The site is full of 'spoilers' for the book

Living Labyrinth

by Ian Stewart and Tim Poston

If you can't read St Matthew's Gospel because St Mark gave away the resurrection, don't explore further.

I like background on books:
let me in, and do not warn me again

or Go to where I can get the book.

Galactic Travel: Karmabhumi and simquakes

If two physically separated events P and Q are labelled as 'simultaneous' by some observer A,there is an observer B for whom P is earlier than Q, and an observer C for whom Q is earlier than P. This was clearly understood on Old Earth, even before Yuri Gagarin kick-danced on the moon.

Consequently, if you have an 'instantaneous jump' technology where you can choose the frame of reference (for instance, by changing the ordinary speed of your spacecraft), you can make an A-jump from P to Q, followed by a B-jump from Q to the past of P. This would allow such paradoctoring as giving your mother a contraceptive implant at puberty: causality suffers.

All physical evidence is against the existence of a privileged observer, whose 'simultaneous' over-rules everybody else's. (Even in Special Relativity: in General Relativity, it's hard even to make sense of the idea.) So, how is jump technology possible?

There is no privileged observer, but there is a privileged tensor, whose magnitude κ ('kappa') is agreed by all observers, and which increases along every time-like curve (every possible history of an object). This is karmabhumi ('fate stuff'), discovered in 71GE by Jayavarmasukihara. The Da Silva drive enables quantum transitions between points of equal κ — if they satisfy a host of other conditions — and no other points. Jumping back to an earlier time, however circuitously, would take you to a lower κ-value: not possible.

However, that "increases along every time-like curve" cannot be everywhere at the same rate. (Defining "at the same rate" would need a privileged observer, again.) Experimentally, it increases at a particular rate for a local 'mean observer' moving at the mean velocity of nearby matter, and that rate increases in proportion to the local mean curvature of spacetime. Einstein's equations connect this to the local density of mass and energy (in and around a sun, scalar curvature is high), though not point-for-point. (In the vacuum around a sun, curvature is strong enough to keep planets in orbit.) Skipping the partial differential equations, we can roughly say that κ increases faster in a matter-rich region, such as near a supergiant star like Rigel, or in a dense matter-cloud, than in the flatter emptiness of the deep space between stars and galaxies.

Suppose this variable increase went on for ever, uniformly, for two locations ten light years apart: for instance, at Starhome (around Rigel) and Sigao (in the deeps). For simplicity, pretend that according to average 'Galaxy is stationary' time, in some year Y they have the same κ-value, 100 in arbitrary units. Suppose also that κ increases twice as fast at Starhome (2 units per year) as it does at Sigao (1 per year), as locally measured.

After one year at Starhome, κ is 102. After two Sigao years (very close to 'Galaxy is stationary' years) Sigao reaches that value, so jumps between 'Starhome after one year' and 'Sigao after two years' are allowed. Similarly, between 'Starhome after five years' and 'Sigao after ten years'. Allow this to continue, and we would have jumps between 'Starhome after forty years' and 'Sigao after eighty years'. But then we could jump from Sigao to Starhome, and by ramjet at half lightspeed reach Sigao after just twenty years… arriving twenty years before we left! A laser message would arrive forty years before we left.

This does not happen.

What prevents it is analogous to a shock wave: here is how the κ-levels change. Along each curve the κ value is the same at each point. Along the moving orange curve, representing the 'karmabhumi Now', the κ value is the same at each point on the curve, but that value increases with time.

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The smooth pattern breaks, and relaxes along the break, giving points (shown red) where κ has a jump increase. At the early end the jump starts from height zero, but at Sigao it is a jump between 108 and 112. No point in the corresponding two years at Starhome can be reached from any moment at Sigao: from a Sigao point of view, the Starhome moment reachable by Da Silva drive or communicator simply jumps forward by two years. During those two years at Starhome, Sigao is unreachable but as if frozen: after passing κ = 112, it can be contacted as if no time had passed since Starhome passed κ = 108. This is a simultaneity quake, or simquake. We usually say that both 'went through' a simquake, though only one has a locally measurable κ-jump.

An R&D program on Starhome can be finished after half the Starhome time, if you outsource it to Sigao (and only dedicated researchers go there, so maybe even faster), as long as you avoid simquakes.

Managing the Concordat is easier if other places don't have bits of history you can't watch, which is why Starhome is at a fast-κ location. But the real Galaxy is much more complicated than our simple picture, with three dimensions of space, unevenly distributed matter, and the non-linear equations of karmabhumi propagation. (No location completely avoids jumps, or out-of-contact periods.) Predicting the karmabhumi field is the Hard Problem of Concordat computation. Especially for the short term details, its non-locality requires long and frustrating numerical exploration before committing to a jump.

Old Earth goes through a κ-jump every century or two, but the effect on most physics is negligible. (There is a hard-to-detect phase twist in the stream of solar neutrinos.) You can safely ignore simquakes unless your life is affected by Da Silva technology.

Or unless you use syntei.