How to pronounce “minkowski” in English

Minkowski's insight is that the time that you measure when you're moving through spacetime is exactly or almost exactly like the distance

Minkowski's equation helps you do it for relativistic spacetime.

when Minkowski really laid it out in a strict spacetime.

So Minkowski had been following along Einstein's progress.

And Minkowski was the one who said, look, I can think of a more elegant mathematical formulation of your theory.

And Minkowski says, if you think about things that way everything in special relativity makes sense.

But Minkowski says, that's separate from what we call the proper time, here labeled tau, the Greek letter tau.

by the name of Minkowski, who looked at Einstein's equations. Minkowski was a little bit more mathematically inclined than Einstein, and he saw that if you look at the equations, you have basically

And what Einstein and then Minkowski later said is, the time that you personally experienced is not universal.

Riemann didn't know about Minkowski's spacetime, but he knew about other examples.

This minus sign is obviously different in Minkowskian geometry versus Euclidean geometry.

So let's be a little bit more quantitative about what Minkowski was actually saying.

It's given by this thing called the Minkowski metric.

time with a unique kind of geometry, which we now call Minkowski spacetime, by the way.

If you think that spacetime has a geometry, a la Minkowski, what about modifying that geometry?

You have Pythagoras' theorem for Euclidean space, and you have Minkowski's equation for relativistic spacetime.

So that is where Einstein and Minkowski really did this

And that came not from Einstein, but from his old math professor at university, Hermann Minkowski.

Here is the formula for the time interval, the proper time, as it is called, the time you personally experience along a path in Minkowski space.