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For the purposes of this question, lets assume that we are in Edwin Abbott Abbott's Flatland, but the world is a disk, with living shapes Above, and 'dead' shapes Below (the underside of the disk). However, time runs in the opposite direction Below, so if A. Square died on Monday, and went Below (let's assume there a 'strip of paper', like a passage, which he traverses to go from the top of the circular plane, to the underside), and was dead for five days, but was then allowed to return the the world of the living, he would arrive the Wednesday before he died.

I'm assuming that time is linear (no parallel universes), and that Cause and Effect operate, but not necessarily in that order. So, for example, A. Square might be able to warn his former living self of his impending death, but would do so knowing it will happen anyway (otherwise his ghost would not be there to give the warning in the first place).

The other assumption is that events unobserved by anyone are indeterminate (i.e. a kind of Copenhagen interpretation of time).

Can anyone see any logical issues with this? One concern is the travel via the 'strip of paper' connecting the top (Above) world with the Below world - would there be a point where A Square's ghost would be existing both in forward time, and backward time? Could this be done non fatally?

incidentally, time Below doesn't involve people walking backwards, and broken glasses reforming; locally, it appears as if time is moving forward, just backwards relative to those Above.

I've thought of one issue concerning computation: Imagine a machine which prints either the letter 'A' or 'B'. However, it is rigged to send this printout to its former self, and when the former self receives that printout, it is programmed to choose the opposite. So if it chooses 'A' it tells it's former self this, so it chooses'B', and visa versa. I'd imagine that such a weird 'paradox engine' would be in a suppositional state, like Schroedinger's cat in the box, until some highly improbable failure occurred to break it out of its loop (such as mechanical failure etc.) Would this mean there is a 'virtual' universe where the machine runs thousands of times before the improbable event occurs? I suspect this would mean our universe would occasionally have very improbable things happen due to such temporal feedback loops occurring in nature...

The motivation for this is a fantasy story, where I'm trying to devise a mechanism for prophecy based on (as in much folklore) the notion of time working differently in 'fairyland'.

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  • $\begingroup$ Does freewill exist, or is everything (that has been / will be observed) predetermined? $\endgroup$ – LindaJeanne Jun 10 '15 at 11:50
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    $\begingroup$ Free will only exists for choices made concerning unobserved future events. Everything else is predetermined (so A. Square cannot avoid his death, whatever he does, if his ghost has forewarned him, assuming the ghost is not lying). Such is the curse of prophecy... $\endgroup$ – Mobeus Jun 10 '15 at 12:00
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If you want your time traveler to be able to change the past (say by killing their past self but maintaining that they're coming from an alternate timeline) you can preserve causality.

If you want history to be locked and unchangeable... causality becomes a problem. If you allow changes it's easy logically speaking.

http://lesswrong.com/lw/fok/causal_universes/

If a time machine does allow for changing history, it's easy to imagine how to compute it; you could easily write a computer program which would simulate that universe and its time travel, given sufficient computing power. You would store the state of the universe in RAM and simulate it under the programmed 'laws of physics'. Every nanosecond, say, you'd save a copy of the universe's state to disk. When the Time-Changer was activated at 9pm, you'd retrieve the saved state of the universe from one hour ago at 8pm, load it into RAM, and then insert the Time-Changer and its user in the appropriate place. This would, of course, dump the rest of the universe from 9pm into oblivion - no processing would continue onward from that point, which is the same as ending that world and killing everyone in it.[1]

Still, if we don't worry about the ethics or the disk space requirements, then a Time-Changer which can restore and then change the past is easy to compute. There's a perfectly clear order of causality in metatime, in the linear time of the simulating computer, even if there are apparent cycles as seen from within the universe. The person who suddenly appears with a Time-Changer is the causal descendant of the older universe that just got dumped from RAM.

But what if instead, reality is always - somehow - perfectly self-consistent, so that there's apparently only one universe with a future and a past that never changes, so that the person who appears at 8PM has always seemingly descended from the very same universe that then develops by 9PM...?

How would you compute that in one sweep-through, without any higher-order metatime?

What would a causal graph for that look like, when the past descends from its very own future?

And the answer is that there isn't any such causal graph. Causal models are sometimes referred to as DAGs, which stands for Directed Acyclic Graph. If instead there's a directed cycle, there's no obvious order in which to compute the joint probability table. Even if you somehow knew that at 8PM somebody was going to appear with a Time-Turner used at 9PM, you still couldn't compute the exact state of the time-traveller without already knowing the future at 9PM, and you couldn't compute the future without knowing the state at 8PM, and you couldn't compute the state at 8PM without knowing the state of the time-traveller who just arrived.

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  • $\begingroup$ Re the last quoted paragraph: I think Hawking was talking about that when he said it would form a Cauchy Horizon. This was a book of essays on time travel, and something related to this is used to support the impossible position. It's more subtle... something about the future light cone of what would hace taken place is blocked by the arrival. Meanwhile, self-consistent cycles have been explored and appear to work out in a wide range of situations. $\endgroup$ – JDługosz Jun 10 '15 at 17:59
  • $\begingroup$ That last paragraph is also interesting, as it reflects my plotting issues! For example, I have to plot ahead, and account for anyone/information passing back through time (by going Below and 'up' again) and account for their effects on the past in the earlier parts of the plot, (which will, in turn, partly define the later plot parts). Talking about making a rod for one's own back (but a fun one, methinks)... $\endgroup$ – Mobeus Jun 11 '15 at 9:08
  • $\begingroup$ In essence, it seems to me to be in effect recursion, which, still leaves (at least the appearance of) free will, as well as predestination, but also leads to things like the above 'Paradox Engine' (which recurses upon itself until it halts due to some improbable breakdown). What twists my mind is 'where' all the recursing occurs, as I assume an observer of the machine would only see the last, breaking, iteration... $\endgroup$ – Mobeus Jun 11 '15 at 9:08
  • $\begingroup$ Just throwing a wild thought out there, but is the 'iteration space' the machine goes through some kind of meta or fractal time? (as it occurs many times, but within the observers percieved time of one iteration of the machine... $\endgroup$ – Mobeus Jun 11 '15 at 9:08
  • $\begingroup$ To put it in terms of a computer, I suppose I'm saying that the iterations of the Paradox Engine are in effect part of a 'stack trace', and not what gets written to disk, but that may be taking the analogy too far... However, it occurs to me, that you could get really unstuck if some how you hit a time-travel variant of the 3-body problem..? $\endgroup$ – Mobeus Jun 11 '15 at 11:33
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Special relativity describes spacetime as a manifold whose metric tensor has one negative eigenvalue, corresponding to a 'timelike' dimension.

There's nothing about Einsteinian physics that restricts spacetime models to only one negative eigenvalue. However, there are solutions with more than one time dimension.

This is relevant for your question because the "strip of paper" connecting the Above with the Below seems to bend in a secondary time dimension (since your vertical axis is timelike), otherwise, by definition, subluminal travel backwards in a time-like dimension is impossible. Think of 'timelike' dimensions as you think of an the fate of an observer falling past a black hole event horizon -- it cannot but go forward.

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  • $\begingroup$ The actual situation I have in mind if a 4-dimensional city, with two 3D 'surfaces', but I wanted to keep the question pure, as I realize that talking about 4+ dimensions bring a whole bag of other issues. Hence, a second time dimension would be acceptable, although I'm trying to pare down the 'extensions' to normal physics as much as possible. But you make an excellent point which I had not considered! I'll need to think about this... Thanks :) $\endgroup$ – Mobeus Jun 10 '15 at 15:22
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If time runs backwards, each dead person will meet ghosts of this who died after them, or even who were born after they died. This would potentially allow harvesting information from the future through some weird suicide scheme.

If that's the wrong interpretation, it seems that everyone would experience the second world alone; the person who died before you wouldn't see you until you died, but you die in their past, meaning your time will never line up.

Since the asker has clarified that the second situation is the accurate one, I want to point out this means that all ghosts that can return to the land of the living will do so, so that they aren't overwhelmed with loneliness. This seems to mean that passing information from the future is still possible, even if the ghosts have a limited life span. The more I think about it though the harder it seems to line people up in backwards land, and it is only a hell of loneliness with everyone clamouring to escape.

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  • $\begingroup$ Nope, you're quite right. It would indeed be a sad side effect that you would not get to meet your loved ones in the afterlife (unless your ghost went above again for a period of time). $\endgroup$ – Mobeus Jun 10 '15 at 15:17
  • $\begingroup$ Actually, I gave this some more thought, and I don't quite agree any more. Let me explain: person A dies on Tuesday, and person B dies on Wednesday. Both start moving back through time (from the perspective of a living observer). So, after a day, person A is at Monday, and person B is at Tuesday, at which point, she will meet person A at the point of their dying. Hence when Person A had died, they'd met person B, who'd been dead for a day already. I think... Now imagine the challenge I've set myself trying to plot all of this. My head hurts so, so much. $\endgroup$ – Mobeus Jun 13 '15 at 23:43
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Cycles & Immortality concepts

Immortality in the sense that everything is neverending, you can die however you can come back to life (basically someone dead(B) dies, and ends up being alive again(A) - otherwise just saying but B side is going to get overcrowded fast.

This being said, prophecy, predestination, foretelling and different time flows can all exist with no world breaking paradoxes if your world is stuck in cycle. If A is destined to find a cure to an incurable condition before A dies. A might find a cure for hiccups. then die. then while dead advance backwards on the B side, do whatever it was destined there, all the way back to its A birth, then is back on A side and this time cures flaky hair.

They are stuck in their prophecised patterns but still retain freedom of choice. Causality and Effect are in full swing.

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What you describe is easiest handled with topology. I like the Flatland approach for studying this, but I'm going to make it even more extreme: I'm going to describe the world as though it was 1 dimensional. That way, I can have an additional dimension for time, and one more dimension for this above/below behavior, and still fit within the 3 dimensions that we can deal with intuitively.

In topology, this system would appear as two flat sheets, one above and one below, with interconnections. On the top, time flows one direction (lets arbitrarily call that "to the right"), and on the bottom it flows in another direction ("to the left"). At each point there are two interconnections, one allowing travel from the bottom to the top, and the other allowing travel from the top to the bottom.

With this structure, there is no issue with a "square" above passing a dead-square below. The only reason there would be any issue with this is if there was a "collision" as an object tried to cross from above to below, or from below to above, intersecting with itself or another.

Using this topological structure, it is easier to show that many time paradoxes are not important because the structure of time allows a living thing and a ghost to cross paths without intersecting.

Computation is tricky, because it is always done in a perfect theoretical space that never exists. Real computers always have faults, but the paradoxical effects of computation and time travel always assume a perfect computation engine exists.

Accordingly, if you were to strive after a paradox, you would have to use your observations to create a more perfect computer. You would have to measure the state of the computer precisely enough to prevent a fault from occurring. Fortunately for you, this time topology lets you get away with a lot. You can see the fault, identify it's cause, then travel back in time as a ghost to prevent that fault from occurring.

Making the paradox interesting is that the fault has already been observed. The only way to stop the fault is to change something which was unobserved into something that "corrects" the fault after it happens. In a way this will "consume" the unknownness of the universe, one loop at a time. Your machine will get larger and larger as it becomes dependent on more and more observed values until something happens.

What happens depends a lot on what your rulesets are for the minds of ghosts. If the minds of your square and ghost-square are unafflicted by the backwards and forwards travel of time, then the only thing that stops this computational paradox is the patience of your square. Is it actually willing to spend an infinite amount of time to compute an undecidable problem (which, incidentally, is not a paradox. Similar decision problems such as The Halting Problem are only paradoxes for turing machines, which by definition run in finite time).

There are a few alternatives which could resolve the issue without this infinity. One is to refuse to allow ghosts to travel back to the above world into a state where said ghost could cause a paradox. Attempting to create the computational paradox above would simply cause the universe to refuse to allow the ghost to return to the living to mess with itself. This would create an interesting "true death" for ghosts, where the universe no longer admits them to the world of the living because there is no point in time where the ghost could return that is incapable of creating a paradox. It also creates an interesting purgatory for a ghost which has created a potential paradox which forbids the universe from allowing it to return more than X seconds in the past. That ghost must cycle repeatedly, trying to avoid the creation of accidental paradoxes which shrink its lifespan. Eventually, it may give up, let time pass it by, and accept a true death.

A more boring but consistent approach could be to take a physicalist approach, and make the mind of the living or dead creature be made of matter, thus subject to the same uncertainty principles as the rest of the world. In these worlds, one could perceive a paradox, but the harder one tries to perceive it, the more one's mind is distrupted - it's far easier on the universe to let a few atoms of one of your neurons misbehave than it is to allow a paradox. This is actually a very traditional solution to the time traveler paradoxes: the universe will simply disallow you from doing anything which creates an inconsistent state. It also creates interesting effects known as Strange Loops, such as the main character from Heinlein's All You Zombies.

Another alternative would be to allow the universe to affect the minds of the ghosts to erase information needed to produce the paradox. In this world, one is in control of one's own mind in the world of the living, but obviously one has limited control over the physical world around it. Measurements a la. Copenhagen are allowed. You are allowed to remember any measurements you please, just like in real life. However, once you travel to the world of the dead, the roles shift. You can go anywhere you please in the dead world, allowing you to find opportunities to shift to the above world and wreak paradoxes. However, there's a catch. As you move in the ghost world, you do not have perfect control over your mind. Travel to a location where you could choose to make the printer print "B" instead of "A," and the laws of the universe may force you to forget which letter you needed to print to cause a paradox.

An interesting side effect of the last one is a twist on the "true death" of a ghost. A ghost may travel back in time far enough that it is forced to lose so much knowledge that it forgets how to transfer itself back to the land of the living. It coasts, oblivious, until something kicks it back into the world of the living against its will. However, if one's knowledge consists of nothing but "universal truths," one could theoretically surf backwards against time forever, never forgetting who one is, free of what could easily be called the "cycle of reincarnation."

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