Anyway, I am now in CNY OT, iLounge OT and iLeaders June Camp OT, four different math and science olympiad training etc. In other words, I stay back every afternoon. Gakkk. I am not so free as to post too regularly now.
Now on to business. Mwahahaha.
A brief introduction to Quantum Mechanics, phrased exceedingly clearly by Wikipedia:
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[Quantum mechanics (QM) is a set of scientific principles describing the known behavior of energy and matter that predominate at the atomic scale. QM gets its name from the notion of quantum, and the quantum value is the Planck constant. The wave–particle duality of energy and matter at the atomic scale provides a unified view of the behavior of particles such as photons and electrons. While the notion of the photon as a quantum of light energy is commonly understood as a particle of light that has an energy value governed by the Planck constant, what is quantized for an electron is the angular momentum it can have as it is bound in an atomic orbital. When not bound to an atom, an electron's energy is no longer quantized, but it displays, like any other massy particle, a Compton wavelength. While a photon does not have mass, it does have linear momentum. The full significance of the Planck constant is expressed in physics through the abstract mathematical notion of action.
The mathematical formulation of quantum mechanics is abstract and its implications are often non-intuitive. The centerpiece of this mathematical system is the wavefunction. The wavefunction is a mathematical function of time and space that can provide information about the position and momentum of a particle, but only as probabilities, as dictated by the constraints imposed by the uncertainty principle. Mathematical manipulations of the wavefunction usually involve the bra-ket notation, which requires an understanding of complex numbers and linear functionals. Many of the results of QM can only be expressed mathematically and do not have models that are as easy to visualize as those of classical mechanics. For instance, the ground state in quantum mechanical model is a non-zero energy state that is the lowest permitted energy state of a system, rather than a more traditional system that is thought of as simple being at rest with zero kinetic energy.
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As you can see, quantum mechanics is an intensely intresting subject. It is also an intensely irritating subject. For example, almost everything about it contradicts classical mechanics. QM says that a cat can be both alive and dead, a person can shoot himself for ever without dying, stuff can be measured without anything measuring it, and a lot of other things like that.
Hawking radiation is a great example. In layman's terms, radiation from a black hole. Big question here: How can an object that by definition does not emit any radiation emit radiation?
Big answer: Because it doesn't. Not directly anyway. Simplified, the explanation is like this: Because of the ridiculous gravity just outside of the black hole's event horizion, virtual particle-antiparticle pairs are created, one with positive and the other with negative energy. Not really created; they are everywhere, but because of the exceptional circumstances there, there is the chance that one of the pair of the particles will be sucked into the black hole while the other escapes. Normally the pairs annihilate each other (sad) and dont give off spectacular explosions (sad again) because of the fact that one has positive and the othe has negative energy therefore they cancel each other out. Because of energy conservation, the one with negative energy will be the one sucked in. To an outside observer, it seems that the black hole has just emitted a particle. Voila.
The amount of radiation emitted is inversely proportional to the surface area of the event horizon (and incidentally the area of the event horizon is directly proportional to the entropy in the black hole).
Cheers,
CY
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