Wednesday, 6 May 2015

Matching Points in Spacetime

What's in a name?The “Beneath” in the name of this blog (and my game) is meant to indicate not just the literal “beneath the surface” of a dungeon, but also meaning intrigue and puzzle solving. Similarly the “Beyond” means literally to travel beyond locked doors or chasms, or to other planes, but also meaning beyond the stars, or beyond human powers, or that there is no limit in RPGs. The name is purposely chosen to work for Fantasy, Space Opera, Mystery, Horror, or Super Heroes.

It’s looking more and more likely that my homebrew Explore will support SciFi as a first class citizen alongside Fantasy. This isn't surprising, since after all the skill system originates in house rules for our Star Frontiers campaign. Hence yesterday's in-game description of how interstellar travel might work in ExploreSciFi (quite influenced by Star Frontiers – but not Knight Hawks) along with a scientific explanation of how this doesn't violate the laws of Relativity. (Truly - it doesn't). Then on the way into work this morning the mathematician in me pondered about the canonical nature of the CMB, why is it the 'unique distinguished exemplar'?

A Recap
To recap, yesterday I was saying that every observer has a concept of what is happening “now” across the universe, and this is applicable to all physical phenomena. This is different for another observer with a different relative velocity; for example the two observers will disagree about whether two events, one occurring next to each observer, are simultaneous or not. The difference is greater the larger the separation between the observers, and the larger the difference between their velocities. This is how come accelerating to faster than the speed of light causes time travel paradoxes.

Secondly I discussed the concept of the “age of the universe”, which measured from any planet in the universe will give almost identical answers, since with only a small velocity change you can match the CMB. A universal time can thus be given to any event in space & time, it is the time since the universe began at the point where the event occurred, measured relative to the CMB. If you jump instantaneously from one point in space to another, appearing at the same universal time as you left, then you can never travel backwards in time, so no paradox.

Why the CMB? 
So, to return to today's question - what is uniquely special about the CMB? Why can I only jump from here to there at the same point in universal time? Why not some other reference frame?

Let's rephrase that: why can I only jump from here to there at the point where the age of the universe is the same?

With this rephrasing it's clear – when space is bent to join A to B, the point in time you must arrive is the moment when the expansion of the universe at B is the same as it was at A when you left. That is, you can only bend space to join “matching points” in space-time.

That not only seems eminently sensible, it looks like it is the only possible answer, and I've no idea why that didn't occur to me before!

Footnote: let’s not forget that relativity is based upon the concept that there is no universal reference frame, and we still have that rule for all physical phenomena except instantaneous interstellar travel. You still cannot accelerate to faster than the speed of light as that would cause time travel paradoxes.

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