How to pronounce “minkow” 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 when Minkowski says, "I have some new math that unifies space and time based on Einstein's theories," Einstein himself was like, "Yeah, I don't need that.

When Einstein and Minkowski figured out that space and time are both two different ways of slicing up spacetime, what does that mean?

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

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

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

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.

Einstein or maybe I should say more properly Minkowski, his teacher and contemporary, offers a vision of space-time as a single thing, as a four dimensional block in which

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.

Well, my ex-professor, Minkowski, says that spacetime has a geometry.

one person's space and time equals some numbers times this person's space and time. And so that's kind of a staggering thing. 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.

And in fact, it wasn't until two years later, when Herman Minkowski, who was a mathematician who had been one of Einstein's professors,

In the case of Albert Einstein, for example, he was thoughtful about the fact that his former professor, Minkowski, said, "You should think of space and time

specialized, something technical. Einstein offers, Einstein or maybe I should say more properly Minkowski, his teacher and