Also my favorite diagram so far, illustrating what happens when you jump out of the John Hancock Tower (i.e., the version we built out of accelerating ships that has fake gravity):

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Part 5:
https://wrog.dreamwidth.org/71989.html
about how to transform between Moving and Stationary People coordinates (Lorentz transformations) and what velocity angles are (they're like rotation angles, but different)

(trying to make this accessible to folks who haven't seen a whole lot of linear algebra [though, as I recall, I *did* know about matrices in 6th grade;... thought they were cool..)

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Part 4:
https://wrog.dreamwidth.org/71432.html

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On the Storrow Drive Theorem

This is on how, having developed how one does spacetime for a 1-dimensional universe, how you put back the 2nd and 3rd spatial dimensions,

and the key question is what happens when you have college students attempting to measure the height of a bridge using rental trucks,

i.e., what differences are there in how the Moving People see it vs. how the Stationary People see it. Do the Moving People see a different height? Or see the truck slanted weirdly? Curiously, the answer to both of these turns out to be NO.

And we have this fun diagram

Part 3:
https://wrog.dreamwidth.org/71271.html

…introduce the _Interval_ between two events

= (Δz, spatial separation)² − (Δt, time lapse)²

and show that this number is an **invariant**, i.e., all slower-than-light observers get the same result calculating this in their own coordinates.

Magic diagram (with ALT text!) below proves this for Moving (upwards) vs. Anti-Moving (downwards, same speed) observers (i.e., using that Intermediate POV from before), and go from there.

Interval is either
(*) (proper distance)² > 0 [events are simultaneous for somebody],
(*) −(proper time)² < 0 [events are co-located for somebody], or
(*) zero [light-speed trajectory]

and then we do Twin Paradox and How FTL Violates Causality.
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I also really like how this diagram came out.

It's another spacetime-with-left-to-right-time grid from the stationary observer POV, showing trajectories of
(*) the stationary observer,
(*) the (velocity v) moving observer, and
(*) all possible in-between trajectories
+
how the two observers measure velocities
+
how the two observers will **not** agree on which trajectory is going v/2
+
how the One True Intermediate Trajectory
(i.e., the one that both see going the same speed) is between the v/2 trajectories **and** seen by both observers as going **faster** than v/2.

...this being the Big Red Flag that velocities don't add the way you'd think.

(also spelled out more fully in Part 2)

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Part 2:
https://wrog.dreamwidth.org/71156.html

In some ways, the following diagram is the whole ball of wax, essentially summarizing why the moving observer will *not* agree with stationary observer on simultaneity of events.

It's a spacetime diagram with time going left to right, depicting someone moving upwards (black line), bouncing a light ray off of a reflector above/below them (yellow lines).

If you get what's going on here, why the moving person''s '"snapshot" (blue line) of what's going on Right Now cannot be vertical (i.e., aligned with the stationary person's snapshots), you can derive everything else.

(see the full post for the actual argument)

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