How Lunar Eclipses Work (Infographic)
At 2:26 p.m. EST (1926 GMT) on Feb. 15, the asteroid 2012 DA14 will fly within 17,200 miles (27,680 kilo- meters) of Earth. This is lower than the communications satellites that orbit 22,000 miles (35,800 km) above the equator.
The asteroid will not hit the Earth on this orbital pass, but asteroid 2012 DA14 is about the size of the object that hit Siberia in 1908 (the “Tunguska Event“). The asteroid was discovered on Feb. 23, 2012, by the La Sagra Sky Survey. [Asteroid 2012 DA14 Flyby: Fact vs. Fiction (Video)]
At 150 feet wide (49 meters), the asteroid is less than half the length of the International Space Station (356 feet wide, or 109 meters). It is about half the size of a football field.
From Earth’s Northern Hemisphere, the asteroid will be below the horizon for most of its approach, but will be well-placed for observing after closest approach. The asteroid passes at a sharp angle to the path of the satellites and is not expected to hit any of them. [Asteroid 2012 DA14 Photos: Earth Flyby of Feb. 15, 2013]
The asteroid’s current orbit is similar to the Earth’s, but tilted. Asteroid 2012 DA14 passes Earth twice per orbit, but February’s pass is the closest approach for many decades. As it whips by at a relative velocity of 4.8 miles per second (7.82 kilometers per second), the Earth’s gravity will slingshot the asteroid into a slightly different orbit.
NEW YORK — Is time real, or the ultimate illusion?
Most physicists would say the latter, but Lee Smolin challenges this orthodoxy in his new book, “Time Reborn” (Houghton Mifflin Harcourt, April 2013), which he discussed here Wednesday (April 24) at the Rubin Museum of Art.
In a conversation with Duke University neuroscientist Warren Meck, theoretical physicist Smolin, who’s based at Canada’s Perimeter Institute for Theoretical Physics, argued for the controversial idea that time is real. “Time is paramount,” he said, “and the experience we all have of reality being in the present moment is not an illusion, but the deepest clue we have to the fundamental nature of reality.”
Smolin said he hadn’t come to this concept lightly. He started out thinking, as most physicists do, that time is subjective and illusory. According to Albert Einstein’s theory of general relativity, time is just another dimension in space, traversable in either direction, and our human perception of moments passing steadily and sequentially is all in our heads.
Over time, though, Smolin became convinced not only that time was real, but that this notion could be the key to understanding the laws of nature.
“If laws are outside of time, then they’re inexplicable,” he said. “If law just simply is, there’s no explanation. If we want to understand law … then law must evolve, law must change, law must be subject to time. Law then emerges from time and is subject to time rather than the reverse.”
Smolin admitted there are objections to this idea, especially what he calls “the meta-law dilemma:” If physical laws are subject to time, and evolve over time, then there must be some larger law that guides their evolution. But wouldn’t this law, then, have to be beyond time, to determine how the other laws change with time? Other physicists have cited this objection in reaction to Smolin’s work.
“The problem I see with the argument for laws that evolve in time is one that you yourself identify in the book: what you call the ‘meta-laws dilemma,’” Columbia University physicist Peter Woit wrote on his blogNot Even Wrong. “You speculate a bit in the book on ways to resolve this, but I don’t see a convincing answer to the criticism that whatever explanation you come up with for what determines how laws evolve, I’m free to characterize that as just another law.”
Smolin admitted this is currently a sticking point, but maintained that there are possible solutions.
“I believe you can resolve the meta-law dilemma,” Smolin said at the Rubin event. “I think the direction of 21st-century cosmology will depend on the right way to resolve the meta-law dilemma.”
Smolin and Meck discussed the consequences of his idea, including what it means for our understanding of human consciousness and free will. One implication of the idea that time is an illusion is the notion that the future is just as decided as the past.
“If I think the future’s already written, then the things that are most valuable about being human are illusions along with time,” Smolin said. “We still aspire to make choices in life. That is a precious part of our humanity. If the real metaphysical picture is that there are just atoms moving in the void, then nothing is ever new and nothing’s ever surprising — it’s just the rearrangement of atoms. There’s a loss of responsibility as well as a loss of human dignity.”
While certain famous equations, such as Albert Einstein’s E = mc^2, hog most of the public glory, many less familiar formulas have their champions among scientists. LiveScience asked physicists, astronomers and mathematicians for their favorite equations; here’s what we found:
The theory can be encapsulated in a main equation called the standard model Lagrangian (named after the 18th-century French mathematician and astronomer Joseph Louis Lagrange), which was chosen by theoretical physicist Lance Dixon of the SLAC National Accelerator Laboratory in California as his favorite formula.
“It has successfully described all elementary particles and forces that we’ve observed in the laboratory to date — except gravity,” Dixon told LiveScience. “That includes, of course, the recently discovered Higgs(like) boson, phi in the formula. It is fully self-consistent with quantum mechanics and special relativity.”
The standard model theory has not yet, however, been united with general relativity, which is why it cannot describe gravity. [Infographic: The Standard Model Explained]
“In simple words, [it] says that the net change of a smooth and continuous quantity, such as a distance travelled, over a given time interval (i.e. the difference in the values of the quantity at the end points of the time interval) is equal to the integral of the rate of change of that quantity, i.e. the integral of the velocity,” said Melkana Brakalova-Trevithick, chair of the math department at Fordham University, who chose this equation as her favorite. “The fundamental theorem of calculus (FTC) allows us to determine the net change over an interval based on the rate of change over the entire interval.”
This formula describes how, for any right-angled triangle, the square of the length of the hypotenuse (the longest side of a right triangle) equals the sum of the squares of the lengths of the other two sides.
“The very first mathematical fact that amazed me was Pythagorean theorem,” said mathematician Daina Taimina of Cornell University. “I was a child then and it seemed to me so amazing that it works in geometry and it works with numbers!” [5 Seriously Mind-Boggling Math Facts]
This simple formula encapsulates something pure about the nature of spheres:
“It says that if you cut the surface of a sphere up into faces, edges and vertices, and let F be the number of faces, E the number of edges and V the number of vertices, you will always get V – E + F = 2,” said Colin Adams, a mathematician at Williams College in Massachusetts.
“So, for example, take a tetrahedron, consisting of four triangles, six edges and four vertices,” Adams explained. “If you blew hard into a tetrahedron with flexible faces, you could round it off into a sphere, so in that sense, a sphere can be cut into four faces, six edges and four vertices. And we see that V – E + F = 2. Same holds for a pyramid with five faces — four triangular, and one square — eight edges and five vertices,” and any other combination of faces, edges and vertices.
“A very cool fact! The combinatorics of the vertices, edges and faces is capturing something very fundamental about the shape of a sphere,” Adams said.
Einstein makes the list again with his formulas for special relativity, which describes how time and space aren’t absolute concepts, but rather are relative depending on the speed of the observer. The equation above shows how time dilates, or slows down, the faster a person is moving in any direction.
“The point is it’s really very simple,” said Bill Murray, a particle physicist at the CERN laboratory in Geneva. “There is nothing there an A-level student cannot do, no complex derivatives and trace algebras. But what it embodies is a whole new way of looking at the world, a whole attitude to reality and our relationship to it. Suddenly, the rigid unchanging cosmos is swept away and replaced with a personal world, related to what you observe. You move from being outside the universe, looking down, to one of the components inside it. But the concepts and the maths can be grasped by anyone that wants to.”
Murray said he preferred the special relativity equations to the more complicated formulas in Einstein’s later theory. “I could never follow the maths of general relativity,” he said.
1 = 0.999999999….
Credit: Shutterstock/Tursunbaev Ruslan
This simple equation, which states that the quantity 0.999, followed by an infinite string of nines, is equivalent to one, is the favorite of mathematician Steven Strogatz of Cornell University.
“I love how simple it is — everyone understands what it says — yet how provocative it is,” Strogatz said. “Many people don’t believe it could be true. It’s also beautifully balanced. The left side represents the beginning of mathematics; the right side represents the mysteries of infinity.”
Here, L stands for the Lagrangian, which is a measure of energy in a physical system, such as springs, or levers or fundamental particles. “Solving this equation tells you how the system will evolve with time,” Cranmer said.
A spinoff of the Lagrangian equation is called Noether’s theorem, after the 20th-century German mathematician Emmy Noether. “This theorem is really fundamental to physics and the role of symmetry,” Cranmer said. ”Informally, the theorem is that if your system has a symmetry, then there is a corresponding conservation law. For example, the idea that the fundamental laws of physics are the same today as tomorrow (time symmetry) implies that energy is conserved. The idea that the laws of physics are the same here as they are in outer space implies that momentum is conserved. Symmetry is perhaps the driving concept in fundamental physics, primarily due to [Noether’s] contribution.”
The equation has numerous applications, including allowing physicists to estimate the mass and size of the proton and neutron, which make up the nuclei of atoms.
Basic physics tells us that the gravitational force, and the electrical force, between two objects is proportional to the inverse of the distance between them squared. On a simple level, the same is true for the strong nuclear force that binds protons and neutrons together to form the nuclei of atoms, and that binds quarks together to form protons and neutrons. However, tiny quantum fluctuations can slightly alter a force’s dependence on distance, which has dramatic consequences for the strong nuclear force.
“It prevents this force from decreasing at long distances, and causes it to trap quarks and to combine them to form the protons and neutrons of our world,” Strassler said. “What the Callan-Symanzik equation does is relate this dramatic and difficult-to-calculate effect, important when [the distance] is roughly the size of a proton, to more subtle but easier-to-calculate effects that can be measured when [the distance] is much smaller than a proton.”
“Start with any triangle,” Whitney explained. “Draw the smallest circle that contains the triangle and find its center. Find the center of mass of the triangle — the point where the triangle, if cut out of a piece of paper, would balance on a pin. Draw the three altitudes of the triangle (the lines from each corner perpendicular to the opposite side), and find the point where they all meet. The theorem is that all three of the points you just found always lie on a single straight line, called the ‘Euler line’ of the triangle.”
Whitney said the theorem encapsulates the beauty and power of mathematics, which often reveals surprising patterns in simple, familiar shapes.