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Perhaps what Lonewulf is speaking of is the existence of an external reality, not any standard of perceived truth.
Perhaps, like Parmenides, he's asking whether our imperfect senses reflect an external, absolute reality. If that's the case, Lonewulf, you've got friends in high places...Parmenides thought that we can't prove that any such thing as an absolute external reality exists. Zeno's paradoxes seem to have been created by Zeno in order to show that "reality" is illogical, and therefore his teacher Parmenides was correct. Socrates' "I know only one thing, and that is that I know nothing" was probably a song on the same fiddle -- admitting that all he really knew was that "reality" was unknowable. On the other hand, everybody behaves like reality really is real. Science assumes that there is something out there to measure. That assumption is that when a tree falls in the forest, something has happened and we can infer from logic and physics that a noise was produced. Parmenides might smile knowingly, but there's a lot to be said for the assumption that reality is real.
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Jim he allowed [the stars] was made, but I allowed they happened; I judged it would have took too long to make so many. Jim said the moon could 'a laid them... --Huckleberry Finn |
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trees make sounds in the same way as fast food is fattening, food is just food until it is eaten.
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Brian's mother: He's not the Messiah. He's a very naughty boy! |
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"All your bias are belong to us." Ara Pacis "A witty saying proves nothing." Voltaire |
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To be honest, there's not much for me to discuss now. Ilya pretty much answered my question, so I don't have much to say overall. I now know there are people that don't believe in objective truth, I know what they call themselves, and I know the links that further explain them.
Though I don't regret being vague, I learned a few minor tidbits and provoked some discussion. I don't regret that.
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"A long habit of not thinking a thing wrong gives it a superficial appearance of being right." -- Thomas Paine Being intelligent is not a felony. But most societies evaluate it as at least a misdemeanor. -- Heinlein Creationists make it sound as though a "theory" is something you dreamt up after being drunk all night. -- Isaac Asimov |
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Next time you decide to be vague, try not to complain about being misunderstood.
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"All your bias are belong to us." Ara Pacis "A witty saying proves nothing." Voltaire |
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Suppose I have a photon, and I'm measuring it's spin. Now, it turns out that if I measure the spin in any given direction, call it x, I'll find the photon to be either aligned with that direction (call it x+), or aligned in the opposite direction (call it x-). Now, it turns out that the spins measured for any orthogonal directions are incompatible observables, just like position and momentum for single particle. If I measure the spin in the x direction, I have no idea what the spin in the y or z direction are. We can actually test this. If I take a stream of photons, and set up a filter that strictly removes any photons that are x-, I'll have a stream of photons that are all x+. If I pass them through the same kind of filter, all of them will pass through, since only the x+ ones are left. If I pass them through the same kind of filter rotated 90 degrees, to instead allow only spin y+ photons through I'll find that half of them will make it, and the other half will be blocked. The thing is, that you might think that the photons left after this second filter are all x+, y+ photons, but it turns out that measuring the spin in the y direction completely destroys any information I had about the x direction. If I measure the x spin again, I'll find that half of the photons are x+ and half are x-. Presumably, the act of measuring the spin in one direction, no matter how carefully done, destroys the information about the spin in the other direction. What if I redefine my axes, and tilt them 45 degrees (let's call this direction x') instead of 90? Quantum mechanics predicts, and experiment bears out, that there will be some amount of correlation (I won't get just half and half like I did when I rotated the filter 90 degrees), but it won't be complete. In fact, I can work out exactly what the probability that a photon I know is x+ will be aligned with any other direction, given the angle between the two directions. Now, Einstein, Podolsky, and Rosen used this, along with the notion of entanglement, to try to show that quantum mechanics was not wrong, but incomplete. It's possible for two photons to be emitted by a source in such a way that they are spin correlated. That is, if one is down in the x direction, the other must be up in the x direction, and vice versa. Now, you take such a pair of photons, and wait until they're a long way away from each other, so there's no chance that they can interact. You measure the spin in the x direction for one of them, and find that it's (say) x+. You measure the spin in the y direction for the other one, and find that it's y+. But you know that the second photon has to also be x-, since it has to be opposite the spin of the first one in the x direction, and "obviously" that first measurement can't have affected the spin of the second one in any way (you could have waited until the photons were light years apart before making the measurements). So now you know the spin in two different directions for these photons (one is x+, y- and the other is x-, y+), more information than quantum mechanics says you can have. EPR claimed this showed that quantum mechanics was incomplete. Each photon must "really know" which way its spin is aligned in each direction. And actually, my choices of x, y, and z were arbitrary; I could have chosen different axes, so technically each photon knows which way it will respond to a measurement of spin in any direction at all. These photons would then be like the shoes: they have specific attributes, we just don't know what they are. So let's follow this assumption, that photons are ordinary objects with real (though possibly unknown) attributes, and see where it leads us. Bell's equality says that, for any collection of objects with any three attributes, A, B, and C, N(A, not B) + N(B, not C) >= N(A, not C), where N(A, not B) is the number of objects that have trait A but not trait B, N(B, not C) is the number of objects that have trait B but not trait C, and so forth. The attributes can be linked or not, but the inequality holds so long as these are real attributes. Let's see why. First, we know that N(A, not B, C) + N(not A, B, not C) >= 0 This is just the statement that either there are no objects that would satisfy one of these conditions or there are some that do. I can move from there to here, just by adding the same thing to both sides of the equation. N(A, not B, C) + N(not A, B, not C) + N(A, not B, not C) + N(A, B, not C) >= N(A, not B, not C) + N(A, B, not C) Now, if these are real attributes, then an object either has some trait, or doesn't have some trait. So N(A, not B, C) + N(A, not B, not C) is just the same as N(A, not B). That is, if you count the objects that have trait A but not trait B, that will be the same as adding up the objects that have trait A, do not have trait B, and have trait C along with those that have trait A, do not have trait B, and do not have trait C. All objects either have trait C or not. Similarly, N(not A, B, not C) + N(A, B, not C) can be replaced by N(B, not C) and N(A, not B, not C) + N(A, B, not C) is just the same as N(A, not C). This gives us Bell's inequality: N(A, not B) + N(B, not C) >= N(A, not C) I'd suggest you go back over that and convince yourself that I haven't made any mistakes here. If you're still not convinced, you might come up with a concrete example (say, a classroom of people, with your traits as being female, having blue eyes, and having dark hair), and check yourself that, however many members of the set there are and which ones have or do not have various traits, this inequality holds. Done with that? Good. ![]() So, now we go try to measure this on some photons. We're going to test whether N(x+, x'-) + N(x'+, y-) >= N(x+, y-). We run into a problem, though. We can't measure the spin in two directions for a single photon, because we know that the measurement in the first direction will mess up the measurement in the second direction. But we can use the trick EPR suggested for using entangled photons to find this out. We measure the spin in the x direction on one of them, and in the x' direction (this was tipped at some angle less than 90 degrees, remember) on the other one, and then we must know both spins for each particle. If we perform the experiment, though, we find out that the inequality is broken. The right side is actually greater than the left. This is also exactly what quantum mechanics predicts, but the fact that experimental results also seem to bear out the result means that even if someday quantum theory is superseded by some deeper theory (as EPR imagined it might), that theory will have the same problem. How can this be? Well, we really only made a few assumptions in our work above. One is that we used basic rules of logic. It's hard to imagine that those are flawed. Another is that we assumed that these photons actually had definite real attributes, we just didn't know what they were. Another is the assumption that our measurements on the photons (separated possibly by light years) did not affect each other. It turns out that, regardless of whether we assume the attributes were real before we measured them, we can't get around the influence question. That is, to explain the results we see, one photon has to "tell" the other one, instantaneously regardless of distance, what it's results were, and the results of the measurements on the second one will be affected by this. Let's revisit the woman and her shoes, with a slight change. Let's say she owns hundreds of shoes, all red, green, or blue, in equal proportion. She always packs one at random. If she does this many times, there will be a 1 in 3 chance for each color. Her husband always picks one of the boxes that she left behind at random and looks at the color. There's always a 1 in 3 chance for him to find each color. But, if they both open their boxes with them oriented the same way (either both vertically or both horizontally), there's a 1 in 2 chance that they picked the same color, whatever it was, while if they open their boxes holding them oriented differently, there's only a 1 in 6 chance that the colors match. The only way for that kind of correlation is if the act of opening the box is instantly communicated to the other pair of shoes somehow, and it has the possibility of changing its color in response. But also note that, since each measurement alone just gives a straight 1 in 3 chance for each color, just as we'd expect, there's no way to see this correlation, or to know which way the other person was holding the box (or even if they've opened it yet), until the woman comes back and they compare the results. |
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Best layman-level explanation of Bell's inequality I have ever read, Grey.
It would appear that quantum properties like photon spin are not "real" properties in the classical sense that the color of a billiard ball is. They can change simply because a linked property is measured. When we measure whether a quantum billiard ball has a stripe or not, we suddenly no longer know what color it is until we re-measure that...and then we don't know anymore if it has a stripe or not! Hehe! So to get back to NanC's questions, at a quantum level there are inevitable unknowns -- aspects of reality that are unavoidably "smeared out" into uncertainty. We can measure a real, classical billiard ball and know for sure that it is purple and has a black stripe. But we cannot know both things about a quantum one. If we know one property, the other really does become uncertain. And we are absolutely sure of that because if we measure the color of a bunch of quantum balls and select all purple ones, then measure whether or not they have stripes, and then measure the color again...we find that the color of our selected group is no longer all purple. ---- We can imagine knowing both the x spin and the y spin simultaneously, and we can imagine a magical machine which knows both, but such a machine is "non-physical" -- it is impossible in our universe. Our excellent ape imaginations, operating on the classical-physics logic which applies to virtually everything we have observed in our long evolutionary history before the twentieth century, persists in visualizing absolute, discrete properties for electrons and quarks. Intuitively. The Universe, however, is laughing up its sleeve. It isn't constrained to behave the way we Earth-apes intuitively believe it does. ---- So the fun part is understanding that in this case our wonderful, useful, and very often accurate commonsense intuition about the universe really really is wrong! How wonderful that is! What great views open up before us if we accept that our intuition is not always right, and we can stretch our imaginations and our calculations beyond it, into new landscapes and new discoveries! One can only say, with Galileo, YAY!
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Jim he allowed [the stars] was made, but I allowed they happened; I judged it would have took too long to make so many. Jim said the moon could 'a laid them... --Huckleberry Finn |
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"A long habit of not thinking a thing wrong gives it a superficial appearance of being right." -- Thomas Paine Being intelligent is not a felony. But most societies evaluate it as at least a misdemeanor. -- Heinlein Creationists make it sound as though a "theory" is something you dreamt up after being drunk all night. -- Isaac Asimov |
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I hope not, that's an awful lot. I always imagined a good murder mystery would be one in which two people were gambling against a dealer, who was spinning a roulette wheel. One of the gamblers bet all his money that a given number would come up, with probability 1/38 (if you know roulette). The other bet all his money that it wouldn't. This much is agreed by both men. The dealer spun the wheel and as a result, one of the men became so angered he grabbed a knife and killed the dealer. Both say the other did it, and the result of the wheel was lost in the melee. Can you convict the guy who bet on the single 1/38 chance based on this evidence? Can't you say that there is more than a 97% chance he is guilty, and that's beyond a reasonable doubt? Meanwhile, he claims that what he thought was his luckiest day ever just ended up getting him in prison...
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"A long habit of not thinking a thing wrong gives it a superficial appearance of being right." -- Thomas Paine Being intelligent is not a felony. But most societies evaluate it as at least a misdemeanor. -- Heinlein Creationists make it sound as though a "theory" is something you dreamt up after being drunk all night. -- Isaac Asimov |
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The Bell inequality stuff is quite interesting, but I would have thought that in the EPR setup, the act of measuring would have imparted the necessary spin, why would they assert that the total spin added up to zero? Or put differently, if you measure the spin of something in a superposition state and get a definite result, does that not impart angular momentum to the measuring device? In principle I mean, of course it would be tough to measure it.
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If you're interested in digging deeper, I can give you a link to a discussion forum where experts who love this stuff will be both very patient in walking you through the maze and very knowledgable about the issues (HINT: they're the folk who you see referenced in the 'discussion' pages of the relevant wiki entries). |
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Thanks for the webpage, though I tried to load the Bell paper and my computer crashed! In any event, I think my question is simpler than the one addressed in that paper, though no doubt there would be insight there. But does anyone know the answer to this simpler QM question:
If you prepare a particle in a pure state of known spin +1/2 in the z direction, and then measure its spin in the x direction and get +1/2, doesn't the measuring instrument have to soak up the +1/2 angular momentum in the z direction and the -1/2 in the x direction? In other words, won't it get an angular momentum of hbar/root(2) in a direction 45 degrees between the z and -x axis? If so, then clearly the measuring instrument gave the particle its angular momentum, and I don't see why EPR would have expected to be able to know both the z and x spin in Grey's very detailed explanation of the EPR paradox in this thread. I do still see the idea of "entangled" wave functions, however, but I'm missing the point of rotating the angle of the spin measurement. |
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I didn't really understand the EPR paradox but I think that if no actual information is being sent between the two then it is just some property of the situation rather than a paradox.
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Brian's mother: He's not the Messiah. He's a very naughty boy! |
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The "truth" of your table is only a temporary truth and not an "absolute truth".
Perhaps, "absolute truth" is timeless and never subject to change. If absolute truth is timeless, then there are no absolute truths about material things (or that IS the only absolute truth regarding temporal items, that there is no materially based absolute [everlasting] truth). 5 years from now you may not have that table. The fact that you have that table now is absolutely truthFULL but not absolute truth. There is a difference between "true meaning" and "absolute truth". The difference is temporal (time based). and that is absolutely true http://www.bautforum.com/images/icons/icon7.gif |
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I think what we mean by "absolute truth" is that there is something with some properties (even if we cannot know them exactly) which we are attempting to observe. That something is objectively there with some objective property. That it isn't some sort of show put on for our senses, or some other slippery philosophical hall of mirrors which we're observing.
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Lonewulf, you undersand not? absolute truth in the mind of a believer
dwells, never a seeker of knowledge, but blind faith, more important, you of science, as am I, Have faith in what your learning tells you. Nokton |