Quantum Mechanics 1b - Birth of the Quantum II ViaScience 2026-09-27 | Quantum Mechanics 1b - Birth of the Quantum II
Quantum Field Theory 7a Oppenheimer and Bethe I ViaScience 2021-09-25 | Two papers, one by J. Robert Oppenheimer and the other by Hans Bethe, "bookend" a period in the development of quantum field theory in which physicists struggled with infinities that kept popping up in calculations and threatened to derail the entire field. Bethe's solution of "mass renormalization" provided a path forward and led to an explanation of the "Lamb shift," a tiny energy shift in the Hydrogen spectrum that was discovered shortly after World War 2.
Quantum Field Theory 6c - Interacting Fields III ViaScience 2021-08-11 | We conclude this video with a discussion of scattering between photons and free electrons.Errors: 12:30 The dV at the end of the H-hat-i double-prime expression is typeset as a superscript. It should have been typeset in a normal-size font.19:29 The final 13-second audio clip was accidentally repeated.
Quantum Field Theory 6b - Interacting Fields II ViaScience 2021-07-26 | Here we outline the process of calculating transition rates for photon absorption and emission by a hydrogen atom.
Quantum Field Theory 6a - Interacting Fields I ViaScience 2021-07-05 | We can now calculate the quantum interaction Hamiltonian for the electron and photon fields. The result is a quantum field theory that can describe the emission and absorption of photons by an atom.Error: At 2:26 omega-sub-k (in the H-hat-sub-r expression) should be outside the parentheses.
Thermodynamics 6e - Heat Capacity and the Third Law V ViaScience 2020-08-11 | We conclude our examination of the Third Law of Thermodynamics. First, we find that anharmonic oscillations explain heat capacities above the classical prediction based on quadratic degrees of freedom and harmonic oscillators. Then we see that systems can have non-zero entropy at absolute zero by considering the ground-state degeneracy of an ice crystal. Finally, we sum up the Third Law. The most generally agreed upon formulation is the Unattainability Principle - that no process can reach absolute zero temperature in a finite number of steps and in a finite amount of time.
Thermodynamics 6d - Heat Capacity and the Third Law IV ViaScience 2020-07-29 | We have seen how quantum mechanical "freezing" of degrees of freedom accounts for heat capacities below the classical prediction. Here we examine how anharmonic oscillations explain heat capacities above the classical prediction.Thermodynamics playlist: youtube.com/playlist?list=PLsp_BbZBIk_4balQI5tY_Xo0y_9i-jYZ2
Thermodynamics 6c - Heat Capacity and the Third Law III ViaScience 2020-07-15 | Previously we developed the concept of quadratic degrees of freedom and equipartition of energy. We also saw how Einstein applied quantum mechanics to atomic vibrations to explain the "freezing" of vibrational degrees of freedom at low temperatures. Here we apply these ideas to develop a theory of the heat capacity of diatomic and more complex molecules.
Thermodynamics 6b - Heat Capacity and the Third Law II ViaScience 2020-07-03 | We develop the Debye model which improves on the Einstein model's prediction of the heat capacity of a solid at low temperatures. Then we begin a discussion of the concept of equipartition of energy and its relation to the classical theory of heat capacity.
Thermodynamics 6a - Heat Capacity and the Third Law I ViaScience 2020-06-12 | In this video, we develop and discuss the final law of thermodynamics - the Third Law. We find that the Third Law is intimately connected with the concept of heat capacity, and fundamentally relies on the quantum-mechanical nature of matter. In this segment, we develop the Einstein Model for the heat capacity of solids.
Quantum Field Theory 5c - Classical Electrodynamics III ViaScience 2020-05-30 | We end with a derivation of the classical interaction Hamiltonian for a charged particle moving in an electromagnetic field. There is a lot of "turn the crank" math in this installment, but the final result will be key to our continued development of quantum field theory.
Quantum Field Theory 5b - Classical Electrodynamics II ViaScience 2020-05-12 | [Reupload to correct color encoding issues] We complete our discussion of the electron self-force problem and introduce the concept of (classical) mass renormalization.
Quantum Field Theory 5a - Classical Electrodynamics I ViaScience 2020-04-09 | In this video we look at two important results from classical electrodynamics that we will need in order to continue with our development of quantum electrodynamics. First is the problem of the electron "self-force." The pieces of a finite distribution of electric charge exert forces on one another. Electromagnetic theory predicts these forces do not cancel out for an accelerating charge, leading to a net self-force. Second, we derive the interaction Hamiltonian that describes the interaction of an electric charge and an electromagnetic field.
Thermodynamics 5e - Statistical Mechanics V ViaScience 2020-03-29 | We end this video with a comparison between experiment and the results of our statistical mechanics analysis.
Thermodynamics 5d - Statistical Mechanics IV ViaScience 2020-03-16 | Previously we worked through some fundamental results of statistical mechanics. We are now in a position to derive the formula for the absolute entropy of an ideal monatomic gas. We find that our first attempt is plagued by the so-called Gibbs Paradox. Revisiting our fundamental statistical assumptions, we modify our entropy expression to resolve this paradox. The result is the Sackur-Tetrode equation, one of the most elegant results in statistical mechanics.
Thermodynamics 5c - Statistical Mechanics III ViaScience 2020-02-27 | We derive the Boltzmann distribution and the partition function for an ideal, monatomic gas.(Maxima, maxima.sf.net, is the free computer algebra system used in this video.)
Thermodynamics 5b - Statistical Mechanics II ViaScience 2020-02-13 | Here we apply our fundamental statistical formula, derived for the toy "balls in boxes" problem, to the states of atoms in a monatomic gas.
Thermodynamics 5a - Statistical Mechanics I ViaScience 2020-02-02 | Previously we've seen that our "colliding billiard balls" model for a monatomic gas has chaotic dynamics. Therefore, it is hopeless to try and describe the exact dynamical evolution of such a system. However, we can turn this to our advantage by treating the system as so unpredictable that it can be treated as a random process. Then, particular dynamical states can be characterized by their probability of occurrence. This is the basic idea of statistical mechanics. We begin with the derivation of the fundamental statistical formula we will need to analyze the statistics of a gas. We achieve this by analyzing the "toy" problems of flipping coins and distributing balls among boxes.
Quantum Field Theory 4d - Second Quantization IV ViaScience 2020-01-17 | We end our discussion of second quantization with the details of perturbation theory.
Quantum Field Theory 4c - Second Quantization III ViaScience 2020-01-07 | Feynman diagrams provide a visual tool we can use to determine the types of terms that must appear in the interaction Hamiltonian. Unfortunately, interacting systems are typically described by equations that are too difficult to solve exactly. This leads us to consider the techniques of perturbation theory that allow us to develop approximate solutions.
Thermodynamics 4b - Entropy and the Second Law II ViaScience 2020-01-03 | We compare the reversibility of the Carnot cycle to the irreversibility of the Stirling cycle and find that they may be accounted for by the constancy or increase of transferred heat divided by temperature. We then consider how conservation laws, including the fundamental laws of mechanics, cannot account for the irreversibility of a system. Note on the definition of a "closed system." I am using the term "closed system" in the sense of the following definition from Thermal Physics by Charles Kittel: "A closed system is defined as a system with constant energy, constant number of particles, and constant volume." Another term for such a system is "isolated system," in which case "closed system" may refer to a system that has a constant number of particles but can exchange energy with its surroundings.
Thermodynamics 4c - Entropy and the Second Law III ViaScience 2020-01-03 | We consider in more detail how the fundamental laws of mechanics cannot account for the irreversibility of a system. Yet we find evidence that "special" states are easily transformed into "non-special" states while transforming a non-special state into a special state requires "fine-tuning" of initial conditions. We end with the conventional statement of the 2nd Law of Thermodynamics and the historic definition of entropy.Note on the definition of a "closed system." I am using the term "closed system" in the sense of the following definition from Thermal Physics by Charles Kittel: "A closed system is defined as a system with constant energy, constant number of particles, and constant volume." Another term for such a system is "isolated system," in which case "closed system" may refer to a system that has a constant number of particles but can exchange energy with its surroundings.
Quantum Field Theory 4b - Second Quantization II ViaScience 2019-12-19 | We work out the details of the fermion creation and destruction operators and summarize the quantum field theories of photons and electrons we have developed so far.This video borrows from Chapter 4 of A Pedestrian Approach to Quantum Field Theory by Edward G. Harris (ISBN-13: 978-0486780221).
Quantum Field Theory 4a - Second Quantization I ViaScience 2019-12-11 | Previously we've seen how to quantize the electromagnetic field. This led us to define operators that create and destroy photons. We want to develop similar operators for electrons. The way we do this is the technique of "second quantization." Photons are bosons, which are not governed by the Pauli exclusion principle. Electrons, however, are fermions, which must satisfy the exclusion principle. Therefore, electron creation and destruction operators cannot be the same operators we used for photons.This video borrows from Chapter 4 of A Pedestrian Approach to Quantum Field Theory by Edward G. Harris (ISBN-13: 978-0486780221).
Thermodynamics 4e - Entropy and the Second Law V ViaScience 2019-12-06 | We conclude our discussion of entropy and the Second Law of Thermodynamics. Consideration of free expansion of an ideal gas leads to the basic concepts of statistical mechanics, which will be the topic of the next video.
Thermodynamics 4d - Entropy and the Second Law IV ViaScience 2019-11-13 | We now have the tools we need to calculate the precise entropy change of an ideal monatomic gas.
Thermodynamics 4a - Entropy and the Second Law I ViaScience 2019-09-23 | The Second Law of Thermodynamics is one of the most important laws in all of physics. But it is also one of the more difficult to understand. Central to it are the concepts of reversibility and entropy.Note on the definition of a "closed system." I am using the term "closed system" in the sense of the following definition from Thermal Physics by Charles Kittel: "A closed system is defined as a system with constant energy, constant number of particles, and constant volume." Another term for such a system is "isolated system," in which case "closed system" may refer to a system that has a constant number of particles but can exchange energy with its surroundings.
Quantum Field Theory 3d - Photons IV ViaScience 2019-09-13 | Here we complete our discussion of the quantum field theory description of the electromagnetic field.
Quantum Field Theory 3c - Photons III ViaScience 2019-08-26 | To see how our quantum field description of photons works, we consider the problem of describing a quasi-classical "coherent" field.
Quantum Field Theory 3b - Photons II ViaScience 2019-06-26 | We consider Fermi's approach to quantizing the electromagnetic field.Errors:At 12:26 I say "plus i a-hat-minus a-hat-plus times ..." I should have said "plus i a-hat-minus minus a-hat-plus times ..."
Thermodynamics 3c - Energy and the First Law III ViaScience 2019-06-14 | Here we complete our discussion of the First Law and thermodynamic cycles.Note on the definition of a "closed system." I am using the term "closed system" in the sense of the following definition from Thermal Physics by Charles Kittel: "A closed system is defined as a system with constant energy, constant number of particles, and constant volume." Another term for such a system is "isolated system," in which case "closed system" may refer to a system that has a constant number of particles but can exchange energy with its surroundings.
Thermodynamics 3b - Energy and the First Law II ViaScience 2019-05-23 | We apply the first law of thermodynamics to understand the Stirling cycle heat engine.Note on the definition of a "closed system." I am using the term "closed system" in the sense of the following definition from Thermal Physics by Charles Kittel: "A closed system is defined as a system with constant energy, constant number of particles, and constant volume." Another term for such a system is "isolated system," in which case "closed system" may refer to a system that has a constant number of particles but can exchange energy with its surroundings.
Quantum Field Theory 3a - Photons I ViaScience 2019-05-15 | In this video we apply the theory we developed in videos 1 & 2, along with some ideas from electromagnetic theory, to develop a rigorous theory of photons.
Thermodynamics 3a - Energy and the First Law I ViaScience 2019-03-23 | Having developed our ideal-gas model in the previous video, we now use that model to understanding the principle and application of the First Law of Thermodynamics.Note on the definition of a "closed system." I am using the term "closed system" in the sense of the following definition from Thermal Physics by Charles Kittel: "A closed system is defined as a system with constant energy, constant number of particles, and constant volume." Another term for such a system is "isolated system," in which case "closed system" may refer to a system that has a constant number of particles but can exchange energy with its surroundings.
Thermodynamics 2d - Ideal Gases IV ViaScience 2019-03-10 | Here we finish our discussion of ideal gases. We consider the chaotic nature of collisions between spherical particles and the implications for begin able to precisely describe the microscopic evolution of a system of gaseous atoms.
Thermodynamics 2c - Ideal Gases III ViaScience 2019-03-09 | Continuing our discussion of the monatomic ideal gas, we consider some of the microscopic properties of a gas.
Thermodynamics 2b - Ideal Gases II ViaScience 2019-01-12 | We continue our discussion of ideal gases. Here we derive the Ideal Gas Law and the heat capacity of an ideal monatomic gas.
Thermodynamics 2a - Ideal Gases I ViaScience 2018-12-12 | The kinetic theory of gases allows us to use a very simple mechanical model to derive the relation between the pressure, volume and temperature of a gas.
Mechanics 3 - Work & Energy ViaScience 2018-11-07 | We have an intuitive feel for the concepts of work and energy. In physics we give these precise definitions. For at least some systems we find that we can define different forms of energy, potential and kinetic, such that the total energy remains constant even as these specific forms vary.
Quantum Field Theory 2b - Field Quantization II ViaScience 2018-10-21 | Here we complete the "quantum field theory" of a vibrating string. (Note: My voice is lower and slower than normal - I was coming down with a cold.)Errors: At 0:42 I say "minus c-squared times q-k..." I should have said, "minus c-squared times quantity k pi over L squared, times q-k..." At 6:00 the last two "kets" on the lower right should have n_k in place of n_k+1. The number operator does not change the photon occupation numbers.
Quantum Field Theory 2a - Field Quantization I ViaScience 2018-10-21 | In the previous video we saw how the quantum harmonic oscillator provides a model system in which we can describe the creation and destruction of energy quanta. In 1925 Born, Heisenberg and Jordan presented a way to apply these ideas to a continuous field. (Note: My voice is lower and slower than normal - I was coming down with a cold.)
Thermodynamics 1b - Heat and Temperature II ViaScience 2018-10-10 | Here we complete our discussion of the concepts of heat and temperature.
Thermodynamics 1a - Heat and Temperature I ViaScience 2018-10-09 | We begin our investigation into thermodynamics with a consideration of the phenomena of heat and temperature. (BTW: I spelled Newton's first name Issac. It's Isaac.)
Mechanics 2 - Force, Mass & Acceleration ViaScience 2018-09-29 | Arguably the most important equation in all of physics is F = ma, force equals mass times acceleration. Newton presented this law of Nature in 1687.Caltech's The Mechanical Universe episode Newton's Laws:youtu.be/tsJMfy2GH0A
Quantum Field Theory 1b - Creation and Destruction II ViaScience 2018-09-04 | A mass attached to spring is an example of a "harmonic oscillator." For the quantum harmonic oscillator we can find creation and destruction operators which create and destroy one quantum of energy. This seems like a promising development in our quest to develop a rigorous quantum description of photons.
Quantum Field Theory 1a - Creation and Destruction I ViaScience 2018-08-27 | The theory of quantum mechanics we developed in the previous series has some loose ends. Notably: 1) We talk about photons being emitted (created) and absorbed (destroyed) but we haven't given a rigorous description of this process. 2) The Dirac equation implies the presence of a "Dirac sea" of invisible, negative-energy electrons. Exciting a negative-energy electron to a positive-energy state appears as the creation of an electron-positron pair. A "better" theory would predict this creation directly without the bizarre, invisible Dirac sea.The theory developed to tie up these loose ends is called Quantum Electrodynamics. It's the first (of several) quantum field theories.
Relativity 5c - twin paradox redux 1 ViaScience 2018-04-15 | Here we extend our video 5a (youtu.be/kN_d7eknfYk) treatment of the twin "paradox" of special relativity.Apologies to Richard Feynman for my typo at 2:46 which renamed him Feynmann. This while I was literally reading my copy of the Feynman Lectures to get the quote in question.
Relativity 13b - cosmology II ViaScience 2017-12-07 | We consider how the empty-space theory we have developed so far will need to be modified in the presence of matter.
Relativity 13a - cosmology I ViaScience 2017-11-15 | In this video we consider the cosmological implications of General Relativity. We start with general considerations and the predictions of Newtonian theory.video on slope and curvature: youtu.be/FqOH42zc9Es
Relativity 12e - gravitational waves V ViaScience 2017-06-26 | Here we consider the technology required to detect gravitational waves.
