Tensors for Beginners 9: The Metric Tensor eigenchris 2026-09-20 | Tensors for Beginners 9: The Metric Tensor
Spinors for Beginners 16: Lie Groups and Lie Algebras eigenchris 2023-12-10 | Full spinors playlist: youtube.com/playlist?list=PLJHszsWbB6hoOo_wMb0b6T44KM_ABZtBsLeave me a tip: ko-fi.com/eigenchrisPowerpoint slide files + Exercise answers: github.com/eigenchris/MathNotes/tree/master/SpinorsForBeginnersVideos on momentum operator generating translations in quantum mechanics:Physics with Elliot: youtube.com/watch?v=_lz1VfI6Wxk&t=596s&pp=ygUecGh5c2ljcyB3aXRoIGVsbGlvdCBjb21tdXRhdG9yProfessor M Does Science's video: youtube.com/watch?v=978mMgGYs1M&t=392s&pp=ygUkcHJvZmVzc29yIG0gZG9lcyBzY2llbmNlIHRyYW5zbGF0aW9uQuantum Sense': youtube.com/watch?v=A7yDvA8VQC8&t=305s&pp=ygUZcXVhbnR1bSBzZW5zZSB0cmFuc2xhdGlvbg%3D%3D0:00 - Introduction2:45 - Groups & Lie Groups4:00 - Exponent of a so(3) Matrix7:40 - Calculating so(3) generators9:50 - Momentum generators translations10:58 - so(3) traceless proof 13:35 - so(3) anti-symmetric proof15:11 - Warning about matrix exponentials16:43 - Lie Algebra Bracket20:24 - Structure coefficients21:48 - Lie Algebras as Tangent Spaces23:30 - Lie Algebra Property Proofs30:15 - Summary of so(3)31:05 - Overview of so+(1,3)32:50 - Spin-1 and Spin-1/2 representations34:40 - Math vs Physics conventions
Spinors for Beginners 15: Nilpotents, Fermions, and Maximally Isotropic Subspaces eigenchris 2023-10-29 | Full spinors playlist: youtube.com/playlist?list=PLJHszsWbB6hoOo_wMb0b6T44KM_ABZtBsLeave me a tip: ko-fi.com/eigenchrisPowerpoint slide files + Exercise answers: github.com/eigenchris/MathNotes/tree/master/SpinorsForBeginnersProfessor M Does Science's playlist on multi-particle quantum mechanics with creation and annihilation operators (second quantization): youtube.com/playlist?list=PL8W2boV7eVfnSqy1fs3CCNALSvnDDd-tbCohl Furey's playlist on Clifford Algebras and particle physics: youtube.com/playlist?list=PLNxhIPHaOTRZMO1VjJcs7_3dgyJ2qU1yZ0:00 - Introduction0:53 - Creation and Annihilation Operators (Bosons)2:14 - Fermions4:58 - Nilpotents7:14 - Projectors10:46 - Example in Cl(1,3)14:18 - More Nilpotents16:11 - Maximally Isotropic Subspaces21:02 - Generalizing to C(n,0) and Cl(p,q)23:57 - Example in Cl(2,0)26:20 - Conclusion
Spinors for Beginners 14: Minimal Left Ideals (and Pacwoman Property) eigenchris 2023-10-22 | Full spinors playlist: youtube.com/playlist?list=PLJHszsWbB6hoOo_wMb0b6T44KM_ABZtBsLeave me a tip: ko-fi.com/eigenchrisPowerpoint slide files + Exercise answers: github.com/eigenchris/MathNotes/tree/master/SpinorsForBeginnersThesis by Crystal-Ann McKenzie: scholar.uwindsor.ca/etd/56520:00 - Introduction2:01 - Review of Cl(3,0)4:28 - Fitting Spinors into Cl(3,0)8:09 - Minimal Left Ideals11:39 - Projectors12:55 - Pacwoman Property14:17 - Calculating Minimal Left Ideal in Cl(3,0)17:45 - Spin Operators in Cl(3,0)19:35 - Dual Spinors and Inner Product24:40 - Spinor Outer Product27:20 - Hestenes Definition of Spinors30:18 - Generalizing to Cl(1,3)37:10 - Generalizing to Cl(p,q)41:00 - Faithful Matrix Representations
Spinors for Beginners 13: Ideals and Projectors (Idempotents) eigenchris 2023-09-30 | Full spinors playlist: youtube.com/playlist?list=PLJHszsWbB6hoOo_wMb0b6T44KM_ABZtBsLeave me a tip: ko-fi.com/eigenchrisPowerpoint slide files + Exercise answers: github.com/eigenchris/MathNotes/tree/master/SpinorsForBeginners0:00 - Matrix Projectors7:23 - Clifford Algebra Projectors11:12 - Ideals18:19 - Projectors create Ideals
Spinors for Beginners 12: How the Spin Group Generalizes Quaternions to any Dimension eigenchris 2023-09-17 | Full spinors playlist: youtube.com/playlist?list=PLJHszsWbB6hoOo_wMb0b6T44KM_ABZtBsLeave me a tip: ko-fi.com/eigenchrisPowerpoint slide files + Exercise answers: github.com/eigenchris/MathNotes/tree/master/SpinorsForBeginners0:00 - Introduction2:45 - Terminology overview4:00 - Reflections in 3D space9:00 - Reflections in 4D spacetime13:20 - Rotations in 3D space22:07- Exponentials26:37 - Rotations + Boosts in 4D spacetime32:07 - Galilean Boosts32:42 - Spin(n) Groups40:27 - Grade Involution42:07 - Spin(p,q) Groups44:15 - Transforming Multi-vectors46:34 - Hestenes Definition of "spinor"
Spinors for Beginners 10: SU(2) double covers SO(3) [ SL(2,C) double covers SO+(1,3) ] eigenchris 2023-08-06 | Full spinors playlist: youtube.com/playlist?list=PLJHszsWbB6hoOo_wMb0b6T44KM_ABZtBsLeave me a tip: ko-fi.com/eigenchrisPowerpoint slide files + Exercise answers: github.com/eigenchris/MathNotes/tree/master/SpinorsForBeginners0:00 - Introduction3:05 - Real projective spaces RP^n7:29 - SU(2) double-covers SO(3)11:02 - Simply Connected spaces 14:34 - SL(2,C) double-covers SO+(1,3)20:34 - Mobius Transformations23:10 - Spin Groups
Spinors for Beginners 11: What is a Clifford Algebra? (and Geometric, Grassmann, Exterior Algebras) eigenchris 2023-07-23 | Full spinors playlist: youtube.com/playlist?list=PLJHszsWbB6hoOo_wMb0b6T44KM_ABZtBsLeave me a tip: ko-fi.com/eigenchrisPowerpoint slide files + Exercise answers: github.com/eigenchris/MathNotes/tree/master/SpinorsForBeginnersSudgylacmoe: youtube.com/c/sudgylacmoe Swift Introduction to Geometric Algebra: youtube.com/watch?v=60z_hpEAtD8Swift Introduction to Spacetime Algebra: youtube.com/watch?v=e7aIVSVc8cIBivector: youtube.com/@bivectorCrystal-Ann McKenzie's thesis: scholar.uwindsor.ca/etd/56520:00 - Introduction2:57 - Grassmann Algebras (wedge product)13:20 - Clifford Algebras22:45 - Grassman vs Clifford Algebras 26:35 - Abstract definitions of Algebras
Why Sabine Hossenfelders video on transgender teens is misleading eigenchris 2023-06-25 | Sources: docs.google.com/document/d/1zHgCEE-3bJWMVr93f6NehlwO5FZY9wQVHk90IJwSjrg/edit?usp=sharing0:00 0: Introduction5:37 1: Gender-Affirming Care11:46 2: Rapid-Onset Gender Dysphoria17:11 2b: Correlation and Causation24:29 3: "Vaccines cause Autism" pseudo-science29:49 4: Special Scrutiny40:40 5: Follow-up ROGD papers47:25 6: Falsifiability50:03 7: Conclusion
Spinors for Beginners 6.1 - Equivalence of Quaternions, Sigma Matrices, and SU(2) eigenchris 2023-05-14 | Full spinors playlist: youtube.com/playlist?list=PLJHszsWbB6hoOo_wMb0b6T44KM_ABZtBsLeave me a tip: ko-fi.com/eigenchrisPowerpoint slide files + Exercise answers: github.com/eigenchris/MathNotes/tree/master/SpinorsForBeginners0:00 Introduction1:06 Quaternions4:16 Sigma Matrices5:08 Equivalence of Quaternions and Sigma Matrices7:59 Double-Sided Rotations12:05 Spin(3) Group and double-cover of SO(3)13:55 Conclusion
Spinors for Beginners 9: Pauli Spinors vs Weyl Spinors vs Dirac Spinors eigenchris 2023-04-30 | Full spinors playlist: youtube.com/playlist?list=PLJHszsWbB6hoOo_wMb0b6T44KM_ABZtBsLeave me a tip: ko-fi.com/eigenchrisPowerpoint slide files + Exercise answers: github.com/eigenchris/MathNotes/tree/master/SpinorsForBeginnersWeyl Spinor and Dirac Spinor transformation rules are covered in pages 13-17 of this PDF: arxiv.org/pdf/1312.3824.pdfReview of Special RelativityLorentz Transformation Derivation 1: youtube.com/watch?v=5bSy18w8Dh0Lorentz Transformation Derivation 2: youtube.com/watch?v=240YGZmV1b0Time Dilation + Length Contraction: youtube.com/watch?v=WOLUSQK1JtkSpacetime Interval: youtube.com/watch?v=km7WTO_6K5s0:00 Intro / Overview3:02 Special Relativity Review4:43 Spacetime Interval6:16 Lorentz Transformations SO(1,3)10:12 Weyl Vectors11:54 Double-Sided Lorentz SL(2,C)17:45 Weyl Spinors Factoring24:26 Spinor Inner Products30:39 Left + Right Chirality34:45 4 Types of Weyl Spinor (Van der Waerden notation)43:06 Dirac Spinors44:17 Conclusion / Review
Spinors for Beginners 8: Are the Pauli Matrices also Vectors? (Intro to Spinor Spaces) eigenchris 2023-03-27 | Full spinors playlist: youtube.com/playlist?list=PLJHszsWbB6hoOo_wMb0b6T44KM_ABZtBsLeave me a tip: ko-fi.com/eigenchrisPowerpoint slide files + Exercise answers: github.com/eigenchris/MathNotes/tree/master/SpinorsForBeginnersMy Tensors for Beginners playlist:youtube.com/playlist?list=PLJHszsWbB6hrkmmq57lX8BV-o-YIOFsiG0:00 Introduction3:07 Vectors5:08 Dual Vectors8:34 Tensor Product 11:22 Spinor Spaces15:00 Sigma as a linear map19:45 Doubling indices; rank 1/220:45 Change of Spinor basis23:00 Summary
Spinors for Beginners 7: Square Root of a Vector (factoring vector into spinors) eigenchris 2023-03-05 | Full spinors playlist: youtube.com/playlist?list=PLJHszsWbB6hoOo_wMb0b6T44KM_ABZtBsLeave me a tip: ko-fi.com/eigenchrisPowerpoint slide files + Exercise answers: github.com/eigenchris/MathNotes/tree/master/SpinorsForBeginnersSources:Spinors in 3D from Wikipedia: en.wikipedia.org/wiki/Spinors_in_three_dimensionsAn Introduction to Spinors: arxiv.org/pdf/1312.3824.pdfSpinors for Everyone PDF: https://hal-cea.archives-ouvertes.fr/cea-01572342/file/1-Spinors-for-every-one-typos.pdfA Child's Guide to Spinors PDF: http://www.weylmann.com/spinor.pdf0:00 Introduction1:46 Factoring 2x2 Matrices 5:45 Factoring Pauli Vector11:31 Relating back to spinors in videos 2-515:10 Factoring matrices with non-zero determinant17:50 Summary
Spinors for Beginners 6: Pauli Vectors and Pauli Matrices eigenchris 2023-02-26 | Full spinors playlist: youtube.com/playlist?list=PLJHszsWbB6hoOo_wMb0b6T44KM_ABZtBsLeave me a tip: ko-fi.com/eigenchrisPowerpoint slide files + Exercise answers: github.com/eigenchris/MathNotes/tree/master/SpinorsForBeginnersSources:Spinors in 3D from Wikipedia: en.wikipedia.org/wiki/Spinors_in_three_dimensionsAn Introduction to Spinors: arxiv.org/pdf/1312.3824.pdfSpinors for Everyone PDF: https://hal-cea.archives-ouvertes.fr/cea-01572342/file/1-Spinors-for-every-one-typos.pdfA Child's Guide to Spinors PDF: http://www.weylmann.com/spinor.pdf0:00 Introduction1:02 Pauli Matrix Properties5:48 Pauli Vector Reflections11:11 Pauli Vector Rotations17:24 Proof of double-sided SU(2) formula23:28 Form of SU(2) matrices, parameter counting25:32 Summary
Spinors for Beginners 5: The Flagpole and Complex Projective Line (CP1) eigenchris 2023-02-08 | Full spinors playlist: youtube.com/playlist?list=PLJHszsWbB6hoOo_wMb0b6T44KM_ABZtBsLeave me a tip: ko-fi.com/eigenchrisPowerpoint slide files + Exercise answers: github.com/eigenchris/MathNotes/tree/master/SpinorsForBeginnersVideo by comparing + contrasting Jones Vectors and Quantum Spin States by Sander Konijnenberg: youtube.com/watch?v=RowMxWt4mVEInteractive Flagpole Visualization: in-theory.net/what-is-a-spinorPDF File on Flagpole visualization of spinors by Andrew M. Steane: arxiv.org/abs/1312.38240:00 Review of Jones Vectors and Quantum States5:04 Flagpole Visualization of Spinors10:12 Real Projective Line13:45 Point at infinity + Opposite points on circle17:55 Real Projective Plane18:54 Complex Projective Line21:33 Summary
Spinors for Beginners 4: Quantum Spin States (Stern-Gerlach Experiment) eigenchris 2023-01-26 | Full spinors playlist: youtube.com/playlist?list=PLJHszsWbB6hoOo_wMb0b6T44KM_ABZtBsLeave me a tip: ko-fi.com/eigenchrisPowerpoint slide files + Exercise answers: github.com/eigenchris/MathNotes/tree/master/SpinorsForBeginnersMinutePhysics video on polarizers: youtube.com/watch?v=zcqZHYo7ONs3Blue1Brown video on polarizers: youtube.com/watch?v=MzRCDLre1b40:00 Introduction + Stern-Gerlach Experiment3:38 Internal Angular Momentum5:34 Bra-Ket notation7:55 State Collapse, Born's Rule10:00 Z-oriented S.G. Experiment12:34 X-oriented S.G. Experiment16:01 Y-oriented S.G. Experiment18:37 Bloch Sphere, U(2) Matrices20:44 Global Phase Shifts with Born's Rule, SU(2)24:10 Conclusion
Spinors for Beginners 3: Polarizations and SU(2) Matrices [and O(3), SO(3), U(2)] eigenchris 2023-01-15 | Full spinors playlist: youtube.com/playlist?list=PLJHszsWbB6hoOo_wMb0b6T44KM_ABZtBsLeave me a tip: ko-fi.com/eigenchrisPowerpoint slide files + Exercise answers: github.com/eigenchris/MathNotes/tree/master/SpinorsForBeginnersMinutePhysics video on polarizers: youtube.com/watch?v=zcqZHYo7ONs3Blue1Brown video on polarizers: youtube.com/watch?v=MzRCDLre1b40:00 Introduction0:57 Waveplates2:25 D-to-L rotation4:43 H-to-L rotation7:32 Ignoring overall phase shifts8:52 H-to-A rotation and the Poincaré Sphere10:08 U(2) Matrices10:49 O(3) Matrices for Real vectors13:25 SO(3) Matrices for 3D Rotations15:12 Hermitian Conjugates17:00 U(2) Matrices for Complex vectors18:33 SU(2) Matrices for Rotating Jones Vectors20:53 Why Jones vectors are Spinors (angle-doubling)23:31 Next Video
Spinors for Beginners 2: Jones Vectors and Light Polarization eigenchris 2022-12-13 | Full spinors playlist: youtube.com/playlist?list=PLJHszsWbB6hoOo_wMb0b6T44KM_ABZtBsLeave me a tip: ko-fi.com/eigenchrisPowerpoint slide files + Exercise answers: github.com/eigenchris/MathNotes/tree/master/SpinorsForBeginners0:00 Introduction1:09 Electromagnetic Waves3:36 EM Wave Equations5:52 Euler's Formula8:21 Jones Vectors H and V10:35 Jones Vectors D and A12:34 Jones Vectors L and R15:28 Sign convention16:00 Conclusion + Exercise
Spinors for Beginners 1: Introduction (Overview +Table of Contents for video series) eigenchris 2022-12-02 | Full spinors playlist: youtube.com/playlist?list=PLJHszsWbB6hoOo_wMb0b6T44KM_ABZtBsLeave me a tip: ko-fi.com/eigenchrisPowerpoint slide files: github.com/eigenchris/MathNotes0:00 Introduction2:55 List of Topics ("Staircase")4:18 Basic Examples of Spinors in Phyiscs7:32 Spinors as Square Roots of Vectors10:22 Spinors as members of Clifford Algebras13:12 Spinors in terms of Lie Groups/Algebras15:40 Spinors in QFT18:09 Conclusion
Tensors for Beginners 1: Forward and Backward Transformations (REMAKE) eigenchris 2022-11-30 | Tensors for Beginners playlist: youtube.com/playlist?list=PLJHszsWbB6hrkmmq57lX8BV-o-YIOFsiGLeave me a tip: ko-fi.com/eigenchrisI made a mistake in the original version of this video that has been confusing people for years. Super late, but trying to make amends.
Relativity 110d: Cosmology - FLRW Geodesics, Cosmological Redshift, Horizons, Comoving Coordinates eigenchris 2022-08-25 | Full relativity playlist: youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQaPowerpoint slide files: github.com/eigenchris/MathNotes/tree/master/RelativityLeave me a tip: ko-fi.com/eigenchrisLinks/Sources:FLRW redshift derivation: https://www.int.washington.edu/users/dbkaplan/555/lecture_03de Sitter-Schwarzschild metric links: en.wikipedia.org/wiki/De_Sitter%E2%80%93Schwarzschild_metricphysics.stackexchange.com/questions/512385/finding-de-sitter-schwarzschild-metricPhantom Energy/Big Rip: en.wikipedia.org/wiki/Phantom_energyHow non-zero cosmological constant affects orbits: physics.stackexchange.com/questions/299152/orbits-in-an-universal-expansion/299162#299162Expanding Hubble Horizon: quora.com/Why-isnt-the-event-horizon-of-the-universe-the-same-as-the-Hubble-Sphere-After-all-after-the-expansion-of-space-crosses-the-speed-of-light-wouldnt-that-be-the-horizon-and-the-Hubble-sphereComputing Cosmological Horizons: physics.stackexchange.com/questions/212023/if-the-expansion-of-the-universe-accelerates-why-its-horizon-does-not-shrink/213675#2136750:00 Intro + FLRW Geodesics7:04 Light-like FLRW Geodesics11:14 Cosmological Redshift16:41 Cosmic Rest Frame18:12 Do we expand along with the universe?24:51 Cosmological Horizons32:12 Summary
Relativity 110f: Cosmology - Friedmann Equations Derivation + Universe Evolution Models (FINALE) eigenchris 2022-07-22 | Full relativity playlist: youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQaPowerpoint slide files: github.com/eigenchris/MathNotes/tree/master/RelativityLeave me a tip: ko-fi.com/eigenchrisLinks/Sources:Sean Carroll's 15-page PDF on cosmology: preposterousuniverse.com/wp-content/uploads/grnotes-eight.pdfPDF with derivation of "3rd" Friedmann Equation based on Adiabatic expansion (page 19): https://www.uio.no/studier/emner/matnat/astro/nedlagte-emner/AST4220/h09/course-material/lectures.pdfArticle on Conservation of Energy in General Relativity: https://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.htmlde Sitter's 1917 paper: academic.oup.com/mnras/article/78/1/3/1239878Video on mathematics of de Sitter space: youtube.com/watch?v=dZ-4REivxRUEquation for de Sitter space: en.wikipedia.org/wiki/De_Sitter_space#DefinitionEquation for embedding Anti-de Sitter space: en.wikipedia.org/wiki/Anti-de_Sitter_space#Definition_and_propertiesPDF building up dS and AdS space from the basics: http://3dhouse.se/ingemar/relteori/Kurs.pdfPhysics Stack exchange post about values of cosmological parameters: physics.stackexchange.com/questions/314660/to-what-accuracy-do-we-know-the-value-of-the-cosmological-constantChronology of the Universe: en.wikipedia.org/wiki/Chronology_of_the_universeDark Energy Survey (estimated cosmological parameters): en.wikipedia.org/wiki/Dark_Energy_SurveyVideo intro to Dark Energy Survey: youtube.com/watch?v=4TkyxLENS5QDr Becky talks about Dark Energy Survey: youtube.com/watch?v=IHMFDxLcMYsCosmic Inflation: en.wikipedia.org/wiki/Inflation_(cosmology)"Gravity in a Nutshell" by A. Zee also has chapters on de Sitter and anti-de Sitter spacetimes (IX.10 and IX.11)Sources for the estimations of cosmological parameters:WMAP: arxiv.org/pdf/0803.0732.pdfBOOMERanG: arxiv.org/pdf/astro-ph/0004404.pdfPlanck: en.wikipedia.org/wiki/Lambda-CDM_model#ParametersOther topics I didn't cover:Killing Vectors: en.wikipedia.org/wiki/Killing_vector_fieldKerr Metric (rotating black holes): en.wikipedia.org/wiki/Kerr_metricEinstein-Hilbert Action (Lagrangian formulation of GR): en.wikipedia.org/wiki/Einstein%E2%80%93Hilbert_action0:00 Introduction1:04 Review of FLRW metric and Perfect Fluid3:09 Friedmann Equations Derivation 7:04 "3rd" Friedmann Equation (conservation of energy)8:25 Universes dominated by matter, radiation, dark energy14:25 Einstein Static Universe17:51 de Sitter / anti-de Sitter Universes25:16 Cosmological parameters28:02 Cosmological Models with Λ = 033:08 Cosmological Models with Λ ≠ 036:43 The model for our universe39:17 Conclusion
Relativity 110b: Cosmology - FLRW Metric Derivation (3 possible geometries) eigenchris 2022-07-05 | Full relativity playlist: youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQaPowerpoint slide files: github.com/eigenchris/MathNotes/tree/master/RelativityLeave me a tip: ko-fi.com/eigenchrisRicci Curvature of 3-sphere: physics.mcgill.ca/~rhb/ph514/10sol6.pdfRicci Curvature of Hyperbolic plane: thatsmaths.files.wordpress.com/2013/10/134-half-plane-curvature.pdfInfo on Hyperboloid Model: en.wikipedia.org/wiki/Hyperboloid_modelHyperbolic Geometry video by Henry Segerman: youtube.com/watch?v=eGEQ_UuQtYsAlex Flournoy video on FLRW metric: youtube.com/watch?v=9WToQrPPeXsDietterich Labs video on FLRW metric: youtube.com/watch?v=cbRy3sXDJ-U0:00 Introduction1:10 Cosmological Principle4:03 Flat universe and scale factor a(t)6:52 Closed/spherical universe12:22 Open/hyperbolic universe17:55 Unifying the 3 metrics22:58 Reduced-Circumference Polar Coordinates
Relativity 108e: Schwarzschild Metric - Gravitational Redshift / Blueshift (via covector fields) eigenchris 2022-06-24 | Full relativity playlist: youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQaPowerpoint slide files: github.com/eigenchris/MathNotes/tree/master/RelativityLeave me a tip: ko-fi.com/eigenchris0:00 Intro1:40 Covectors / Doppler Shift Review4:57 Covector Field for a light wave13:21 Getting the frequency from a covector field18:21 Gravitational vs Doppler Frequency Shift24:56 Extra derivations25:44 Summary
Relativity 110e: Cosmology - Perfect Fluids, Cosmic Rest Frame, Equation of State eigenchris 2022-06-07 | Full relativity playlist: youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQaPowerpoint slide files: github.com/eigenchris/MathNotes/tree/master/RelativityLeave me a tip: ko-fi.com/eigenchris0:00 Intro1:43 Review of Energy-Momentum Tensor4:07 Perfect Fluid Energy-Momentum Tensor10:45 Cosmic Rest Frame18:37 Equation of State22:40 Summary
Relativity 108d: Schwazrschild Metric - Eddington-Finkelstein, Kruskal-Szekeres, White/Wormholes eigenchris 2022-05-31 | Full relativity playlist: youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQaPowerpoint slide files: github.com/eigenchris/MathNotes/tree/master/RelativityLeave me a tip: ko-fi.com/eigenchrisAdditional Resources:Sean Carroll: preposterousuniverse.com/wp-content/uploads/grnotes-seven.pdfDiscussion about above notes: physicsforums.com/threads/outgoing-eddington-finkelstein-coordinates.628702Notes using +--- metric: http://www.physik.uni-regensburg.de/forschung/gebhardt/gebhardt_files/skripten/Lect04KruskalCoord.pdfhttp://www.physik.uni-regensburg.de/forschung/gebhardt/gebhardt_files/skripten/Lect04KruskalCoord.pdfPenrose Diagrams:Wikipedia: en.wikipedia.org/wiki/Penrose_diagramPBS spacetime #1: youtube.com/watch?v=mht-1c4wc0QPBS spacetime #2: youtube.com/watch?v=4v9A9hQUcBQRead more about Flamm's Parabaloid:en.wikipedia.org/wiki/Schwarzschild_metric#Flamm's_paraboloidOther Videos on EF/KS coordinates:Schuller/Winter School: youtube.com/watch?v=7VJzouE9rNE&list=PLFeEvEPtX_0S6vxxiiNPrJbLu9aK1UVC_&index=22GRSS: youtube.com/watch?v=SkWLg3pBwGY&list=PL9_n3Tqzq9iWtgD8POJFdnVUCZ_zw6OiB&index=188Arindam Kumar Chatterjee:youtube.com/watch?v=4PI4jI6sxb8Arindam Kumar Chatterjee: youtube.com/watch?v=PMXkptjAdOoK Raviteja: youtube.com/watch?v=gMnKRVT-QmU0:00 Intro2:58 Non-orthogonal + Light-like Vectors Review7:16 Ingoing Eddington-Finkelstein Coordinates15:36 Outgoing Eddington-Finkelstein Coordinates17:19 Kruskal-Szekeres Coordinates28:03 KS 4 Spacetime Regions33:01 Wormholes (Einstein-Rosen Bridge)36:06 Summary
Relativity 110c: Cosmology - FLRW Tensor/Coefficient Derivations eigenchris 2022-04-24 | Full relativity playlist: youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQaPowerpoint slide files: github.com/eigenchris/MathNotes/tree/master/RelativityLeave me a tip: ko-fi.com/eigenchrisSome other sources for the tensor formulas are:- Sean Carroll GR Cosmology notes: preposterousuniverse.com/wp-content/uploads/grnotes-eight.pdf- Section 2.9 of the Catalogue of Spacetimes (note they they take the g_tt metric term to be c^2 instead of 1, so the locations of c in the formulas are different: arxiv.org/pdf/0904.4184.pdf0:00 Intro + Notation2:48 Connection Coefficients10:08 Ricci Tensor19:04 Ricci Scalar
Relativity 110a: Cosmology - Introduction to Modern Cosmology eigenchris 2022-04-05 | Full relativity playlist: youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQaPowerpoint slide files: github.com/eigenchris/MathNotes/tree/master/RelativityLeave me a tip: ko-fi.com/eigenchrisEinstein's 1917 paper: https://einsteinpapers.press.princeton.edu/vol6-trans/433Friedmann's 1922 paper: https://wwwphy.princeton.edu//~steinh/ph563/friedmann.pdfEinstein's objection + retraction: https://einsteinpapers.press.princeton.edu/vol13-trans/301https://einsteinpapers.press.princeton.edu/vol14-trans/77Lemaître's 1927 paper: academic.oup.com/mnras/article/91/5/483/985165?login=falseHubble's 1929 paper: pnas.org/doi/full/10.1073/pnas.15.3.168 Ralph Alpher's 1948 CMB prediction paper: sci-hub.hkvisa.net/10.1103/PhysRev.74.15770:00 Introduction1:35 Einstein's 1917 cosmology paper9:46 Friedmann Equations14:38 Galactic Redshift18:54 Lemaitre & Hubble propose an expanding universe22:44 Cosmic Microwave Background28:10 Dark Energy and Universe's Accelerating Expansion31:41 Summary
Relativity 109e: Gravitational Waves - How Gravitational Wave Affect Free Particles eigenchris 2022-02-27 | Full relativity playlist: youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQaPowerpoint slide files: github.com/eigenchris/MathNotes/tree/master/RelativityLeave me a tip: ko-fi.com/eigenchrisSome PDFs on calculating the components of the Riemann Curvature Tensor for gravitational waves:See Section 5.2 of: https://pages.pomona.edu/~tmoore/LesHouches/les-houches-5.pdfSee Section 8.2 of: http://star-www.st-and.ac.uk/~hz4/gr/hendry_GRwaves.pdfSome helpful PDFs on the Lorenz Gauge:https://pages.pomona.edu/~tmoore/LesHouches/les-houches-4.pdfhttps://pages.pomona.edu/~tmoore/LesHouches/les-houches-5.pdfOther Sources on Gravitational Waves:Sean Carroll: preposterousuniverse.com/wp-content/uploads/grnotes-six.pdfWikipedia: en.wikipedia.org/wiki/Linearized_gravityYouTube: youtube.com/watch?v=kIBdtbCszB0PDF 1: http://star-www.st-and.ac.uk/~hz4/gr/hendry_GRwaves.pdfPDF 2: https://www.tat.physik.uni-tuebingen.de/~kokkotas/Teaching/NS.BH.GW_files/GW_Physics.pdf0:00 Review1:35 Gravitational Waves vs Wavy Coordinates3:56 Geodesics for Gravitational Waves7:19Proper Distance between Geodesics11:50 Interpreting + and x Polarizations15:49 Visualizing Gravitational Waves17:23 Summary
Relativity 109d: Gravitational Waves - Transverse-Traceless Gauge (Plus and Cross Polarizations) eigenchris 2022-02-24 | Full relativity playlist: youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQaPowerpoint slide files: github.com/eigenchris/MathNotes/tree/master/RelativityLeave me a tip: ko-fi.com/eigenchrisSome helpful PDFs on the Lorenz Gauge:https://pages.pomona.edu/~tmoore/LesHouches/les-houches-4.pdfhttps://pages.pomona.edu/~tmoore/LesHouches/les-houches-5.pdfOther Sources on Gravitational Waves:Sean Carroll: preposterousuniverse.com/wp-content/uploads/grnotes-six.pdfWikipedia: en.wikipedia.org/wiki/Linearized_gravityYouTube: youtube.com/watch?v=kIBdtbCszB0PDF 1: http://star-www.st-and.ac.uk/~hz4/gr/hendry_GRwaves.pdfPDF 2: https://www.tat.physik.uni-tuebingen.de/~kokkotas/Teaching/NS.BH.GW_files/GW_Physics.pdf0:00 Polarization1:58 Intro to Transverse Traceless Gauge3:13 Review of Plane Waves 7:44 The components of the wave amplitude9:38 The Transverse-Traceless Gauge13:18 h-bar equals h14:31 Determining components of Wave Amplitude17:12 + and x polarizations18:07 Summary
Relativity 109c: Gravitational Waves - Wave Derivation (The Lorenz Gauge) eigenchris 2022-02-07 | Full relativity playlist: youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQaPowerpoint slide files: github.com/eigenchris/MathNotes/tree/master/RelativityLeave me a tip: ko-fi.com/eigenchrisSome helpful PDFs on the Lorenz Gauge:https://pages.pomona.edu/~tmoore/LesHouches/les-houches-4.pdfhttps://pages.pomona.edu/~tmoore/LesHouches/les-houches-5.pdfOther Sources on Gravitational Waves:Sean Carroll: preposterousuniverse.com/wp-content/uploads/grnotes-six.pdfWikipedia: en.wikipedia.org/wiki/Linearized_gravityYouTube: youtube.com/watch?v=kIBdtbCszB0PDF 1: http://star-www.st-and.ac.uk/~hz4/gr/hendry_GRwaves.pdfPDF 2: https://www.tat.physik.uni-tuebingen.de/~kokkotas/Teaching/NS.BH.GW_files/GW_Physics.pdf0:00 Introduction to Lorenz Gauge2:10 Proving 3 terms in G go to zero5:09 Displacement Field8:03 Metric Tensor transformation10:30 Riemann Tensor transformation12:05 h-bar transformation14:43 Lorenz gauge gives the Wave Equation17:57 Gauge Transformations in Electricity and Magnetism22:12 Gauge Transformations in Linearized Gravity
Relativity 109b: Gravitational Waves - Linearized Gravity / Weak Gravity eigenchris 2022-01-31 | Full relativity playlist: youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQaPowerpoint slide files: github.com/eigenchris/MathNotes/tree/master/RelativityLeave me a tip: ko-fi.com/eigenchrisBinary System orbit described in section 9.2 of this PDF: http://star-www.st-and.ac.uk/~hz4/gr/hendry_GRwaves.pdfEinstein's 1916 paper on Gravitational waves: https://einsteinpapers.press.princeton.edu/vol6-trans/213Official LIGO site: https://www.ligo.caltech.edu/LIGO FAQ: https://www.ligo.caltech.edu/page/faqOther Sources:Sean Carroll: preposterousuniverse.com/wp-content/uploads/grnotes-six.pdfWikipedia: en.wikipedia.org/wiki/Linearized_gravityYouTube: youtube.com/watch?v=kIBdtbCszB0PDF 1: http://star-www.st-and.ac.uk/~hz4/gr/hendry_GRwaves.pdfPDF 2: https://www.tat.physik.uni-tuebingen.de/~kokkotas/Teaching/NS.BH.GW_files/GW_Physics.pdfPhysics Stack Exchange question about the derivatives of h (comment response by Valter Moretti, who is a university professor): physics.stackexchange.com/questions/593298/linearized-gravity-derivatives-of-the-metric-perturbation0:00 Introduction to Linearized Gravity2:26 Inverse Metric5:03 Connection Coefficients6:15 Riemann Tensor7:39 Ricci Tensor8:53 Ricci Scalar9:58 Einstein Tensor13:02 Summary
Relativity 109a - Gravitational Waves: Introduction (LIGO, Wave Equation) eigenchris 2022-01-26 | Full relativity playlist: youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQaPowerpoint slide files: github.com/eigenchris/MathNotes/tree/master/RelativityLeave me a tip: ko-fi.com/eigenchrisBinary System orbit described in section 9.2 of this PDF: http://star-www.st-and.ac.uk/~hz4/gr/hendry_GRwaves.pdfEinstein's 1916 paper on Gravitational waves: https://einsteinpapers.press.princeton.edu/vol6-trans/213Official LIGO site: https://www.ligo.caltech.edu/LIGO FAQ: https://www.ligo.caltech.edu/page/faqOther Sources:Sean Caroll: preposterousuniverse.com/wp-content/uploads/grnotes-six.pdfWikipedia: en.wikipedia.org/wiki/Linearized_gravityPhysics Unsimplified Video: youtube.com/watch?v=kIBdtbCszB0Other helpful PDF: https://www.tat.physik.uni-tuebingen.de/~kokkotas/Teaching/NS.BH.GW_files/GW_Physics.pdf0:00 Introduction to Waves2:10 Gravitational Waves4:24 History of Gravitational Waves5:30 LIGO detectors9:32 Wave Equation12:45 Wave Equation Notation
eigenchriss Math/Physics YouTube Channel Recommendations eigenchris 2022-01-23 | [A1] Robert Davie youtube.com/channel/UCm7lQ5bSq6yBHVPYJ7J561w[A2] Dietterich Labs youtube.com/c/DietterichLabs/videos[A3] dXoverdteqprogress youtube.com/user/dXoverdteqprogress/videos[A4] XylyXylyX youtube.com/user/XylyXylyX/videos[A5] Noah Explains Physics youtube.com/channel/UCZSC7wgBq3RSLKoJDfGL0Rg/videos[A6] Physics with Elliot: youtube.com/c/PhysicswithElliot/videos[A7] Sander Konijnenberg youtube.com/channel/UCb4KzvTvz-9kMuL3-9Nj_fA/videos[B1] Alex Flournoy youtube.com/channel/UCHAwDVSS8oDLLln07cNdU6A/videos[B2] Frederic P Schuller youtube.com/c/FredericSchuller/videos[B2 also] Schuller's General Relativity playlist on a separate channel: youtube.com/playlist?list=PLFeEvEPtX_0S6vxxiiNPrJbLu9aK1UVC_ [B3] Hitoshi Murayama youtube.com/channel/UCoIq8T6hxfk6ZtLBv9CMCnQ/videos[B4] Peter Woit youtube.com/channel/UCdSEKN94Jo1xjUHVyfEfIjgPeter Woit's work-in-progress text: https://www.math.columbia.edu/~woit/QMbook/qmbook-latest.pdf[B5] Leonard Susskind (individual courses are 10 videos each) youtube.com/playlist?list=PLLjeznqO-C0AVy5P39Hbybl0ew_03IkIx[B6] Tadashi Tokieda youtube.com/watch?v=SXHHvoaSctc&list=PLTBqohhFNBE_09L0i-lf3fYXF5woAbrzJ[B7] Introduction to differential forms playlist youtube.com/playlist?list=PLB8F2D70E034E9C29[C1] Snoopy Topology Notes https://www.math.colostate.edu/~renzo/teaching/Topology10/Notes.pdf[C2] Quick and Dirty Introduction to Exterior Algebraweb.archive.org/web/20191221153300/http://brickisland.net/cs177/?p=174web.archive.org/web/20191221153400/http://brickisland.net/cs177/?p=184web.archive.org/web/20191221195625/http://brickisland.net/cs177/?p=200web.archive.org/web/20191222002003/http://brickisland.net/cs177/?p=248web.archive.org/web/20191221104907/http://brickisland.net/cs177/?p=264[C2 also] The author of the above has a YouTube channel: youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS[C3] Sean Carroll GR Lecture Notes preposterousuniverse.com/grnotes[C4] Exploring Black Holes: eftaylor.com/exploringblackholes[C5] Catalogue of Spacetimes arxiv.org/pdf/0904.4184.pdf[C6] Einstein's Papers Onlinehttps://einsteinpapers.press.princeton.edu/
Relativity 108c: Schwarzschild Metric - Geodesics (Mercury perihelion advance, photon sphere) eigenchris 2021-11-19 | Full relativity playlist: youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQaPowerpoint slide files: github.com/eigenchris/MathNotes/tree/master/RelativityLeave me a tip: ko-fi.com/eigenchrisAlso see dXoverdteqprogress's video on the perihelion of Mercury: youtube.com/watch?v=pjD0Sa2_kK40:00 Introduction1:14 Geodesics Review5:28 Newtonian Orbits Review9:55 Constants of Motion (Geodesics)16:20 Tangent Vector Length (Geodesics)18:27 Timelike Geodesics (massive bodies)20:21 Graphing Effective Potentials26:38 Lightlike Geodesics (photon sphere)28:24 Perihelion Advance of Mercury 34:48 Summary
Relativity 108b: Schwarzschild Metric - Interpretation (Gravitational Time Dilation, Event Horizon) eigenchris 2021-11-11 | Full relativity playlist: youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQaPowerpoint slide files: github.com/eigenchris/MathNotes/tree/master/RelativityLeave me a tip: ko-fi.com/eigenchris0:00 Introduction0:53 Gravitational Time Dilation9:55 r-coordinate interpretation (radius)15:26 r-coordinate interpretation (circumference)18:24 Singularities20:23 Schwarzschild Radius + Event Horizon21:41 Light-like geodesics26:00 Light rays on spacetime diagrams31:36 SummaryRead more about Flamm's Parabaloid:en.wikipedia.org/wiki/Schwarzschild_metric#Flamm's_paraboloidFree "Exploring Black Holes" Textbook (look for "PDF" link under "Download Options" on the right side of the page):archive.org/details/exploringblackholesAnother source for the radial integral (see section 4.3): https://pages.pomona.edu/~tmoore/LesHouches/les-houches-4.pdfViewer phugoidoscillations commented that the integral can also be found in "Anton Calculus 6th ed", Table of Integrals #96.
Relativity 108a: Schwarzschild Metric - Derivation eigenchris 2021-10-10 | Full relativity playlist: youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQaPowerpoint slide files: github.com/eigenchris/MathNotes/tree/master/RelativityLeave me a tip: ko-fi.com/eigenchrisKarl Schwarzschild's 1916 paper: arxiv.org/pdf/physics/9905030.pdf0:00 Introduction to Schwarzschild metric5:12 Spherical Coordinates Review7:30 Schwarzschild Metric Assumptions10:59 Connection Coefficient Calculation17:24 Ricci Tensor Calculation22:35 Solving for A(r) and B(r)24:47 Solving for Schwarzschild Radius28:56 Warning + Conclusion
Relativity 107f: General Relativity Basics - Einstein Field Equation Derivation (w/ sign convention) eigenchris 2021-09-05 | Full relativity playlist: youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQaPowerpoint slide files: github.com/eigenchris/MathNotes/tree/master/RelativityLeave me a tip: ko-fi.com/eigenchrisGeneral Proof of 2nd Bianchi Identity: youtu.be/hhhYzfozon0?t=613Einstein Papers:https://einsteinpapers.press.princeton.edu/vol6-trans/115https://einsteinpapers.press.princeton.edu/vol6-trans/1210:00 Overview of Derivation6:42 Metric Compatibility + Cosmological Constant term12:53 Contracted Bianchi Identity20:54 Solving for Kappa (Einstein Constant)28:08 Trace-Reversed Form29:46 Sign Conventions35:09 Summary
Tensors for Relativity Explained in 1 Minute (#VeritasiumContest) eigenchris 2021-08-27 | Tensors for Beginners Playlist: youtube.com/playlist?list=PLJHszsWbB6hrkmmq57lX8BV-o-YIOFsiGTensor Calculus Playlist: youtube.com/playlist?list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCxRelativity Playlist: youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQaContact: eigenchris.videos@gmail.com#VeritasiumContest
Relativity 107e: General Relativity Basics - Stress-Energy-Momentum Tensor eigenchris 2021-08-16 | Full relativity playlist: youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQaPowerpoint slide files: github.com/eigenchris/MathNotes/tree/master/RelativityLeave me a tip: ko-fi.com/eigenchris0:00 Introduction2:22 Number-flux 4-vector N9:58 Conservation of Particle Number11:11 Galilean Transformation for N12:57 Lorentz Transformation for N15:41 Energy-Momentum Tensor T21:51 Interpreting Components of T23:47 Conservation of Energy-Momentum28:28 Dust and Perfect Fluid32:21 Conclusion
Relativity 107d: General Relativity Basics - Curved Spacetime for Newtonian Gravity (Newton Cartan) eigenchris 2021-06-27 | Full relativity playlist: youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQaPowerpoint slide files: github.com/eigenchris/MathNotes/tree/master/RelativityLeave me a tip: ko-fi.com/eigenchris0:00 Introduction to Newton-Cartan Theory1:47 Poisson's Equation6:30 Geodesic Equation for Newtonian Gravity11:10 Riemann Tensor for Newtonian Gravity15:50 Tidal Forces Tensor18:50 Ricci Tensor for Newtonian Gravity22:49 Conclusion + SummaryFYI, I'm using the sign convention for the Riemann Tensor used in section 12.2 of "Gravitation" by Misner, Thorne and Wheeler.
Introduction to Mathematics of Spinors (from a self-learner) eigenchris 2021-06-20 | Parts 1 and 2 (Block Sphere, Pauli Vectors): youtube.com/watch?v=QOl8EL7H7QIParts 3 and 4 (Clifford Algebras, Minimal Ideals): youtube.com/watch?v=_5o0Bc66fikParts 5, 6 and 7 (Lie Groups/Algebras, Double Covers, Representation Theory): youtube.com/watch?v=v87AXrdHAkQResources for learning spinors: Introduction to Spinors: arxiv.org/pdf/1312.3824.pdfSpinors and Clifford Algebras: https://hal.archives-ouvertes.fr/hal-00502337/documentThesis by Crystal-Ann McKenzie (does the best job at explaining spinors as members of minimal ideals): scholar.uwindsor.ca/cgi/viewcontent.cgi?article=6651&context=etdVideo showing all the different types of spinor invariants found in a Lagrangian from QFT: youtube.com/watch?v=uhox3P99GigReview of the 4 types of spinor indices (covariant, contravariant, covariant-dot, contravariant-dot): https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.697.1657&rep=rep1&type=pdfBooks:"Introduction to 2-Spinors in General Relativity" by Peter J. O'Donnell"Introduction to Supersymmetry" by Wiedamann"The Theory of Spinors. The Geometry of Minkowski Spacetime" by Naber, G. L.
Relativity 107c: General Relativity Basics - Curvature, Riemann Tensor, Ricci Tensor, Ricci Scalar eigenchris 2021-06-08 | Full relativity playlist: youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQaPowerpoint slide files: github.com/eigenchris/MathNotes/tree/master/RelativityLeave me a tip: ko-fi.com/eigenchrisYou are free to continue watching to the next video, but if you feel you are getting confused, here are some other videos on curvature here:TC 21 - Lie Bracket, Flow, Torsion: youtube.com/watch?v=SfOiOPuS2_U&list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx&index=24TC 22 - Riemann Curvature Tensor Meaning: youtube.com/watch?v=-Il2FrmJtcQ&list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx&index=25TC 23 - Riemann Curvature Tensor Symmetries: youtube.com/watch?v=optrC-0HhMI&list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx&index=26TC 24 - Ricci Tensor Meaning: youtube.com/watch?v=ZhDNijOEw0Y&list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx&index=27TC 25 - Ricci Tensor/Scalar Meaning: youtube.com/watch?v=oQZTYt_Pxcc&list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx&index=28TC 26 - Ricci Tensor/Scalar Properties: youtube.com/watch?v=hhhYzfozon0&list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx&index=290:00 Introduction1:56 Riemann Curvature Tensor8:12 Riemann Tensor Components + Symmetries15:29 Riemann Tensor - Geodesic Deviation19:04 Ricci Curvature Tensor23:46 Ricci Curvature Scalar25:46 Curvature of Rindler Metric 33:19 Summary
Error Correcting Codes 4a: Finite Fields - Introduction to Non-Binary Codes eigenchris 2021-06-07 | Full ECC playlist: youtube.com/playlist?list=PLJHszsWbB6hqkOyFCQOAlQtfzC1G9sf2_Definition of a field: en.wikipedia.org/wiki/Field_(mathematics)#Classic_definition
Relativity 107b: General Relativity Basics - Manifolds, Covariant Derivative, Geodesics eigenchris 2021-05-11 | Full relativity playlist: youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQaPowerpoint slide files: github.com/eigenchris/MathNotes/tree/master/RelativityLeave me a tip: ko-fi.com/eigenchrisYou are free to continue watching to the next video, but if you feel you are getting confused, here are some other videos on geodesics and the covariant derivative:TC 15 - Geodesics + Christoffel Symbols on Sphere: youtube.com/watch?v=1CuTNveXJRc&list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx&index=17TC 16 - Geodesics on Sphere example: youtube.com/watch?v=8sVDceI70HM&list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx&index=18TC 17 - Flat Space Definition: youtube.com/watch?v=U5iMpOn5IHw&list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx&index=19TC 17.5 - Component Definition: youtube.com/watch?v=8S_XOjd5Mec&list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx&index=20TC 18 - Extrinsic Definition: youtube.com/watch?v=Af9JUiQtV1k&list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx&index=21TC 19 - Intrinsic Definition: youtube.com/watch?v=EFKBp52LtDM&list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx&index=22TC 20 - Abstract Definition: youtube.com/watch?v=cEEahoUUGyc&list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx&index=230:00 Introduction1:35 Equivalence Principle and Manifolds6:15 Extrinsic vs Intrinsic views of Manifolds10:29 Tangent Vectors on Manifolds16:20 Covariant Derivative Notation22:10 Levi Civita Connection28:58 Geodesics33:44 Summary
Relativity 107a: General Relativity Basics - Equivalence Principle and Proper Acceleration eigenchris 2021-04-10 | Full relativity playlist: youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQaPowerpoint slide files: github.com/eigenchris/MathNotes/tree/master/RelativityLeave me a tip: ko-fi.com/eigenchrisOther resources on the various equivalence principles:Sean Carrol Notes, Chapter 4: preposterousuniverse.com/wp-content/uploads/grnotes-four.pdf(full notes at: preposterousuniverse.com/grnotes)Alex Flournoy Video Lectures: youtube.com/watch?v=UMOrzZ2igdw&list=PLDlWMHnDwyliMevB36wgRbjXhJkoN_RUQ&index=10Wikipedia: en.wikipedia.org/wiki/Equivalence_principle#Modern_usage0:00 Introduction0:57 Equivalence Principle7:28 Proper Acceleration / Gravity is different17:02 Tidal Forces21:37 Summary
What Is Momentum? (joke video) eigenchris 2021-04-01 | My math/physics playlists:Tensors for Beginners: youtube.com/playlist?list=PLJHszsWbB6hrkmmq57lX8BV-o-YIOFsiGTensor Calculus: youtube.com/playlist?list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCxError Correcting Codes: youtube.com/playlist?list=PLJHszsWbB6hqkOyFCQOAlQtfzC1G9sf2_Relativity: youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQa
Relativity 106a: Tensors - Frequency Wave Covectors and Doppler Shift (with accelerating frames) eigenchris 2021-03-14 | Full relativity playlist: youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQaPowerpoint slide files: github.com/eigenchris/MathNotes/tree/master/RelativityLeave me a tip: ko-fi.com/eigenchrisPrevious videos on covectors:Tensors for Beginners 4: youtube.com/watch?v=LNoQ_Q5JQMYTensors for Beginners 5: youtube.com/watch?v=rG2q77qunSwTensors for Beginners 6: youtube.com/watch?v=d5da-mcVJ200:00 Intro1:59 Covector Basics3:51 Covector Laws6:33 Covector Components9:25 Basis Covectors13:02 Covectors Summary14:30 Doppler Effect / Waves Intro16:40 Wave Covector18:26 Galilean Doppler Effect23:02 Relativistic Doppler Effect (Inertial Frames)28:20 Relativistic Doppler Effect (Accelerating Frame)31:44 Conclusion
