Time

What are the main points of Chapter 1 of Rovelli's Order of Time?

In Einstein's general theory of relativity, gravitational acceleration is related to the rate at which physical time passes.

The rate of physical time varies, depending on relative motion of clocks that measure time.

In Chapter 2 of Order of Time, Rovelli explains that, among the equations of physics, there is no asymmetry between past and future, except in the equation for "entropy."  During the 19th and 20th Centuries, physicists gradually found that with respect to this equation, everything in the universe was to that extent similar to the things originally described by "entropy."

What was the first thing that a 19th Century scientist used this equation to describe?

The flow of energy through a steam engine (such as an internal combustion automobile engine), when heated gas expands and drives a piston.

In Chapter 2 of Order of Time, Rovelli introduces statistical mechanics, which explains heat as the motion of molecules.  A greatly simplified mathematical picture of this motion is a random process, such as shuffling a deck of cards.  Or flipping a coin.

Suppose we use a very small deck of just 4 cards, the ace of each of the four suits.  Two suits are red, and two are black.  Any particular sequence of cards is equally probable as any other.  These are what Rovelli calls "configurations" (pp. 31-32). 

Four cards have 4 possible first choices, then 3 possible second choices for each of the 4 first choices, then 2 third choices.  4x3x2 = 24.  

Make a list of all 24 configurations of the four cards in order to visualize all the possibilities.  Giving each card a letter from a to d.  Do this in a systematic order.

How many configurations have the two red cards followed by the two black cards?  How unusual is this orderly pattern?

4, or one sixth of all configurations.

Suppose two clocks are moving at relative velocity equal to seven-eighths the speed of light.  Use the equation for time dilation to calculate how much longer between ticks of the moving clock, when viewed from the other clock. (Speed of light = c)When the moving clock ticks once (or light bounces once back and forth between its mirrors), how many ticks on the clock by which the measurement is made?

Slightly more than two ticks.