EldwinSchrodinger @ Feynman Diagrams
Feynman diagrams are graphical ways to represent exchange forces. Each point at which lines come together is called a vertex, and at each vertex one may examine the conservation laws which govern particle interactions. Each vertex must conserve charge, baryon number and lepton number.
Developed by Feynman to decribe the interactions in quantum electrodynamics (QED), the diagrams have found use in describing a variety of particle interactions. They are spacetime diagrams, ct vs x. The time axis points upward and the space axis to the right. (Particle physicists often reverse that orientation.) Particles are represented by lines with arrows to denote the direction of their travel, with antiparticles having their arrows reversed. Virtual particles are represented by wavy or broken lines and have no arrows. All electromagnetic interactions can be described with combinations of primitive diagrams like this one.
Only lines entering or leaving the diagram represent observable particles. Here two electrons enter, exchange a photon, and then exit. The time and space axes are usually not indicated. The vertical direction indicates the progress of time upward, but the horizontal spacing does not give the distance between the particles.
Other electromagnetic process can be represented, as in the examples below. A backward arrow represents the antiparticle, in these cases a positron. Keep in mind that time progresses upward, and that a downward arrow is not a particle progressing downward, but an antiparticle progressing upward ( forward in time).
After being introduced for electromagnetic processes, Feynman diagrams were developed for the weak and strong interactions as well. Forms of primitive vertices for these three interactions are
Particle interactions can be represented by diagrams with at least two vertices. They can be drawn for protons, neutrons, etc. even though they are composite objects and the interaction can be visualized as being between their constituent quarks.
Labels: Quantum Mechanics
EldwinSchrodinger @ Quantum Teleportation
Teleportation is the name given by science fiction writers to the feat of making an object or person disintegrate in one place while a perfect replica appears somewhere else. How this is accomplished is usually not explained in detail, but the general idea seems to be that the original object is scanned in such a way as to extract all the information from it, then this information is transmitted to the receiving location and used to construct the replica, not necessarily from the actual material of the original, but perhaps from atoms of the same kinds, arranged in exactly the same pattern as the original. A teleportation machine would be like a fax machine, except that it would work on 3-dimensional objects as well as documents, it would produce an exact copy rather than an approximate facsimile, and it would destroy the original in the process of scanning it. A few science fiction writers consider teleporters that preserve the original, and the plot gets complicated when the original and teleported versions of the same person meet; but the more common kind of teleporter destroys the original, functioning as a super transportation device, not as a perfect replicator of souls and bodies.
In 1993 an international group of six scientists, including IBM Fellow Charles H. Bennett, confirmed the intuitions of the majority of science fiction writers by showing that perfect teleportation is indeed possible in principle, but only if the original is destroyed. In subsequent years, other scientists have demonstrated teleportation experimentally in a variety of systems, including single photons, coherent light fields, nuclear spins, and trapped ions. Teleportation promises to be quite useful as an information processing primitive, facilitating long range quantum communication (perhaps unltimately leading to a "quantum internet"), and making it much easier to build a working quantum computer. But science fiction fans will be disappointed to learn that no one expects to be able to teleport people or other macroscopic objects in the foreseeable future, for a variety of engineering reasons, even though it would not violate any fundamental law to do so.
In the past, the idea of teleportation was not taken very seriously by scientists, because it was thought to violate the uncertainty principle of quantum mechanics, which forbids any measuring or scanning process from extracting all the information in an atom or other object. According to the uncertainty principle, the more accurately an object is scanned, the more it is disturbed by the scanning process, until one reaches a point where the object's original state has been completely disrupted, still without having extracted enough information to make a perfect replica. This sounds like a solid argument against teleportation: if one cannot extract enough information from an object to make a perfect copy, it would seem that a perfect copy cannot be made. But the six scientists found a way to make an end run around this logic, using a celebrated and paradoxical feature of quantum mechanics known as the Einstein-Podolsky-Rosen effect. In brief, they found a way to scan out part of the information from an object A, which one wishes to teleport, while causing the remaining, unscanned, part of the information to pass, via the Einstein-Podolsky-Rosen effect, into another object C which has
never been in contact with A. Later, by applying to C a treatment depending on the scanned-out information, it is possible to maneuver C into exactly the same state as A was in before it was scanned. A itself is no longer in that state, having been thoroughly disrupted by the scanning, so what has been achieved is teleportation, not replication.
As the figure to the left suggests, the unscanned part of the information is conveyed from A to C by an intermediary object B, which interacts first with C and then with A. What? Can it really be correct to say "first with C and then with A"? Surely, in order to convey something from A to C, the delivery vehicle must visit A before C, not the other way around. But there is a subtle, unscannable kind of information that, unlike any material cargo, and even unlike ordinary information, can indeed be delivered in such a backward fashion. This subtle kind of information, also called "Einstein-Podolsky-Rosen (EPR) correlation" or "entanglement", has been at least partly understood since the 1930s when it was discussed in a famous paper by Albert Einstein, Boris Podolsky, and Nathan Rosen. In the 1960s John Bell showed that a pair of entangled particles, which were once in contact but later move too far apart to interact directly, can exhibit individually random behavior that is too strongly correlated to be explained by classical statistics. Experiments on photons and other particles have repeatedly confirmed these correlations, thereby providing strong evidence for the validity of quantum mechanics, which neatly explains them. Another well-known fact about EPR correlations is that they cannot by themselves deliver a meaningful and controllable message. It was thought that their only usefulness was in proving the validity of quantum mechanics. But now it is known that, through the phenomenon of quantum teleportation, they can deliver exactly that part of the information in an object which is too delicate to be scanned out and delivered by conventional methods.
This figure compares conventional facsimile transmission with quantum teleportation (see above). In conventional facsimile transmission the original is scanned, extracting partial information about it, but remains more or less intact after the scanning process. The scanned information is sent to the receiving station, where it is imprinted on some raw material (eg paper) to produce an approximate copy of the original. By contrast, in quantum teleportation, two objects B and C are first brought into contact and then separated. Object B is taken to the sending station, while object C is taken to the receiving station. At the sending station object B is scanned together with the original object A which one wishes to teleport, yielding some information and totally disrupting the state of A and B. The scanned information is sent to the receiving station, where it is used to select one of several treatments to be applied to object C, thereby putting C into an exact replica of the former state of A.
Labels: Quantum Mechanics
EldwinSchrodinger @ Quantum Theory - Thermodynamics
to understand paradoxes in the universe, we would first need some background in thermodynamics and of course statistics which are important to the development of quantum theory.
first of all, when i first started on quantum theory, i would ask myself. what the heck is thermodynamics and entropy? its actually not as tough as you would think :) it actually means the movement of heat from a body with higher temperature
to a body with lower temperature. till the temperatures of the two bodies are the same. and thats called thermal equilibrium.
here's a simple example. this particular girl leaves her seat after sitting for about 10 minutes, and you sit on that same sit. you'll find that the seat is warm. now why? its because the molecules in the seat are still vibrating at the same rate as in that girl's body. which is apparently faster than that yours. hence, the seat feels warm to you. and when it doesn't feel warm, it reaches thermal equilibrium! =)
here' the first law of thermodynamics - law of the conservation of energy. " the quantity of heat can be equated to a certain amount of mechanical work ". thus. heat can be converted into work and must be a form of energy. and when a certain amount of energy disappears somewhere, an equal amount must appear elsewhere in the same system.
for the 2nd law of thermodynamics, it is said that when time is elapsed, all energy would eventually be transformed into heat at a uniform temperature and all natural process would stop. this is also based on the principle of the dissipation of energy or just entropy. "the total entropy of a system always increases whenever heat flows from a hot body to a cold body" AND, it also increases whenever mechanical energy is changed into thermal energy in certain collision and frictional processes.
according to physicist ludwig boltzmann, entropy dependson the probabilities of molecular arrangements. for eg, if a state has a very large number of different ways its molecules could be arranged, then it has a very large entropy. thats why, if an egg were to fall on the floor and breaks, it is very unlikely to reform into its original shape.
if the entropy of an isolated system increase, what does that mean? it actually means that heat does not flow on its own from the cold body to the hot body. like a ball cannot bounce higher than its original position by converting heat to mechanical energy. likewise an egg cannot unscramble itself. if that happens, that would not violate the newtonian mechanics. but to instead, decrease the entropy of a system and thus forbidden by this 2nd law of thermodynamics. and this law tells time which way to go! =D
Labels: Quantum Mechanics
