# Introduction: what is quantum field theory?

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Introduction: what is quantum field theory? Asaf Pe er 1 January 13, 2015 This part of the course is based on Ref. [1] 1. Relativistic quantum mechanics By the mid 1920 s, the basics of quantum mechanics were already discovered by people like de Broglie, Bohr, Schrödinger, Pauli and Heisenberg. However, in its basic form, quantum mechanics is inconsistent with the already known theory of special relativity. Therearevariousways toseethis: for example, theamplitudefor afreeparticletopropagate from x 0 to x is U(t) = x e iht x 0, (1) which is nonzero for all x and t, indicating that a particle can propagate between any two points at arbitrary short time; this is in contradiction, of course, to the requirement set by special relativity, that nothing travels faster than the speed of light, c. Thus, Schrödinger equation needs to be replaced by a relativistic equation (known as Klein-Gordon equation). A different, yet related question is the question of particle interaction. Schrödinger equation, for example, explains how a single particle evolves under the influence of an external potential; however, it does not describe interactions between particles, such as electronphoton scattering (Compton scattering), or the production of new particles that take place when relativistic particles interact. A classical example is the prediction of the anti-electron particle (the positron) by Dirac in 1928, that results when two energetic photons interact (γ +γ e + +e ). The positron was discovered by Anderson in In following years, a plethora of new particles were discovered. 2. The electron-photon duality The concept of wave-particle duality tells us that the properties of electrons and photons are fundamentally very similar. Despite obvious differences in their mass and charge, under the right circumstances both suffer wave-like diffraction and both behave like particle. 1 Physics Dep., University College Cork

2 2 Yet the appearance of these objects in classical physics is very different. Electrons and other matter particles are postulated to be elementary constituents of Nature. In contrast, light is a derived concept: in classical EM, the fundamental entities are the electromagnetic fields. Maxwell thought of photons as a ripple of these fields. Ifphotonsandparticlesaretruelytobeplacedonequalfooting, howshouldwereconcile this difference in the quantum world? One possibility is that we view particle as fundamental, with the electromagnetic field arising only in some classical limit from a collection of quantum photons. Alternatively, we may consider field as fundamental, with the photon appearing only when we correctly treat the field in a manner consistent with quantum theory. In this case, we may want to introduce an analogue electron field, whose ripples give rise to particles with mass and charge. But why then didn t Faraday, Maxwell and other classical physicists find it useful to introduce the concept of matter fields, analogous to the electromagnetic field? In this course, we will take the second viewpoint, namely that the field is primary and particles are derived concepts, appearing only after quantization. We will show how photons arise from the quantization of the electromagnetic field and how massive, charged particles such as electrons arise from the quantization of matter fields. We will learn that in order to describe the fundamental laws of Nature, we must in fact introduce a field to every fundamental particle in nature: not only introduce electron fields, but also quark fields, neutrino fields, gluon fields, W and Z-boson fields, Higgs fields and a whole slew of others. The advantage of the field is fundamental view point can be understood as due to the following reasons: (1) locality; (2) the ability to create and annihilate particles; and (3) the fact that all particles of the same type are identical. 3. Locality One key concept which I am afraid is not properly emphasized is the concept that the laws of nature are local. The old laws of Coulomb and Newton involve action at a distance. This means that the force felt by an electron (or planet) changes immediately if a distant proton (or star) moves. This is wrong!!. It is both philosophically unsatisfactory, and, more importantly, experimentally wrong - it is inconsistent with the basic concept that no signal can travel faster than the speed of light, which is finite. Thus, we are seeking a theory in which all interactions are mediated in a local fashion by the field.

3 3 4. Particle number is not conserved Another reason to treat the field, rather than the particle as the fundamental quantity is the experimental fact that when particles interact, new particles can be created (or annihilated) - the particle number is not conserved. This fact is demonstrated at a daily basis in CERN and other accelerators. It is a direct consequence of the combination of quantum mechanics and special relativity. Particles are not indestructible objects, made at the beginning of the universe and here for good. They can be created and destroyed. They are, in fact, mostly ephemeral and fleeting. This experimentally verified fact was first predicted by Dirac who understood how relativity implies the necessity of anti-particles. We will review Dirac s argument for anti-particles later in this course, together with the better understanding that we get from viewing particles in the framework of quantum field theory. For now, we will quickly sketch the circumstances in which we expect the number of particles to change. Consider a particle of mass m trapped in a box of size L. Heisenberg tells us that the uncertainty in the momentum is p /L. In a relativistic setting, momentum and energy are on an equivalent footing, so we should also have an uncertainty in the energy of order E c/l. When the uncertainty in the energy exceeds E = 2mc 2, we cross the barrier to pop particle anti-particle pairs out of the vacuum. We learn that particle-anti-particle pairs are expected to be important when a particle of mass m is localized within a distance of order λ = mc. (2) The distance λ is called Compton wavelength. At distances shorter than this, there is a high probability that we will detect particle- anti-particle pairs swarming around the original particle that we put in. Note that Compton wavelength is always smaller than the de Broglie wavelength, λ db = h/ p : the de Broglie wavelength indicates the distance at which the wave nature of the particle becomes apparent, while Compton wavelength is the distance at which the concept of a single pointlike particle breaks down completely. The presence of a multitude of particles and antiparticles at short distances implies that any attempt to write down a relativistic version of the one-particle Schrödinger equation is doomed to failure. There is no mechanism in standard non-relativistic quantum mechanics to deal with changes in the particle number. We thus need a new formalism to treat states with an unspecified number of particles, as is expected in the relativistic regime. This formalism is quantum field theory (QFT).

4 4 5. All particles of the same type are the same A third reason to treat fields as the fundamental physical quantity is that all particles of the same type are the same. This is much more serious than it initially sounds. For example, two electrons are identical in every way, regardless of where they came from and what they ve been through. The same is true of every other fundamental particle. Suppose we capture a proton from a cosmic ray which we identify as coming from a supernova lying 8 billion lightyears away. We compare this proton with one freshly minted in a particle accelerator here on Earth. And the two are exactly the same! How is this possible? Why aren t there errors in proton production? How can two objects, manufactured so far apart in space and time, be identical in all respects? One explanation that might be offered is that there s a sea of proton stuff filling the universe and when we make a proton we somehow dip our hand into this stuff and from it mould a proton. Then its not surprising that protons produced in different parts of the universe are identical: they are made of the same stuff. It turns out that this is roughly what happens. The stuff is the proton field or, if you look closely enough, the quark field. In fact, there is more to this tale. Being the same in the quantum world is not like being the same in the classical world: quantum particles that are the same are truely indistinguishable. Swapping two particles around leaves the state completely unchanged - apart from a possible minus sign. This minus sign determines the statistics of the particle. In quantum mechanics you have to put these statistics in by hand and, to agree with experiment, should choose Bose statistics (no minus sign) for integer spin particles, and Fermi statistics (yes minus sign) for half-integer spin particles. In quantum field theory, this relationship between spin and statistics is not something that you have to put in by hand. Rather, it is a consequence of the framework. 6. What is quantum field theory? After (hopefully) convincing you that QFT is necessary, it is time to define it. The clue is in the name: it is the quantization of a classical field, the most familiar example of which is the electromagnetic field. In standard quantum mechanics, we are taught to take the classical degrees of freedom and promote them to operators acting on a Hilbert space. In QFT, we are doing essentially the same - for fields. Thus the basic degrees of freedom in quantum field theory are operator valued functions of space and time. Classically, every point in space has a field value associated with it; in QFT, every point in space has an operator associated with it. These operators are going to operate on

5 5 Hilbert space. This means that we are dealing with an infinite number of degrees of freedom - at least one for every point in space, and there are infinite number of such points. This infinity will come back to bite on several occasions. It will turn out that the possible interactions in quantum field theory are governed by a few basic principles: locality, symmetry and renormalization group flow (the decoupling of short distance phenomena from physics at larger scales). These ideas make QFT a very robust framework: given a set of fields there is very often an almost unique way to couple them together. As it turns out, QFT is an extremely useful tool not only for relativistic systems (where it is necessary), but also for non-relativistic systems with many particles, such as in condensed matter physics (where collective excitations, known as phonons exist). It is obviously the fundamental basis for particle physics, high energy physics, and plays a major role in quantum gravity and cosmology - as well as in pure mathematics. 7. Units and scales Nature presents us with three fundamental dimensionful constants; the speed of light c, Planck s constant (divided by 2π), and Newton s gravitation constant G. They have dimensions: [c] = LT 1 [ ] = L 2 MT 1 (3) [G] = L 3 M 1 T 2 (L - length, T - time and M - mass). Throughout this course, we will work with natural units, defined by c = = 1 (4) which allows us to express all dimensionful quantities in terms of a single scale which we choose to be mass or, equivalently, energy (since E = mc 2 has become E = m). The usual choice of energy unit is ev, the electron volt or, more often GeV = 10 9 ev or TeV = ev. To convert the unit of energy back to a unit of length or time, we need to insert the relevant powers of c and. For example, the length scale λ associated to a mass m is the Compton wavelength λ = mc. (5) With this conversion factor, the electron mass m e = ev translates to a length scale λ e = cm.

6 6 Throughout this course we will refer to the dimension of a quantity, meaning the mass dimension. If X has dimensions of (mass) d we will write [X] = d. In particular, the surviving natural quantity G has dimensions [G] = 2 and defines a mass scale, G = c M 2 p = 1 M 2 p (6) where M p GeV is the Planck scale. It corresponds to a length l p cm. The Planck scale is thought to be the smallest length scale that makes sense: beyond this quantum gravity effects become important and it is no longer clear that the concept of spacetime makes sense. The largest length scale we can talk of is the size of the cosmological horizon, roughly l p. Fig. 1. Energy and distance scales in the known universe Some useful scales in the universe are shown in Figure 1. This is a logarithmic plot, with energy increasing to the right and, correspondingly, length increasing to the left. The smallest and largest scales known are shown on the figure, together with other relevant energy scales. The standard model of particle physics is expected to hold up to about the TeV energies. This is precisely the regime that is currently being probed by the Large Hadron Collider (LHC) at CERN. There is a general belief that the framework of quantum field theory will continue to hold to energy scales only slightly below the Planck scale - for example, there are experimental hints that the coupling constants of electromagnetism, and the weak and strong forces unify at around GeV. For comparison, the rough masses of some elementary (and not so elementary) particles are shown in the table:

7 7 Particle photon neutrino electron Muon Pions Proton, Neutron W,Z Bosons Higgs Boson Mass < ev 10 2 ev 0.5 MeV 100 MeV 140 MeV 1 GeV GeV 125 GeV REFERENCES [1] D. Tong, Lectures on Quantum Field Theory (

### Concepts in Theoretical Physics

Concepts in Theoretical Physics Lecture 6: Particle Physics David Tong e 2 The Structure of Things 4πc 1 137 e d ν u Four fundamental particles Repeated twice! va, 9608085, 9902033 Four fundamental forces

### Fundamental Particles, Fundamental Questions. Elizabeth H. Simmons Dean and Professor, Lyman Briggs College

Fundamental Particles, Fundamental Questions Elizabeth H. Simmons Dean and Professor, Lyman Briggs College The smallest pieces of matter Nuclear physics and particle physics study the smallest known building

### REALIZING EINSTEIN S DREAM Exploring Our Mysterious Universe

REALIZING EINSTEIN S DREAM Exploring Our Mysterious Universe The End of Physics Albert A. Michelson, at the dedication of Ryerson Physics Lab, U. of Chicago, 1894 The Miracle Year - 1905 Relativity Quantum

### The Standard Model or Particle Physics 101. Nick Hadley Quarknet, July 7, 2003

The Standard Model or Particle Physics 101 Nick Hadley Quarknet, July 7, 2003 Thanks Thanks to Don Lincoln of Fermilab who provided some of the pictures and slides used in this talk. Any errors are mine

### STRING THEORY: Past, Present, and Future

STRING THEORY: Past, Present, and Future John H. Schwarz Simons Center March 25, 2014 1 OUTLINE I) Early History and Basic Concepts II) String Theory for Unification III) Superstring Revolutions IV) Remaining

### Theory of electrons and positrons

P AUL A. M. DIRAC Theory of electrons and positrons Nobel Lecture, December 12, 1933 Matter has been found by experimental physicists to be made up of small particles of various kinds, the particles of

### PX434 Physics of the Standard Model Dr Steven Boyd : P448. ATLAS Event Display

PX434 Physics of the Standard Model Dr Steven Boyd : P448 ATLAS Event Display Intro Stuff Lectures are divided in chapters each chapter has a writeup which will be put online There is a module homepage

### Lecture 2 - The current state of fundamental physics

Lecture 2 - The current state of fundamental physics 1) Einstein & General Relativity Gravity as Spacetime Curvature Gravitational Radiation, LIGO & LISA Cosmology & the Expanding Universe Dark Energy

### Where is Fundamental Physics Heading? Nathan Seiberg IAS Apr. 30, 2014

Where is Fundamental Physics Heading? Nathan Seiberg IAS Apr. 30, 2014 Disclaimer We do not know what will be discovered. This is the reason we perform experiments. This is the reason scientific research

### Feynman diagrams. 1 Aim of the game 2

Feynman diagrams Contents 1 Aim of the game 2 2 Rules 2 2.1 Vertices................................ 3 2.2 Anti-particles............................. 3 2.3 Distinct diagrams...........................

### Subatomic Physics: Particle Physics Lecture 4. Quantum Electro-Dynamics & Feynman Diagrams. Antimatter. Virtual Particles. Yukawa Potential for QED

Ψ e (r, t) exp i/ (E)(t) (p) (r) Subatomic Physics: Particle Physics Lecture Quantum ElectroDynamics & Feynman Diagrams Antimatter Feynman Diagram and Feynman Rules Quantum description of electromagnetism

### W-boson production in association with jets at the ATLAS experiment at LHC

W-boson production in association with jets at the ATLAS experiment at LHC Seth Zenz Qualifying Examination Talk January 14 2008 (Introductory section only; modified slightly for public distribution.)

### 1 Introduction. 1 There may, of course, in principle, exist other universes, but they are not accessible to our

1 1 Introduction Cosmology is the study of the universe as a whole, its structure, its origin, and its evolution. Cosmology is soundly based on observations, mostly astronomical, and laws of physics. These

### 1D 3D 1D 3D. is called eigenstate or state function. When an operator act on a state, it can be written as

Chapter 3 (Lecture 4-5) Postulates of Quantum Mechanics Now we turn to an application of the preceding material, and move into the foundations of quantum mechanics. Quantum mechanics is based on a series

### Particle Physics. The Standard Model. A New Periodic Table

5 Particle Physics This lecture is about particle physics, the study of the fundamental building blocks of Nature and the forces between them. We call our best theory of particle physics the Standard Model

### The Fundamental Forces of Nature

Gravity The Fundamental Forces of Nature There exist only four fundamental forces Electromagnetism Strong force Weak force Gravity Gravity 2 The Hierarchy Problem Gravity is far weaker than any of the

### Special Relativity and Electromagnetism Yannis PAPAPHILIPPOU CERN

Special Relativity and Electromagnetism Yannis PAPAPHILIPPOU CERN United States Particle Accelerator School, University of California - Santa Cruz, Santa Rosa, CA 14 th 18 th January 2008 1 Outline Notions

### The Higgs Boson. Linac08 Victoria BC, Canada CANADA S NATIONAL LABORATORY FOR PARTICLE AND NUCLEAR PHYSICS

CANADA S NATIONAL LABORATORY FOR PARTICLE AND NUCLEAR PHYSICS Owned and operated as a joint venture by a consortium of Canadian universities via a contribution through the National Research Council Canada

### Laws of Motion and Conservation Laws

Laws of Motion and Conservation Laws The first astrophysics we ll consider will be gravity, which we ll address in the next class. First, though, we need to set the stage by talking about some of the basic

### Chapter 18: The Structure of the Atom

Chapter 18: The Structure of the Atom 1. For most elements, an atom has A. no neutrons in the nucleus. B. more protons than electrons. C. less neutrons than electrons. D. just as many electrons as protons.

### Generally Covariant Quantum Mechanics

Chapter 15 Generally Covariant Quantum Mechanics by Myron W. Evans, Alpha Foundation s Institutute for Advance Study (AIAS). (emyrone@oal.com, www.aias.us, www.atomicprecision.com) Dedicated to the Late

### THE MEANING OF THE FINE STRUCTURE CONSTANT

THE MEANING OF THE FINE STRUCTURE CONSTANT Robert L. Oldershaw Amherst College Amherst, MA 01002 USA rloldershaw@amherst.edu Abstract: A possible explanation is offered for the longstanding mystery surrounding

### SubAtomic Physics Nuclear Physics

SubAtomic Physics Nuclear Physics Lecture 4 Main points of Lecture 3 Strong and coulomb interaction processes conserve angular momentum and parity External properties 1) Charge number of protons (ze) 2)

### The Early History of Quantum Mechanics

Chapter 2 The Early History of Quantum Mechanics In the early years of the twentieth century, Max Planck, Albert Einstein, Louis de Broglie, Neils Bohr, Werner Heisenberg, Erwin Schrödinger, Max Born,

### University of Cambridge Part III Mathematical Tripos

Preprint typeset in JHEP style - HYPER VERSION Michaelmas Term, 2006 and 2007 Quantum Field Theory University of Cambridge Part III Mathematical Tripos Dr David Tong Department of Applied Mathematics and

### Evolution of the Universe from 13 to 4 Billion Years Ago

Evolution of the Universe from 13 to 4 Billion Years Ago Prof. Dr. Harold Geller hgeller@gmu.edu http://physics.gmu.edu/~hgeller/ Department of Physics and Astronomy George Mason University Unity in the

### Introduction to Elementary Particle Physics. Note 01 Page 1 of 8. Natural Units

Introduction to Elementary Particle Physics. Note 01 Page 1 of 8 Natural Units There are 4 primary SI units: three kinematical (meter, second, kilogram) and one electrical (Ampere 1 ) It is common in the

### Chapter S3 Spacetime and Gravity

Chapter S3 Spacetime and Gravity What are the major ideas of special relativity? Spacetime Special relativity showed that space and time are not absolute Instead they are inextricably linked in a four-dimensional

### Supersymmetry Supergravity Superstring Supercolliders

The Super Era of Sub-Atomic Particle Physics Jay Hauser Abstract: Particle physics has now moved into the "Super" era, in which Supersymmetry, Supergravity, and Superstring theories will be investigated

### One of the primary goals of physics is to understand the wonderful variety of nature in a

A Unified Physics by by Steven Weinberg 2050? Experiments at CERN and elsewhere should let us complete the Standard Model of particle physics, but a unified theory of all forces will probably require radically

### A Theory for the Cosmological Constant and its Explanation of the Gravitational Constant

A Theory for the Cosmological Constant and its Explanation of the Gravitational Constant H.M.Mok Radiation Health Unit, 3/F., Saiwanho Health Centre, Hong Kong SAR Govt, 8 Tai Hong St., Saiwanho, Hong

### 8. Newton's Law of Gravitation

2 8. Newton's Law Gravitation Rev.nb 8. Newton's Law of Gravitation Introduction and Summary There is one other major law due to Newton that will be used in this course and this is his famous Law of Universal

### Chapter 27: The Early Universe

Chapter 27: The Early Universe The plan: 1. A brief survey of the entire history of the big bang universe. 2. A more detailed discussion of each phase, or epoch, from the Planck era through particle production,

### 0.33 d down 1 1. 0.33 c charm + 2 3. 0 0 1.5 s strange 1 3. 0 0 0.5 t top + 2 3. 0 0 172 b bottom 1 3

Chapter 16 Constituent Quark Model Quarks are fundamental spin- 1 particles from which all hadrons are made up. Baryons consist of three quarks, whereas mesons consist of a quark and an anti-quark. There

### Pearson Physics Level 30 Unit VIII Atomic Physics: Chapter 17 Solutions

Pearson Physics Level 30 Unit VIII Atomic Physics: Chapter 17 Solutions Student Book page 831 Concept Check Since neutrons have no charge, they do not create ions when passing through the liquid in a bubble

### Theoretical Particle Physics FYTN04: Oral Exam Questions, version ht15

Theoretical Particle Physics FYTN04: Oral Exam Questions, version ht15 Examples of The questions are roughly ordered by chapter but are often connected across the different chapters. Ordering is as in

### Chapter 23 The Beginning of Time

Chapter 23 The Beginning of Time 23.1 The Big Bang Our goals for learning What were conditions like in the early universe? What is the history of the universe according to the Big Bang theory? What were

### The High Redshift Universe Reprise

The High Redshift Universe Reprise Planck time Particle physics stuff Inflation Element creation All in first 1000 seconds Bit of a snooze for the next 400000 years Atoms form from the ions and electrons

### Chapter 1 Units, Physical Quantities, and Vectors

Chapter 1 Units, Physical Quantities, and Vectors 1 The Nature of Physics Physics is an experimental science. Physicists make observations of physical phenomena. They try to find patterns and principles

### 13- What is the maximum number of electrons that can occupy the subshell 3d? a) 1 b) 3 c) 5 d) 2

Assignment 06 A 1- What is the energy in joules of an electron undergoing a transition from n = 3 to n = 5 in a Bohr hydrogen atom? a) -3.48 x 10-17 J b) 2.18 x 10-19 J c) 1.55 x 10-19 J d) -2.56 x 10-19

### JANVIDA ROU. Introduction

HANBURY BROWN-TWISS INTERFEROMETRY IN SUBATOMIC PARTICLES JANVIDA ROU Introduction Many different experiments utilizing collisions have been developed to study nuclei and elementary particles. For example,

### Atomic Structure: Chapter Problems

Atomic Structure: Chapter Problems Bohr Model Class Work 1. Describe the nuclear model of the atom. 2. Explain the problems with the nuclear model of the atom. 3. According to Niels Bohr, what does n stand

### Wave Function, ψ. Chapter 28 Atomic Physics. The Heisenberg Uncertainty Principle. Line Spectrum

Wave Function, ψ Chapter 28 Atomic Physics The Hydrogen Atom The Bohr Model Electron Waves in the Atom The value of Ψ 2 for a particular object at a certain place and time is proportional to the probability

### Chapter 7: The Quantum-Mechanical Model of the Atom

C h e m i s t r y 1 A : C h a p t e r 7 P a g e 1 Chapter 7: The Quantum-Mechanical Model of the Atom Homework: Read Chapter 7. Work out sample/practice exercises Suggested Chapter 7 Problems: 37, 39,

### Cross section, Flux, Luminosity, Scattering Rates

Cross section, Flux, Luminosity, Scattering Rates Table of Contents Paul Avery (Andrey Korytov) Sep. 9, 013 1 Introduction... 1 Cross section, flux and scattering... 1 3 Scattering length λ and λ ρ...

### Lecture Outlines. Chapter 27. Astronomy Today 7th Edition Chaisson/McMillan. 2011 Pearson Education, Inc.

Lecture Outlines Chapter 27 Astronomy Today 7th Edition Chaisson/McMillan Chapter 27 The Early Universe Units of Chapter 27 27.1 Back to the Big Bang 27.2 The Evolution of the Universe More on Fundamental

### ASTR/PHYS 109 Dr. David Toback Lectures 18 & 19

ASTR/PHYS 109 Dr. David Toback Lectures 18 & 19 1 Was due Today L19 Reading: (Unit 4) Pre-Lecture Reading Questions: Unit 4, Stage 2: Due before class today Unit 3 Revision (if desired), Stage 2: Due today

### University of Cambridge Part III Mathematical Tripos

Preprint typeset in JHEP style - HYPER VERSION Michaelmas Term, 2006 and 2007 Quantum Field Theory University of Cambridge Part III Mathematical Tripos Dr David Tong Department of Applied Mathematics and

### Physics 121: Optics, Electricity & Magnetism

Physics 121: Optics, Electricity & Magnetism Neil Alberding SFU Physics Spring 2010 Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 1 / 1 Outline I Neil Alberding

### The Bohr model for the electrons

The Bohr model for the electrons Electronic structure how the electrons are arranged inside the atom Applying the quantum principle of energy Two parameters: Energy Position Learning objectives Describe

### Special Theory of Relativity. A Brief introduction

Special Theory of Relativity A Brief introduction Classical Physics At the end of the 19th century it looked as if Physics was pretty well wrapped up. Newtonian mechanics and the law of Gravitation had

### The Higgs Particle, Pivot of the Standard Model of the Subatomic Particles

The Higgs Particle, Pivot of the Standard Model of the Subatomic Particles Utrecht University Gerard t Hooft, Public Lecture, Sendai, April 24, 2015 CERN European Center for Nuclear Research LHC Large

### Session 42 Review The Universe, and its Dark Side

95% Session 42 Review The Universe, and its Dark Side Dec 9, 2011 Email: ph116@u.washington.edu Announcements Final exam: Monday 12/12, 2:30-4:20 pm Same length/format as previous exams (but you can have

### Lecture 7: Light Waves. Newton s Laws of Motion (1666) Newton s First Law of Motion

Lecture 7: Light Waves Isaac Newton (1643-1727) was born in the year Galileo died He discovered the Law of Gravitation in 1665 He developed the Laws of Mechanics that govern all motions In order to solve

### Masses in Atomic Units

Nuclear Composition - the forces binding protons and neutrons in the nucleus are much stronger (binding energy of MeV) than the forces binding electrons to the atom (binding energy of ev) - the constituents

### Basic Nuclear Concepts

Section 7: In this section, we present a basic description of atomic nuclei, the stored energy contained within them, their occurrence and stability Basic Nuclear Concepts EARLY DISCOVERIES [see also Section

### 1 Anomalies and the Standard Model

1 Anomalies and the Standard Model The Glashow-Weinberg-Salam model of the electroweak interactions has been very successful in explaining a wide range of experimental observations. The only major prediction

### DO PHYSICS ONLINE FROM QUANTA TO QUARKS QUANTUM (WAVE) MECHANICS

DO PHYSICS ONLINE FROM QUANTA TO QUARKS QUANTUM (WAVE) MECHANICS Quantum Mechanics or wave mechanics is the best mathematical theory used today to describe and predict the behaviour of particles and waves.

### The spin of an elementary particle would appear, on the surface, to be little different from the

Chapter 6 Particle Spin and the Stern-Gerlach Experiment The spin of an elementary particle would appear, on the surface, to be little different from the spin of a macroscopic object the image of a microscopic

### 23. The Beginning of Time. Agenda. Agenda. ESA s Venus Express. Conditions in the Early Universe. 23.1 Running the Expansion Backward

23. The Beginning of Time Somewhere, something incredible is waiting to be known. Agenda Announce: Solar Altitude Lab (#2) due today Read Ch. 24 for Thursday Observation make-up next week Project Presentations

### LHC discoveries and Particle Physics Concepts for Education

LHC discoveries and Particle Physics Concepts for Education Farid Ould- Saada, University of Oslo On behalf of IPPOG EPS- HEP, Vienna, 25.07.2015 A successful program LHC data are successfully deployed

### TIME, SYMMETRY OF. Although everyday experience leads us to believe that time "flows" in one direction, the

TIME, SYMMETRY OF Although everyday experience leads us to believe that time "flows" in one direction, the equations of both classical and modern physics work equally well in either time direction. Since

### Periodic Table of Particles/Forces in the Standard Model. Three Generations of Fermions: Pattern of Masses

Introduction to Elementary Particle Physics. Note 01 Page 1 of 8 Periodic Table of Particles/Forces in the Standard Model Three Generations of Fermions: Pattern of Masses 1.0E+06 1.0E+05 1.0E+04 1.0E+03

LIGHT AND ELECTROMAGNETIC RADIATION Light is a Wave Light is a wave motion of radiation energy in space. We can characterize a wave by three numbers: - wavelength - frequency - speed Shown here is precisely

### The Dawn of PHYSICS BEYOND THE. By Gordon Kane 68 SCIENTIFIC AMERICAN

The Dawn of PHYSICS BEYOND THE By Gordon Kane 68 SCIENTIFIC AMERICAN STANDARD MODEL The Standard Model of particle physics is at a pivotal moment in its history: it is both at the height of its success

### PX408: Relativistic Quantum Mechanics

January 2016 PX408: Relativistic Quantum Mechanics Tim Gershon (T.J.Gershon@warwick.ac.uk) Handout 1: Revision & Notation Relativistic quantum mechanics, as its name implies, can be thought of as the bringing

### The Early Universe. Lecture 27-1

The Early Universe Lecture 27-1 Back to the Big Bang The total energy of the universe consists of both radiation and matter. As the Universe cooled, it went from being radiation dominated to being matter

### Summary of Important Ideas in Quantum Physics

Summary of Important Ideas in Quantum Physics 1) The Universe is quantized. Familiar quantities such as energy, momentum, electric charge, mass possibly even time and space are not continuous. They occur

### Atomic Structure Ron Robertson

Atomic Structure Ron Robertson r2 n:\files\courses\1110-20\2010 possible slides for web\atomicstructuretrans.doc I. What is Light? Debate in 1600's: Since waves or particles can transfer energy, what is

### A Summary of Particle Physics for Teachers

A Summary of Particle Physics for Teachers Particles Prior to Accelerators By the mid 1930s, the understanding of the fundamental structure of matter seemed almost complete. Decades before, Rutherford

### The Schrödinger Equation

The Schrödinger Equation When we talked about the axioms of quantum mechanics, we gave a reduced list. We did not talk about how to determine the eigenfunctions for a given situation, or the time development

### Level 3 Achievement Scale

Unit 1: Atoms Level 3 Achievement Scale Can state the key results of the experiments associated with Dalton, Rutherford, Thomson, Chadwick, and Bohr and what this lead each to conclude. Can explain that

### Thomson and Rayleigh Scattering

Thomson and Rayleigh Scattering Initial questions: What produces the shapes of emission and absorption lines? What information can we get from them regarding the environment or other conditions? In this

### ATOMIC STRUCTURE AND THE PROPERTIES OF MATTER

SUBAREA I. ATOMIC STRUCTURE AND THE PROPERTIES OF MATTER COMPETENCY 1.0 UNDERSTAND THE VARIOUS MODELS OF ATOMIC STRUCTURE, THE PRINCIPLES OF QUANTUM THEORY, AND THE PROPERTIES AND INTERACTIONS OF SUBATOMIC

### emission of light from atoms discrete line spectra - energy levels, Franck-Hertz experiment

Introduction Until the early 20 th century physicists used to explain the phenomena in the physical world around them using theories such a mechanics, electromagnetism, thermodynamics and statistical physics

### PHOTOELECTRIC EFFECT AND DUAL NATURE OF MATTER AND RADIATIONS

PHOTOELECTRIC EFFECT AND DUAL NATURE OF MATTER AND RADIATIONS 1. Photons 2. Photoelectric Effect 3. Experimental Set-up to study Photoelectric Effect 4. Effect of Intensity, Frequency, Potential on P.E.

### Unification - The Standard Model

Unification - The Standard Model Information on Physics level 4 Undergraduate Course PT.4.6 K.S. Stelle, Office Huxley 519 November 9, 2015 Rapid Feedback to be handed in to the UG office Level 3 (day

### Curriculum for Excellence. Higher Physics. Success Guide

Curriculum for Excellence Higher Physics Success Guide Electricity Our Dynamic Universe Particles and Waves Electricity Key Area Monitoring and Measuring A.C. Monitoring alternating current signals with

### Lectures on the Higgs Boson

Lectures on the Higgs Boson Lecture 1: From X-rays to the Higgs Boson The World of Subatomic Particles Lecture 2: The Big Bang Factory Story of the World s Largest Machine Lecture 3: The Higgs Boson and

### hypothesis of Louis de Broglie (1924): particles may have wave-like properties

Wave properties of particles hypothesis of Louis de Broglie (1924): particles may have wave-like properties note: it took almost 20 years after noting that waves have particle like properties that particles

### Lecture 17: Dark Energy & The Big Bang

Lecture 17: Dark Energy & The Big Bang As with all course material (including homework, exams), these lecture notes are not be reproduced, redistributed, or sold in any form. Solution? ~1998 astronomers

Nuclear Fusion and Radiation Lecture 2 (Meetings 3 & 4) Eugenio Schuster schuster@lehigh.edu Mechanical Engineering and Mechanics Lehigh University Nuclear Fusion and Radiation p. 1/40 Modern Physics Concepts

### AP Chemistry A. Allan Chapter 7 Notes - Atomic Structure and Periodicity

AP Chemistry A. Allan Chapter 7 Notes - Atomic Structure and Periodicity 7.1 Electromagnetic Radiation A. Types of EM Radiation (wavelengths in meters) 10-1 10-10 10-8 4 to 7x10-7 10-4 10-1 10 10 4 gamma

### 2. 빈공간 (empty space) 에서질량이 0 인 real photon이 pair production을할수없음을보이시오. photoelectron current 와 retarding potential 의관계를그래프를이용해설명하시오.

현대물리학 ( 김충선교수님 ) 2 차시험 2009. 05. 04 월요일 1. A photon whose energy equals the rest mass of the electron undergoes a Compton collision with an electron at rest. If the electron moves off at an angle of 60

### Particle Physics. Michaelmas Term 2011 Prof Mark Thomson. Handout 7 : Symmetries and the Quark Model. Introduction/Aims

Particle Physics Michaelmas Term 2011 Prof Mark Thomson Handout 7 : Symmetries and the Quark Model Prof. M.A. Thomson Michaelmas 2011 206 Introduction/Aims Symmetries play a central role in particle physics;

### The speed of the ball relative to O, which we call u, is found. u u' O'

Einstein s Theory of relativity The theory of relativity has two parts. The Special Theory of Relativity relates the measurements of the same events made by two different observers moving relative to each

### Interesting note: When the Big Bang theory came out, many Christians embraced it. Why?

Cosmology Interesting note: When the Big Bang theory came out, many Christians embraced it. Why? Because the prevailing scientific view about the Universe in the early 1900 s was: The Universe is infinite

### Pretest Ch 20: Origins of the Universe

Name: _Answer key Pretest: _2_/ 58 Posttest: _58_/ 58 Pretest Ch 20: Origins of the Universe Vocab/Matching: Match the definition on the left with the term on the right by placing the letter of the term

### - develop a theory that describes the wave properties of particles correctly

Quantum Mechanics Bohr's model: BUT: In 1925-26: by 1930s: - one of the first ones to use idea of matter waves to solve a problem - gives good explanation of spectrum of single electron atoms, like hydrogen

### TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES. PHYS 3650, Exam 2 Section 1 Version 1 October 31, 2005 Total Weight: 100 points

TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES PHYS 3650, Exam 2 Section 1 Version 1 October 31, 2005 Total Weight: 100 points 1. Check your examination for completeness prior to starting.

### Your years of toil Said Ryle to Hoyle Are wasted years, believe me. The Steady State Is out of date Unless my eyes deceive me.

Your years of toil Said Ryle to Hoyle Are wasted years, believe me. The Steady State Is out of date Unless my eyes deceive me. My telescope Has dashed your hope; Your tenets are refuted. Let me be terse:

### The Big Bang Theory David Terr, Ph.D 4/10/13

The Big Bang Theory David Terr, Ph.D 4/10/13 The Big Bang theory is the currently accepted theory of the origin of the universe. According to this theory, the observable universe was formed approximately

### Chapter 7 Neutron Stars

Chapter 7 Neutron Stars 7.1 White dwarfs We consider an old star, below the mass necessary for a supernova, that exhausts its fuel and begins to cool and contract. At a sufficiently low temperature the

### 10. Our violent origin Cosmology and the nuclear processes in the Big Bang

10. Our violent origin Cosmology and the nuclear processes in the Big Bang Our Universe is getting larger. The space between the galaxies is expanding so that we see distant galaxies in all directions

### Chapter 15 Cosmology: Will the universe end?

Cosmology: Will the universe end? 1. Who first showed that the Milky Way is not the only galaxy in the universe? a. Kepler b. Copernicus c. Newton d. Hubble e. Galileo Ans: d 2. The big bang theory and

### 1. Coordinates (x, t) in one frame are related to coordinates (x, t ) in another frame by the Lorentz transformation formulas.

Physics 00 Problem Set 7 Solution Quick overview: Although relativity can be a little bewildering, this problem set uses just a few ideas over and over again, namely. Coordinates x, t in one frame are

### Calculating particle properties of a wave

Calculating particle properties of a wave A light wave consists of particles (photons): The energy E of the particle is calculated from the frequency f of the wave via Planck: E = h f (1) A particle can

### Thomson and Rayleigh Scattering

Thomson and Rayleigh Scattering In this and the next several lectures, we re going to explore in more detail some specific radiative processes. The simplest, and the first we ll do, involves scattering.