@Exocytosis Sorry about the delay. I didn't realise that you had posted in here because you didn't use the @UserName syntax to "ping" me.

I can't think of a simple way to explain that minus sign (apart from what I've already said). Its significance is that space and time have different character, despite being intimately related. To see how the minus sign arises mathematically, you need to work through the standard derivation of the basic Lorentz factor equation, 1/gamma^2 = 1 - beta^2. And that's usually done as a stage of deriving the 2D Lorentz transformations (time + 1 space dimension).

That derivation uses the 2 postulates of SR: that the laws of physics are identical in all inertial frames, and that the speed of light is always c when measured locally in an inertial frame.

The usual procedure is that in frame 1 you have a light clock, a beam of light bouncing in a vertical line (Y axis) from floor to ceiling between a pair of mirrors. Frame 2 is moving horizontally (X axis) at constant speed v relative to frame 1. The spacetime interval between the events of the light leaving one mirror & hitting the other is identical in both frames, but the space & time components are different.

Take a look at Greg Egan's Foundations article on Special Relativity. IMHO, he's a great science & maths writer, as well as a good programmer and excellent science fiction author. But maybe I'm a little biased because he's a fellow Australian. :)