In our universe, when you change from a non-moving perspective to a moving one, or vice versa, that change of perspective is represented by a what's called Lorentz transformation, which is a kind of squeeze-stretch rotation of spacetime that I've mechanically implemented with this spacetime globe.

00:27

A quick reminder - spacetime diagrams plot position on the horizontal axis and time on the vertical axis, and something moving as time passes traces out a path through spacetime called a worldline.

00:38

One of the first things you might notice about Lorentz transformations is that events that were at different places at the same time before the transformation aren't at the same time after the transformation.

00:49

This means that from the perspectives of people going different speeds, simultaneous events for one person won't be simultaneous for the other, and vice versa.

00:57

For example, if from my perspective these two boxes spontaneously combust at the same time, and you're moving at a third the speed of light to my right, then from your perspective, that is, the perpective from which you're not moving so your worldline is purely vertical, from your perspective the box on the right will combust first, and the box on the left will combust second.

01:16

The takeaway here is that our universe has neither an absolute notion of time nor an absolute sense of simultaneous events, and that simultaneity breaks down more the farther away from each other two things are – a box even farther to the left that from my perspective simultaneously spontaneously combusts with the others will, from your moving perspective, be even farther out of sync with the box on the right.

01:37

This is described by the time part of the Lorentz Transformation equations, the part that says t new = gamma times t minus v times x over c squared).

01:47

Because of the x in there, the farther away an event is from you, the more its time from the new perspective will be out of sync with events closer to you.

01:54

Though because of the factor of c squared in the denominator, which is huge, it's hard to notice anything being out of sync until either your speed or distance to the object in question are really really really big – like, you'd have to be going half the speed of light and be comparing things farther apart than the earth and moon before things would become more than 1 second out of sync.

02:11

But in that case, events that were simultaneous from my perspective really would be out of sync for you!

02:16

As surprising as this may seem, it might feel more familiar and comfortable when you remember that this “getting out of alignment” phenomenon happens to points at the same place in space, too, which is literally what we think of as defining motion – from my perspective, this box is at the same position at different times – that is, it's not moving&59; maybe, “simulspacious”– but from your moving perspective it's at different positions at different times – it is moving.

02:36

Relativity of simultaneity is just the other side of the coin – the fact that events that happen at the same time at different spatial positions happen at different times when viewed from a moving perspective.

02:47

All together, in our universe, the takeaway is this: events that were previously either all at the same place or all at the same time get out of alignment with each other when you change to a moving perspective.

02:58

A big thanks again to Mark Rober for making the spacetime globe a reality, and to dive more into the details of relativity of simultaneity, I highly recommend heading over to Brilliant.org's course on special relativity that they've been developing simultaneously with this video series (well, at least, simultaneous from my perspective).

03:16

There, you can explore custom scenarios and do actual puzzles and problems that help you build on what you learned in this video, like figuring out how laser tag would work at relativistic speeds!

03:26

The special relativity questions on Brilliant.org are specifically designed to help you go deeper on the topics I'm including in this series, and you can get 20% off of a Brilliant subscription by going to Brilliant.org/minutephysics.

03:37

Again, that's Brilliant.org/minutephysics which gets you 20% off premium access to all of Brilliant's courses and puzzles, and lets Brilliant know you came from here.

Relativity of Simultaneity | Special Relativity Ch. 4

A Lorentz transformation of coordinates of the events in question, enacted with a mechanical minkowski diagram, aka mechanical Lorentz transformation, aka spacetime globe.