I’ve been pretty interested in quantum technology (information, computing, encryption, etc) and in order to really get into those concepts I think I need to brush up on my physics. Rather than taking the traditional textbook approach, or starting directly at quantum theory, I decided to have a read through a book by Sean Carroll called “The Biggest Ideas in the Universe: space, time and motion”. This is supposed to be the first in a three part series taking you all the way up the chain to quantum (hopefully) but the next two books haven’t been written yet. In any event, I’m interested. I hope to capture my notes here for reference later on.

Conservation

The first chapter starts us at the idea of conservation within physics. Effectively, physics is all about predictability, and following laws of conservation is one of the easiest ways to predict what will happen in the future. Sean takes a brief detour to talk about Aristotle’s view of physics which can be summed up as:

• There is a concept of natural and unnatural motion
• The natural state of an object is to be at rest
• Based on the concept of teleology, or, that motion is orientated towards a future goal

This view was eventually surpassed and we started to understand that objects don’t evolve to an ultimate state, but rather, follow a set of patterns/laws that can be used to predict what happens next.

Momentum

The first law of conservation that he discusses is that of momentum. Mass can be though of as the resistance an object has to being accelerated, and if you multiple this value by the velocity of the object, you get momentum.

$$ \overrightarrow p=m \overrightarrow v $$

Another way to describe this is that momentum is proportional to velocity via the mass quality of the object (assuming the mass is constant).

Classical Mechanics

The discussion then turns to the idea of classical mechanics and touches on the idea of Newtonian Mechanics. Effectively, classical mechanics view the world as made up of things with defined values that obey deterministic laws of motion. This is in contrast to quantum mechanics. Newtonian mechanics is a specific model within this framework that deals with the ideas of space time and is in contrast with concepts around relavistic mechanics. This is a step forward from the Aristotle days as we are now discussing physics in terms of a discussion of patterns that are obeyed rather than the sole idea of cause and effect.

There are a couple of other conservations laws that we can discuss, and they step out of the idea of symmetries. Symmetries is effectively the idea that you can perform a transformation on a system that leaves its essential qualities/features unchanged. The example given in the book is the idea of rotating a circle. Effectively, because of this concept of symmetries, we can conclude that every symmetry is associated with the conservation of a given quality. For example:

Symmetry	Conserved Quality
Temporal	Energy
Spatial	Momentum
Rotations	Angular Momentum

Spherical Cow

The first chapter ends with the idea of the spherical cow. In physics, we tend to simplify a problem down by ignoring all the “complicated” things about that problem that we possible can. This allows us to develop a theory/equations about the simplified model, and then simply add back in “the complexity” later on. I had not heard this joke before, but I totally understand how physics does this.

Stay tuned for part 2!