The Einsteinian UniverseSzydagis 02.09.2015

Photo of Albert Einstein circa 1916.

1/13

(Wikipedia user MissMJ)

Twentieth Century Fox, Planet of the Apes

Einstein’s 1905 epiphany: c = ?!Recall Maxwell: his famed equations included a term

for the speed of light (c) in several placesBut 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 magnetismThe solution: the speed of light must be the same in ALL

reference frames (points of view) for all observersSpace & time are two sides of same coin. Another view:

time just 4th dimension, on top of length, width, height

2/13

Far-reaching consequencesEinstein’s solution implied that the speed of light is

the maximum speed for *anything* within our UniverseThere are subtle technicalities and exceptions we’ll

discuss later. Most importantly, information transfer limited

In order to forge a self-consistent picture (c a true constant), then as you approach light speed…Outside observers see your length contractingThey also see time moving more slowly for youYou 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 = mc2)

Cannot accelerate past c, as would require an infinite force or amount of energy to do. Can only asymptote

Aníbal Pées Labory

3/13

E = mc2 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)

4/13

preventionofdiscontent.tumblr.com

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)

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!

Particle categories in relativity

https://www.youtube.com/watch?v=pa0Fmcv83nw

5/13

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

6/13

The Twin “Paradox”

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

7/13

(see Planet of the Apes screenshot from first slide)

Special -> General RelativityEinstein 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 utilityFirst 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)

8/13

http://onlinephys.com/relativity.html

Gravity: Force as geometry (GR)

Another class demo: geometry of space (two volunteers)

Force of gravity no longer the spooky (abstract) “action-at-a- distance” of Newton: masses just attract each other from afarRiemann 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

9/13

Gravitational distortion of light

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)

Image credit: Francesco Iacopino of Learning is Beautiful.

Can get very complex: gravitational lensing (the Einstein lens): images of whole galaxies twisted into funny shapes, multiplied (1st observed 1979)

(also apparent position without sun)

(apparent position during eclipse)

10/13

…of the passage of timeTime passes more slowly closer to a

gravitational field, viewed from afarYou 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

http://25.media.tumblr.com

11/13

Sears Tower, downtown Chicago

Conclusion & HWEinstein’s conception of the

universe: still staticHis 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

Read about the discovery he was wrong (course site)

Work on written homework 3

Start studying for this Friday’s class-long test!!

12/13

The Worlds of Physics

Slow and big: Classical (Newtonian) mechanics, improved upon with General Relativity (GR)

Slow and small: Standard Model (SM) of particle physics, quantum mechanics (QM), atomic physics (AMO), nuclear physics, quantum field theory (QFT)

Fast and big: Special Relativity (SR), GR (includes SR) if big

Fast and small: High-energy physics (HEP), relativistic quantum mechanics (RQM) and field theory

What combines all of them? A “Theory of Everything,” or GUT (Grand Unified Theory): string theory?

massspeed

size

13/13