Eleven dimension, parallel universes, and a world made out of strings. It's not science fiction. It's String Theory.
Part I
Part II
Part III
Source: PBS
Showing posts with label Science. Show all posts
Showing posts with label Science. Show all posts
Monday, February 11, 2008
The Elegant Universe
Quantum Mechanics
Quantum Mechanics is the successful theory of the fundamental forces and particles of the Universe and also the theory behind Quantum Field Theory,the main component of the Standard Model, the general theory that unifies 3 of the 4 fundamental forces in a coherent and predictable model of the Universe.
In his website Andrew Thomas gives a full account of the main concepts of Quantum Mechanics in an easy and accessible manner.
Quantum Mechanics: An Introduction
Introducing the peculiar world of the quantum, where a particle is a wave, and a wave is a particle. Considers the Heisenberg Uncertainty Principle.
The Quantum Casino
At its most basic level, nature appears to be fundamentally random. Are we all players in a game of chance at the Quantum Casino?
Quantum Entanglement
Quantum states can become entangled in astonishing ways. Welcome to the strange world of "qubits", faster-than-light communication, and Einstein's first definition of reality.
Quantum Decoherence
At last it would appear a solution has been found to the riddle of the apparent collapse of the wavefunction. Includes an interactive simulation of decoherence in an ensemble of particles.
Quantum Reality
A review of our study of quantum mechanics, the Copenhagen Interpretation, and the first indications of a deeper "veiled" reality.
It's a Small World
Introducing the Standard Model of particle physics, and string theory. But are these theories truly fundamental, or do they rest on a infinite tower of turtles?
The Cosmic Universe
What happened at the start of the universe? Could Arnold Schwarzenegger's Terminator arm hold the key? Also considers quantum gravity and the "wavefunction of the universe".
The Anthropic Principle
Some of the fundamental physical constants in the universe appear to have been fine-tuned, otherwise life could not exist. Are "multiverse" solutions the answer to this mystery?
The Arrow of Time
All fundamental physical processes appear to be time-reversible - so why don't we see broken eggs mending themselves? And why can't we remember the future?
The Mathematical Universe
The universe appears to have an uncanny connection with the world of mathematics. Why is this? And do mathematical structures have a reality all of their own?
The Big Brother Universe
An examination of the evidence that our universe is the product of an advanced civilisation. Are we living in a computer simulation? Are we all "housemates" in the ultimate reality show?
Monday, January 14, 2008
Large Hadron Collider
The Large Hadron Collider Project was approved by CERN Council in December 1994. Because of initial funding difficulties it was proposed initially as a 2-phase project, the first stage with an energy of 10 TeV in the center-of-mass, to be operational by 2004, with an upgrade to its final energy of 14 TeV by 2008.
During the years 1995-1996, intense negotiations with non-Member States secured a substantial commitment to participate financially in the construction of the Machine. Consequently, in December 1996, Council passed a Resolution approving the construction of the 14 TeV accelerator in a single stage. The LHC will be the first machine built at CERN with substantial material contribution from non-Member States. Machine hardware is being constructed in National Laboratories in Canada, India, Japan, Russia and the USA.
The LHC will ultimately collide beams of protons at an energy of 14 TeV . Beams of lead nuclei will be also accelerated, smashing together with a collision energy of 1150 TeV.
A TeV is a unit of energy used in particle physics. 1 TeV is about the energy of motion of a flying mosquito. What makes the LHC so extraordinary is that it squeezes energy into a space about a million million times smaller than a mosquito.
The experiments will be carried out deep inside the earth in a circular tunnel 27 kilometers long, 100 meters below the surface of the Earth, where CERN physicists will crash sub-atomic particles whirring around at the speed of light and monitor the debris of these tiny crashes, to calibrate the relationship between matter and energy and learn more about how matter came into existence in the first few seconds of the Big Bang.
The ultimate prize is to find an almost particle, the Higgs-Boson, a key part of what physicists call the Standard Model of the subatomic world. CERN's Large Hadron Collider will be supplied with protons from the injector chain Linac2 - Proton Synchrotron Booster (PSB) - Proton Synchrotron (PS) - Super Proton Synchrotron (SPS). These accelerators were upgraded to meet the very stringent needs of the LHC.
The tunnel was formerly used to house the LEP, an electron-positron collider. The underground infrastructure of LEP included experimental areas at four points, each incorporating experimental and service caverns, plus an equipment cavern with injection tunnels connected to allow particle transfer from the SPS machine. Plus additional galleries parallel to the main tunnel were used to house klystrons and their power supplies. On the surface a total of 37 buildings housed all the necessary equipment and services for the LEP machine and experimental operations. The LEP-2 upgrade consisted essentially of the addition of two sets of galleries thus allowing a doubling of the number of klystrons and related power supplies.
For the LHC project, the existing LEP tunnel has been re-used after the complete dismantling of the LEP machine. In addition new structures have been added including experimental and service caverns destined to accommodate two new experiments two transfer tunnels of about 2.5 km each in length and beam dump facilities comprising two sets of straight tunnels and caverns. 32 new surface buildings of various sizes have also been constructed.
LHC@Home, a distributed computing project, was started to support the construction and calibration of the LHC. The project uses the BOINC platform to simulate how particles will travel in the tunnel. With this information, the scientists will be able to determine how the magnets should be calibrated to gain the most stable "orbit" of the beams in the ring.
While many have voiced concerns that the LHC will destroy the Universe, engineers close to the project admit that the possibility is infinitesimally small. As CERN has pointed out, if the Earth were in danger of any such fate, it would have happened billions of years ago from the bombardment of protons the planet receives that are millions of times more energetic than anything that could be produced by the LHC.
The Large Hadron Collider is expected to create tiny black holes within the Earth. However there exists an entirely theoretical phenomenon known as Hawking Radiation, which some physicists expect to cause these black holes to dissipate. The primary cause for concern is the fact that Hawking Radiation - the only means by which these black holes could be dissipated, is entirely theoretical.
CERN performed a study to investigate whether such dangerous events as micro black holes, strangelets, or magnetic monopoles could occur. The report concluded, "We find no basis for any conceivable threat". It has been claimed that a strong argument for the safety of colliders such as the LHC comes from the simple fact that cosmic rays with energies up to twenty million times the LHC's 1.4×10¹³ eV capacity have been bombarding the Earth, Moon and other objects in the solar system for billions of years with no such effects. Yet CERN themselves claim that the Hadron Collider is to recreate conditions that haven't existed since a fraction of a second after the big bang, making it difficult to accept that the conditions within the collider are quite as everyday.
As with any new and untested experiment, it is not possible to say with utter certainty what will happen. John Nelson at the University of Birmingham stated of RHIC that "it is astonishingly unlikely that there is any risk-but I could not prove it." Furthermore, in academia there is some question, albeit among a minority of scientists, of whether the Hawking radiation theory is correct.
Souces: Daily Galaxy, CERN, Wikipedia
Thursday, January 10, 2008
Monday, January 7, 2008
Whale Song
The mechanisms used to produce sound vary from one family of cetaceans to another. Marine mammals, such as whales, dolphins, and porpoises, are much more dependent on sound for communication and sensation than land mammals are , as other senses are of limited effectiveness in water. Sight is limited for marine mammals because of the way water absorbs light. Smell is also limited, as molecules diffuse more slowly in water than air, which makes smelling less effective. In addition, the speed of sound in water is roughly four times that in the atmosphere at sea level. Because sea-mammals are so dependent on hearing to communicate and feed, environmentalists and cetologists are concerned that they are being harmed by the increased ambient noise in the world's oceans caused by ships and marine seismic surveys. (read Wikipedia full article)
Prof. Richard A. Muller course Physics for Future Presidents at Berkeley has a lecture about waves where he talks about the ocean sound channel and whales communication. Forward the video to about 35 min to watch his explanation.
Carl.Sagan's Cosmos series also talks about this issue at chapter 11, The Persistence Of Memory.
Friday, December 28, 2007
DARPA Grand Challenge
The DARPA Urban Challenge features autonomous ground vehicles conducting simulated military supply missions in a mock urban area. Safe operation in traffic is essential to U.S. military plans to use autonomous ground vehicles to conduct important missions. (see more information)
Tuesday, December 18, 2007
Alan Turing
Being as i am interested in computers and mathematics i have to begin this 'on the shoulders of giants' series with one of the most prolific and influent thinkers of our time: Alan Turing. In this brief essay i'll try to explain how come he singled ed invented the computer, the modern conception of one, by his conceptual thought of the Universal Turing Machine, an abstract device that gived enough time and space could implement any algorithm. The Turing Machine came to be as the conceptual formulation of the modern computer and a powerful instrument in the study of the foundations of mathematics in the footsteps of The Entscheidungsproblem proposed by Hilbert.
When i say that Alan Turing invented the computer i'm not trying to imply that he is the only one who have contributed to the actual invention and construction of the modern computer, i'm only saying that his work on the Turing Machine is at the fundamental level of what is the modern conception of a computer and it would be enough starting from that to actually build one.
One of my heroes, Leibniz, was near achieving that goal, but he missed in linking all his ideas to a coherent and precise definition of a computer. In spite of that, lets not forget that he develop the pascal adding machine into a full calculating device.
Turing's work, besides all is implications in the development of the computer, was also a step further in the achievement reached by Kurt Godel in his famous incompleteness theorem, by stating the foundations of mathematics in terms of the halting problem, meaning that no turing machine could decide if all programs halt or not and consequently any system of formal logic is incomplete if coherent. More recently Gregory Chaitin stated the halting problem in terms of the probability that a program halts and reached the perturbant conclusion that even at a fundamental level of mathematics as in algebra there are mathematical facts that are unproven unless we take them has an axiom; they are uncompressable truths with maximum entropy or randomness.
The Entscheidungsproblem mentioned above, question whether there exists a definite method which, at least in principle, can be applied to a given proposition to decide whether that proposition is provable. Turing's great insight in his 1936 paper 'On computable numbers, with an application to the Entscheidungsproblem' was to perceive Hilbert's question in terms not of proofs, but of computing numbers. As his title said, the Entscheidungsproblem was only an application of a new idea, that of computability.
His paper starts by asking how can we specify the infinite in finite terms? In particular, how can we specify the infinite sequence of digits in a 'real number', such as n = 3. 141592, 653...? What does it mean to say that there is a definite method for calculating such a number? Turing's answer lies in defining the concept of the Turing machine.
How Turing got his result? He use'd a version of Cantor's diagonal method from set theory. He first defined a turing machine as a device capable of a very simple set of operations gived by a 'table of behavior', each one being a specific turing machine, and in some state unequivocally gived by it's current configuration plus the symbol scanned on tape. (more details)Then he defines a computable number as an infinity sequence of symbols that can be printed on a turing machine starting with a blank tape. He then rationalizes that if we order all the turing machines in a sequence we can obtain a number that differs in the Nth digit of the Nth turing machine - the diagonal method - so it's uncomputable. But if it can be defined how is it uncomputable? The problem lies in knowing if a turing machine actually produce an infinite number; Turing prove that there is no turing machine which can be applied to another turing machine proving that it will ever produce an infinite number, so that the problem itself - know known as the halting problem - is not computable. Turing states that if there was such a machine it could be applied to itself raising a contradiction - another instance of the self referencing problem finded in Godel's proof and Russel's paradox. So the question of defining something to which that is no mechanical procedure to solve it can be easily translated to an abstract mathematical question and formal logic and therefore to give a negative answer to Hilbert's Entscheidungsproblem.
The Universal Turing Machine
Besides given a definitive answer to the Entscheidungsproblem and defining the field of computability in new terms Turing's work had a practical implication: it laid out the principle of the computer through the concept of the universal Turing machine.
Given that there is a mechanical procedure capable of implementing any 'table of behaviour' in a Turing machine then there is also a more abstract one capable of implementing any Turing machine, what Turing called a Universal Turing Machine.
Today we can not but associate Turing original ideas with the concept of the modern computer. It's easy to correlate the universal Turing machine, a specific Turing machine and is configurations respectively with the computer, a computer program and the instruction blocks of a computer program. Turing also gave an algorithmic view of computation applied to the human mind which makes him also a prominent thinker in the philosophy of mind, because in spite of his pioneer work in the development of the concept of the computer, the subject of his study was the human brain as a start point from which would eventually emerge a computer.
Starting with Godel's proof of incompleteness and Alonzo Church lambda calculus we already had the answers to the questions Turing set to solve in his own work at the time he published his results, but the novel approach he devised was so ingenious and new that he achieved the conception and definition of the computer on paper before it would be physically implemented so that we might even say that he invented it.
World War II
The advent of the World War II had a profound impact in Turing´s live. Earlier, he developed an interest and some ideas about codes, cyphers and the global field of cryptanalysis. Armed with that skills he naturally achieve a position in UK effort to break German codes and their Enigma machine at Bletcheley Park. This also related with his previous experience in constructing computers: at Princeton he spent time in building a machine out of electromagnetic relays which effected binary multiplication as an encoding device, with some theory of immunity to cryptanalysis. When back at Cambridge, Turing also designed and partially built another machine, which approximated by gear-wheel motion a Fourier series for the Riemann zeta-function. It was intended to shorten the hard labor of finding the possible locations of zeros - the subject of the Riemann hypothesis, which remains today perhaps the most important unsolved problem in mathematics.
In Bletcheley Park he participated in the design of a machine called 'the Bombe' and had direct contact with the Colossus which was used in breaking the german Enigma successor, the Lorenz cipher. Due to the classified nature of his war effort to reengenering german ciphers and codes, that facet of his life was keeped secret until much after the war ended. But we can now recognize the great impact of that work simultaneous in the war outcome and to the evolution, use and recognition of the intrinsic advantages of electronic computers as a tool to solve problems.
Post War
Following his war experience, Turing went to the National Physical Laboratory and worked on his detailed design for a computer, submitting it for approval in March 1946. Turing's Automatic Computing Engine (ACE), as it was dubbed was chronologically second to the June 1945 EDVAC report bearing von Neumann's name, but in addition to the originality of its hardware design, it was ideologically independent: for (i) it was conceived from the outset as a universal machine for which arithmetic would be just one application, and (ii) Turing sketched a theory of programming, in which instructions could be manipulated as well as data, a foresight vision of the metaprograming approach.
This is also related with Turing later interest in machine intelligence and learning in the broad field of Artificial Intelligence. In Manchester, where he got his first full academic post, he and the small group around him published articles under the heading 'Digital computers applied to games' in 1953, which mark pioneering research into machine intelligence. But this lead made no impact on the fresh start to artificial intelligence made by Newell, Simon, Minsky and McCarthy in the United States. Nevertheless in his famous 1950 paper 'Computing machinery and intelligence' he presents the idea of an 'imitation game' also known as the Turing test, in which a human has to interact with 'someone' in a closer room through a teletype device and tell if it is a human. Turing says that if a machine can play the human role well, it can elude his human interactor in thinking his talking to a human rather a machine, then the machine must exhibit intelligence behavior, human intelligence. Turing predicts that by the final of 20th century we should be able to construct such a machine, a bold assumption that we are yet to achieve.
Nevertheless much of his other contributions to philosophy, logic, mathematics, and the emergent field of computation provided invaluable tools of thought that enable us to progress the state of civilization and maybe, in the proper time, the fulfillment of his vision about computers, intelligence and their expression in an artificial intelligence synthesis and in doing so perhaps we be able to know a little more about ourselfs and answer the primordial philosophical question about who we are.
Monday, December 10, 2007
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