Einstein's Hypotenuse: Unraveling the Mystery of Minus Signs

[epmc2]

i was watching a lecture and the professor started explaining how einstein's hypotenuse was used in explaining dimensions. but failed to explain how einstein arrived at:

H²=c²*t²-d₁²-d₂²-d₃²

i was wondering where the minus signs came from?

 

[phyzguy]

I think we all wonder at some level why things are this way, but the fact is that this is how the universe works. While we can treat time as a fourth dimension, it is not equivalent to the three spatial dimensions. While it is obvious to us from our everyday experience that time is different from the spatial dimensions, it is not obvious that this is the way to treat it mathematically. I think Einstein, Lorentz, Minkowski, and others arrived at this mathematical formulation from studying the Maxwell equations, which transform in this way. Maxwell's equations of course have their basis in empirical measurements of electricity and magnetism.