Understanding Spacetime Diagrams

[NoahsArk]

I see in your otherwise well drawn diagram that the rocket’s worldline goes over 2 units for every 3 units up, which means the lines of simultaneity should go over 3 units for every 2 units up

This is a very helpful tip! So, to get the slope of the line of simultaneity given the X and Y coordinates of the worldline, we just flip the numbers. E.g. if the car is moving at .1 c, then for every movement of .1 to the right, the y movement is 1 (.1, 1). The line of simultaneity, then, would have coordinates of (1, .1) and the slope is .1?

The rotated grid lines represent light-cones, which in my opinion is at the heart of special relativity

It was through watching a video about light cones that I first started to understand the rule about why two events can never occur in reverse order, no matter which frame of reference is observing them, when the first event had caused the second event to occur:

 

[Mister T]

It was through watching a video about light cones that I first started to understand the rule about why two events can never occur in reverse order, no matter which frame of reference is observing them, when the first event had caused the second event to occur:

If the first event caused the second event then their separation is timelike and what you say about the order is true. If the events have a spacelike separation then the order of the events varies with different reference frames. In particular, there will be a frame where the events are simultaneous.

 

[Pencilvester]

the slope is .1?

Yes, ##\frac{dt}{dx}=0.1## for the lines of simultaneity of an object moving with ##\frac{dx}{dt}=0.1##.