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Posted: Mon May 01, 2006 10:26 pm
Shroedinger said: if you put a cat in a box which is completly isolated from the outside. The cat can breath obviously, that is not the issue, but from the outside there is no method for observing what is going on inside. Ok, well, we put this cat in a box, and we put in with the cat a substance which has exactly a 50% chance of decaying, and IF it decays it will turn into a poison which will kill the cat. Now, is the cat DEAD or ALIVE?
The explaination provided by the Copenhagen Interpretation and that which is accepted by the Physics Community is that the Cat is in both states at the same time. I was also informed that it was not pragmatic to think of the cat in such a way, but that the example is used a mental expercise for students and used to illustrate the interaction of the quantum and the macro.
I understand the correlations of this tought experiment with that of Electron Diffraction, and also how the Electron Diffraction experiments portrays's the electron's wave/particle duality well. HOWEVER, I have one more question.
If the diffraction pattern was modelled by Shroedinger's wave equation, and it is said to represent the probability of all the paths that the electron can take, then isn't it implied that the electron is a particle? I mean if we talk about diffraction as the result of the existance of multiple states at once, then are we not talking about the electron as if it was a particle?
Discuss: Electron Diffraction and how it relates to Shroedinger's Cat More interesting ideas and explaination related to the above mentioned topics.
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Posted: Mon May 01, 2006 10:35 pm
This is hardly my area of expertise and all, however, I believe the interference patterns are indicitive of the wave like property, being as particles are unable to constructively or destructively interfere.
I could very well be wrong though of course.
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Posted: Tue May 02, 2006 12:06 am
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Posted: Tue May 02, 2006 1:27 am
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Posted: Tue May 02, 2006 3:56 pm
Yes, I understand much better now what the probability wave is - it's just that, the probability wave. And as VorpalNeko has said, the electron and other elementary particles are just epiphenomena.
How did Weinberg exactly argue that the spacetime manifold is damaging to physics?
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Posted: Tue May 02, 2006 7:32 pm
poweroutage Yes, I understand much better now what the probability wave is - it's just that, the probability wave. And as VorpalNeko has said, the electron and other elementary particles are just epiphenomena. Well, that one interpretation, anyway, and it happens to be the one I happen to prefer. It should be noted, however, that this is definitely not the only view. Certain variants of the Copenhagen interpretation, for example, reverse this--the particles are what is physically real and the wavefunctions are mere mathematical constructs. Personally I find that the almost-arbitrary wavefunction collapse under that view to be impersuasive. There is, of course, the Feynman interpretation, which is simply "shut up and calculate." poweroutage How did Weinberg exactly argue that the spacetime manifold is damaging to physics? I'll have to look into his GTR book again to see if he provides any detailed reasoning, but roughly the disagreement can be described as follows. Immediately after GTR, it was once hoped by some that physics can be reduced to geometry, and not without good reason, as both gravity and electromagnetism are amenable to that treatment (cf. Kaluza-Klein). Weinberg sees that approach as a failure, although I'm not clear on his reasons for doing so; gauge theories, after all, are laden with the language of differential geometry. Weinberg believes that geometry obscures the physics, particuarly connections to other areas (presumably he means particle physics), but to me it just looks like he just forcibly supresses such an interpretation to the equations, despite the fact that such a move is costly, as the tools of differential geometry are rather powerful. Take that with a grain of salt. Differential geometry is one of my favorite areas of mathematics, and general relativity is one of my favority areas of physics, so I am not without bias. If I were to try psychoanalyze the physics community on this issue, I'd say that in general the particle physicists place theire hopes in string theory, which (in)famously has a fixed background--something that GTR absolutely rejects. Others, particularly general relativists like Penrose, would say that the string theorists are fooling themselves by ignoring GTR in such a manner, and that geometrical approaches to quantification (e.g., loop quantum gravity) are more likely to succeed.
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Posted: Wed May 03, 2006 1:55 pm
[Psst, GTR is General Theory of Relativity ^_~ ... oh, you edited XD]
Poweroutage, if you condemn GUTs not accounting for gravity then you are mistaking your terminology from where I stand. Grand Unification, at least from inside the particle physics approach, only seeks to unite the electroweak force [Glashow-Weinberg-Salam model, it united Quantum Electrodynamics with the weak force by use of Weinberg Higgs mechanism] with Quantum Chromodynamics. They were not supposed to consider gravity, that is some more suited to the "Theory of Everything" label.
I have little time for string theorists at the moment, their heads are in the clouds, a view shared, informally, by John Ellis in a seminar he gave last year. At the moment we are only pushing into the EWKB [Electroweak Symmetry Breaking] energy regime [the LHC will have an centre-of-mass energy of about 14,000 GeV] whereas the Planck scale is up at 10^19 GeV. Again, I speak with my bias, I would prefer more theorists in the particle physics community to work on more particle physics phenomonelogy at lower energy scales so that current theoretical uncertainties are reduced.
Some people are trying to fly before we can even jog.
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Posted: Wed May 03, 2006 2:36 pm
VorpalNeko poweroutage Yes, I understand much better now what the probability wave is - it's just that, the probability wave. And as VorpalNeko has said, the electron and other elementary particles are just epiphenomena. Well, that one interpretation, anyway, and it happens to be the one I happen to prefer. It should be noted, however, that this is definitely not the only view. Certain variants of the Copenhagen interpretation, for example, reverse this--the particles are what is physically real and the wavefunctions are mere mathematical constructs. Personally I find that the almost-arbitrary wavefunction collapse under that view to be impersuasive. There is, of course, the Feynman interpretation, which is simply "shut up and calculate." you see that is what I was asking, that the existance of the Shroedinger wave function as a 'probability' wave implied that the particles are physically real and any wave properties that we may observe are simply due to their "spectral" nature, and the necessity for observation. I did not realize that the other intepretation (that of Feynman) was that we should take the wave function as it is and not think about the underlying meanings. However, let's not have a bill Nye the science guy "now you know" moment. Isn't it important to know what is really going on? I mean to an extent you can always apply equaitons, but if you don't understand why you are applying those equations isn't it possible that at one point, if the equations fail you, you will not know what is wrong with them, or how to modyfy them? Couldn't it all be a fluke? Or are you just saying you don't care if its a fluke now, if that turns out to be the case, we'll find out eventually? VorpalNeko poweroutage How did Weinberg exactly argue that the spacetime manifold is damaging to physics? I'll have to look into his GTR book again to see if he provides any detailed reasoning, but roughly the disagreement can be described as follows. Immediately after GTR, it was once hoped by some that physics can be reduced to geometry, and not without good reason, as both gravity and electromagnetism are amenable to that treatment (cf. Kaluza-Klein). Weinberg sees that approach as a failure, although I'm not clear on his reasons for doing so; gauge theories, after all, are laden with the language of differential geometry. Weinberg believes that geometry obscures the physics, particuarly connections to other areas (presumably he means particle physics), but to me it just looks like he just forcibly supresses such an interpretation to the equations, despite the fact that such a move is costly, as the tools of differential geometry are rather powerful. The Kaluza-Klein theory just an early form of string theory, and it seems to me that QM would benefit from it's 'alliance' with GR, he might dislike it, but he can't negate the fact that GUT's have been unsucessful in uniting all the other forces with Gravity. QM isn't perfect, and neither is relativity of course, they're powerful and all their predictions are correct but clearly neither of them is as of yet 'complete'. VorpalNeko Take that with a grain of salt. Differential geometry is one of my favorite areas of mathematics, and general relativity is one of my favority areas of physics, so I am not without bias. If I were to try psychoanalyze the physics community on this issue, I'd say that in general the particle physicists place theire hopes in string theory, which (in)famously has a fixed background--something that GTR absolutely rejects. Others, particularly general relativists like Penrose, would say that the string theorists are fooling themselves by ignoring GTR in such a manner, and that geometrical approaches to quantification (e.g., loop quantum gravity) are more likely to succeed. Just to make sure, are you using GTR as an acronym for General Relativity? How does string theory have a 'fixed background'?
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Posted: Wed May 03, 2006 5:41 pm
poweroutage However, let's not have a bill Nye the science guy "now you know" moment. Isn't it important to know what is really going on? I mean to an extent you can always apply equaitons, but if you don't understand why you are applying those equations isn't it possible that at one point, if the equations fail you, you will not know what is wrong with them, or how to modyfy them? Turning that around, the multitude of interpretations might each suggest a certain modification. poweroutage Couldn't it all be a fluke? Or are you just saying you don't care if its a fluke now, if that turns out to be the case, we'll find out eventually? I'm saying simply this: get used to many mutually contradictory interpretations of QM. They're all observationally equivalent, but not ontologically so. poweroutage The Kaluza-Klein theory just an early form of string theory, and it seems to me that QM would benefit from it's 'alliance' with GR, he might dislike it, but he can't negate the fact that GUT's have been unsucessful in uniting all the other forces with Gravity. TOEs. poweroutage QM isn't perfect, and neither is relativity of course, they're powerful and all their predictions are correct but clearly neither of them is as of yet 'complete'. No argument there. poweroutage Just to make sure, are you using GTR as an acronym for General Relativity? Yes-- general theory of relativity. poweroutage How does string theory have a 'fixed background'? In GTR, the metric couples to the stress-energy-momentum tensor T, as can be seen directly from Einstein's field equation. The metric thus evolves dynamically, in turn affecting how the stress-energy-momentum behaves. String theory has no mechanism for this--one assumes a fixed background metric instead. This kind of 'symbiotic' relationship between the metric and matter distribution is such an essential feature of GTR that some (evidently a minority among those actually working on TOEs, however) see this as an indication that string theory has a fundamentally flawed approach to unification.
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Posted: Sat May 06, 2006 4:59 pm
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Posted: Sat May 06, 2006 5:03 pm
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Posted: Sun May 07, 2006 12:03 am
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Posted: Thu Jun 08, 2006 6:07 pm
OMG that's cute.... Anyways I read (about a year ago so some of the information might be a little off, I'm trying to remember it) a really good book entitled Shrondiger's Kittens. I forgot who wrote it but if you're intrested pick it up, Shrondiger's paradox always was a little freakey in my mind. Anyways the whole premise of Shrondiger's kittens is this: Take the shrondiger's cat model but put it in a space ship and make two. So there is two cats, put into two spaceships with the deadly set-up with one diffrence. Only one cat will die, however it cannot be determened which cat it will be. Now send the rockets into two opposite directions of the universe and have them travel for months. (Let's assume that the cats can only die by the poison.) One of the rockets crash into a planet with intellegent life. They pop open the hatch and what do they find? The whole point of this is when they open the hatch and see if the cat is alive or dead (let's just say the cat they see is dead) the cat billions of miles away is automatically alive because the other cat was observed. I think they called it the electron probiblity wave that collapses once one of the cat's is viewed. Well long story short it goes to say that something exists in the universe because it is observed, before that there is an infinate number of posibilites for where it is and the state that it's in. Essentally the universe exists because the universe is looking in on itself. If that isn't a headache (but a fun headache at that) I don't know what is.
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Posted: Thu Jun 08, 2006 9:14 pm
The cats-on-spaceships thing is called entanglement, and is more common in say, photons, than in cats. But essentially the same thing happens. You stick a pair of entangle photons in boxes and send them in different directions. Open one box, and you know what the other box contains. Note that this doesn't violate relativity because no new information is being sent from the other box.
The long story ought to read that an object exists in a certain place/state once it's observed. This is the basis for quantum computing, in that the bits (qbits) can have any of a number of states before observation, and thus operations can be carried out on all of those states simultaneously. Note that Heisenberg forbids us from observing everything about a particle at a given instance.
Schrodinger's cat can be turned into the safe: we don't know anything about things we haven't examined. To me at least, that sounds perfectly reasonable. So, to deal with things we haven't observed, we must assume that they are in every possible state, and go from there. Again, sounds reasonable. The real problem arises when you try to differentiate between "what is true" and "what we know and/or are forced to assume" which are equivalent in QM.
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Posted: Wed Aug 16, 2006 9:40 pm
Schroedinger, Erwin! Professor of physics! Wrote daring equations! Confounded his critics! (Not bad, eh? Don't worry. This part of the verse Starts off pretty good, but it gets a lot worse.) Win saw that the theory that Newton'd invented By Einstein's discov'ries had been badly dented. What now? wailed his colleagues. Said Erwin, "Don't panic, No grease monkey I, but a quantum mechanic. Consider electrons. Now, these teeny articles Are sometimes like waves, and then sometimes like particles. If that's not confusing, the nuclear dance Of electrons and suchlike is governed by chance! No sweat, though--my theory permits us to judge Where some of 'em is and the rest of 'em was." Not everyone bought this. It threatened to wreck The comforting linkage of cause and effect. E'en Einstein had doubts, and so Schroedinger tried To tell him what quantum mechanics implied. Said Win to Al, "Brother, suppose we've a cat, And inside a tube we have put that cat at-- Along with a solitaire deck and some Fritos, A bottle of Night Train, a couple mosquitoes (Or something else rhyming) and, oh, if you got 'em, One vial prussic acid, one decaying ottom Or atom--whatever--but when it emits, A trigger device blasts the vial into bits Which snuffs our poor kitty. The odds of this crime Are 50 to 50 per hour each time. The cylinder's sealed. The hour's passed away. Is Our p***y still purring--or pushing up daisies? Now, you'd say the cat either lives or it don't But quantum mechanics is stubborn and won't. Statistically speaking, the cat (goes the joke), Is half a cat breathing and half a cat croaked. To some this may seem a ridiculous split, But quantum mechanics must answer, "Tough @#&! We may not know much, but one thing's fo' sho': There's things in the cosmos that we cannot know. Shine light on electrons--you'll cause them to swerve. The act of observing disturbs the observed-- Which ruins your test. But then if there's no testing To see if a particle's moving or resting Why try to conjecture? Pure useless endeavor! We know probability--certainty, never.' The effect of this notion? I very much fear 'Twill make doubtful all things that were formerly clear. Till soon the cat doctors will say in reports, "We've just flipped a coin and we've learned he's a corpse."' So saith Herr Erwin. Quoth Albert, "You're nuts. God doesn't play dice with the universe, putz. I'll prove it!" he said, and the Lord knows he tried-- In vain--until fin'ly he more or less died. Win spoke at the funeral: "Listen, dear friends, Sweet Al was my buddy. I must make amends. Though he doubted my theory, I'll say of this saint: Ten-to-one he's in heaven--but five bucks says he ain't." http://www.straightdope.com/classics/a1_122.html
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