Lecture 8 61507 Astro 1001 Relativity Two kinds

Lecture 8 6/15/07 Astro 1001

Relativity • Two kinds: one with gravity (general relativity) and one without (special relativity) • Thought experiments play a critical role in understanding SR

Some Results • No information can travel faster than the speed of light • You would conclude that time runs more slowly for any person that is moving • Simultaneity doesn’t strictly exist • Something’s size changes as its speed changes • Mass changes as the speed changes also

What is Relative? • Motion is only relative – Moon vs Earth viewpoints • Only two facts (axioms) – The laws of nature are the same for everybody – The speed of light is the same for everybody • We have no common sense in the situations in which relativity is important

Some Basics • SR makes heavy use of reference frames – Two people share a reference frame if they are not moving with respect to one another • Speed of light axiom is somewhat surprising – Experimentally true

Thought Experiment 1 (page 415) • Jackie is moving away from you at 90 km/hr • Jackie has no reason to believe that she is moving – Jackie sees you moving away at 90 km/hr

Thought Experiment 2 (page 415) • Same as TE 1, but now you throw a baseball at Jackie at 100 km/hr • Jackie sees the ball coming at 10 km/hr towards her • Ball is moving at 100 km/hr according to one person, at 10 km/hr according to another

Thought Experiment 5 (page 416) • You are moving at. 9 c and shine a flashlight at Jackie – Would naively think that it approaches Jackie at. 1 c • Beam approaches Jackie at c

Thought Experiment 6 (page 418) • Image you are on a rocket traveling faster and faster: do you ever exceed the speed of light – In what reference frame? • Turn on headlights: lights are traveling away from you at c • Everybody else sees them moving away from you at c

Reference Frames and Distance (page 418) • Imagine you are throwing a ball up and down in a moving train – You see the ball go straight up and then come straight down • An observer by the side of the track sees the ball go up and down, but also sideways – Ball travels a greater distance in the same amount of time, so it appears to be moving faster

Thought Experiment 7 (page 419) • Jackie flashes a laser off of a mirror on the ceiling of her moving spaceship – The light appears to travel a longer distance to you – Light must be traveling at the same speed in both cases – Thus, time must be traveling slower in Jackie’s moving spaceship

Group Work • Jackie is now in a very long spaceship with a red light at one end a green light at the other. She is traveling past you at. 9 c. The lights both flash at the moment the middle of the spaceship passes you. What do you see, and what does Jackie see? What does this say about simultaneity?

Experiments • In 1887 Michelson and Morley showed that the speed of light is not affected by the Earth’s motion around the Sun. • Particle accelerators can demonstrate time dilation – Particles have known halflives, but those are modified by time dilation

Thought Experiment 12 • Jackie moves away from you at nearly the speed of light and both record each others movements – Jackie will say that you are moving in slow motion, you will say that Jackie is moving in slow motion • The book compares this to the Moon being up or down

On To General Relativity • If you send two people in exactly opposite directions, they will eventually meet since the Earth is round • If you send two people in space in opposite directions, they might meat because of gravity, or because space is curved

Major Ideas • The three spatial dimensions and the time dimension form a four dimensional spacetime • We can envision changes in the shape of spacetime by thinking of a rubber sheet

Ideas from GR • Gravity arises from distortions of spacetime • Time runs more slowly in gravitational fields • The universe has no boundaries or center, but it might have a finite volume • Large masses that undergo changes in structure or motion emit gravitational waves

Acceleration is Different • Acceleration causes forces, so you can tell who is accelerating and who is not • The effects of gravity are exactly equivalent to the effects of acceleration – Called the Equivalence Principle

Geometry • Consider the Earth’s surface: there is no such thing as a straight line on Earth • Great circles are the straightest possible path between two points on the Earth’s surface – Philadelphia to Beijing great circle does NOT just follow a line of latitude

Different Geometries • Flat geometry (Euclidean geometry) is what you learn about in high school • Spherical geometry is similar to that of the Earth’s surface • Hyperbolic geometry goes the opposite way and is shaped like a saddle

The Universe • The four dimensional universe has to have one of these geometries • The straightest possible path feels no force, but curved paths represent forces • Gravity curves spacetime, creating a force

Testing General Relativity • Mercury – Newton’s Laws incorrectly predicted the orbit of Mercury, while GR did it correctly • Gravitational Lensing – Uniquely predicted by GR – Observed in 1919 • Gravity Probe B

Weird Stuff • Gravitational Waves – Ripples in spacetime • Wormholes – Create lots of paradoxes

The Quantum Revolution • Protons, neutron, and electrons are not the most basic particles – Quarks and leptons • Antimatter is real • Four fundamental forces – Gravity, weak and strong nuclear, electromagnetic • All particles exhibit wave particle duality

Basic Properties of Particles • Most important properties are mass, charge, and spin • Spin is analogous to spin angular momentum – Used to describe angular momentum that belongs to particles inherently – Divides all particles into two groups: fermions and bosons – Spin can be orientated in different directions

Quarks • Six “flavors” of quarks: up, down, top, bottom, strange, and charmed • Different combinations of 2 or 3 quarks produce all of the fermions except for the leptons • Leptons are very small particles that appear to be fundamental – Electrons, neutrinos are the best examples

The Four Forces • Gravity – Weakest force by far – Works at very large distances • Electromagnetism – Important in biology and chemistry – Stays constant in strength • Weak Nuclear – Weak pretty much everywhere – Important in radioactive decays • Strong Nuclear – Exceptionally strong in atomic nucleus, weak everywhere else

The Uncertainty Principle • The more we know about where a particle is located, the less we can know about its momentum and vice versa • Example with electrons – If we use visible light, we can only pin its location to within 500 nm (5000 x the size of an atom) – If we use high energy light, we kick the electron too hard when we observe it

Wave Particle Duality • Particles don’t even really follow a specific path, their paths are smeared out • We can tell exactly (within the limits of the HUP) where a particle is when we measure it, but no idea what its doing when we aren’t observing it

Exclusion Principle • Simply stated: two particles can’t be in the same place at the same time – We use the phrase “quantum state” to describe the current conditions of an object – More precisely: two particles can’t occupy the same quantum state at the same time – Example: energy levels of an atom

Group Work • Determinism is the thinking that the universe can be predicted from its initial state. In what ways is quantum physics deterministic and in what ways is it not deterministic?

Quantum Tunneling • HUP means you can’t know exactly where a particle is – Maybe the particle will appear on the other side of a barrier • Seems silly, but its of critical importance – Many electronics rely on it – Many stars wouldn’t exist without it