Admin. 11/2/17 1. Class website http://www.astro.ufl.edu/~jt/teaching/ast1002/ 2. Optional Discussion sections: Tue. ~11.30am (period 5), Bryant 3; Thur. ~12.30pm (end of period 5 and period 6), start in Pugh 170, then Bryant 3 [if just a small group we move to my office - 302 Bryant]. 3. Office hr: Tuesday 12.30-1pm; Wed. 12.30-1.00pm, Bryant 302 (but email me if coming on Wed.). 4. Homework 9: is due Fri. Nov. 10th 11.59pm via Canvas e-learning under Quizzes 5. Reading this week: Ch. 0, 1, 2.1-2.7, 3, 4.1-4.3, 5-10, 13, 14 6. Midterm 2: results via Canvas e-learning soon. 7. Observing project deadline: extended to Thur. Nov. 2nd 2017 8. Email me Astro-news, jokes, tunes, images: ast1002_tan-l@lists.ufl.edu 9. Printed class notes? Name tags? Space and Time Before Einstein Galileo and Newton Space and time are absolute same grid independent of velocity Velocities simply add together Nolan sees the ball going 50+40 feet/second 0 Position 10 9 8 7 6 5 4 3 2 1 0 Event #1 1 2 3 4 5 6 7 8 9 10 Time Event #2 Key Concepts: Lecture 28: Relativity Special Relativity The Problem with Light General Relativity Falling into a Black Hole Speed of light Galileo tried to measure it - by timing a light flash Danish astronomer Olaus Roemer (1675) - Timing moons of Jupiter Americans Michelson and Morley (1887) The speed of light is the same no matter how fast the observer is moving: EXPERIMENTAL RESULT
Michelson-Morley Experiment Einstein s Special Relativity Velocities do not simply add Light must appear to move at the same speed! Space and time are relative Distances between and times of events must be different as viewed by different moving observers. Einstein s Special Relativity -1905 Special relativity only applies for situations with no acceleration An inertial reference frame First Postulate The physical laws of nature are the same in every inertial reference frame First stated by Poincaré (1898, 1904) Second Postulate The speed of light is the same in every inertial reference frame Space-Time Time can be considered as a natural dimension, like the 3 dimensions of space the 4 th dimension The distance between events in space-time will change depending on how fast you move! Space and time are Relative, not absolute
An Example: a light clock A parked train Light moves up and down in the same amount of time for each observer Consequences of Special Relativity Contraction of space A moving object will appear shorter in its direction of motion Something moving at the speed of light would appear to have zero length A moving train Light moves further as seen by the stationary observer Consequences of Special Relativity Time Dilation (slowing of time) A clock will appear to tick more slowly on a moving object At the speed of light a clock will seem to stop Time/Time(rest) 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 V/C The Twin Paradox You fly off in a space rocket at 99% of the speed of light to visit a star 100 light years away, while your twin stays on Earth. After a short stay of a few days, you return from the star at the same speed. What do you find when you return to the Earth? (answer discussed in class).
Another consequence of special relativity Mass and Energy Mass and energy are the same things A little mass can be converted into a lot of energy Energy can be converted to mass E=mc 2 The General Theory of Relativity General Theory of Relativity (1916) Einstein wanted to understand how gravity affects light A new theory to explain gravity not as a force but rather as the curvature of space-time The Principle of Equivalence You can not tell the difference between acceleration and gravity Acceleration by gravity is independent of the mass being accelerated The Cosmic Speed Limit Einstein s Universe As an object moves faster its energy increases It behaves as if it is more massive It becomes harder to accelerate At the speed of light its mass becomes infinite It will require infinite force to accelerate it Nothing can go faster than the speed of light Mass/Mass(rest) 21 19 17 15 13 11 9 7 5 3 1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 V/C Newton s notion of space Is an absolute grid of coordinates Einstein s notion of space Space describes the motion of objects with no forces on them Space is altered by matter
Curved 2D Space Tests of General Relativity Bending of star light by the Sun s mass May 29, 1919 Solar eclipse Precession of Mercury s orbit Due to strong curvature of space near the Sun Gravitational redshift Stronger the gravity the slower the clock Tested by clocks in buildings & space Gravitational Lens
An Object Falling Into a Black Hole -Time appears to slow down for an object in a strong gravitational field. At the event horizon, time appears to stop, as viewed from outside. -Light from the object falling into the black hole gets redshifted further and further to longer wavelengths. Photons emitted from the event horizon are infinitely stretched out: infinite wavelength, zero energy, impossible to detect. Tidal Shredding Near Black Holes Strength of gravity depends on distance as 1/r 2 If you were to approach a black hole feet first, your feet would be pulled more strongly than your head. Near a black hole this difference in force can be enough to stretch you out, into something resembling spaghetti Dropping a clock into a Black Hole Black Holes What if remnant mass > 3 M sun? Neutron pressure can not hold it up Collapses even further Escape velocity is greater than speed of light Density is so high even light cannot escape light & matter go in but they don t come out Essentially completely cutoff from our universe
Black Holes Schwarzschild Radius is where the escape speed = speed of light Event Horizon is a sphere of radius = Schwarzschild radius For 3M sun core this is 9km General Relativity predicts there is a singularity inside the event horizon density and gravity become infinite Laws of physics break down - need new physics Worm holes? New matter? Causality violated? Energy conservation violated? Interstellar video Supermassive Black Holes Gravitational Waves video
Astronomy Picture of the Day Feb. 11th 2016 LIGO Detects Gravitational Waves from Merging Black Holes