The Einsteinian Universe

Transcription

1 1/13 (Wikipedia user MissMJ) The Einsteinian Universe Szydagis Photo of Albert Einstein circa Twentieth Century Fox, Planet of the Apes

2 Einstein s 1905 epiphany: c =?! 2/13 Recall Maxwell: his famed equations included a term for the speed of light (c) in several places But something didn t make any sense: this was the speed of light in what frame of reference? Not a variable! Perform this thought experiment: you are driving along in your car at 40 mph and catch up to another vehicle also moving at 40 mph. You will appear stationary to each other Einstein: so, why is there no such thing as frozen light? Galilean relativity (car example) and Newtonian physics clearly in contradiction with Maxwell s equations governing electricity and magnetism The solution: the speed of light must be the same in ALL reference frames (points of view) for all observers Space & time are two sides of same coin. Another view: time just 4 th dimension, on top of length, width, height

3 Far-reaching consequences Einstein s solution implied that the speed of light is the maximum speed for *anything* within our Universe There are subtle technicalities and exceptions we ll discuss later. Most importantly, information transfer limited 3/13 In order to forge a self-consistent picture (c a true constant), then as you approach light speed Outside observers see your length contracting They also see time moving more slowly for you You see the same thing happening, not to yourself (you feel no different), but to the external observers! Your apparent mass (really your kinetic energy, as you would not feel heavier ) increases (E = mc 2 ) Cannot accelerate past c, as would require an infinite force or amount of energy to do. Can only asymptote Aníbal Pées Labory

4 4/13 E = mc 2 What does it mean? If space and time are equivalent not completely independent as per common sense, could matter/energy be as well? Yes! One can think of matter as solidified energy (and energy as vaporized matter). Since speed of light c is a big number, that s a lot of energy that s stored in matter. Conversion of matter into pure energy is a really big deal Another great simplification, like treating time as another dimension was: the old principles of conservation of mass and conversation of energy are one and the same thing! Beautiful, symmetric. Mass (matter) can neither be created nor destroyed but can be changed into energy, and vice versa Originally could only change form (matter: solid, liquid, gas, plasma, quark-gluon mix; energy: kinetic, potential)

5 Particle categories in relativity 5/13 Bradyons (POSITIVE rest mass): speeds variable, slower than light (the default), all matter particles, like protons, neutrons, electrons, etc. Can travel faster than light when not in a vacuum, but in a particular medium though (water for instance) where n > 1. They then produce Cherenkov radiation (blue light) watch?v=pa0fmcv83nw Photons (ZERO rest mass, literal not small ): light travels at the speed of light, of course Any particle with zero mass *must* travel at c (whenever in vacuum). Cannot slacken Tachyons (NEGATIVE rest mass): existence never shown. A catch: you can travel faster than light if you always were Unable to slow down below light speed. In fact, always speeding up and losing energy that way, not gaining. Not very logical!

6 6/13 Special relativity: demonstration Two volunteers required! (Class participation credit) A traditional thought (gedanken) experiment Can generalize this to *all clocks*: time itself bending! Copyright 2015 Hackaday, Hack A Day, and the Skull and Wrenches Logo are Trademarks of Hackaday.com

7 7/13 The Twin Paradox (see Planet of the Apes screenshot from first slide) If one twin takes a trip to a distant planet on a rocket traveling close to the speed of light and returns to Earth, she will have aged less than her sister who had stayed behind. (There should be a visual difference in appearance). According to special relativity, that s the stationary sister s point of view, but according to the traveling twin, it s the other way around: her Earth-bound sister is the younger one! It s not really a paradox. The solution is that the traveling twin actually did age less (time passed more slowly for her relative to her sister). The trick is you need general relativity: the astronaut twin *accelerated* (changed velocity by slowing down and turning around) xigrimxreaperix

8 8/13 Special -> General Relativity Einstein generalized his theory of relativity to explain acceleration and gravity (and modern nav sats need it!) Special relativity, which we just covered, was worked out for straight-line, constant-speed paths. Limited utility First new theory of gravity since Newton centuries passed! If you are traveling at constant velocity (with no external points of reference like passing trees seen through a window), you cannot tell the difference between that and standing still (both cases are inertial reference frames) If you are accelerating OR in a gravitational field, you cannot tell the difference either, but it s definitely different than the zero/constant speed case above (these situations are called non-inertial reference frames)

9 Gravity: Force as geometry (GR) 9/13 Another class demo: geometry of space (two volunteers) Force of gravity no longer the spooky (abstract) action-at-adistance of Newton: masses just attract each other from afar Riemann metric tensors key, math from half-century earlier Space-time is shaped by matter-energy, which in turn affects underlying space-time (*the* Einstein equation) Starting with either, can find configuration match in other General relativity (GR) is predictive (remember: the hallmark of a good scientific theory), so this was not just idle speculation. Explained anomaly in orbit of Mercury (closest to Sun, gravity big) that Newton s math misses

10 Gravitational distortion of light (also apparent position without sun) Image credit: Francesco Iacopino of Learning is Beautiful. (apparent position during eclipse) Can get very complex: gravitational lensing (the Einstein lens): images of whole galaxies twisted into funny shapes, multiplied (1 st observed 1979) Starlight can get measurably deflected by an intervening large mass, like our Sun Light still always follows straight lines (geodesics), taking the shortest possible path in space and time (Fermat s principle) But *space itself* can be warped/curved A solar eclipse lets you see stars in daytime and prove this (Sir Arthur Eddington, 1919) 10/13

11 of the passage of time 11/13 Time passes more slowly closer to a gravitational field, viewed from afar You age more rapidly at the top of a skyscraper than at the bottom of it (though that is an extremely small effect non-scientific timepieces won t show) Verified with empirical measurements using vast distances and very precise clocks; easiest to see close to big mass More proofs of GR: Gravity Probe B (gravitomagnetism and frame dragging) caused by mass in motion, the Earth; gravitational redshift (light again), heavy binary stars, universe expansion Sears Tower, downtown Chicago

12 Conclusion & HW 12/13 Einstein s conception of the universe: still static His equations predicted an expanding or contracting universe (uncomfortable) He inserted a fudge factor (the cosmological constant, lambda) that he later called his greatest blunder Like Copernicus and his circles, just couldn t let go Quiz on this topic, relativity

13 The Worlds of Physics speed mass 13/13 Slow and big: Classical (Newtonian) mechanics, improved upon with General Relativity (GR) size Slow and small: Standard Model (SM) of particle physics, quantum mechanics (QM), atomic physics (AMO), nuclear physics Fast and big: Special Relativity (SR), GR (includes SR) if big Fast and small: High-energy physics (HEP) -- relativistic quantum mechanics (RQM) and quantum field theory (QFT) What combines all of them? A Theory of Everything, or GUT (Grand Unified Theory): string theory?