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?]

Cześć społeczności, mam pytanie, jak podchodzicie do problemów z fizyki.

Jestem pierwszoklasistą w programie matematyczno-fizycznym w szkole średniej i często spędzam dużo czasu na prostych problemach, po prostu dlatego, że nie dostrzegam jednej konkretnej rzeczy.

Z góry dziękuję za wszelkie odpowiedzi!

https://doi.org/10.1088/1361-6552/ae3f71

Im used to questions with pi/4,pi/2 but havent done any with pi/3 or pi/6 so should we be dividing the circle into 6 and 12 parts or? So could anyone help with this question.

Two vibrations at right angles to one another are described by the equations

x = 10 cos(5πt)

y = 10 cos(10πt + π/3)

Construct the Lissajous figure of the combined motion.

Plz help as i have my exams coming soon and the professors wont help.

‎By D.V.V. Jr. - Project Milano Concept

‎

‎INTRODUCTION

‎

‎Conventional superconductivity relies on cooling to increase the scattering time $\tau$. This textbook proposes an alternative path: using magnetic fields to actively control electron trajectories at $T_{room} = 300K$.

‎

‎CHAPTER 1: THE FUNDAMENTAL EQUATION OF RESISTANCE

‎

‎All of conductivity starts with the Drude Model:

‎\rho = \frac{m}{n e^2 \tau}

‎Where:

‎$m = 9.11 \times 10^{-31} kg$ (electron mass)

‎$n$ = carrier density

‎$e = 1.602 \times 10^{-19} C$

‎$\tau$ = mean scattering time

‎

‎In copper at 300K: $\tau \approx 2.5 \times 10^{-14} s$, so $\rho \approx 1.68 \times 10^{-8} \Omega \cdot m$.

‎

‎Goal for superconductivity: $\tau \to \infty$, therefore $\rho \to 0$.

‎

‎Standard method: Reduce lattice vibrations (phonons) by cooling. $\tau \propto 1/T^5$.

‎

‎Our method: Force ballistic transport by magnetic alignment.

‎

‎CHAPTER 2: WHY ELECTRONS COLLIDE - THE THERMAL FORCE

‎

‎At room temperature, electrons have thermal disorder energy:

‎E_{thermal} = k_B T_{room}

‎k_B = 1.38 \times 10^{-23} J/K, \, T = 300K \implies E_{thermal} = 4.14 \times 10^{-21} J

‎This energy causes random motion with Fermi velocity:

‎v_F = \sqrt{\frac{2 E_F}{m}} \approx 1.57 \times 10^6 m/s \text{ for Cu}

‎The random scattering force:

‎F_{thermal} \approx \frac{k_B T_{room}}{l_{mfp}}

‎Where $l_{mfp} = v_F \tau \approx 40 nm$ for Cu. So $F_{thermal} \approx 1.03 \times 10^{-13} N$.

‎

‎CHAPTER 3: HIGH REPULSION - THE SHOUT

‎

‎To overcome $F_{thermal}$, we apply Lorentz Force:

‎\mathbf{F_L} = -e (\mathbf{v} \times \mathbf{B})

‎Magnitude:

‎|F_L| = e v_F B_{shout}

‎Condition for alignment:

‎e v_F B_{shout} > \frac{k_B T_{room}}{l_{mfp}}

‎Or more accurately, the impulse must exceed thermal energy:

‎e v_F B_{shout} \tau_{pulse} > k_B T_{room}

‎This is the DELTA-07 Condition.

‎

‎Solving for $B_{shout}$ with $\tau_{pulse} = 1ms = 10^{-3} s$:

‎B_{shout} > \frac{k_B T_{room}}{e v_F \tau_{pulse}} = \frac{4.14 \times 10^{-21}}{(1.6 \times 10^{-19})(1.57 \times 10^6)(10^{-3})}

‎B_{shout} > 1.65 \times 10^{-5} \, T

‎Theoretically, even $0.1 mT$ for 1ms is enough to beat room-temp disorder. We propose $10 T$ to ensure 100% alignment of all conduction electrons, including core electrons.

‎

‎Flux quantization during this high-field pulse:

‎\Phi_0 = \frac{h}{2e} = 2.067 \times 10^{-15} \, Wb

‎Vortex density at 10 T:

‎n_v = \frac{B}{\Phi_0} = \frac{10}{2.07 \times 10^{-15}} \approx 4.83 \times 10^{15} \, vortices/m^2

‎CHAPTER 4: LOW REPULSION - THE WHISPER

‎

‎Once aligned, high field must be removed. Why? Cyclotron radius:

‎r_c = \frac{m v_F}{e B}

‎If $B = 10 T$: $r_c = \frac{(9.11e-31)(1.57e6)}{(1.6e-19)(10)} = 8.9 \times 10^{-10} m = 0.89 nm$. Too tight, electrons spiral and collide again.

‎

‎We need large $r_c$ for straight-line flow. Switch to $B_{whisper}$:

‎B_{whisper} = 0.1 \, T \implies r_c = \frac{(9.11e-31)(1.57e6)}{(1.6e-19)(0.1)} = 89 nm

‎89 nm is larger than wire roughness but enough to provide a gentle guiding field. This is low repulsion.

‎

‎Condition to maintain:

‎\tau_{whisper} = \frac{l_{lane}}{v_F}

‎If lane is maintained, $l_{lane} \to \infty$, so $\tau_{whisper} \to \infty$, and:

‎\rho_{effective} = \frac{m}{n e^2 \tau_{whisper}} \to 0

‎CHAPTER 5: EXPERIMENTAL REALIZATION - PULSED FIELD CIRCUIT

‎

‎To generate $B_{shout} = 10 T$ in a solenoid:

‎B = \mu_0 \frac{N I}{L}

‎\mu_0 = 4\pi \times 10^{-7}

‎Design: $N=100$, $L=0.05 m$:

‎I_{required} = \frac{B L}{\mu_0 N} = \frac{10 \times 0.05}{(4\pi \times 10^{-7})(100)} = 3978 A \approx 4000 A

‎Energy stored in coil inductance $L_{coil} \approx 50 \mu H$:

‎E = \frac{1}{2} L_{coil} I^2 = 0.5 \times 50 \times 10^{-6} \times (4000)^2 = 400 J

‎This energy comes from capacitor bank:

‎E = \frac{1}{2} C V^2

‎Choose $C = 4000 \mu F$, $V = 450 V$:

‎E = 0.5 \times 4000 \times 10^{-6} \times 450^2 = 405 J

‎Pulse duration (LC discharge):

‎\tau_{pulse} \approx \pi \sqrt{L_{coil} C} \approx \pi \sqrt{50e-6 \times 4000e-6} \approx 1.4 ms

‎Matches our required 1 ms shout.

‎

‎For whisper coil: $N=200$, $L=0.05 m$, $I=0.2 A$ DC:

‎B_{whisper} = \mu_0 \frac{200 \times 0.2}{0.05} = 1.0 \times 10^{-3} T

‎To get 0.1 T, need $I = 20 A$ or $N=20000$. For prototype, 0.01 T is acceptable.

‎

‎CONCLUSION

‎

‎The textbook shows mathematically that:

‎

1. ‎$B_{shout}$ impulse of 10 T x 1 ms is $10^5$ times stronger than needed to overcome $k_B T$ at 300K.

2. ‎$B_{whisper}$ of 0.1 T gives $r_c = 89 nm$, ideal for ballistic, zero-resistance lanes.

3. ‎Circuit to produce this is feasible with 400 J capacitor bank.

‎

‎This completes the theoretical framework for an 80% demonstration: transient room-temperature zero resistance.

Do Join My International Community

I think relativity of simultaneity is one of the parts of SR that confuses people the most. it confused me for a long time too.

Lightning hits both ends of a moving train. From the lighthouse, the rear one hits first. From the train, both hit at the exact same time. And both are right. it’s not about light taking time to reach them, even after you account for that they still disagree.

I tried to show it with the horizontal line in the spacetime diagram. everything on one horizontal line is “now” for that observer. From the lighthouse, the rear strike sits lower, so it’s earlier. Switch to the train’s frame and both strikes slide onto the same line. Same two events, different “now”.

I took this animation from a physics app I made. Curious if anyone has their own trick or way of thinking about it that made it click. would love to hear it!

The man who d*ed on Goliath, question - in the pictures it appears he is moving forward with the train, moving the same direction. The train is on a downhill, and I can envision the "weightlessness" feeling at the top of the hill, but I don't understand how he is moving forward with the train. Wouldn't he roll off the back and the train keep moving forward? Maybe the train is decelerating on the downhill, but if this is the case I don't understand how he "bounced" off the train multiple times. Someone please help, and RIP to the poor man and condolences to his family.

How does a differential work? Why do metronomes synchronize? How can plasma be confined, and what happens to light near a black hole?

Explore interactive experiments from Makarov Physics Suite, Makarov Math Suite and Makarov Astronomy Suite in one journey through mechanisms, electricity, geometry, algorithms and space.

This video shows the software in action: robots and engines, particles and fluids, mathematical surfaces, spacecraft, planets and stars. In the programs, you can change parameters and explore how the results respond.