Last night, I headed down to the beautiful Bell House, in the Gowanus section of Brooklyn, for this month's Secret Science Club lecture featuring Princeton University physicists Steven Scott Gubser and Frans Pretorius, whose latest book, The Little Book of Black Holes, is literally hot off the presses. The two doctors lectured in a 'tag team' style, taking turns at the microphone and occasionally engaging in physical demonstrations of concepts.
While setting up, Dr Gubser joked that, while living in a two-religion household is fine, living in a two-operating system is more difficult, so he made the switch from Linux to Apple at the behest of his brother-in-law. He then began the lecture by discussing time dilation- according to the Theory of General Relativity, time moves more slowly for a moving observer than for a stationary observer. He confessed that the demonstration would be 'slightly fake', because he's not the Flash and could not run near the speed of light, then the two demonstrated the Twin Paradox, as one ran across the stage and the other remained stationary. At the end of the jog, he joked that, at this pace, the jogger would be one femtosecond younger than the stationary observer. The Twin Paradox is not an optimal frame of reference, general relativity doesn't take into account acceleration, and the 'paradox' is a red herring- a better analogy is a pair of hypothetical light clocks, using a photon traveling between two sensors. The speed of light being constant, the photon of a moving time clock would appear to an outside observer to be moving on diagonals, moving a greater distance than a stationary clock:
At greater speeds, the photon would move greater distances. The photon trajectory forms a right triangle relative to the 'clock' and its trajectory, so the Pythagorean theorem can be used to derive the value of Tau (proper time). At any rate, a moving observer would experience slower time relative to a stationary observer.
The lecture then shifted to the subject of gravity. According to the Theory of General Relativity, gravity is a product of the curvature of space- mass bends space, and gravitational forces can also produce a time dilation, with time moving faster the further an observer gets from a source of gravitation. The mass of an object determines the degree to which it can curve space, and the good doctors displayed a graphic which contrasted the amount of curvature among different heavenly bodies, ranging from our sun to a white dwarf to a neutron star to a black hole. Each of these objects represents a degree of compression of mass- a white dwarf is the remnants of a star approximately the size of our sun compressed to a diameter of approximately a few thousand kilometers (thanks, Smut). A neutron star is the remains of a supermassive star which has collapsed under its own gravity- a star with two times the mass of the sun would collapse into a two-kilometer diameter. On Earth, gravitational time dilation effects GPS units.
Stellar black holes are stars which have collapsed into a small enough radius that they cause spacetime to undergo a gravitational collapse within a radius known as an event horizon. This collapse of spacetime is the ultimate expression of curvature, a condition in which a singularity is formed. The spacetime dilation at a singularity is infinite, a hypothetical clock would stop. The Schwartzschild radius is the radius at which a body's mass, compressed into a sphere, would result in gravitational forces which had escape velocities which exceed the speed of light. At the Schwarzschild radius, time dilation is reversed- a stationary observer would find that time moved slower than a moving observer would. One of the pillars of the Theory of General Relativity is that there's no such thing as gravity, just the movement of time in space.
At the event horizon of a black hole, the curvature of space becomes infinite in 'a nasty way'. Crossing an event horizon, an observer would experience an 'oh, damn, what do I do now?' moment. With the stopping of a clock at the singularity, escape would always be in the victim's future... there would be a spaghettification as a subject is stretched out by gravitational forces.
Einstein initially doubted the existence of black holes. As Carl Sagan quipped, extraordinary claims need extraordinary evidence. Evidence for black holes was circumstantial... observations of the center of the galaxy revealed that the stars were orbiting an object four million times the mass of the sun, but no such object was observed. Strong-but-circumstantial evidence pointed to the existence of a supermassive black hole at the center of the galaxy.
The way in which the waves chirped helped researchers infer the size of the black holes. If the collision of the two black holes had been visible, it would have outshone all of the stars for a fraction of a second.
The lecture was followed by a Q&A session- the Bastard did not have an opportunity to get a question in, but Drs Gubser and Pretorius fielded a wide variety of questions. A question about the evidence for relativity led to a discussion of the eclipse observations of bent light which resulted from gravitational effects. A question about GPS systems elicited response that the systems need to take time dilation into account. A discussion of pulsars, spinning neutron stars, revealed that they pulse at regular frequencies, so they are good clocks. A question about the fate of the universe elicited the response that time ends- relativity predicts its own demise, but that a collapse could possibly be followed by a re-expansion. A question about whether a racecar driver would age more slowly than an avid jogger was answered by the assertion that extreme velocities are needed to make an observable difference in aging. Another audience member asked about Hawking radiation- black holes emit dim and faint radiation, but it is swamped by the Cosmic Microwave Background Radiation. Asked about his 'fantasy' experiment, Dr Gubser answered that he would want a range of interferometers measuring a range of interference pattern up to the ten kilometer ranges, and more sensitive detectors. He also wanted to explore the analogs between black hole collisions and heavy ion collisions (PDF).
Once again, the Secret Science Club has dished out a fantastic lecture. Kudos to Margaret and Dorian, Drs Gubser and Pretorius, and the staff of the beautiful Bell House yet again.