Albert Einstein and 100 Years of Relativity Christopher M. Johns-Krull Rice University, Dept. of Physics and Astronomy October 17, 2016

The eternal mystery of the word is its comprehensibility The eternal mystery of the word is its comprehensibility. The fact that it is comprehensible is a miracle. -- Albert Einstein He actually first tried an offset circle. 2

The laws of physics are the same for all observers Special Relativity’s Postulates The laws of physics are the same for all observers The speed of light is the same for all observes He actually first tried an offset circle. 3

The Laws of Physics He actually first tried an offset circle. 4

Is the Speed of Sound Constant? He actually first tried an offset circle. 5

Is the Speed of Sound Constant? He actually first tried an offset circle. 6

The Speed of Light He actually first tried an offset circle. 7 By The original uploader was Stigmatella aurantiaca at English Wikipedia - Transferred from en.wikipedia to Commons., CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=22446309 7

Relative Speeds Change How They Add He actually first tried an offset circle. 8

Special Relativity

Faster than Light Travel – NO! He actually first tried an offset circle. 10

Time Dilation: Normal Objects Moving – Speed Changes He actually first tried an offset circle. 11

Time Dilation: Light Moving D = T x V V = D/T c = D/T He actually first tried an offset circle. 12

Time Dilation – Leads to Length Contraction Can measure distance with speed and velocity: D = T x V He actually first tried an offset circle. 13

Length Contraction

When Simultaneous Things Aren’t He actually first tried an offset circle. 15

And Mass Goes Up He actually first tried an offset circle. 16

Some Formulas He actually first tried an offset circle. 17

E = m c2 He actually first tried an offset circle. 18

Experimental Tests He actually first tried an offset circle. 19 By The original uploader was Stigmatella aurantiaca at English Wikipedia - Transferred from en.wikipedia to Commons., CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=22446309 19

Experimental Tests He actually first tried an offset circle. 20

Experimental Tests He actually first tried an offset circle. 21

We Can Kind of Do It! He actually first tried an offset circle. 22

Twin Paradox He actually first tried an offset circle. 23

But Motion is Relative He actually first tried an offset circle. 24

Working Through the Paradox 6.0 lyr away He actually first tried an offset circle. 25

Working Through the Paradox 6.0 lyr away At the start of the journey, your clocks are the same. Han Solo then accelerates to 0.6c and travels to the distant star at this speed. We will not worry about the details of acceleration or deceleration. On Earth you have a telescope that allows you to see Han’s closk, and he has one that allows him to see yours. He actually first tried an offset circle. 26

On the Way… 6.0 lyr away Han uses the length contraction formula and finds that the distance he has to travel is 4.8 lyr. γ = 0.8 and 6 * 0.8 = 4.8 He actually first tried an offset circle. 27

Han Arrives 6.0 lyr away Han traveled for 4.8 lyr at 0.6c and took 4.8/0.6 = 8 years You observe that he traveled 6.0 lyr at 0.6c and it took 6/0.6 = 10 years He actually first tried an offset circle. 28

Han’s Clock When He Arrives 6.0 lyr away Han records 8 years. You see 8 years on Han’s clock but 16 on yours – 10 to get there plus 6 for the light to get back to you. Han’s clock is running at ½ the speed of yours He actually first tried an offset circle. 29

Your Clock When Han Arrives 6.0 lyr away Han sees 8 years on his clock. Han sees 4 years on your clock because he is seeing yours as it was 6 years ago when he gets there. Your clock is running ½ the speed of Han’s. He actually first tried an offset circle. 30

Now Han Comes Home 6.0 lyr away Han’s clock goes from 8 to 16. Your clock goes from 10 to 20. He actually first tried an offset circle. 31

Now Han Comes Home 6.0 lyr away But you see Han’s clock go from 8 to 16 while yours went from 16 to 20, so you see Han’s clock running twice as fast as yours. He actually first tried an offset circle. 32

Now Han Comes Home 6.0 lyr away But Han sees your clock go from 4 to 20 while his went from 8 to 16, so Han sees your clock running twice as fast as his. He actually first tried an offset circle. 33

Working Through the Paradox 6.0 lyr away He actually first tried an offset circle. 34

Superluminal Motion M 87 He actually first tried an offset circle. 35

Simple Measure of Speed v = d/t

Superluminal Motion Explained He actually first tried an offset circle. 37

Moving to General Relativity He actually first tried an offset circle. 38

In Essence GR Works with Geometry He actually first tried an offset circle. 39

Is All Motion Relative? He actually first tried an offset circle. 40

It Can be Made to be! He actually first tried an offset circle. 41

The Equivalence Principle The effects of gravity are exactly equivalent to the effects of accelerations He actually first tried an offset circle. 42

The Equivalence Principle And its corollary He actually first tried an offset circle. 43

Spacetime instead of Space & Time He actually first tried an offset circle. 44

A Spacetime Diagram He actually first tried an offset circle. 45

A Spacetime Diagram He actually first tried an offset circle. 46

More Worldlines He actually first tried an offset circle. 47

More Worldlines He actually first tried an offset circle. 48

Shortest Distance – Straight Lines He actually first tried an offset circle. 49

Shortest Distance – Straight Lines He actually first tried an offset circle. 50

Shortest Distance on a Sphere He actually first tried an offset circle. 51

Shortest Distance on a Sphere He actually first tried an offset circle. 52

The Geometry of the Universe He actually first tried an offset circle. 53

“Straight” Lines in Curved Spacetime If you are floating freely, then your worldline is following the straightest possible path through spacetime. If you feel weight, then you are not on the straightest possible path. He actually first tried an offset circle. 54

What is an Orbit? He actually first tried an offset circle.

A New Understanding of Gravity

An Orbit is a Straight Path Through Curved Spacetime He actually first tried an offset circle.

A New Understanding of Gravity