any logical argument without external-to-the-argument premises cannot have external-to-the-argument conclusions you wind up with no justifiable external definites. You absolutely have no reason to believe there is anything that has a probability of 1 or 0 - past, present or future - outside of your own head. This makes an idea of an external natural law that tells you how something is going to (or is, or did) behave exactly completely absurd, and that little change should make modern physics a lot easier to grasp.
Getting back to something more concrete, like duality - observing effects of particles does not necessitate any further existence of particles other than the concept of a particle you just formed. Observing both wave-like and object-like behavior does not in any way imply anything you *have not observed. * In other words, simply because you have an idea of an object and that objects have certain properties, and you observe properties it does not automatically create an object to have them. The consistent observable that behaves like solids and waves at the same time is not something that has the property of being and then acting funny, the observable behavior is the entirety of its existence.
When you observe something as a solid, you expect to observe other properties in the future that are expected of solids. When you suddenly do not, there can’t be a how or a why to it simply because your expectation was broken - your expectation s are not guarantees. Trying to think of duality as funny waves that act like particles or funny particles that act like waves is silly, you’re taking two things you’ve observed and assigning one of them more weight for no other reason than that you fancy it more.
Err…sorry for the rant. I gotta go let the cat out of the box, it’s probably hungry and we need to bury it 
I stopped reading at this:
I have read of versions of the twin-slit experiment that establish that interference can be prevented by a measurement made after the particle (photon/electron?) must have passed through the slit(s). I can’t see that there is any common sense way to describe what the heck is going on there.
I’m sure you’ve heard this:
Anyone who is not shocked by quantum theory has not understood it. Neils Bohr
Actually it makes perfect sense. It’s not like you measure interference, write it down in the notebook, take pictures of the patterns and then can do a subsequent measurement that will change all your notes, pictures, etc. to not have interference.
A) You do an interaction A (I don’t like the word measurement). You detect interference.
X) You do an interaction X, you detect particle.
XA) You do an interaction X. Then you do interaction A and the result is different from what you would expect of A. The result of A is consistent with the result of X and not with the result of experiment 1 above.
To tell you the truth that’s about as common sense as you can get, what else do you expect it to do?
Because the alternative everybody considers is
This is simply silly and violates causality in EITHER time direction.
The part about the particle passing through the slit BEFORE you do interaction X or A is exactly the kind of extra ‘existence’ that I was talking about and seems to be completely counter-intuititve to me . You didn’t do an experiment B before X or A that shows that it passes through the slit, hence your sequence is XA and not BXA, so you can’t invent a hypothetical B and then tell me BXA makes no sense - B is fictional. XA makes sense. A makes sense. X makes sense. What else do you need?
Note that 4) above should be XA*) for clarity.
I don’t claim to understand quantum theory. I’m not a physicist. I dabble here and there, but with all due respect to Niels Bohr, when relativity/quantum is what your dad explains to you when you’re 4 years old - the time when you don’t really question or attempt to comprehend the axioms thrown at you by your parents - they’re just truths. Wash your hands. Things fall down because of bent space and nothing travels faster than the speed of light. Existence is interaction. Eat your vegetables.
As a kid I always dreamed of observing a macroscopic quantum event - I didn’t know the probabilities involved and the probability of toys materializing right in front of me was so intriguing. People looked at me funny, and then twenty years later I see something along the lines of “so this immovable object meets this unstoppable force” and my eyebrow goes up. What the hell? Now THAT, my friends, defies every type of common sense.
Huh?
I mean to replace the word “complicated” with the word “nonsensical”. Path-integration in quantum mechanics is more of a heuristic than anything remotely approaching a rigorous method. Simply put: what the physicists say you’re supposed to do just doesn’t work that way. They’ve found ways of interpreting “what we really mean” in various special cases but the method itself, as written, is mathematical garbage.
I’m not entirely sure what you mean but I’ll clarify what I was on about (on the grounds that it’s better to be wrong than vague).
The experiment I had in mind is rather more complicated than the plain twin slits, it involves a bunch of mirrors and beam-splitters but the essence is this.
In the traditional twin slits experiment you decide to detect (or not) the particle as it goes through one of the slits, detect particle => no interference, don’t detect => interference. This we know from nothing 
The extended experiment means that you delay the decision to detect to a time at which the particle has already passed though the slit(s) and you get the same results. Which means that whatever it is that the quantum entity does when it does the wave/particle switch, it can do retrospectively.
The difficulty isn’t with describing/accepting the results, it’s with picturing what is going on between firing the particle and observing the final behaviour. Isn’t this the point at which sensible (real) physicists throw up their hands and say don’t ask!
Since we’re on the topic of quantum physics being so counter intuitive, may I ask a side question? I once read an online book by a physicists — one whose notions, while interesting, seemed to be over the top — that addressed the EPR paradox or Bell’s experiments (??). Anyway, he said that because of relativistic foreshortening (if that’s the right term…how length in the direction of travel shrinks…Lorentz Contraction?), if we consider two particles moving away from each other at light speed and if we consider them from their reference frames, they’ve not actually even separated from one another, even though in our frame of reference they have. Thus there’s no need action at a distance, since the particles haven’t separated in their own frames of reference.
It sounded a bit crazy, but I’m not qualified to evaluate it myself. So, is that a reasonable interpretation to posit?
Thanks.
[/hijack]
I can’t say that I will help you understand, but I can offer a few personal clarifications that have helped me understand what’s going on in QM, specifically the double-slit experiment.
First off, I believe it is technically incorrect to say that a single particle is passing thru both slits at once. My problem with this statement is that the language is contradictory: Particles by definition do not exist in two places at once.
Now before a host of QM experts descend on me for denying a particle can behave this way, let me first say that the statement is perhaps better phrased as “The state function associated with a particle for its entire path thru the experimental apparatus allows for trajectories that pass thru either slit”. The electron always follows one and only one of these potential paths, but the path is chosen randomly (as far as we can tell) based on the probabilities allowed by the state function. Given this interpretation, if the experiment is conducted with a single electron (and you had an extremely sensitive detecting plate), you would not see a single electron smeared out in an interference pattern, but a single dot. Repeat the single-electron experiment (e.g. send one every second or so), and the pattern of dots would create the expected interference pattern.
Classically, you’d expect each single electron to follow the same chosen path and create a single cluster of dots on the plate (if the path was good enough for the first, it should be good enough–assuming similar conditions–for any subsequent one). In fact, if the experiment is altered such that efforts are made to detect which slit the electron passes thru, the results conform to classical expectations. QM balks at this, saying this effort to detect is also part of the experimental apparatus; since the apparatus of the experiment is what determines the value of the particle’s state function, and the state function determines the probability of possible paths, its no surprise adding this element would affect the outcome.
As noted, this appears to fly in the face of traditional science. Well-designed experiments ought to be repeatable; if all physical parameters in a macroscopic-world projectile experiment are held constant, the same results will always occur. This deterministic assumption is so pervasive that it is built into Newton’s laws of physics: With a knowledge of all physical parameters of an experiment at time t, you can determine these same parameters at time t+dt, and with a little calculus for all time after t. There are of course errors that must be considered in any physical experiment, but the basis of Newton’s laws are such that if you could account for every error term (i.e. if you had the mind of God), you could determine a body’s exact postion at any moment in the future.
The linked article’s point, I think, is to reveal this interpretation at the heart of traditional physics. Beyond that, the article notes that a second way of understanding basic physics is provided by the Hamiltonian interpretation of motion, where of all possible paths an object can take, nature selects the one that involves the “least effort”. This is somewhat different than the deterministic scheme of Newton–where one moment flows inexorably into the next–in that it assumes some sort of “foreknowledge” (a loaded word, I know, but the best I can do) about the path prior to the start of motion. A strict Newtonian interpretation would find this idea absurd: if, e.g. you’re putting a ball on an undulated green, how can the ball know about the forces produced by rolling up or down a bump in the green before the ball is struck? And just how is this “evaluation” of alternate paths made?
The very words I’ve used to describe these ideas–“foreknowledge” and “evaluation”–seem to underscore the classical need for complete knowledge of all physical parameters at time t before moving into time t+dt. In fact, classically the Hamiltonian interpretation of mechanics has relied on a pre-defined concept of “energy”, a quantity somehow possessed by the object in motion and traded/augmented/diminished according to specific physical rules (the Hamiltonian equivalent of Newtonian laws) while the object moves thru an experiment.
But the other possible interpretation–that some kind of “path evaluation” is done in advance of motion–seems to be confirmed by the results of QM experiments. I say “seems” because I don’t believe paths are actually evaluated by a conscious electron, but at some level alternate paths are a possibility before the electron follows one. Moreover, it would be a mistake to think these alternate paths exist merely because there was some error at the atomic level we were not accounting for, because the math of the Heisenberg Uncertainty relation shows that this “error” is built into the fabric of reality (at least the reality interpreted by QM).
This, I think, is at the heart of the interpretation dilemma: Classical physics has trained us to such an extent that we inherently approach any physics problem such that if perfectly understand all possible phyical parameters at time t, there are laws which tell us exactly what state these same parameters will be in at time t+dt, and hence for all time in the future. Alternate interpretations–such as the one offered by QM–fly in the face of this assumption because they support randomness, not a randomness associated with expected error, but one built into the interpretation itself.
I order to limit a lengthy post, I did not include discussion of another common QM misconception–one I fear the language Ireinforces. This invloves the “particle-wave duality” of the electron.
We often say the electron is a particle, but it is more correct to say it has properties which resemble a particle. If QM has taught us anything, it is that its best to leave it at that; “particle” may be a convenient shorthand, but it should not be pressed too hard. Similarly, there are some properties of an electron which resemble a wave, and a similar understanding that we should limit our interpretation to observable properties is the best tack to take.
We simply don’t know what the “fundamental nature” of the electron is; such a question is metaphysical, and QM makes a point of eschewing metaphysical interpretations (like the one illustrated above at the heart of Newtonian physics). The best we can say is, whatever the electron is, it is neither a strict particle nor a strict wave, and that it has properties associated with both these metaphysical concepts.
Still, discarding metaphysics entirely would mean discarding useful concepts like “path”; I’m not suggesting we go that far, but I am suggesting that we realize these terms are metaphors only. If they help us grasp what is happening, great, but i wouldn’t want to stake my life on them.
I guess this is the point I’ve been trying to make all along.
Emission --> Slits —> Interaction A or Interaction B
Interaction A results in an interference pattern (Result A)
Interaction B results in a spotted particle pattern (or whatever it is) (Result B)
You can’t do both on the same particle. Interaction A or B only affects how the particle will act AFTER the interaction, not before. Whatever event happened to the particle at the slits has the property of causing Result A after Interaction A or Result B after Interaction B.
A classical physics analogy would be, imagine magic color photo film onto which you project two things, a green text “Result A” and a red text “Result B”. Now this film has the property of not showing anything until dunked in some developer-fixer mix, and this chemical both develops and fixes the film. However, you have one that only does green colors and one that only does red (I said it was magic). You can only use one after which the film is fixed and cannot be developed further.
Now, say you have a whole bunch of these undeveloped slides that somebody projected “Result A” and “Result B” onto but you don’t know that. All you have is these slides and a developer. You develop some in the green developer and some in the red, and get slides that say either “Result A” or “Result B” but never both. It’s not reasonable to suddenly assume your developer affects what picture was projected on the film in the past, just like it’s not reasonable to assume your interaction affects how the particle went through the slits.
I know, that’s sort of the whole point, it isn’t reasonable. But that is exactly what happens. You can force the experiment into particle or wave like behaviour after it (the quantum thingy) has interacted with the slits.
I think what you’re describing with the red vs green text is what is dissmissed by QM as proposing hidden variables, that is the quantum entity actually has a state before you measure it which your measurement reveals. QM says this isn’t so. In your analogy this means that the text is both green and red until you devleop it.
Does Stranger on a Train still post here? Or would a real Quantum Mechanic care to stop by and straighten us out?
And I am not a Quantum Mechanic, but I think this statement is incorrect according to most people’s view of it. You were doing OK in my opinion up until this sentence. If we don’t observe which path it went through, then the state function goes through both paths at once, and, at least in my way of thinking, the electron as a particle does not exist at that instant, so it’s incorrect to say it goes through one and only one slit. The wave function went through both, then when it hits the detector screen it becomes a particle again, with a more definite position.
No. You eliminate one of the dimensions of the state using your measurement, and the remaining one is the one that is “revealed”. What I’m saying is that the particle essentially interfered AND didn’t, and an interaction picks one and destroys the other. I don’t like those terms though.
The particle is in itself “a high probability” of observing certain predictable behaviors given certain experiments. There is no more “is” to it’s “is”. Our language is limited in this regard, but expectation of existence or behavior is merely a predictor for a future experiment.
Yes a particle is emitted and then interacted with in an experiment usings slits and a detector (A) and gives different results in different cases. Saying that it passes through the slit is a dangerous statement for it is essentially saying that in a future experiment with an additional detector (B) at the slit we would observe it passing through the slit using B and then get the same results using A. We already know we won’t, so saying it passes through the slit is only useful when it is a helpful model. Things do not possess unobserved properties, which includes existence.
You are correct about the results of the single electron experiment, but your statement about the electron trajectory is wrong. The measurement of a single dot does not mean that the electron has in fact travelled through the apparatus as a point particle. The interference pattern can only arise if the electron is in fact interfering with itself, as each electron is completely decoupled from all past and future electrons. So the electron remains in a delocalized combination of states until it interacts with something that requires it to be in a single state, such as a detector. If that detector is over the slits, it will pass through only one of them as a particle and no interference will be observed. If that detector is at the final screen, it will occupy states which correspond to an interference pattern and choose one of them based on the relative probabilities. Repeat this enough times and statistics will take over, producing the full interference pattern.