B Drawing a Minkowski diagram to show multiple Points of View

[DaveC426913]

TL;DR Summary

Can I use a single Minkowski diagram to show the subjective experiences of multiple observers?

Caveats:

• I'm sure this is kind of putting the cart before the horse here, because if I have to ask this question, it surely means I ought to be reading up on it first.
• This is for a story, but that should not mean this is the wrong forum; I'm really just asking about the basics of Minkowski Diagrams. (but if it should be moved to the sci-fi forum, that's fine too).

I want to be able to represent the subjective experiences of multiple observers moving relativistically WRT to each other. Simplistically: two stars (Earth and another nearby star) and two or more ships interacting in the space between at relativistic speeds. It's more complex than that, but that's the gist. I want to rigorously nail down when each POV observes events and can react to them.

eg. Will a diagram that shows the experience of a shipboard observer be able to also show the experiences of an Earth observer and an observer on a third ship? Or shoud I make a diagram for each (or each pair?)

 

[Orodruin]

Sure it can, you just need to draw their corresponding time and space axes into the diagram.

If you are looking for something like the twin paradox though - be mindful that such a diagram can get quite busy with stuff.

 

[Ibix]

I'd ask what you mean by "subjective experience" first. I'd tend to interpret it as "what they see directly", in which case the answer is yes. If you mean their interpretation (questions like "what's happening at the same time as we're being menaced by this sehlat") then you would need to think first about simultaneity conventions for any observer who isn't permanently floating along at constant speed, and a Minkowski diagram may not be the best tool for that. It could certainly be done anyway, but there might be better options.

I'd second @Orodruin's comment that these diagrams might get very busy very fast. Multiple copies with different elements, or an electronic version where you can turn on only relevant elements, might be wise.

 

[Orodruin]

For reference, this is the full twin paradox diagram from my hand-written lecture notes (the ones I lecture from as opposed to the ones I put into LaTeX, which I suggest students read):

The axes of three inertial frames are shown: S - rest frame of "staying" twin, S' - rest frame of "travelling" twin in the outbound leg, S'' - rest frame of "travelling" twin in the inbound leg.
It shows the "staying" twin's world line in blue and the "travelling" twin's world line in red. A/B/C are events on the "staying" twin's world line that are simultaneous to the turn around in S/S'/S'' and the dashed lines are the corresponding simultaneities.
The yellow lines mark the parts of the "staying" twin's world line that are covered by the "paradox" argument where time dilation is applied without taking relativity of simultaneity into account.

 

[DaveC426913]

No, not the twin paradox. I just want to ensure events happen within the right time frame. If boosting-out ship sees braking-in ship passing it at, say, .8c, how much lead time can they give Earth, given a bunch of extenuating circumstances? But complicated-er. Anybody recall that school grade problem about a fly that goes back and forth between two approaching trains, like a pinball? That sort of thing.

And ... I just realized that I don't need a Minkowski diagram at all for that. I can simply plot events in one coordinate system, say, Earth's. The time dilation effects themselves are limited to below .9c.

 

[Orodruin]

The twin paradox diagram is just an example of how things start looking pretty busy once you start drawing several frames in one diagram.

 

[Ibix]

can simply plot events in one coordinate system, say, Earth's.

Well, that's still a Minkowski diagram...

The time dilation effects themselves are limited to below .9c.

That's a factor of two and a bit, which might be relevant to the story. Probably best to include tick marks along the worldlines for their proper time, so as not to get caught out.

 

[robphy]

From my Insight,
https://www.physicsforums.com/insights/relativity-rotated-graph-paper/

Note that there are six reference frames here: Alice, the four incoming and outgoing particles, and the COM frame. Since the k-factors of the particles (and Alice) are rational numbers, we can easily draw (and thus count) their unit-mass-diamonds on Alice’s diagram. However, since the COM frame does not have a rational k-factor (and thus not a perfect square for its square-mass) we can’t easily draw the unit-diamonds in that frame… but we can calculate practically everything of physical importance.

Source: https://www.physicsforums.com/insights/relativity-rotated-graph-paper/