The story of Relativity

1. The story of Relativity WHS Honors Physics Spring, 2011

2. Before we begin • Most of what we will discuss goes against “common sense”. If you accept Einstein’s ideas, it will dramatically change the way you view reality • That said, Einstein’s predictions have been validated and tested to unimaginable precision. Without his theories, we wouldn’t have GPS, along with many other recent technological luxuries. • Claiming you don’t “believe” Einstein’s relativity places the burden of proof on you. Whether or not it defies your intuition is irrelevant when compared to the immense body of scientific study that’s validated its merit.

4. Two Great Revolutions for the New Physics • Quantum Mechanics and Relativity • The latter, exclusively due to the work of Einstein, deals with space, time, and motion. Its consequences are just as baffling and profound as the quantum theory, and challenge many of our old notions about the nature of the universe.

5. Two Theorys • Special Relativity • Time is NOT absolute. Your watch ticks at a different rate than mine • Spacetime is a “fabric”, and time and space can be thought of as “intertwined” • Everything moves at light speed. • General Relativity • Einstein’s famous equation • Spacetime curves and warps in response to gravitational fields

6. Space, time, and the eye of the beholder • 1905 • A 26-year old patent clerk sends a paper he has written in his free time to the German “Annals of Physics”, a publication ran by Max Planck, one of the most famous scientists in the world • Upon finishing the paper, Max Planck realized that classical physics had been overthrown

7. Physics at the time of Einstein • NEWTON • Still professed as the “king of physics” • Laws of motion and gravity were accepted as absolute • JAMES MAXWELL • Discovered electromagnetism • Discovered that EM waves never slow down, never speed up, and always travel “light speed”

8. Albert Einstein • In his teens, Einstein began pondering a simple question: • What happens if you chased after a beam of light at light speed?

9. Intuition and It’s Flaws • Example: You are driving • From your perspective, the trees and houses outside your car are moving. However, a hitchhiker on the side of the road sees them as standing still • From your perspective, your hood and dashboard are motionless, but from the hitchhikers perspective they are moving.

10. So what? • Observers in “relative motion” will have different perceptions of space and time • As we will see, your stereo clock ticks more slowly than this wristwatch, and your car looks compacted (or, more specifically, shorter) to him as you drive by. • This fact is not a flaw in measurements or your watches. This is a fact of the universe! • See illustration on page 845 of your book

11. Why don’t we “see” and “feel” relativity? • Relativity depends on how fast an object (or person) moves • For the speeds of cars, planes, or even spaceships, these effects are miniscule and hardly even detectable. • Clever experiments have proven relativity to be one of the most monumental properties of our universe • Let’s read sample story ONE…Ty and Garrett go super-charge a camaro

12. The Principle of Relativity • Two simple structures form the foundation of special relativity • The properties of light • Light ALWAYS travels at 299792458 m/s, regardless of reference frame! • Who or what is doing the measuring? • We call this the “Principle of Relativity” • All laws of physics are the same for all observers, regardless of reference frame. • Read sample story TWO

13. The Speed of light • Contrary to our claim that there is no meaning to the statement “Cheryl is traveling 10 miles per hour”, light always travels 670 miles per hour, regardless of benchmarks for comparison! • Read sample story THREE

14. Truth and consequences • Speed is a measure of how far an object can travel in a given duration of time • If a car goes 65 mph, it would travel 65 miles in one hour. Similarly, it would travel 130 miles in two hours. • Distance is a notion about space, or how much space there is between two objects • Duration is a notion of time, or how much time passes between two events

15. The effect on time (Part I) • The speed of light can easily show us that our everyday conception of time is wrong. • TIME IS NOT UNIVERSAL! • Simultaneity depends on the motion of the observer, and is NOT absolute • Read sample story FOUR

16. The effect on time (part II) • It’s hard to define time • Attempts in dong so usually invoke the word time itself • Some might try to define time as being measured by clocks…but this shifts the burden to defining a clock. • We shall define a clock as an object that displays perfectly regular cycles

17. TIME • “Regular cycles of motion” require equal time durations. • Our goal is to understand how motion affects the passage of “time”. • Under constant motion, we will consider simple “ticking light clocks”. These clocks are highly accurate and easily explainable, being as they involve just two mirrors and a photon.

18. The Light Clock • If a photon bounces back and forth one billion times in a second, we can time events based on how many times the light bounces back and forth. • If a horse starts and finishes a race in 55 billion cycles, it took 55 seconds to cross the finish line. • If Leo fell asleep during notes today in 120 billion cycles, he fell asleep in 2 minutes

19. But what if the light clock is in motion? • Notice that if our light clock moves eastwest, the photon moves too. Because it is moving NorthSouth as well as EW, it must travel further to complete one cycle. This slows the clock.

20. Suppose our "light clock" were traveling sideways at a very high (but constant) speed. Now the photons would follow the "saw tooth" path shown on the right side of the drawing. The light must travel a greater distance now to make a round trip. Since its speed is the same as before (remember, the speed of light is not changed by the speed of its source), it will take longer to make a round trip.

21. Life on the run? • So, if moving fast makes time tick slowly, can I live longer going faster? • Well, yes AND no • You will live longer, but you will also be living in slow motion relative to others. Let’s say a stationary person can read 100 books in a lifetime. You would also read 100 books in your lifetime because everything you do in your reference frame will be at a slower rate according to a stationary observer, including your rate of reading.

22. So, who’s moving, anyway? • You may have noticed that reversing the roll of who is watching reverses the image of who’s clock is ticking slower… • With all the seeming paradoxes in relativity, we gain a great deal of insight into the workings of the universe. • Read Sample Story FIVE

23. Motion’s effect on space • As you saw in Ashley and Cheryl’s example, time is affected by motion. We will now see the effect that motion has on time. • Read Sample Story SIX

24. The sharing of motion through dimensions • Let’s consider three dimensions • The corner of Wentworth and Halsted, 8th floor…three dimensions in real-life. • Everything around us is aging, moving from one moment in time to the next (Einstein and many other physicists think of time as the 4th dimension) • Remember, time doesn’t “move”, just like spatial dimensions don’t move. • We move through THEM, but they don’t move!

25. Einstein’s bold claim • Every object travels through space-time at the speed of light • It’s combined speed through all four dimensions will equal exactly that of light • This one fixed speed can be shared between dimensions

26. How Space-time works • As you sit motionless in your chair, all of your movement through space-time is in the TIME dimension (your time ticks away as fast as it can here on Earth) • As you run about half the speed of light, half of your speed is taking place in 3-D space, while half is in time (your clock ticks twice as slow as someone not moving) • Light, which clearly moves light speed, has ALL of it’s speed through space-time locked up in motion, and because of this light does not experience time!

27. About light… • Light never “ages” • A photon that emerged at the big bang is the same age today as it was when it was created. • There is no passage of time at light speed. Time can be thought of as forever frozen at that rate. • The age of light is a universal minimum (0) while something not moving at all ages at a maximum rate.

28. What E = mc2 says about motion • The higher the mass of a particle, the more energy it has, and vice versa. • The faster something moves, the greater its energy (Think of the KE equation) • Objects moving extremely fast become more massive, and hence harder to get going faster

29. It’s fun to think about traveling light speed, but… • It’s easy to accelerate a shopping cart, but harder to accelerate a truck. • According to Einstein’s famous equation, the faster something gets, the more it weighs, and the harder it becomes to make it go faster. • In fact, you can never pass the speed of light because the weight of the object moving will approach infinity!! Nothing can travel faster than the speed of light.

30. Part II General Relativity …if you thought Special Relativity was stupid…this will be REALLY exciting!

31. Through special relativity, Einstein realized that Newton’s idea that you could “catch up” to a ray of light was wrong. Newton’s law of universal gravitation seemed to have been violated. For the next years, Einstein nearly drove himself mad through his constant work and study. Finally, Einstein’s “GENERAL THEORY of Relativity” was born, and this theory revolutionized our understand of space and time by showing how they warp and distort to communicate the force of gravity.

32. Newton’s Perspective on Gravity • Everything exerts gravitational force on everything else. Regardless of physical composition, every object in our universe exerts an attractive gravitational force on everything else. • Every object exerts AND feels the force of gravity. • The gravitational force is communicated instantaneously, according to Newton.

33. Newton’s Law of Gravity • Gravitational force between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. • Newton’s law successfully predicted orbits, baseball flights, cliff divers, and apples falling. • It’s important to know that Newton wasn’t technically “wrong”. His laws were just an incomplete description of nature! • Einstein’s new discoveries proved to be more accurate representations of the universe.

34. Relativity vs. Newtonian Gravity • Special relativity is built on the fact that light sets the absolute speed barrier. • This also applies to signals (cell phones and radio waves) just as much as particles • Nothing truly occurs “instantaneously”, and signaling always requires a time lag • Things can go slower than light, but nothing goes faster.

35. The flaw of Newtonian Gravity • According to his equation, if the separation between two objects changed, they would instantaneously feel a change in their mutual gravitation. • For instance, if our sun exploded… • Earth, which is 93 million miles away, would instantly be thrown out of orbit. Although light and signals would take nearly nine minutes to reach us, Newton claimed we would instantly lose orbit. • Einstein knew that information cannot travel faster than the speed of light. A tree cannot be heard hitting the ground before it actually hits it!

36. Newton’s Embarrassing Secret • Newton developed equations that predicted gravitational attraction, but he never actually offered insight to HOW it works or WHAT it is. • His equation was like the “Owners Manuel”, but he left the inner workings locked up in the “black box”.

37. Einstein’s Happiest Thought • In 1907, while sitting at his patent clerk desk, Einstein had an idea. He fully explained “constant-velocity” motion, as we talked about during our special relativity examples 1-6. But what about ACCELERATED motion? Perhaps this troubled you…once again, we shall turn to an example! • Read Sample Story SEVEN!

38. Acceleration • The force of gravity is indistinguishable from the force of acceleration. • When adjusted properly, you could not tell the difference between a rocket accelerating at 9.8 m/s/s and the Earth pulling down on you at 9.8 m/s/s, assuming you did not know the direction you were facing.

40. DISCUSSION: Consider a universe in which the speed of light is just 4.0 mph (typical walking speeds). How would the laws of physics change? When Done: Quietly read sample story 7 Today: 1) Finish Notes 2) consider the justification of invariance 3) math WS

41. The essence of Relativity • Special: • The laws of physics appear identical to all observers undergoing constant-velocity motion • When in motion relative to another, your experiences in spacetime are NOT on equal grounds!!! • General: • There is no difference between an accelerated vantage point WITHOUT a gravitational field and a non-accelerated vantage point WITH a gravitational field • Gravity and acceleration are the same thing! • All observers, regardless of their state of motion, may claim that they are at rest while the rest of the world moves by them, so long as they include a suitable gravitational field in the description of their surroundings.

42. The stronger the gravity, the more time-warping that occurs. The more time-warping, the more slowly time progresses. • What happens to time near a black hole?

43. Acceleration and the warping of space-time • Recall that an object is “accelerating” if its speed or direction is changing. • We will consider DIRECTIONAL change, as in circular motion • Think of the “Gravitron Ride” at the amusement park. • A circle drawn on a sphere (3-D) will have a shorter circumference than a 2-D “Greek circle”.

45. The Moral to Acceleration and space… • The familiar geometric relationships established by the Greeks hold true on paper, but in our universe, accelerated motion curves space-time 3-D • Einstein now had a description of gravity (something Newton could not achieve), and it was visual as well as theoretical

46. The inaccuracy of “bowling ball” visualization • When the sun causes the fabric of space to be warped, it really does not pull downward, as the image shows. There is no Earth-like gravity working on the sun.

47. Experimental Verification of G.R. • During an eclipse, Einstein predicted that we could see light being bent around the sun’s gravitational field from a distant star.

48. Our stunning conclusions • The theory of GR has brought about one of the most dramatic upheavals ever to occur in our understanding of the universe. • Space and time, long considered to be a simple fixed background for all events, are now seen as dynamic, curving and changing in response to the matter and energy within them.

49. The “Cone of Causality” • Think of the future as being the top cone and the past as the bottom cone • Only so many past events could “cause” what we see now • What we do this moment can only affect so much of the spatial expanse • Imagine light speed as the “edge” of the cones

50. Quantum Theory and Relativity • Taken together, these two theories—GR and quantum mechanics—form our best current understanding of the physical laws of the universe. • The problem is that you can't mathematically merge them together. • Every attempt that has been made so far to reconcile the geometric view of space-time in GR with the fuzziness of quantum mechanics has led to contradictions. • The search for a single theory that could bring these two pieces together—a theory of quantum gravity—occupied Einstein for much of his life and is still one of the greatest outstanding challenges in science today.