Understanding the Quantum World

Begin your journey into the quantum world by focusing on one of its most baffling features: the behavior of quantum entities as both particles and waves. Following her approach of presenting analogies over equations, Professor Carlson gives a handy way of visualizing this paradox. Then she takes you further into quantum weirdness by using a slinky to show how waves can be quantized.

Investigate one of the most famous demonstrations in physics: the double-slit experiment. See how electrons behave as both particles and waves when passing through two parallel slits in a plate and then striking a screen. Bizarrely, the wave properties disappear when the electrons are monitored as they pass through each slit, showing our inability to have complete information of a quantum state.

Consider what life would be like if quantum effects held at our everyday scale. For instance, there would be no trouble sitting in three chairs at once! Learn what happens when a particle in such a mixed state is forced by measurement to assume a definite position—a situation known as wave function collapse. This leads to the important quantum principle that observers disturb what they measure.

Ponder two celebrated and thought-provoking responses to the apparent incompatibility of quantum mechanics and classical physics. Bell’s theorem shows that attempts to reconcile the two systems are futile in a certain class of theories. Next, Schrödinger’s cat is a thought experiment implying that a cat could be both dead and alive if the standard interpretation of quantum mechanics holds.

Review the major theories proposed by physicists trying to make sense of the paradoxes of the quantum world. Look at the Copenhagen interpretation, Einstein’s realist view, the many worlds interpretation, quantum Bayesianism, non-local hidden variables, and other creative attempts to explain what is going on in a realm that seems to be governed by probability alone.

Heisenberg’s uncertainty principle sets a fundamental limit on how much we can know about an object’s position and momentum at the same time. Professor Carlson introduces this simple equation, showing how it explains why atoms have structure and come in the diverse forms of the periodic table of elements. Surprisingly, the stability of our everyday world rests on uncertainty at the quantum level.

Electrons don’t just orbit the nucleus—they simultaneously exist as standing waves. Go deeper into what standing wave modes look like in one, two, and three dimensions, discovering that these shapes explain the quantization of energy states in an atom. As usual, Professor Carlson introduces useful analogies, including the standing waves produced in a vibrating drum head.

Focus on standing waves of electrons around nuclei, seeing how the periodic table of elements results from what electrons do naturally: fall into the lowest energy state given the total electric charge, existing electron population, and other features of an atom. Learn the Pauli exclusion principle and a handy mnemonic for remembering the terminology for atomic orbitals, such as 1s, 2p, 3d, etc.

Watch what happens when electrons are put into wave forms that differ from standing waves. Your goal is to understand why some of these superposition states are unstable. Professor Carlson notes that the sloshing of an electron back and forth in an unstable state causes it to act like an antenna, radiating away energy until it falls to a lower energy level.

What accounts for the dramatic difference between diamond and graphene (a sheet of graphite one atom thick), both of which are composed of pure carbon? Study the role of electrons in molecular bonds, applying your knowledge of electron standing waves. In carbon, such waves make possible several types of bonds, which in diamond and graphene result in remarkably different physical properties.

A clock pendulum is an example of a classical harmonic oscillator. Extend this concept to the atomic realm to see how quantum waves behave like harmonic oscillators. Then learn how quantum physics was born at the turn of the 20th century in Max Planck’s solution to a paradox in the classical picture of oscillating atoms. His conclusion was that the energies of oscillation had to be quantized.

Return to the Heisenberg uncertainty principle from Lecture 6 to see how quantum uncertainty also extends to energy and time. This has a startling implication for energy conservation, suggesting that short-lived “virtual” particles can pop into existence out of nothing—as long as they don’t stay around for long. Consider evidence for this phenomenon in the Lamb shift and Casimir effect.

Continue your investigation of the counterintuitive quantum world by contrasting angular momentum for planets and other classical objects with analogous phenomena in quantum particles. Cover the celebrated Stern–Gerlach experiment, which in the 1920s showed that spin is quantized for atoms and can only take on a very limited number of discrete values.

Having covered electron spin in the previous lecture, now turn to orbital angular momentum. Again, a phenomenon familiar in classical physics relating to planets has an analogue in the quantum domain—although with profound differences. This leads to a discussion of permanent magnets, which Professor Carlson calls “a piece of quantum physics that you can hold in your hand.”

Among Einstein’s insights was that light comes in discrete packets of energy called photons. Explore the photoelectric effect, which prompted Einstein’s discovery. See a do-it-yourself project that demonstrates the photoelectric effect. Close by surveying applications of the quantum theory of light to phenomena such as lasers, fluorescent dyes, photosynthesis, and vitamin D production in skin.

Dive deeper into the interactions of light with matter. Starting with a hydrogen atom, examine the changes in energy and angular momentum when an electron transitions from one orbital to another. See how the diverse possibilities create a “fingerprint” specific to every type of atom, and how this is the basis for spectroscopy, which can determine the composition of stars by analyzing their light.

Peer into the structure of a cesium atom to see what makes it ideal for measuring the length of a second and serving as the basis for atomic clocks. Then head into space to learn how GPS satellites use atomic clocks to triangulate positions on the ground. Finally, delve into Einstein’s special and general theories of relativity to understand the corrections that GPS must make to stay accurate.

Probe the quantum events that underlie color vision, discovering the role of the retinal molecule in detecting different frequencies of photons as they strike cone cells in the eye’s retina. Also investigate the source of color blindness, most common in men, as well as its inverse, tetrachromacy, which is the ability to see an extra channel of color information, possessed by some women.

Now turn to the sources of color in the world around us, from the yellow glow of sodium street lights to the brilliant red of a ruby pendant. Grasp the secret of the aurora, the difference between fluorescence and phosphorescence, and the reason neon dyes look brighter than their surroundings. It turns out that our entire experience of color is governed by the quantum world.

Anyone who makes use of a memory stick, a solid-state hard drive, or a smartphone relies on one of the most baffling aspects of the quantum world: quantum tunneling. Professor Carlson uses a roller coaster analogy, combined with your newly acquired insight into wave mechanics, to make this feat of quantum sorcery—the equivalent of walking through walls—perfectly logical.

Investigate why two pieces of matter cannot occupy the same space at the same time, reaching the conclusion that this is only true for fermions, which are particles with half-integer spin. The other class of particles, bosons, with integer spin, can be in the same place at the same time. Learn how this feature of bosons has been exploited in lasers and in superfluids such as liquid helium.

Study the most celebrated challenge to the Copenhagen interpretation of quantum mechanics: the paradox proposed by Albert Einstein and his collaborators Boris Podolsky and Nathan Rosen—later updated by David Bohm. Is quantum mechanics an incomplete theory due to hidden variables that guide the outcome of quantum interactions? Examine this idea and the experiments designed to test it.

Analyze how metals conduct electricity, discovering that, in a sense, electrons “surf” from one metal atom to the next on a quantum mechanical wave. Probe the causes of electrical resistance and why metals can never be perfect conductors. Finally, use the Pauli exclusion principle to understand the optimum distribution of electrons in the different quantum states of metal atoms.

Close with one of Professor Carlson’s favorite topics: superconductivity. As noted in Lecture 23, when electrons flow through a metal, they lose energy to resistance. But this is not true of superconductors, whose amazing properties trace to the difference between bosons and fermions. Learn how quantum stability allows superconductors to conduct electricity with zero resistance, then step back and summarize the high points of your quantum tour.