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Introduction to Quantum Mechanics

Introduction to Quantum Mechanics

milkyrain
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Posted 12/05/07 - 09:54 AM: Subject: Introduction to Quantum Mechanics	#1
The nature of light as understood in terms of the Maxwell's electromagnetic wave theory of light says that light is made of an electric and a magnetic force moving perpendicularly to each other towards the lights direction. The force fields oscillate periodically and are detected as waves. This can be shown by the pattern of interference shown when light passes through two or more slits. The double slit experiment, used to show interference in waves, can be performed on one photon, one packet of light, at a time. You would expect that no interference pattern be seen as unlike a wave one photon must travel through either one slit or the other and have nothing to interfere with. However this experiment has been performed numerous times, and after letting a stream of photons through one at a time the random dots on the screen soon revel an interference pattern. This implies that the photons split when going through the two slits and reforms to be detected as one photon on the screen. The photons can also be measured by placing a detector on each slit measuring which one it goes through, when this is done an interference pattern is not formed. The light beam behaves as a particle when equipment that tests for particles is used, and as a wave when a wave is being tested for. The question then rose of how the quanta knew what number of tunnels to pass through when the particle detector is placed at the other side of the door. The fact that everything had the potential to act like waves of energy and particles of mass was explained by Einstein. It was shown that electrons can act like particles when they collide but when they orbit a nucleus they travel as a wave, always a whole number of waves from the nucleus. It can only travel at a completed wavelength and so it has a non zero minimum energy. If the electron is given more it will try to reach it's lowest state emitting any access energy as photons. Measuring which slit the photon travels through is measuring it's position and measuring the interference pattern is a measurement of it's wavelength from which you can work out it's velocity, that is it's direction and speed. Because it can not be measured as both a wave and a particle at the same time properties of both can not be measured simultaneously, they are non-commuting. The more accurately you can measure the position then the less accurately you can measure the velocity and the same is true the other way around. The uncertainty could never be less than a certain number worked out by Heisenberg. Quantum mechanics can not predict what something will do in the future, it can only give a probability. Like throwing dice it can not be known what the outcome will be all we can determine are the probabilities of the quanta having each position and velocity which is described by something called the wave function which we can predict over time. Previous to this people had thought that the future was predictable. Laplace suggested that if we knew the positions and velocities of all of the atoms in the universe then we could predict it's whole future and work out it's whole past but the Heisenberg uncertainty principle showed that it is a fundamental law of the universe that you can not know both these things. It is not just the limitation of our knowledge, it simply can't be done. Two photons can be connected together and separated to the other side of the world and still the measurement of one will change the state of the other instantly irrelevant of location. If two quanta were formed which had to propagate at right angles to each other in all planes then measuring one would determine that the other was 90 degrees from it. The property did not exist until it was measured and yet simultaneously the other quanta changed to correspond with the measured result. This happened even if they were so far apart that not even light could travel between them, no message could be sent. Quantum physics explains this by stating that there is a non-locality whereby the photon knows how to behave how ever far away the apparatus is from it, location is irrelevant. However this knowledge can not be sent as a message as it can be so far away that not even light, the fastest possible thing, could travel there in time. This implies instantaneous communication 'Spooky action at a distance' Einstein called it. The Copenhagen theory accepts these aspects of quantum physics as merely factual information about the universe that we have discovered, this is in contrast to Einstein's view which was that the consequences of quantum physics shows an incompleteness of the theory. In 1935 as part of an on going debate with Bohr, who advocated the Copenhagen theory Einstein and his colleagues Podolski and Rosen presented a paper (known as EPR) that claimed locality must be preserved. The EPR paper stated that quantum physics has an incompleteness which can be explained by 'hidden variables'. An experiment can be set up whereby the energy states of electrons are altered so that there is a release of photons. It has been found that in certain atoms the photons released are always done so at perpendicular angles. This can be measured in the x, y and z planes, and so measuring the polarisation in plane x of photon A determines that the same result in photon B would be perpendicular to this. This is country to the above statement that two non-commuting variables can not be known simultaneously. If this is true then there need not be a theory of non-locality, the photons simply have fixed but opposite polarities when they leave the electron. Bell's theory explains the probabilities of specific measurements of the polarities in the x, y and z planes of two photons if Einstein was correct. In practice the probabilities recorded did not agree with this inequality, assuming the laws of logic hold, that special relativity holds, and that locality holds there is no explanation for the recorded results. The assumption that must be wrong is locality, our idea of space, and therefore only quantum physics can account for the fact that the probability is different - the measure of x in Photon A disturbs the measurement of y in Photon B. The random as apposed to deterministic nature of the photons, and the idea that it is only in measuring a feature that the feature exists is troubling to the classically held view of reality as holding fundamentally predictable and logically explainable empirical and a priori properties. Perhaps space is an illusion, or perhaps the illusion is time. If this experiment is carried out with a time delay on the photon that is measured then it must affect the other photon even though it should have already chosen what to be. The message is sent backwards in time. Another idea is that perhaps it is not random whether or not we view an ordinary quanta as a wave or a particle. Perhaps every time this decision has to be made the universe branches off into two, in one world it is a wave and in another a particle. The new parallel world and an infinite amount of others are all contained inside something else. It seems that what is random is not what the quanta does but in which world your consciousness lands in. Some believe that this means that the observation which defines the quanta's existence must be by a conscious observer. This would mean that the universe would not exist if we were not here to observe it and would lead to the question of how we could have then evolved in it.
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hyena in petticoat
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Posted 12/10/07 - 10:55 PM:	#2
You know, I have just been reading a book a mentioned in the Off topic part of this forum. Timeline by Michael Crichton. Ever came across it? I've been wondering if the stuff written there about QM are true or are they fiction? Anyway, I read about some of the stuff you mentioned in the book. Seems interesting.
_____________________ Running running run. If you can't say anything nice about someone, say nothing. Then creep up behind them with a baseball bat and really let 'em have it. "What's the point of goin' out and riding if you're gona be a pussy..." - Ecce

kkiiji
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Posted 02/22/08 - 11:04 PM:	#3
I don't think the conclusion would be the universe lacks existence without observation. I think it's more like something I once read by Kant, that what exists in the universe without observation is simply beyond human understanding. Our observations simply dissect the universe into time and space, making it appear deterministic. I should have read this topic before making my other one, but I'm still quite confused by the entanglement thing. How exactly was the entanglement phenomenon derived? I'm almost certain it was derived and not observed, but how? How is it related to the uncertain path of a wave function? I can understand the conclusion of a lack of local realism, but that's derived from the entanglement phenomenon, which almost seems to be a whole other thing from the earlier uncertainty principle.

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