Spacetime ☄️ for Idiots ❡

Spacetime is not the same as the 4D euclidian space on Krei.se

I admit that it threw me totally off to see it does NOT work like my 4D. And that i have no idea how STA works.

I know the algebra! But that does not mean anything :D

So here's how i tackle this from a coder/system architects POV.

It's "just" 3D ❡

Even though STA has 4 coordinates you always experience 3D and time.

Block universe ❡

Forget for a moment about the taught assumption you would need to keep track of all observers in the universe somehow. NOT TRUE.

A block of data is kept globally with 4 coordinates which are 3 spatial and 1 temporal. No squaring to -1 yet!!!

Now think of this like a game tick. Do not start to think about trains moving or wristwatches of astronauts!!!

-> There is a global event log with 4 coordinates and the global timestamp/coordinate is counting up.

This is true for a person on earth and the aliens on a remote planet far far away. BOTH HAVE THE SAME GLOBAL TIME 4th coord.

The origin or 0,0,0 place is not important, but ofc you need to assign one and stay with it on the server.

Notation and Vocabulary ❡

SERVER

• 🕰️ coordinate or global time is the 4th coordinate on the server

CLIENT

• ⌚ "proper time" is what an observer sees on his watch. I think that's bonkers as the proper time ofc should be whats kept in the log.

• (when you move as an observer your proper time will tick slower than the servers time.) later!!

Danger zone not sure 👷👷 ❡

Projection to 3D ❡

Now when you want to know what the 3D space right now looks to this observer you can do that with:

v γ₀ = v · γ₀ + v ∧ γ₀

=   v · γ₀      - scalar time you read on your clock
+   v ∧ γ₀      - 3D spatial position

But that is true also for the room 1 meter around you - you will need to measure this still in a distance including time. You always see the past when looking at an object 1m away from you. And it always experiences YOUR past.

So technically all points in space have a time offset relative (there it is!) to each other.

but because t squares to -1 it's

interval² = x² + y² + z² - (c t)²

This can give a positive or negative result

4th coordinate / time continuously goes up ❡

[x,y,z,t] every interval you choose, like 1 second you have to distribute across these 4.

So when you do NOT move in x,y,z - t will go up by a const (speed of light) c

now when you distribute it`s not a euclidian metric where this DISTANCE or INTERVAL is the √ of x² + y² + z² + w²