Dr. Matt O'Dowd on the geometry of causality in Einstein's tenseless block universe (i.e. timeless spaceless spacetime)

[Eckhart Aurelius Hughes]

Here is a great video produced by PBS featuring Dr. Matt O'Dowd (PhD):

Here are some selected excerpts:

The special theory of relativity tells us that one person's past may be another's future.

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Special relativity tells us that our experience of both distance and time are, well, relative. If I accelerate my rocket ship to half the speed of light, the distance I need to travel to a neighboring star shrinks dramatically from my point of view. An observer I leave behind, with an amazing telescope, observes me traveling the entire original distance but will perceive my clock as having slowed. The combination of this length contraction and time dilation allows both moving and stationary observers to agree on how much older everyone looks at the end of the journey. Everyone agrees on the number of ticks that occurred on everyone else's clock; they just don't agree on the duration of all of those ticks.

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In relativity, 3D space and 1D time become a 4D entity called [timeless spaceless] spacetime. To preserve our sanity, we represent this on a spacetime diagram, plotting time and only one dimension of space. We'll see our causal geometry emerge plain as day, even in this simplified picture. There is no standing still on a spacetime diagram. If I don't move through space, I still travel forward in time at a speed of exactly one second per second according to [my own watch].

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The traveler infers a set of simultaneous events that, to me, are not simultaneous, but there is no preferred reference frame. Their sloped x-axis is right for them. Even just doing this graphically, we see that the traveler's x-axis is rotated by the same angle as their time axis. That comes from insisting that we all see the same speed of light, 45 degrees on the spacetime diagram. Moving between these reference frames is now a simple matter of squaring up our traveler's axes.

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Now, we can finally get to why this thing is so important and what it really represents. It may seem counterintuitive that an event very close to the origin in both space and time can be separated from that origin by the same spacetime interval as an event that is very distant in both space and time. The hyperbolic shape seems to demand that, but remember, it takes the same amount of proper time to travel from the origin to a nearby near-future event compared to a distant far-future event on the same contour. From the point of view of a particle communicating some causal influence, those points are equivalent. The spacetime interval tracks this causal proximity.

Due to the "Relativity of Simultaneity" which Einstein discovered, we now know that your entire life and death can be in someone's past even if their entire life and death is in your past.