light quanta

The equation explained

W = \left( \frac{v}{v_0} \right)^n ;

In wordsThe probability that all the n points are found in the part v of the volume v₀ at a moment chosen at random is the fraction v over v₀, raised to the power n.OverviewThe probability that, at a randomly chosen moment, all n independently moving points are in the part v of the volume v₀ is the fraction v/v₀ multiplied by itself n times.Full explanationThe special case of section 5: a volume

v_0

holds

n

movable points, molecules for example. Nothing is assumed about the law of their motion except that no part of the space, and no direction, is preferred. The points are also few enough that their action on one another can be ignored. The paper asks how probable it is, relative to the original state, that at a moment chosen at random all

n

points are in a given part

v

of the volume. For one point the answer is the fraction of the volume,

v/v_0

, because no part of the space is preferred. The points move independently, so as in the third display the probabilities multiply. The paper calls this a statistical probability.Every step

\frac{v}{v_0}

One point: no part of the space is preferred, so the chance that it is in the part

v

at a random moment is the fraction of the volume that

v

takes up.

W = \frac{v}{v_0} \cdot \frac{v}{v_0} \cdots \frac{v}{v_0}

The

n

points move independently of one another, so the chance that all are in

v

at once is the product of their separate chances, one factor for each point.

W = \left( \frac{v}{v_0} \right)^n

The same factor

n

times is a power: the printed line.AlsoOverviewFull explanationEvery step

Read it in the paper