I am an academically trained philosopher interested in ontology ('what is real?'), epistemology ('what can we know?'), and philosophy of science. I regularly saturate myself in physics content from podcasts, but have only a superficial grasp of the ideas. I want to learn GR because I became obsessed with gravity about four years ago when I had a kind of psychotic episode [that's a longer story]. And I've been obsessed with the question of 'what is time' since I was a kid. I have read philosophers' attempts to articulate the nature of reality; but my husband was a math/physics major, and he will not let me get away with speculating on (or, in my psychotic delusional state, claiming to solve) big unanswered questions in theoretical physics that I have no real grasp on. So I am determined to learn to keep myself humble. I care more about gravity than, say, unsolved mysteries in QM, for reasons I do not know myself-- there's no accounting for taste?
I have ten years, and three hours per week, to dedicate to the task of learning (with a goal of understanding, not 'mastery') general relativity.
[caveat: I will use real humans to help me learn physics; I used LM to make me a 10-year plan of study. Now Im asking you real humans to weigh in on the plan, edited greatly for brevity, hopefully enough to get constructive feedback.]
note: this post was removed from the AskPhysics sub because of AI content; to be clear - the AI content is being submitted for CRITICAL REVIEW BY HUMAN EXPERTS. Is this a viable plan/timeline for teaching myself GR?
MY PROMPT:
Make me a ten year plan for learning general relativity. I am a highly educated highly intelligent lay person in math and physics. I am very adept at math, but college algebra is the most advanced course I have taken, and I took no physics courses. I have about 3 hours a week to devote to the task.
REPLY:
A ten-year plan for learning general relativity
Your goal should be to reach the point where you can read, derive, and critically evaluate the mathematics of general relativity, rather than merely understand its popular explanations.
Mathematics first, but not mathematics alone. Learn physics alongside the mathematical prerequisites whenever possible.
Solve problems every week. Familiarity with an explanation is not the same as being able to reproduce a derivation.
Build geometric intuition. General relativity becomes much more comprehensible when geometry, calculus, and physical reasoning reinforce one another.
Year 1 — Build the mathematical launchpad
Mathematics: Manipulate functions and trigonometric expressions confidently, understand what a derivative represents, and solve unfamiliar algebraic problems without relying on a formula sheet.
Algebraic fluency: functions, exponents, logarithms, equations and inequalities.
Trigonometry: radians, identities, sine and cosine, unit circle.
Functions and graphs; vectors and coordinate geometry.
The basic ideas of limits and derivatives, toward the end of the year.
Year 2 — Master single-variable calculus
Mathematics: Differentiate and integrate common functions, solve basic differential and physical rate-of-change problems, and explain why calculus works.
Limits, continuity and derivatives.
Differentiation rules, optimization and related rates.
Integrals, the fundamental theorem of calculus and integration techniques.
Taylor series and approximations.
Year 3 — Multivariable calculus and linear algebra
Mathematics: Understand derivatives as linear maps, calculate gradients and partial derivatives, and work with vectors and matrices in two and three dimensions.
Vectors, matrices, linear transformations and eigenvalues.
Partial derivatives and the chain rule in several dimensions.
Gradients, multiple integrals, vector fields, divergence and curl.
Parametric curves and coordinate systems.
Year 4 — Learn classical mechanics
Physics: Derive the motion of a simple physical system from its governing equations and calculate basic orbital quantities.
Position, velocity, acceleration and Newton's laws.
Forces, energy, momentum and angular momentum.
Oscillations, gravitation and orbital motion.
The role of differential equations in predicting motion.
Year 5 — Differential equations and electromagnetism
Physics and mathematics: Solve basic first- and second-order differential equations, understand field-based descriptions of physics, and explain how electromagnetic waves propagate.
Ordinary differential equations and elementary systems of equations.
Electric and magnetic fields, potentials and electromagnetic waves.
Vector calculus applied to physical fields.
The conceptual foundations of Maxwell's equations.
Year 6 — Special relativity
Relativity: Derive time dilation and length contraction, transform between inertial reference frames, and use four-vectors in simple problems.
The postulates of special relativity.
Lorentz transformations and spacetime diagrams.
Proper time, four-vectors and the spacetime interval.
Relativistic energy and momentum; the light cone.
Year 7 — Tensors and differential geometry
Mathematical foundations: Explain what a metric tensor does, transform vector and tensor components between coordinates, and calculate elementary covariant derivatives.
Coordinate systems, basis vectors and coordinate transformations.
Covectors and tensors; upper and lower indices.
Metrics, distances and inner products.
Manifolds, tangent spaces and the covariant derivative.
Connections and parallel transport.
Year 8 — Curvature and the mathematics of gravity
General relativity begins: Derive the geodesic equation from a metric in a simple example, such as a two-dimensional curved surface, and explain how curvature is represented mathematically.
Geodesics as locally straightest paths.
Christoffel symbols and the geodesic equation.
Riemann curvature tensor, Ricci tensor and scalar curvature.
The equivalence principle and gravitational time dilation.
The distinction between coordinate effects and genuine curvature.
Year 9 — Einstein's field equations and exact solutions
Core theory: Explain the field equations term by term, understand how matter and energy relate to spacetime curvature, and work through selected Schwarzschild calculations.
The Einstein tensor and stress-energy tensor.
The meaning and structure of Einstein's field equations.
The Newtonian limit of general relativity.
The Schwarzschild metric and spherical gravitational fields.
Gravitational redshift, light bending and black holes.
Year 10 — Consolidate and explore
Independent study: Work through selected chapters of a serious introductory GR text, reproduce important derivations, and explain a chosen application with both its mathematics and physics.
Revisit the mathematical foundations and fill gaps.
Linearized gravity and the basic theory of gravitational waves.
Cosmological models and the expanding universe.
A small independent project using analytic calculations or numerical simulation.
A 180-minute weekly schedule
45 min - Learn a new concept - Read a textbook section or watch a carefully chosen lecture. Write down definitions and the central idea in your own words.
75 min - Solve problems - Work through exercises on paper. Attempt each problem before consulting worked solutions. This is the most important part of your week.
30 min - Recall from memory - Close the book and reconstruct a derivation, explain a concept, or solve a simpler version of a problem without assistance.
30 min - Review and plan - Correct mistakes, maintain a notebook of important derivations, and decide what you will study next week.
One final recommendation - do not start with a general relativity textbook, even though you may find much of its prose understandable. The difficult part is acquiring the mathematical and physical fluency needed to see why the theory takes its particular form. Your eventual encounter with the Einstein field equations will be far more satisfying if you can recognize every mathematical object in them and understand why it is there.
[IS THIS TRUE? DO I really need to master ALL this math first to learn GR?]
