Modern Physics: PHYS 344 Professor Michael Manfra Office: Physics 84 Phone: 494-3016 Email: mmanfra@purdue.edu Lecture schedule: MWF 2:30am to 3:20am in Physics 203 Office hours: Fridays, Physics 84 from 9:00am to 10:00am or appointments via email

Course description for PHYS344 Modern Physics will introduce you to some of the most amazing developments in our understanding of Nature that took place in the beginning of the 20th century Principal among these: Relativity theory: fundamentally changed our understanding of the notions of space and time from those of Newtonian mechanics Quantum theory: a completely new way to understand the behavior of matter at small (atomic) length scales

Prerequisites PHYS 272H, or 241 Everyone should have completed a course in classical mechanics Everyone should have completed a course in electricity and magnetism This course also requires a bit of mathematical sophistication: complex numbers, simple differential equations including wave equations

Examinations and Grading A problem set will be given each week. Total points available for all problem sets (combined) 100 points There will be two exams given in class: tentative schedule: the 1st on Monday Oct. 5th and the 2nd on Monday Nov. 16th. These exams will be graded on a 100 point scale. The final exam will occur during finals week at the normally scheduled time and will be graded on a 200 point scale. The final grade will be determined as follows: Average of problem sets: 100 points max Two in-class exams: 200 points max (total) Final exam: 200 points max Total: 500 points max

TA and graders TA: Nirajan Mandal Email: nmandal@purdue.edu Office: Physics 104 Graders: Kui Zhang (grader) Email: zhan2382@purdue.edu   Dohyung Ro (grader) Email: rod@purdue.edu

Bedtime reading Course required text: Modern Physics, Kenneth Krane, 3rd Edition, Wiley & Sons You should start by reading Chapter 1: Review of Classical Mechanics You should also review some basic mathematics of complex numbers, simple differential equations including wave equations, e.g. Maxwell’s equations

Problem Sets Problem sets will be assigned on Wednesday and due in class the following Wednesday. Problem sets must be turned in on time to receive full credit. We will try to return graded problem sets within one week. Students are encouraged to work together and discuss problems – this is a good way to learn. Nevertheless, blind copying of another student’s work is not acceptable – Don’t do this – we will spot it. Problem sets shouldn’t be torture, so if you’re having trouble, talk to us.

EMERGENCY PREPAREDNESS – A MESSAGE FROM PURDUE To report an emergency, call 911. To obtain updates regarding an ongoing emergency, sign up for Purdue Alert text messages, view www.purdue.edu/ea. There are nearly 300 Emergency Telephones outdoors across campus and in parking garages that connect directly to the PUPD. If you feel threatened or need help, push the button and you will be connected immediately. If we hear a fire alarm during class we will immediately suspend class, evacuate the building, and proceed outdoors. Do not use the elevator. If we are notified during class of a Shelter in Place requirement for a tornado warning, we will suspend class and shelter in [the basement]. If we are notified during class of a Shelter in Place requirement for a hazardous materials release, or a civil disturbance, including a shooting or other use of weapons, we will suspend class and shelter in the classroom, shutting the door and turning off the lights. Please review the Emergency Preparedness website for additional information. http://www.purdue.edu/ehps/emergency_preparedness/index.html One final piece of Purdue business before we begin: as we start this semester I want to take a few minutes to discuss emergency preparedness. Purdue University is a very safe campus and there is a low probability that a serious incident will occur here. However, just as we receive a safety briefing each time we get on an aircraft, we want to emphasize our emergency procedures for evacuation and shelter in place incidents. Our preparedness will be critical if an unexpected event occurs.   Purdue prepares for natural disasters or human‑caused incidents with the ultimate goal of maintaining a safe and secure campus, but nin the end, emergency preparedness is your personal responsibility. Let’s quickly review the following procedures:

Modern Physics has very some unintuitive ideas. In fact, this course will hit you with more than any other course you’ll ever take. The goal is simply to expose you to them, and later courses will cover them on more detail.

Understanding the ideas of each lecture requires the knowledge of the previous lectures. If you keep up, you won’t end up looking like this the night before the exams! Image from http://groups.msn.com/AGODFIGHTforallreligions/membersinformationrules.msnw (I don’t recommend this site for anything other than this picture.)

Modern Physics is 20th century physics (maybe not so modern….) We’ll start with Einstein’s Special Theory of Relativity Then move to Quantum Theory

Before Special Relativity One frame moving at velocity v with respect to another x’ z’ y’ x z y Basically, this seems so obvious as to not to be necessary to say it. Unfortunately, it’s wrong.

James Clerk Maxwell (1831-1879) Why is this a problem? In the mid-19th century, Maxwell unified electricity and magnetism with his now famous equations and showed that light is an electromagnetic wave. The Scottish physicist James Clerk Maxwell, b. Nov. 13, 1831, d. Nov. 5, 1879, did revolutionary work in electromagnetism and the kinetic theory of gases. After graduating (1854) with a degree in mathematics from Trinity College, Cambridge, he held professorships at Marischal College in Aberdeen (1856) and King's College in London (1860) and became the first Cavendish Professor of Physics at Cambridge in 1871. Maxwell's first major contribution to science was a study of the planet Saturn's rings, the nature of which was much debated. Maxwell showed that stability could be achieved only if the rings consisted of numerous small solid particles, an explanation still accepted. Maxwell next considered molecules of gases in rapid motion. By treating them statistically he was able to formulate (1866), independently of Ludwig Boltzmann, the Maxwell-Boltzmann kinetic theory of gases. This theory showed that temperatures and heat involved only molecular movement. Philosophically, this theory meant a change from a concept of certainty--heat viewed as flowing from hot to cold--to one of statistics--molecules at high temperature have only a high probability of moving toward those at low temperature. This new approach did not reject the earlier studies of thermodynamics; rather, it used a better theory of the basis of thermodynamics to explain these observations and experiments. Maxwell's most important achievement was his extension and mathematical formulation of Michael Faraday's theories of electricity and magnetic lines of force. In his research, conducted between 1864 and 1873, Maxwell showed that a few relatively simple mathematical equations could express the behavior of electric and magnetic fields and their interrelated nature; that is, an oscillating electric charge produces an electromagnetic field. These four partial differential equations first appeared in fully developed form in Electricity and Magnetism (1873). Since known as Maxwell's equations they are one of the great achievements of 19th-century physics. Maxwell also calculated that the speed of propagation of an electromagnetic field is approximately that of the speed of light. He proposed that the phenomenon of light is therefore an electromagnetic phenomenon. Because charges can oscillate with any frequency, Maxwell concluded that visible light forms only a small part of the entire spectrum of possible electromagnetic radiation. Maxwell used the later-abandoned concept of the ether to explain that electromagnetic radiation did not involve action at a distance. He proposed that electromagnetic-radiation waves were carried by the ether and that magnetic lines of force were disturbances of the ether. James Clerk Maxwell (1831-1879) where is the electric field, is the magnetic field, and c is the velocity of light.

Light is an electromagnetic wave. The electric (E) and magnetic (B) fields are in phase. The electric field, the magnetic field, and the propagation direction are all perpendicular.

Michelson & Morley Waves typically occur in a medium. So in 1887 Michelson and Morley attempted to measure the earth's velocity with respect to what was then called the aether and found it always to be zero, effectively disproving the existence of the aether. Albert Michelson (1852-1931) Edward Morley (1838-1923) http://en.wikipedia.org

In 1905, Einstein had a very good year. In 1905, Einstein explained Brownian motion and the photoelectric effect (for which he later won the Nobel prize). Einstein also explained Michelson’s and Morley’s experiment: he realized that light didn’t need a medium and was a property of free space. And it traveled at the same velocity no matter what speed you were going. This idea forms the basis of the Theory of Special Relativity. Albert Einstein (1879-1955)

With Special Relativity x’ z’ y’ x z y The Lorentz transformations are the correct way to transform from one frame to the other. They yield a constant speed of light and are NOT at all obvious! Lorentz himself didn’t believe them.

Quantum Theory

Blackbody Radiation When matter is heated, it not only absorbs light, but it also spontaneously emits it. A blackbody is a medium that’s black when it’s cool and so can spontaneously emit and absorb all colors. Blackbodies are interesting because their optical properties are independent of the material and only depend on the temperature.

The Ultraviolet Catastrophe Lord Rayleigh used the classical theories of electromagnetism and thermodynamics to show that the blackbody spectrum should be: Rayleigh-Jeans Formula This worked at longer wavelengths but deviates badly at short ones. This problem became known as the ultraviolet catastrophe and was one of the many effects classical physics couldn’t explain.

Max Planck showed that if light is considered as a particle, bye bye Ultraviolet Catastrophe. Indeed, photographs taken in dimmer light look grainier. Very very dim Very dim Dim Bright Very bright Very very bright When we detect very weak light, we find that it’s made up of particles. We call them photons.

19th-century scientists could not explain spectra. www.uoregon.edu 1/Wavelength 

The Planetary model for the atom was also a problem. From classical E&M theory, an accelerated electric charge radiates energy (electromagnetic radiation), which means total energy must decrease. And the radius r must decrease! Why doesn’t the electron crash into the nucleus?

If a light-wave also acted like a particle, why shouldn’t matter-particles also act like waves? In his thesis in 1923, Prince Louis V. de Broglie suggested that mass particles should have wave properties similar to light. The wavelength of a matter wave is called the de Broglie wavelength: where h = Planck’s constant and p is the particle’s momentum De Broglie’s dissertation was only 16 pages long. And the mass particles would be subject to their own Uncertainty Principle!

Quantum theory explains the Periodic Table.