How to be a Great Amateur Theoretical Physicist

This page is an homage to the great theorist and Nobel laureate Gerard t'Hooft (see his web page for where this all started).

Philosophy

I have been looking over Gerard t'Hooft's web page for several years. Something has been bothering me about it. It is not his selection of things, but more their ordering that bothers me. Of course, he is a professional and I am an amateur; perhaps that is the problem—he did things the traditional way and I didn't, that gives me at least one case where a system of self-instruction worked. I will present that below.

Instead of listing resources solely on the web, I will include purchased items if they are very good.

If you follow these fairly carefully, you will do well.

The Approach

Begin a notebook and on the first page you intend to use, write page 1 and begin. Use the techniques from Skills for Learning from the self-study course as a guide. With each topic from the list write a brief description and give at least one example. If you think something is important, even if you know it, write that down, too. You must be completely honest with yourself; if you do not understand something or its properties stop and make a detailed study of it. Some places you will be able to proceed quickly, others will take a frustratingly long time to complete.

Here is an overview of the methods you should use:

Developing Study Skills

The first step is to acquire strong study skills. These will only be mastered with practice.

  1. Every time you encounter a new word attempt to define it. Guess it if you have to. Avoid being misled by technical terms that you think you understand. Do not expect your definition to be correct the first time. Come back to it as you learn more and refine the definition from ever more sophisticated viewpoints.
  2. Every time you encounter a fact or an idea ask yourself, "What is the justification of that idea? Why should you believe it? What is the proof of it, if there is any? If the idea is conjecture, what is the justification for it? How do we know this to be true?
  3. When you encounter an idea try to figure out how it relates to other similar ideas you have encountered. How is it similar? How is it different?
  4. When you encounter an idea or fact, can you tell if it is based on some observation of reality? Or is it based on inference from other ideas?
  5. When you encounter an idea or an argument, can you determine their underlying assumptions?
  6. When you encounter an idea is it the result of applying a specific idea to more general situations? Such an application is called induction. Or is it a case where general ideas are applied to specific situations? This type of application is called deduction.
  7. Given that certain facts will be established in the course of your study, make some predictions by applying what you have learned to situations not covered by your study so far. What do you predict will happen in these situations? Can you verify these predictions?
  8. Inevitably you will encounter gaps in your available information. This is true in school, and it is especially true in self-study. You will certainly encounter a situation where a fact or idea is put forward without complete information. This should not become a roadblock! To settle such occurances we note our ignorance and make an assumption that temporarily settles the matter until we can get back to it. So, when we encounter such confused issues do two things: first, make a note of the ambiguity that you are encountering; and second; determine what information or assumption on your part needs to be provided to settle it; and move on.
  9. In doing science we try to understand nature. The first step in this is to remove all complications and treat the object of study in the most simple and abstract way possible. Then we explore this idealized idea until we think we understand it. Beginning with such idealized and oversimplified ideas can you slowly add levels of complexity and reality until you develop your ideas into deep levels of understanding?

An Opening Statement on the Nature of Physics, Mathematics, and Computation

This requires either Mathematica 8 or later, or the free Mathematica CDF Viewer, though the viewer cannot run the programs, (you can find that here). You will also need to download the MAST Writing Style into the folder SystemFiles/Front End/Stylesheets. You can download that here. Once you load this file into the folder rename it MAST Writing Style 3. Reload Mathematica and it will be there.

Opening Statement

The List of Topics

I am including a ranking system: (1) Means that this is an absolute must-have for any theoretical physicist. (2) Means that the topic is important, and you should have it, but you need not get it on the first pass through the list. (3) Means that the topic is for specialists, and need not be studied by everyone.

Basics:

Basic Mathematics and Physics (1): This is an introduction to the basic ideas of mathematics and physics.

Introduction to Theoretical Physics

Basic Ideas of Mathematica (2)

The Problem of Motion and The Methods to Solve It (1)

The Problem of Gravity and The Methods to Solve it (1)

The Problem of Matter and The Methods to Solve It (1)

The Problem of Heat and The Methods to Solve It (1)

The Problem of Electricity and The Methods to Solve It (1)

The Problem of Magnetism and The Methods to Solve It (1)

The Problem of Light and The Methods to Solve It (1)

Classical Mechanics:

Classical Mechanics (1)

Mathematical Mechanics (2)

Computational Mechanics (2)

Advanced Classical Mechanics (2)

Applied Classical Mechanics (3)

Computational Physics

Computational Physics with Mathematica (2)

Programming in Mathematica (2)

Numerical Methods (3)

Symbolic Methods (3)

Advanced Computational Physics (3)

Classical Electrodynamics and Optics

Classical Electrodynamics (1)

Mathematical Electrodynamics (2)

Computational Electrodynamics (2)

Advanced Classical Electrodynamics (2)

Applied Classical Electrodynamics (3)

Quantum Mechanics and Fields

Quantum Mechanics (1)

Mathematical Quantum Mechanics (2)

Computational Quantum Mechanics (2)

Advanced Quantum Mechanics (2)

Applied Quantum Mechanics (3)

Quantum Field Theory (1)

Mathematical Quanfum Field Theory (2)

Computational Quantum Field Theory (2)

Advanced Quantum Field Theory (2)

Applied Quantum Field Theory (3)

Thermal Physics

Thermal Physics (1)

Mathematical Thermoal Physics (2)

Computational Thermal Physics (2)

Applied Thermal Physics (3)

Thermodynamics (2)

Mathematical Thermodynamics (3)

Computational Themodynamics (3)

Advanced Thermodynamics (3)

Applied Thermodynamics (3)

Kinetic Theory (2)

Mathematical Kinetic Theory (3)

Computational Kinetic Theory (3)

Advanced Kinetic Theory (3)

Applied Kinetic Theory (3)

Statistical Mechanics (2)

Mathematical Statistical Mechanics (3)

Computational Statistical Mechanics (3)

Advanced Statistical Mechanics (3)

Applied Statistical Mechanics (3)

Relativity

Gravitational Physics (1)

Mathematical Gravitational Physics (2)

Computational Gravitational Physics (2)

Classical Gravity Theory and Special Relativity (2)

General Relativity (2)

Applied General Relativity (3)

Advanced General Relativity (3)

Quantum Gravity (3)

Mathematical Methods

Advanced Mathematical Methods (1)

Mathematical Physics (1)

Applied Algebra (2)

Applied Geometry and Topology (2)

Applied Analysis (2)

Applied Discrete Mathematics (2)

Applied Probability and Statistics (2)

The Physics of Matter and Waves

The Physics of Matter (1)

Mathematical Physics of Matter (2)

Computational Physics of Matter (2)

Classical Physics of Matter (2)

Quantum Physics of Matter (2)

Applied Physics of Matter (3)

Elasticity (3)

Fluid Dynamics (3)

Heat Transfer (3)

Plasma Physics (3)

Mesoscopic Physics (3)

Atomic and Molecular Physics (3)

Nuclear Physics (3)

Particla Physics (3)

Applied Theoretical Physics

Astrophysics (3)

Atmospheric Science (3)

Biophysics (3)

Chemical Physics (3)

Engineering Physics (3)

Geophysics (3)

Oceanic Science (3)

Stellar Physics (3)

Interstellar Physics (3)

Galactic Physics (3)

Cosmology (3)

Atmospheric Dynamics (3)

Atmospheric Thermal Physics (3)

Atmospheric Electrodynamics (3)

Atmospheric Radiation (3)

Climate Science (3)

Cellular Biophysics (3)

Molecular Biophysics (3)

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