1. Modern Physics Waves and Optics Special Relativity Quantum Mechanics
Wave, particles, and weirdness
Atoms, molecules, and nuclei
Particle physics
General Relativity
Cosmology
Prof. Rick Trebino
Georgia Tech

2. Modern Physics is 20th century physics.
By 1900, physicists thought they had it all together. They had Physics I and II (“classical physics”) down and thought that that was about it. All that remained was to dot the i’s and cross the t’s.
Scanning-tunneling microscope image of individual atoms
Man, were they in for a surprise! Several of them actually. Modern physics is the story of these surprises (quantum mechanics and special and general relativity), surprises—revolutions, actually—that have changed the world beyond all recognition.
The purpose of this course is to introduce you to all this fun new stuff.

3. The Beginnings of Modern Physics
These new discoveries and the many resulting complications required a massive revision of fundamental physical assumptions and theories.
The introduction (~1905) of the modern theories of special relativity and quantum mechanics became the starting point of this most fascinating revision. General relativity (~1915) continued it. c
Special relativity
Speed
Quantum mechanics
General relativity
19th-century physics
Huge
Size

4. In 1900, it was well-known that the universe contained only particles.
Waves, on the other hand, were simply collective motions of particles—a much less fundamental phenomenon.
A human wave

5. More differences between particles and waves
Particles are highly localized in space and time.
Particles have well-defined trajectories.
Particles are either there (1) or not (0).
Particles cannot cancel each other out.
Waves are extended in space and time.
Waves have poorly defined trajectories.
Waves can be kind of there (~1/2) or even the opposite of there (<0).
Waves can cancel out.

6. We’ll begin our story with the age-old subjects of waves and optics, which hold the key to it all.
“I procured me a triangular glass prism to try therewith the celebrated phenomena of colours.” Isaac Newton, 1665
Isaac Newton ( )
Is light a particle or a wave? After remaining ambivalent for many years, Newton concluded that light was made up of particles.

7. While particles travel in straight lines, waves bend around corners.
Ocean waves passing through wave-breaks in Tel Aviv, Israel:
This is diffraction, and it occurs for all types of waves—but not for particles.

8. Light passing through a hole bends around the edges.
Thomas Young  ( )
Light pattern after passing through a small square hole
In 1803, Thomas Young showed that light diffracted precisely as predicted by Fresnel’s wave theory.

9. James Clerk Maxwell (1831-1879)
In the mid-19th century, Maxwell unified electricity and magnetism into a single force with his now famous equations.
In free space:
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 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.
where is the electric field, is the magnetic field, and c is the velocity of light.
James Clerk Maxwell ( )

10. In addition, Maxwell showed that light is an electromagnetic wave.
The electric (E) and magnetic (B) fields obey the wave equation: x z y
Electric field (E)
Magnetic field (B)
Wavelength (l)
Different wavelengths (distances between the peaks) or frequencies (2p times the rate at which the peaks pass by) correspond to different colors, many of which we can’t see.

11. But exactly what was waving?
It seemed that electromagnetic waves could propagate through empty space!
Indeed, precisely what was electromagnetically waving was unknown at the time. Scientists decided to call it aether and figure out what it was later.

12. Waves also interfere.
The color you see is the one for which the light reflected from the front and back of the bubble surface are in phase.
By the mid-19th century, light was well-known to be a wave.

13. The Michelson Interferometer
Input
beam L2
The Michelson Interferometer deliberately interferes two beams and so yields a sinusoidal output intensity vs. the difference in path lengths.
Output
beam
Mirror L1
Beam-
splitter
Delay
Mirror
Output beam intensity vs. relative path length I l
DL = 2(L2 – L1)
It can also measure velocity.

14. Michelson & Morley
In 1887 Michelson and Morley attempted simply to measure the earth's velocity with respect to the aether and found it always to be zero—no matter which direction the earth was moving—effectively disproving the existence of the aether and providing a great crack in the foun- dations of physics.
Albert Michelson ( )
Edward Morley ( )

15. In 1905, Einstein had a very good year.
That year, Einstein explained Michelson’s and Morley’s experiment: he realized that light didn’t need a medium and was a property of free space. It’s a wave—but not collective motion of particles!
And light has the odd property that it travels at the same velocity no matter what speed you’re going. This is Special Relativity.
Albert Einstein ( )
Oh, and he graduated from grad school that year, too.

16. Before Special Relativity
One frame moving at velocity v with respect to another x’ z’ y’ x z y
Basically, this seems so obvious that we almost shouldn’t even have to say it.
Unfortunately, it’s wrong.

17. With Special Relativityx’ z’ y’ x z y
The Lorentz transformations follow directly from the constant-speed-of-light assumption and are the correct way to transform from one frame to the other. They yield the speed of light in all frames and are NOT at all obvious!
Lorentz himself didn’t believe them.

18. Relativistic and Classical Kinetic Energies
K = ½ mv2
You cannot exceed the speed of light. It’s the law.
v/c
You need an infinite amount of energy to go the speed of light…

19. Measurements of time confirm Special Relativity
In Special Relativity, time passes at a rate that depends on your velocity.
Two airplanes traveled east and west around Earth as it rotated. Atomic clocks on the airplanes were compared with similar clocks kept at the observatory to show that the moving clocks in the airplanes ticked at different rates.

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

21. The Ultraviolet Catastrophe
In 1900, Lord Rayleigh used the classical theories of electromagnetism and thermodynamics to show that the blackbody spectrum should be:
UV Visible IR
Rayleigh-Jeans Formula
This worked at longer wavelengths but deviated badly at short ones. This problem became known as the ultraviolet catastrophe and was one of many effects that classical physics couldn’t explain.

22. Shortly afterward, Max Planck found that he could obtain the correct blackbody result if light was actually a particle.
where h is a constant now known as Planck’s constant.
But, of course, he didn’t really believe such a crazy idea.
No one else did either.
Max Planck (1858–1947)

23. Photo-electric Effect: Classical Theory
Illuminate a surface with light.
Look at the electrons that emerge.
Initial observations by Heinrich Hertz 1887
Image from
Classically, the kinetic energy (K) of the electrons should increase with the light intensity and not depend on the light frequency (w).

24. Photo-electric effect observations
The actual kinetic energy of the electrons is independent of the light intensity.
The kinetic energy of the electrons, for a given emitting material, actually depends only on the frequency of the light (w).
There was also a threshold frequency of the light, below which no electrons were ejected. No one had any idea how this could happen.
Electron kinetic energy K
Light frequency w a w0
Picture from

25. In 1905, Einstein decided Planck wasn’t crazy.
Einstein explained the photoelectric effect by requiring that light be composed of particles of energy ħw, where ħ = h/2π, and w is the frequency.
Energy after = Energy before
Electron kinetic energy
Photon energy
Electron potential energy to be overcome before escaping.
So light is simultaneously a wave and a particle!
We call light particles photons.

26. It’s now easy to see that light also behaves like a particle.
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—photons.

27. 19th-century scientists also could not explain spectra of light emitted by gases.
Wavelength

28. Spectra could be partially explained by the planetary model for the atom.
The electron orbital frequency should be the light frequency.
But from classical electromagnetic theory, an accelerated electric charge radiates energy (electromagnetic radiation), which means that its energy must decrease.
Electron
Nucleus
So the radius of its orbit around the nucleus must decrease.
Why doesn’t the electron crash into the nucleus?

29. Fourier decomposing functions plays a big role in physics.
a1sin(t)
Here, we write a square wave as a sum of sine waves of different frequencies.
a3sin(3t)
Fourier developed the Fourier transform to model heat-flow problems.
a5sin(5t)
Joseph Fourier

30. Fourier extended the idea to a continuous range of frequencies.
The Fourier transform converts a function of time to one of frequency:
and converting back uses almost the same formula:
The spectrum of a wave is given by:

31. f(t)
F(w)
The Uncertainty Principle is a simple classical property of the Fourier transform. t w
Short pulse t w
Medium- length pulse
If Dt is the width of a wave in time, and Dw is its spectral width, then: t w
Long pulse
This relation will play an important role in modern physics!

32. 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 those of light. The wavelength of a matter wave is called the de Broglie wavelength:
Louis de Broglie ( )
where h = Planck’s constant and p is the particle’s momentum.
De Broglie’s dissertation was only 16 pages long.
where E is the particle’s energy.
They would also have frequency:
And the matter-particles would be subject to their own Uncertainty Principle!

33. The Schrödinger Equation
At about the same time, Schrödinger introduced his Wave Equation, which nicely explained atoms and their properties and is the fundamental equation of Quantum Mechanics. For a particle moving in a potential V in one dimension, it’s:
Erwin Schrödinger ( )
And Y is called the particle’s wave function.
where:

34. What on earth is Y? Indeed, what is waving?
Probability! The probability P(x) dx of a particle being between x and x + dx is:
The probability of the particle being between x1 and x2 is:
And quantum mechanics says that particles can remain in stationary states forever without emitting any energy! Quantum mechanics has its own laws, which need only approach classical laws as the system increases in size to classical dimensions.

35. Y yields probability distribution functions
The probability density for the hydrogen atom for three different stationary electron states.

36. Quantum mechanics is essential to understand semiconductors.
Essentially all modern technology is a direct result of semiconductors and so is due to quantum mechanics.
Economists estimate that quantum mechanics is responsible for ~80% of the entire US economy.

37. Nuclear Physics
The nucleus of an atom is made up of positively charged protons and electrically neutral neutrons. So there’s no negative charge!
How can a nucleus hold together?
The strong force!

38. Elementary Particle Physics
If nuclei are made up of protons and neutrons, what are protons and neutrons made of?
Physicists have discovered a zoo of elementary particles, including quarks of 1/3 the charge of a proton.
angelfire.com

39. While there were clearly some problems in 19th- century physics, everyone remained happy with Newton’s Law of Gravitation. Except Einstein.
Einstein was also unsatisfied with his Theory of Special Relativity; it didn’t include acceleration. And because acceleration seemed similar to gravity, in 1915 he lost interest in the quantum mechanical revolution he had begun, and decided to pursue a geometrical theory of gravity, in which acceleration and gravity were equivalent.

40. General Relativity and the Curvature of Space
Einstein considered the possibility that the effect of mass (i.e., gravity) was to curve space.
At the time, no one thought that this was a good idea.
So if space-time is not flat, then the apparent straight line path of light will actually be curved.

41. The verification of GR was a sensation.
In a 1919 eclipse, light from a star was indeed bent by the sun, causing it to appear displaced.
Einstein’s theory predicted a deflection of 1.75 seconds of arc, and two measurements found 1.98 ± 0.16 and 1.61 ± 0.40 seconds.
Telegram:
Newspaper:
Eclipse:
Many more experiments, using starlight and radio waves from quasars, have confirmed Einstein’s predictions about the bending of light with increasing accuracy.

42. Gravitational lensing by galaxies
When light from a distant object like a quasar passes by a nearby galaxy on its way to us on Earth, the light can be bent multiple times as it passes in different directions around the galaxy.
The Cosmic Horseshoe

43. General Relativity also predicts Black Holes
While a star is burning, the heat and pressure produced by the thermonuclear reactions balance its gravity. When the star’s fuel is depleted, gravity dominates. The star’s mass can collapse into a black hole that warps space-time enough to not allow light to escape.
A star greater than 25 solar masses will collapse to a black hole.
Karl Schwarzschild determined the radius of a black hole, now known as the event horizon.

44. The Ultimate Goal of Physics: Unification of All Forces into a Single Force
ELECTRICITY
MAGNETISM
ELECTROMAGNETISM
SINGLE FORCE?
GRAVITATION
WEAK
ELECTROWEAK
STRONG
GRAND
UNIFICATION

45. General Relativity models the entire universe.
Closed
Flat
Open
The density, r, of matter in the universe determines its shape and future.
W0 ≡ r / rcrit
wikipedia
where rcrit = 3H2/8pG is the critical density for which the universe is flat.