Posts Tagged ‘antimatter’
“Chance, too, which seems to rush along with slack reins, is bridled and governed by law”*…
… though that law can sometimes be less than obvious. Erica Klarreich reports on one creative mathematician’s efforts to help us learn…
In late January, Daniel Litt [pictured above] posed an innocent probability puzzle on the social media platform X (formerly known as Twitter) — and set a corner of the Twitterverse on fire.
Imagine, he wrote, that you have an urn filled with 100 balls, some red and some green. You can’t see inside; all you know is that someone determined the number of red balls by picking a number between zero and 100 from a hat. You reach into the urn and pull out a ball. It’s red. If you now pull out a second ball, is it more likely to be red or green (or are the two colors equally likely)?
Of the tens of thousands of people who voted on an answer to Litt’s problem, only about 22% chose correctly. (We’ll reveal the solution below, in case you want to think it over first.) In the months since, Litt, a mathematician at the University of Toronto, has continued to confound Twitter users with a series of probability puzzles about urns and coin tosses.
His posts have prompted lively online discussions among research mathematicians, computer scientists and economists — as well as philosophers, financiers, sports analysts and anonymous fans. Some joked that the puzzles were distracting them from their real work — “actively slowing down economic research,” as one economist put it. Others have posted papers exploring the puzzles’ mathematical ramifications.
Litt’s online project doesn’t just highlight the enduring allure of brainteasers. It also demonstrates the limits of our mathematical intuition, and the counterintuitive nature of probabilistic reasoning. As Litt wrote, there’s “nothing more exhilarating than posing a multiple-choice problem on which 50,000 people do substantially worse than random chance.”…
The answer to this puzzle, other puzzles, and Litt on what makes a great puzzle, and why simple probability questions can be so deceptively difficult: “Perplexing the Web, One Probability Puzzle at a Time,” from @EricaKlarreich in @QuantaMagazine.
Vaguely related (but also very interesting): “The Bookmaker,” via @annfriedman, who observes: “Leif Weatherby and Ben Recht on Nate Silver and the addiction to prediction: ‘Silver insists that viewing all decisions through this lens of gambling is the underappreciated characteristic of Very Successful People,’ they write. ‘But what Silver willfully ignores is that the successful players in this world aren’t the bettors. They are the bookies and casino owners—the house that never loses.'”
* Boethius, The Consolation of Philosophy
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As we contemplate chance, we might send confirmatory birthday greetings to Carl David Anderson; he was born on this date in 1905. An experimental physicist, he shared the 1936 Nobel Prize in Physics for his discovery (that’s to say, confirmation of the existence) of the positron, the first known particle of antimatter… which had been predicted by mathematician and physicist Paul Dirac, whose “Dirac Equation“– in part a product of its author’s application of probability theory– had predicted (among many other features of quantum theory as we know it) the existence of the particle (and antimatter).
“It is difficult to fully appreciate how much our picture of the universe has changed in the span of a single human lifetime”*…
… and it continues to change…
Our universe could be the mirror image of an antimatter universe extending backwards in time before the Big Bang. So claim physicists in Canada, who have devised a new cosmological model positing the existence of an “antiuniverse” which, paired to our own, preserves a fundamental rule of physics called CPT symmetry. The researchers still need to work out many details of their theory, but they say it naturally explains the existence of dark matter.
Standard cosmological models tell us that the universe – space, time and mass/energy – exploded into existence some 14 billion years ago and has since expanded and cooled, leading to the progressive formation of subatomic particles, atoms, stars and planets.
However, Neil Turok of the Perimeter Institute for Theoretical Physics in Ontario reckons that these models’ reliance on ad-hoc parameters means they increasingly resemble Ptolemy’s description of the solar system. One such parameter, he says, is the brief period of rapid expansion known as inflation that can account for the universe’s large-scale uniformity. “There is this frame of mind that you explain a new phenomenon by inventing a new particle or field,” he says. “I think that may turn out to be misguided.”
nstead, Turok and his Perimeter Institute colleague Latham Boyle set out to develop a model of the universe that can explain all observable phenomena based only on the known particles and fields. They asked themselves whether there is a natural way to extend the universe beyond the Big Bang – a singularity where general relativity breaks down – and then out the other side. “We found that there was,” he says.
The answer was to assume that the universe as a whole obeys CPT symmetry. This fundamental principle requires that any physical process remains the same if time is reversed, space inverted and particles replaced by antiparticles. Turok says that this is not the case for the universe that we see around us, where time runs forward as space expands, and there’s more matter than antimatter.
Instead, says Turok, the entity that respects the symmetry is a universe–antiuniverse pair. The antiuniverse would stretch back in time from the Big Bang, getting bigger as it does so, and would be dominated by antimatter as well as having its spatial properties inverted compared to those in our universe [as per the illustration above]…
More at “Our universe has antimatter partner on the other side of the Big Bang, say physicists,” in @PhysicsWorld.
Apposite: “The Big Bang no longer means what it used to.”
* Lawrence M. Krauss, A Universe from Nothing: Why There Is Something Rather Than Nothing
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As we debate doppelgangers, we might send chronologically-accurate birthday greetings to Louis Essen; he was born on this date in 1908. A physicist, he is best remembered for his measurements of time– he invented the quartz crystal ring clock and the first practical atomic clock. His cesium-beam atomic clock ultimately changed the way time is measured: the cesium atom’s natural frequency was formally recognized as the new international unit of time in 1967; the second was defined as exactly 9,192,631,770 oscillations or cycles of the cesium atom’s resonant frequency, replacing the old “second” which had been defined in terms of the Earth’s motion.
Perhaps unsurprisingly, given Essen’s punctilious dedication to accuracy, he was a critic of Einstein’s theory of relativity, particularly as it related to time dilation. Moreover, we note (with an eye to the item above) that Essen’s clocks measured time in only one direction…
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