Feynman Lectures Simplified 2D

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Robert L. Piccioni, Ph.D.

Feynman Lectures

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2D: Magnetic Matter, Elasticity,
Fluids, & Curved Spacetime

Feynman Simplified 2D covers the last quarter of Volume 2, the freshman course, of The Feynman Lectures on Physics. The topics we explore include:
  • Principle of Least Action
  • Tensors in 3-D and 4-D Spacetime
  • Magnetic Materials
  • Diamagnetism & Paramagnetism
  • Ferromagnetism
  • Elasticity & Elastic Matter
  • Viscosity & Liquid Flow
  • Gravity and Curved Spacetime


What is a Tensor?

Tensors are a generalization of vectors. Tensor calculus is a beautiful branch of mathematics that empowers us to elegantly and effectively describe many complex, multi-dimensional phenomena.

Tensors are essential in general relativity, where 4-D spacetime curves, twists, and stretches differently at every point, at every instant, and in every direction.

Tensors are also employed in 3-D analyses of mechanics and wave propagation in anisotropic materials, those whose properties are different in different directions.

The most important thing to know about tensors is that any tensor equation that is valid in one coordinate system is automatically valid without any modifications in all coordinate systems, regardless of their rotation or motion relative to the original coordinate system.

That generality is one reason that the mathematics of general relativity is so challenging, but it is also one of the most powerful tools in solving problems. If we can identify a coordinate system in which we can solve a complex problem with a tensor equation, we have immediately solved the problem in all coordinate systems. General relativity is the only major branch of physics in which tensor equations are universally employed.

Tensors are arrays of components that transform properly between coordinate systems. In 3-D, they transform according to Euclidian coordinate rotations. In 4-D spacetime, they also transform according to the Lorentz transformation.

Let’s consider some quantities that are not tensors.

Temperature is a simple quantity that changes with time and location, making it a function of the four coordinates of spacetime. Its values are different in different coordinate systems, but the values do not change according to the rotation matrices or the Lorentz transformation. Hence, temperature is not a tensor.

Similarly, energy by itself is not a tensor. But, the proper combination of energy and momentum — (E/c, px, py, pz) — is a tensor because its components do transform properly.