Speed of Light and Black Holes Alfred Xue

Speed of Light  Its value is 299,792,458 meters per second

History of the Speed of Light  Galileo’s Simplicio, states the Aristotelian (and Descartes) position,  “Everyday experience shows that the propagation of light is instantaneous; for when we see a piece of artillery fired at great distance, the flash reaches our eyes without lapse of time; but the sound reaches the ear only after a noticeable interval.”

Galileo’s lanterns  In 1638, Galileo used a simple lantern set up to find that light traveled at a speed that was ten times faster than sound, concluding that “if not instantaneous, it is extraordinarily rapid”

Fizeau’s rotating wheel  1849  303,000 km/s

Foucault’s rotating wheel  299,796 km/s

Michelson Morley  1887  Wanted to prove the existence of luminiferours aether

Einstein’s influence  “light is always propagated in empty space with a definite velocity [speed] c which is independent of the state of motion of the emitting body.”  No absolute reference frame  Maxwell’s equations indicated that light was constant in all frames as well, which contradicted Galilean invariance

Conclusions from c  If the speed of light is constant then we have to create a new understanding of time and space.  Time-Dilation  Length Contraction  Relativity of Simultaneity

Time-Dilation

Length Contraction

Space-time diagrams

Twin Paradox  Jane and Joe are twins. Jane travels in a straight line at a relativistic speed v to some distant location. She then decelerates and returns. Her twin brother Joe stays at home on Earth. The situation is shown in the diagram, which is not to scale.  Joe observes that Jane's on-board clocks (including her biological one), which run at Jane's proper time, run slowly on both outbound and return leg. He therefore concludes that she will be younger than he will be when she returns. On the outward leg, Jane observes Joe's clock to run slowly, and she observes that it ticks slowly on the return run. So will Jane conclude that Joe will have aged less? And if she does, who is correct? According to the proponents of the paradox, there is a symmetry between the two observers, so, just plugging in the equations of relativity, each will predict that the other is younger. This cannot be simultaneously true for both so, if the argument is correct, relativity is wrong.

The Paradox resolved

Ladder Paradox  The paradox goes like this: let a long ladder fly lengthwise at great velocity past a normal garage. The proper length of the ladder is more than the length of the garage. Due to the length contraction of special relativity, the passing ladder can for an instant (or two) fit into the garage, as observed by the garage owner.  However, for an observer riding on the ladder, it is the garage that moves at high speed and is length contracted. For the ladder observer there is no way that the ladder can fit into the garage, even for the briefest of moments. Hence, the whole idea seems paradoxical.

A King and a Queen  A king and a queen are set to be executed, on two different planets, with the same blade. The blade is held and dropped from the center. A group trying to save the king and queen have devised a plan to save them both, splitting into two groups to stop each execution. The queen’s group will only react if they see that the King is saved. What happens?

Ladder Paradox Resolved  In the context of the paradox, when the ladder enters the garage and is contained within it, it must either continue out the back or come to a complete stop. When the ladder comes to a complete stop, it accelerates into the reference frame of the garage. From the reference frame of the garage, all parts of the ladder come to a complete stop simultaneously, and thus all parts must accelerate simultaneously.  From the reference frame of the ladder, it is the garage that is moving, and so in order to be stopped with respect to the garage, the ladder must accelerate into the reference frame of the garage. All parts of the ladder cannot accelerate simultaneously because of relative simultaneity. What happens is that each part of the ladder accelerates sequentially, front to back, until finally the back end of the ladder accelerates when it is within the garage, the result of which is that, from the reference frame of the ladder, the front parts undergo length contraction sequentially until the entire ladder fits into the garage.

 e.com/watch?v=o z5qa1tueYk  e.com/watch?v=3 pAnRKD4raY