PHYS 180 Ch 1 Special Relativity PDF

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Download PHYS 180 Ch 1 Special Relativity PDF

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Einstein developed the theory of special relativity in 1905, which was a new way of looking at space and time.

The nature of light ● Light has wave properties, and different wavelengths correspond to different colours. ● Regarding sound: when a radio produces sound, the air from the radio isn’t carried to one’s ears, but rather, the radio creates vibrations in the air that travel to one’s ears. Similarly, waves in the ocean don’t cause the water to move per se, but cause vibrations in the water. ● As one reaches the low-frequency end of the EMR spectrum, there’s an asymptotic decrease in energy that becomes virtually zero. Conversely, as one reaches the highfrequency end, there’s an asymptotic increase in energy that is beyond comprehension. ● Our eyes are the correct size to detect waves of visible light. To see radio waves, we would need eyes the size of mountains. Young’s Double Slit Experiment (1801) proved that light has wave properties. ● Had Young been firing particles through the slits, there should have been two small groups of particles hitting the screen, corresponding to each slit. However, an interference pattern was created, instead. ● Spots at which a peak and trough met caused destructive interference, since they cancelled each other out. Spots at which two peaks or two troughs met caused constructive interference, and were twice as bright. This pattern could be observed on the screen. ● (If we were to shine light on a sheet of paper with two holes, we would see to spots of light on the other side, since the holes we would make would be far bigger than the wavelengths of light.) ● Young’s experiment took place a full century before the theory of relativity was developed.

Monday, September 12, 2016 The modern theory of light was developed by James Clerk Maxwell in 1859 ● Maxwell developed four equations ● Maxwell realized that light is made of electromagnetic waves ○ Moving electric fields cause magnetic fields, and moving magnetic fields cause electric fields ○ This creates an infinite circular effect, where x causes y which causes x which causes y…. ● Maxwell also knew that the speed of light is constant ● Magnetic and electric fields are produced perpendicular to each other ●

Waves propagate in a medium (eg water, air); what is the medium for light? ○ The led to the theory of the Aether, which said that surrounding us everywhere, in empty space, is stuff called ‘the Aether’ ○ This also defines our ‘frame of reference’ for the velocity of light ○ Theory of the Aether; the Aether: ■ Permeates all of space (ie is everywhere) ■ Propagates light waves ■ Other things easily move through it, as if it’s not there ■ The Aether moves as a whole entity, and everything in the Universe (including the Earth and Sun) move through it; in the Spring, the Earth moves with the Aether, in the Autumn, it moves against it

The Michelson Morley Experiment (1887) tried to detect the Aether, and the velocity thereof ● Was conducted by Michelson and Morley ● Was the first experiment to determine the nature of empty space ● If the Aether were to exist and move, then the two beams of light should have reached the microscope detector at different moments ● In fact, the two beams of light arrived at the same time no matter what, so that the speed of light appeared to be constant for all frames of reference (ie regardless of where it’s moving with or against the Aether) Albert Einstein developed the theory of special relativity in 1905 ● Two postulates: a. The laws of physics are invariant in all inertial reference frames ■ It doesn’t matter if the Aether is moving; Maxwell’s equations have to hold true regardless of whether light is moving with or against the Aether b. The speed of light in a vacuum is a constant for all observers, regardless of the motion of the light source. ■ I.e. the speed of light doesn’t change with the motion of the emitter. Even if a car is moving towards a person with its headlights on, the light is still moving at the same speed as if the car had not been in motion.

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Einstein essentially postulated that there is no Aether, and that light is different from anything else, and always moves at a constant speed. Implications of special relativity: ● In order for velocity measurements to agree for light from all frames of reference, space and time must be relative. ○ Instead of the measured velocity depending on the observer, the measured time and length depends on the observer. ○ This is known as time dilation and length contraction ● (Supplementary reading: Brian Greene, The Fabric of the Cosmos) ● Time dilation (moving clocks run slow): t2 = t1 / (1-v^2/c^2)^½ ○ Time flows differently for different ‘observers’ ○ Depending on motion, clocks can tick slower, people can age slower, etc. ○ When velocity = c, then t2 = ∞, ie at the speed of light, time stops. In other words, light doesn’t experience time. ○ From our perspective, sunlight that we see is ~8 minutes old. But from the light’s perspective, it’s simultaneously at the Sun and on Earth. ● Length contraction (moving objects contract along a length of motion): ○ L2 = L1 / (1-v^2/c^2)^½ ● This gives rise to the concept of space-time ○ One’s velocity through spacetime is constant* ● Special relativity states that an object’s combined motion through space and time equals the speed of light. Thus, if something is moving through space, its motion through time must slow down. ○ Light goes through spacetime, but has a zero component of time Wednesday, September 14, 2016 ● Time dilation: v = d/t = c ○ If the velocity is always c, then as distance changes, so does time have to change Monday, September 19, 2016 ● GPS technology applies the theory of special relativity (and general relativity) ○ Three satellites use triangulation to determine one’s location ○ The key to GPS is time: one’s distance from each satellite is the speed of light times the time difference (ie the time light has been travelling) ■ Each satellite has an atomic clock, and sends out signals to indicate its time ○ The satellites are orbiting the Earth so fast that if special relativity weren’t taken into account, the atomic clocks therein would lose approximately seven microseconds in relation to clocks on Earth, each day. ■ This means that every day they would become less accurate by approximately two kilometres. ○ The signals that the satellites send out are radio waves, and thus travel at the speed of light....