Among physics students, March 14 is known as “π-Day” (“Pi-Day”) the day that Albert Einstein was born in Ulm, Germany in 1879. The venerable physicist is known for changing the very paradigm of physics, rejecting the three “fundamental undefinables” of length, mass and time as invariant, and positing in their place the speed of light as the unique invariant. (Thus, measuring the speed of a light beam while traveling in the same direction as the beam, and measuring it while traveling in the opposite direction would yield precisely the same relative velocities; this in distinction to common sense, which would call for adding and subtracting the speed of light from the speed of the observer.) The ramifications of this shift in paradigm lead to fascinating effects at relativistic speeds — including, a contraction of length, an increase of mass, and the slowing down of time. Lying down in the direction of motion in a rocket ship traveling at 50% of the speed of light, a 6′ man would shrink to 5’3”; if his weight were 180 pounds normally, it would increase to 207 pounds. And if he traveled for one earth-year, he would age 47 days less than if he had remained stationary. Launched on March 14, 2012, and brought back one year later, on March 14, 2013, it would be only January 25, 2013 for him. Einstein’s special theory of relativity was published in 1905, and the far more complex general theory of relativity in 1915. Special relativity gives the equivalence of energy and mass in the most famous equation in science, E=mc^2. General relativity, based on the equivalent effects of gravitation and acceleration, leads to explanations of the large-scale universe — a violent universe that has its origin in a “Big Bang” 13.7 billion years ago; of light bending around massive bodies such as stars and galaxies; of stars that collapse into black holes; of “worm holes” that connect different locations of space-time in the universe. Isaac Newton’s dynamics, formulated two centuries earlier in the Principia are still valid, but at relativistic velocities they have to be modified. Einstein’s work has to be regarded as buttressing Newton’s physics and not in any way subverting it. A spaceship can still be sent to land on the moon with Newton’s physics, but Einstein’s corrections would make it a softer landing.
THE INDIVIDUAL OF THE CENTURY
Late in 1999, the editors of Time Magazine, used to selecting the “Individual of the Year,” found themselves with a much more difficult task — selecting the individual of the century. After what must have called for considerable deliberation, they made their announcement. It would not be a spiritual leader, such as Pope John Paul II, Gandhi or Mother Teresa. And it would not be a political leader, such as FDR, Stalin or Churchill, in a century that had seen two World Wars. The editors’ choice for the “Individual of the Century” would be Albert Einstein. They explained the reasoning in their selection: the 20th century had been the ‘Century of Science’ and Albert Einstein was its greatest practitioner, and the very symbol of science.
π is the symbol for the irrational number representing the ratio of the circumference of a circle divided by its diameter. To seven places after the decimal, its value is 3.141 592 7 As an irrational number π cannot be expressed exactly by the ratio of two numbers; however, elementary school students are often taught 22/7, as a crude approximation. It yields 3.142 857, good to two places after the decimal. A much better approximation is 355/113, a ratio that equals 3.141 592 9, good to six places. A better approximation still comes from the mnemonic, “How I need a drink, alcoholic of course, after the heavy lectures involving quantum mechanics,” 3.141 592 653 589 79… Good to 15 places, it comes from counting the letters in each successive word. (For children, substitute “pepsicola” for “alcoholic”.)
NEXT. EINSTEIN Part II: A BUNDLE OF CONTRADICTIONS