The Character of Physical Law

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In my opinion, when it comes to physics, Richard Feynmen is the daddy. He was known as ‘the great explainer’ for a reason. This book is taken from a lecture series he did at Cornell university. And true to his nickname, he explains each concept brilliantly.

Each idea is explained conceptually and in a way that makes sense to the layman. It’s not mathematical at all. In fact I would say this is one of the best top-down primers to the subject of Physics that you can get.

My notes are below, but honestly, it isn’t a long book and you’d do much better to get the explanations from Feynman than you would from my second hand interpretations.

Introduction

  • Feynman was against formalisms

  • He treated life like a big game

  • The role of symmetry and conservation are present throughout the book

  • He discovered a physical law regarding the weak force

The Law Of Gravitation

  • Gravitation is described by 2 equations
    1. F = G(mm’/r2)
    2. F = ma

  • Kepler’s laws:
    1. Orbits follow an ellipsis
    2. Area between two radial vectors is always equal over the same stretch of time
    3. Time to complete an orbit is proportional to (size of orbit)3/2

  • Physical laws allow us to discover new laws

  • Einstein made changes to Newton’s laws to account for relativity

  • The law of gravitation does not apply on the quantum scale – there is no strong theory of quantum gravity

  • Physical laws are:
    1. Mathematical in expression
    2. Not exact
    3. Simple, hence they apply widely

  • Stars are formed by gaseous blobs of dust grouping together thanks to gravity

The Relation Of Mathematics To Physics

  • Maths allows us to explain how things work, not why

  • Physics is inefficient in the sense that it does not build up from fundamental axioms like maths does

  • There are many ways to look at and think about the same theory
    1. Newtons law
    2. Local field theorem
    3. Minimum principle

  • Mathematics is very generalist (eg. For n dimensions) whereas physics is applied (eg. N=3 dimensions)

The Great Conservation Principles

  • Almost all physical laws have the conservation laws in common

  • These laws allow physicists too discover new particles/laws by assuming the conservation laws hold

  • Conservation of energy can explain most of the other conservation laws

  • How does the theory of relativity impact the conservation principles? – pp65

Symmetry In Physical Law

  • Defn: Changes which have no effect on the physical laws

  • Symmetry and conservation laws are interlinked

Working symmetries:
1. Translation in space
2. Translation in time
3. Rotation in space
4. Relativity (uniform velocity in a straight line)

Not working symmetries:
1. Change in scale (minimum limit due to particles)
2. Change in angular speed
3. Reflection in space

  • Electrons exit a beta decay spinning to the left

  • The world is not symmetrical if right and left are not the same – reflection in space does not work

The Disctinction Of Past And Future

On a fundamental level, all physical laws should work when time is moving backward. Take the coloured water example:

  • Even though light blue water would look weird splitting back up into clear and blue, it wouldn’t look weird if a blue atom collided with a white one (it would look the same as if you played it forward)

  • A collision is random, so will look the same going backward

  • The water does not split back up into blue and clear, but it is not impossible, just highly unlikely

We have also reason to believe that Beta decay may not be time sensitive either.

Finally a fun side note. 7.82m volts = an energy level in carbon. If this energy level did not exist then we would not have more than half the elements in the periodic table (nb: what is an energy level?)

Probability And Uncertainty

This chapter relates to the quantum mechanical view of nature

  • Particles – Discrete, experience no interference (“bullets”)

  • Waves – Continuous, experience interference

  • Electrons are discrete, but experience interference unless you observe them by exposing them to light

Wave particle duality is best explained by the double-slit experiment (shout-out to my A level physics teacher Mr Rice)

  • There are two particles which have this feature
    1. Light (photons)
    2. Electrons

  • The probability of arrival of the electrons is distributed like the intensity of a wave

  • In this experiment, there is no way of predicting which hole the electron will pass through

Seeking New Laws

  • Particles explain most phenomena (at low energy)

  • If you combine all known laws of physics then you break some equations (things = infinity or divide by 0 etc) and so we know that they are missing something / something is wrong

  • To get new laws:
    1. Guess
    2. Compute results
    3. Compare to the experiment

  • Most phenomena can be explained by:

    1. Electrons
    2. Photons
    3. Gravitons
    4. Neutrinos
    5. Protons
    6. Neutrons
    7. … And their anti particles

  • Sometimes, when looking for new laws you have to choose some of the existing laws to drop

  • Any good physicist knows multple theories for the same thing

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