The Search for a Fundamental Theory of the Universe

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Roberta Chambers
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1 The Search for a Fundamental Theory of the Universe Lecture 1- History & basic concepts, including Newton, Maxwell, Einstein & Quantum Mechanics Lecture 2 - Where are we now? General relativity & the Standard Model of particle physics Lecture 3 - Where are we going? Quantum Gravity, Supersymmetry, String Theory& Extra Dimensions 1

2 Fundamental questions in physics involve both the very small and the very big. What are nature s smallest building blocks? How do these building blocks interact in order to build up the world as we experience it? What laws govern the evolution the Universe as a whole? How did the Universe begin? Did time & space exist before the big bang? How did it get to look the way we see it, with galaxies, clusters and superclusters of galaxies? Will it have an end? 2

3 What experimental tools do we use to study these questions? 3

4 To study the very small - we smash things into the smallest possible bits. We call these smallest bits elementary particles. At Fermilab, near Chicago, protons & anti-protons circulate in opposite directions around the main ring at nearly the speed of light. They collide at two interaction points, where large detectors analyze what results from a collision. 4

5 The CDF detector at Fermilab weighs 100 tons and contains many layers of instrumentation to record and study the particles shooting out from the interaction point 5

6 A single collision event in the CDF detector. Each track represents the path of a particle produced in the collision. 6

7 A cartoon version of this same event. We ll learn about all these particles in lecture 2. 7

8 To study the very big we use telescopes and satellites of various sorts WMAP Satellite 8

9 The WMAP satellite makes precision maps of the Cosmic Microwave Background Radiation, a remnant of the hot big bang that fills the universe. 9

10 The colors indicate hot and cold spots in the 2.73K CMB. The lines represent polarization of the CMB. This data gives cosmologists a view into the very early universe. 10

11 A Brief History of Fundamental Physics 1. Isaac Newton & Gravity 2. Maxwell & Electromagnetism 3. Einstein & Special Relativity Focus on a series of puzzles & quandaries 4. Quantum Mechanics 11

12 Sir Isaac Newton ( ) The founder of modern physics 1. Calculus 2. Laws of Motion 3. Gravity 12

13 Newton wanted to know how things moved What makes them follow the paths they do, and not some other paths? For everyday objects? And in the heavens? 13

14 In order to study motion, Newton first had to make great advances in mathematics! The natural philosopher Descartes had taught how to describe positions mathematically. Use 3 coordinates (x,y,z) to specify the position of an object in space - Cartesian Coordinates 14

15 TO DESCRIBE MOTION, WE NEED A 4TH COORDINATE - TIME The path of an object is given by its cartesian coordinates as a function of time - x(t), y(t), z(t) r v = dr x dt Newton went on to invent calculus to Mathematically tackle the problem of motion 15

16 A very brief introduction to calculus. Velocity is the rate of change of position with time. For example - the Ford Model T could go about 40 miles/hour. Acceleration is the rate of change of velocity with time. For example - A cheetah can accelerate from 0 mile/hour up to 50 miles/hour in 3 seconds 16

17 Equipped with the tools of calculus, Newton was able to formulate his famous law of motion. F=ma Force = (mass) x (acceleration) 17

Newton found that elliptical orbits result if the sun exerts a force on the planets that follows an inverse square law.

18 Newton s Law of Gravity - the first landmark in fundamental physics. Kepler discovered that planetary orbits are ellipses, with the sun at one focus. Newton found that elliptical orbits result if the sun exerts a force on the planets that follows an inverse square law. From the moon s orbit around the earth and the known radius of the earth, Newton calculated the gravitational acceleration at the surface of the earth... how fast things accelerate when they fall! Newton had shown that physics is the same on the earth and in the heavens! 18

19 The next great landmark in fundamental physics James Clerk Maxell ( ) & Electromagnetism Besides gravity which holds us to the earth, E&M is the most influential force in our day to day modern life. 19

. and also a very important force at the

20 . and also a very important force at the microscopic level Atoms are held together by the attractive electric force between positively charged nuclei and negatively charged electrons We are also familiar with magnetic fields in various forms.. 20

21 Maxwell s 4 equations give a unified description of electric and magnetic phenomena Electric currents - moving charges - produce magnetic fields. Electromagnets. Changing magnetic fields produce electric fields 21

22 Maxwell found that his equations have wave solutions that move at a fixed speed.. When he calculated that speed, he found it was the speed of light! c = 3x10 8 m / s 22

23 Maxwell s electromagnetic theory of light was a tremendous achievement, but it also had some unsettling aspects. In Maxwell s theory all observers measure the speed of light to be the same, independent of their own velocity. If you run fast enough, you can catch a train - but you can never run fast enough to catch up with light! THIS IS NOT HOW THINGS WORK IN NEWTONIAN PHYSICS!! IF YOU RUN FAST ENOUGH YOU CAN ALWAYS CATCH UP. 23

24 Einstein took this theoretical puzzle very seriously and the result was his theory of Special Relativity. The basic postulate that the speed of light is the same for all observers has many interesting consequences.. Different observers will disagree about lengths and time intervals - length contraction & time dilation. Twin paradox - if one twin stays on earth and the other goes off on a rocket ship at very high velocity and then returns, then when they meet again, the one who stayed will be older Strange but true. 24

25 These effects are only important near light speed, which is why we don t notice them in our everyday lives. Einstein s boldness of thought told him they must be real nonetheless The predictions of special relativity have been verified to high precision in particle physics experiments, where velocities do come close to the speed of light. 25

26 other important consequences. Nothing can move faster than light! Physicists call this causality, because faster than light travel is equivalent to moving backwards in time! The equivalence of mass and energy, which yields a great deal of important physics and also physics most famous equation! A heavy nucleus can split into two lighter bits with energy left over.. Nuclear Fission Two light nuclei can join into a heavier nuclei with energy left over.. Nuclear Fusion 26

27 The early part of the 20th century was a busy time for physicists. THERE WERE MANY TROUBLING QUESTIONS ABOUT MICROSCOPIC PHYSICS, LIKE WHY IS THE ATOM STABLE? The atom is pictured as a nucleus surrounded by orbiting electrons, but according to Maxwell s E&M the electrons should radiate and lose energy. Atoms should decay.but they don t! 27

28 Physicists took this very seriously. The theoretical resolution they devised is known as Quantum Mechanics. QUANTUM MECHANICS, OF COURSE COMES WITH ITS OWN UNSETTLING ASPECTS THAT HAVE CHANGED OUR FUNDAMENTAL UNDERSTANDING OF NATURE... 28

THREE EXAMPLES 1) Heisenberg Uncertainty Relation: In quantum mechanics, one cannot know both the position and the momentum of a particle to high accuracy.

29 THREE EXAMPLES 1) Heisenberg Uncertainty Relation: In quantum mechanics, one cannot know both the position and the momentum of a particle to high accuracy. If one knows the position to very high accuracy, then the momentum is very uncertain, and vice-versa. Planck s constant is small enough, that these uncertainties are important only for very microscopic objects Planck s Constant!p!x " h 2# 2) Probabilistic nature of quantum mechanics: In Newtonian physics, if we know where an object is, how fast it s moving and the forces acting on it, then we can predict exactly where it will be in the future. In quantum mechanics, we can only predict a probability distribution for where it will be in the future. 29

3) The dual wave nature of matter: All objects have a natural quantum mechanical wavelength, known as the debroglie wavelength, that is inversely

h = Planck s constant p = momentum One can observe interference patterns in the scattering of small particles like electrons.

30 3) The dual wave nature of matter: All objects have a natural quantum mechanical wavelength, known as the debroglie wavelength, that is inversely proportional to the object s momentum. h = Planck s constant p = momentum One can observe interference patterns in the scattering of small particles like electrons. For macroscopic objects the debroglie wavelength is unobservably small. The debroglie relation is enormously important. It tells us that high momenta, or equivalently high energies, can be used to probe short distance scales. This is what happens at high energy accelerators. Wave Interference 30

What is the 'cosmological principle'?

What is the 'cosmological principle'? Modern cosmology always starts from this basic assumption the Universe is homogeneous and isotropic. This idea seems strange there's empty space between me and the