# Relativity (special)

## 1. Minkowski

trell.org interactive Minkowski spacetime diagram

## 2. Lorentz factor γ (gamma)

The single most important metaphysical fact (e.g., beyond the straight mathematical description of the physical facts) about the Lorentz factor is this: it is a premise. Harvey Brown has put a huge amount of work into re-popularizing this idea in the early 2000s; it was widely known prior to Einstein’s 1905 work, and a major reason that Lorentz was metpahysically unimpressed with his own factor prior to 1905. Physics went through a long period of blandly accepting that the Lorentz factor is a premise, but Brown and others have become increasingly dissatisfied with the metaphysical state of affairs.

What I mean by premise is this: we lack a physical explanation of why it should be the case that that the Lorentz factor is so useful in explaining how the physical world looks to those moving through it. It is not derived from any physical facts. That it empirically explains the world is not an explanation — as is the case for any mere mathematical equation. That’s why Newton said hypotheses non fingo (“I frame no hypotheses”) about his own gravitational equations, which he was keenly aware implied instantaneous movement of information through spacetime, which was physically ridiculous. That an equation describes the world is not equivalent to having an explanation of why the world is as it is, any more than a picture of your friend in a red shirt explains why he is wearing red today rather than blue or purple.

The premise that drives the Lorentz equation is simply that c is identical in all frames of reference. Thus we know that

$c=x$

### 1.1 Derivations of γ

Here are multiple thoughtful derivations of the Lorentz factor (gamma):

## 2. Online Resources

### 2.1 Harvey Brown

Martinez review of Brown’s book