Quantum Mechanics |
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As in the last essay, the purpose of this essay is not to do even a qualitative discussion of the whole topic. Rather it is to present a couple of key results that are philosophically important. The quantum world does not behave like the world we are familiar with. One demonstration of that is the classic 2-slit experiment. You can see a simple explanation of that here: http://www.colorado.edu/physics/2000/schroedinger/two-slit2.html At less than a certain limit, the exact position and momentum of particles becomes uncertain. This is known as the uncertainty principle. The product of the uncertainty in the momentum and the uncertainty in the position must be grater than a fixed quantity, Plank’s constant, usually represented by h. This uncertainty is an inherent property of the particles, not a limitation in our ability to measure. This uncertainty can explain the results of the 2-slit experiment, above. A different way of stating the uncertainty principle, is that the product of uncertainty in time, and uncertainty is energy must be larger than the same fixed quantity h. This allows for temporary violation of the principle of conservation of energy. A small particle of energy can appear out of the vacuum and disappear again. As long as it exists for a very short time, allowed by the uncertainty principle, there is no violation of the classical law of conservation of energy. For a photon, it turns out that it may exist for less than one full wave cycle. These are known as virtual photons. Virtual particles play an important role in quantum field theory. Quantum field theory is a product of the second half of the 20th century. It attributes the various forces in nature to virtual particles. The electromagnetic force is the result of the action of virtual photons. Quantum field theory has been called one of the most successful theories ever in science, and is now very firmly established. These virtual particles have also come to be connected with the “dark energy” in the universe, which we will talk about more when we get to cosmology. For our purposes, we just want to note that these quantum events are totally random, and not caused by any event that precedes them, at least in this universe, in their locally defined time. Next we have to consider Bell’s theorem. A more complete discussion of the topic can be found here: http://www.upscale.utoronto.ca/GeneralInterest/Harrison/BellsTheorem/BellsTheorem.html At the quantum scale, particles are better described as probability waves, spreading out in all directions. However, if the particle interacts at a specific point is space, the probability of it being somewhere else goes to zero. We say the probability wave has collapsed. The problem is that this seems to take place instantaneously at a distance, which would seem to violate the principle of special relativity described in the last essay. Experimentation has shown that this instantaneous connection at a distance is real. http://www.aip.org/enews/physnews/1998/split/pnu399-1.htm Imagine particle A and particle B zooming in opposite directions, and “quantumly entangled”. That is their states are connected but are unknown, and in fact, undetermined. We can measure A and B, in different detectors at the same time, so that there is no chance for a signal traveling at the speed of light to be transmitted between these two events. We find that the way one measurement is resolved effects the other, even though there has not been enough time for a signal to be transmitted. We can also eliminate the possibility of hidden variables that were set before the particles separated.The result is that instantaneous correlation at a distance can take place in the quantum world. We say correlation, and not causation, because it is not at all clear which event takes place first. Since a message at the speed of light could not be transmitted between the two events, according to special relativity, different observers can disagree about the order of these two events. Also, given that information can only be transferred at the speed of light, particle A “sees” itself as being resolved first, without any information from B. But particle B sees itself as being resolved without any input from A. The result from this, that we want to take forward, is that different events that are causally related can happen in different orders according to different observers, and neither observer is “wrong”. For more information:http://www.cosmopolis.com/topics/quantum-nonlocality.html http://www.gilestv.com/tutorials/nonlocal.html The non-local universe. http://www.teach12.com/ttc/assets/coursedescriptions/153.asp |
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