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Full article here: http://www.sciencedaily.com/releases/2010/07/100722142640.htm "ScienceDaily (July 23, 2010) — When waves -- regardless of whether light or sound -- collide, they overlap creating interferences. Austrian and Canadian quantum physicists have now been able to rule out the existence of higher-order interferences experimentally and thereby confirmed an axiom in quantum physics: Born's rule."

Full article here: http://www.scientificamerican.com/article.cfm?id=large-hadron-collider-goals "Landsberg hopes to trump the standard model in grander style. He is presenting an ambitious new theory in which the number of dimensions in the Universe increases as it grows in size. He and his colleagues propose that the Universe began with just one spatial dimension and one time dimension. "Think of the Universe as a one-dimensional thread that gradually wove itself into a two-dimensional tapestry as it grew, and then wrapped itself up further to create three dimensions," he says. Reducing the spatial dimensions of the early Universe avoids the problems with the standard model, because the unwanted infinities arise only for equations describing three dimensions, says Landsberg. The team has also calculated that a fourth spatial dimension would show up as an intrinsic energy that pushes the three-dimensional Universe outwards. The effect roughly matches the acceleration of cosmic expansion, currently attributed to the mysterious "dark energy." "Dark energy is an echo of the fourth dimension of space," Landsberg argues."

Full article here: http://www.firstscience.com/home/articles/big-theories/a-new-form-of-matter-2-fermionic-condensates_1229.html " Researchers have discovered a weird new phase of matter called fermionic condensates. We learned it in grade school. There are three forms of matter: solids, liquids and gases. But that's not even half right. There are at least six: solids, liquids, gases, plasmas, Bose-Einstein condensates, and a new form of matter called "fermionic condensates" discovered by NASA-supported researchers."

Article found on www.sciencedaily.com.Here is the full article: http://www.sciencedaily.com/releases/2010/07/100720101349.htm "The reason is that many physicists believe that electrons have a permanent electric dipole moment. An electric dipole moment is usually created when positive and negative charges are spatially separated. Similar to the north and south poles of a magnet, there are two electric poles. In the case of electrons, the situation is much more complicated because electrons should not actually have any spatial dimension. Despite this, an entire range of physical theories that go beyond the standard model of elementary particle physics are based upon the existence of dipole moment. These theories in turn would explain how the universe in the form that we know it could have been created in the first place."

A great article I discovered on fark.com from the Huffington post, regarding consciousness, duality, etc. First, an excerpt, then the whole article via a link: "In the words of physicist Wheeler: "Nothing is more important about the quantum principle than this, that it destroys the concept of the world as "sitting out there," with the observer safely separated from it ... To describe what has happened, one has to cross out that old word "observer," and put in its place the new word "participator." In some strange sense the universe is a participatory universe."3 Physicist Henry P. Stapp of UC-Berkeley, a leading authority in the theoretical foundations of quantum physics, takes a similar view: "The new physics presents prima facie evidence that our human thoughts are linked to nature by non-local connections: what a person chooses to do in one region seems immediately to affect what is true elsewhere in the universe ... [O]ur thoughts ... DO something [his emphasis]."4 http://www.huffingtonpost.com/dr-larry-dossey/is-consciousness-the-cent_b_645069.html

Hoping someone can help me out here. Light can arise as either particle or wave. Would like clarification on the difference between the two. Have read up on this over and over, but need a simple differentiation. My mind has taken particles as being "things"...a thing one can point to, just as with a rock or Xbox360 and say,"It's right there. It has shape and mass." But, do waves have mass? Is a wave a physical "thing," or, is a light wave similar to a wave of water...it moves, you can point to it and say "there's a wave," but it's really just a mass of h20? Does it have dimension? Any and all clarification would be greatly appreciated.

First off, just want to reiterate, am considering it good fortune to have discovered this group. In a weird way, shows there's hope for humanity. In anycase, a question. How do you define "consciousness?" Not looking for Merriam-Webster definition here. Have studied the mind and it's functions, on many levels, for many years. Even within the neurobiology community, there's much debate. Is it physical or non-physical? Simply synaptic nerve endings firing off? Something you think we don't have the knowledge or technology to truly define yet? All views accepted and respected. Thanks!

Just one question to answer. Let t_{k+1} = t_k / 2 if t_k is even, t_{k+1} = (3*t_k + 1) / 2 if t_k is odd, for positive integers t_k. Prove or disprove: For every t_0 = 1, 2, ... there exists some k such that t_k = 1. Prize for first good answer + proof is a fine chess.com trophy :)

Just one question to answer. What is the most expensive substance manufactured by humans, and how much would a gram of it cost to make? Prize for first good answer is a fine chess.com trophy, as always.

I was wondering how much we can rely on such statements. According to Wikipedia: (http://en.wikipedia.org/wiki/Vacuous_truth#Arguments_that_only_some_vacuously_true_statements_are_true) [edit] Arguments that only some vacuously true statements are true One objection to saying that all vacuously true statements are true is that this makes the following deduction valid: Many people have trouble with or are bothered by this because, unless we know about some a priori connection between P and Q, what should the truth of P have to do with the implication of P and Q? Shouldn’t the truth value of P in this situation be irrelevant? Logicians bothered by this have developed alternative logics (e.g. relevant logic) where this sort of deduction is valid only when P is known a priori to be relevant to the truth of Q. Note that this "relevance" objection really applies to logical implication as a whole, and not merely to the case of vacuous truth. For example, it’s commonly accepted that the sun is made of gas, on one hand, and that 3 is a prime number, on the other. By the standard definition of implication, we can conclude that: the sun’s being made of gas implies that 3 is a prime number. Note that since the premise is indeed true, this is not a case of vacuous truth. Nonetheless, there seems to be something fishy about this assertion. [edit] Summary So there are a number of justifications for saying that vacuously true statements are indeed true. Nonetheless, there is still something odd about the choice. There seems to be no direct reason to pick true; it’s just that things blow up in our face if we don’t. Thus we say S is vacuously true; it is true, but in a way that doesn’t seem entirely free from arbitrariness. Furthermore, the fact that S is true doesn’t really provide us with any information, nor can we make useful deductions from it; it is only a choice we made about how our logical system works, and can’t represent any fact of the real world. [edit] Difficulties with the use of vacuous truth All pink rhinoceros are carnivores. All pink rhinoceros are herbivores. Both of these seemingly contradictory statements are true using classical or two-valued logic – so long as the set of pink rhinoceros remains empty. Question: What do you think of vacuous truths? How does the weak anthropic principle qualify here since it also is a vacuously true statement?

I heard from somewhere that an experiment was conducted by shooting bacteria through the double slit, which when electrons/photons go through, a wave interference pattern is created, but it was thought that any macro thingy would make a normal two slit pattern, and when the bacteria were shot, the scientists detected a (very subtle) interference pattern. Has anyone heard of something like this and know where I can get an article on it? I've been searching google scholar but it was no avail.

Looking for any and all input on neutrinos. What significance do they hold? Why study them? Does knowledge of their existence in any way serve a functional purpose? Once read something along the lines that if a scientist can't explain something to a five year old, he doesn't know what he's talking about. Keep that in mind when discussing this topic. Am not looking for expansive theoretical models. Looking at function and purpose here. Thanks!

Hi everybody (hi Doctor Nic), I am looking for a book or two on PDEs. One that gives a nice and friendly introduction, and one that provides qualitative theory of PDEs or, if possible, one that does both. All answers are welcome! Thanks, Summum Malum P.S. I downloaded one called Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations by a guy called Vicentiu D. Rădulescu, but it does not contain any excersises

I am interested to hear opinions of what my fellow teammates may have concerning whether or not the continuum hypothesis may still be provable in a different set theory besides ZFC. As far as I know, undecideability of the c hypothesis has also been proven for one other model (Peano's Postulates? not sure), but there are plenty of models left, of course. Some, unfortunately, have different definitions of sets that make it harder to ground the original Cantorian question. Anyways, there's plenty of other set theories and I want to know what you think about them! For example, is it harder to work with set theories that have higher consistency strengths, such as Ramsey, or n-Huge? Is there another set theoretic framework that has an even greater consistency than n-Huge? All questions are up for grabs! Take your pick and I'd be interested in knowing.

.. "Some theorists suggest that the Big Bang was not so much a birth as a transition, a "quantum leap" from some formless era of imaginary time, or from nothing at all. Still others are exploring models in which cosmic history begins with a collision with a universe from another dimension."

Experiments have been done to measure the diameter of the proton by its subtle effect on the energy levels in both normal hydrogen atoms and in atoms where the electron has been replaced by a meson. Surprisingly, the measured diameters differ by 4%. As this is much greater than experimental accuracy, the models used for the interaction of these simple particles appear to be wrong. Nobel prize probably available for anyone who can fix them. See wired magazine article.

Very recently, the earliest yet multicellular fossil has been found. It can hardly be a co-incidence that this occurred only a few million years after photosynthesis changes Earth's atmosphere from anaerobic to aerobic (which must have been a huge crisis to all the organisms at the time, necessitating radical adaptation. Oxygen would surely have been extremely toxic to creatures with no experience of it, or protection against uncontrolled oxidation). Even after developing many levels of protection, oxygen is still the source of most damage to our cells today. Perhaps multicellular colonies initially used their outer cells sacrificially to protect the inner ones from oxygen. Also striking is how slow the development of complex life was from this point (not much for 1.5 billion years after the first two examples. A red algae was the other one). This suggests how very difficult it was to develop the specialisation and organisation of different cell-types in large organisms. It is likely it was a lot easier to evolve from a fish to us than from the first multicellular organisms to a fish, since it took a lot less time for the former.

Russian mathematician rejects $1 million prize AP – This undated file photo released by the International Mathematician Congress shows Grigory Perelman. … By MALCOLM RITTER, AP Science Writer Malcolm Ritter, Ap Science Writer – Thu Jul 1, 12:13 pm ET NEW YORK – He said nyet to $1 million. Grigory Perelman, a reclusive Russian mathematics genius who made headlines earlier this year for not immediately embracing a lucrative math prize, has decided to decline the cash. Perelman's decision was announced Thursday by the Clay Mathematics Institute in Cambridge, Mass., which had awarded Perelman its Millennium Prize. The award honors his solving of the Poincare (pwan-kah-RAY) conjecture, which deals with shapes that exist in four or more dimensions. Jim Carlson, institute president, said Perelman's decision was not a complete surprise, since he had declined some previous math prizes. Carlson said Perelman had told him by telephone last week of his decision and gave no reason. But the Interfax news agency quoted Perelman as saying he believed the prize was unfair. Perelman told Interfax he considered his contribution to solving the Poincare conjecture no greater than that of Columbia University mathematician Richard Hamilton. "To put it short, the main reason is my disagreement with the organized mathematical community," Perelman, 43, told Interfax. "I don't like their decisions, I consider them unjust." Attempts by The Associated Press to reach Perelman, a resident of St. Petersburg, were unsuccessful. Carlson said institute officials will meet this fall to decide what to do with the prize money. "We have some ideas in mind," he said. "We want to consider that carefully and make the best use possible of the money for the benefit of mathematics."