Why haven’t time travelers prevented the 100% likely depredations of [pending event]? Why hasn’t anyone come back in time to kill Hitler or save the dodo or smother the members of Nickelback in the cradle? Why in a universe of fermion asymmetry and higher-than-three-dimensional branes have we not seen the real-life equivalent of Booster Gold, Ripley Hunter, Max Mercury, Nate Summers, or the crew of the retrofitted RMS Bounty (after replacing the Klingon meal packs)?

Why has no one saved us?

Before I propose an answer to this question, let me first state my assumptions, as the comment that prompted this inquiry came from Oz of The Damn Woods:

Thesis: Time travel works and can change the flow of events but creates parallel timelines without interrupting or changing the existing one

— ODO OFFICIAL (@OzKFodrotski) November 13, 2016

I take this as the premise of what follows. This is the multiverse theory, somewhat popular in science fiction worlds. We find multiverses in the DC continuities (which is one possible explanation for why Batman seems to have so many different personalities), the Marvel multiverse (with the added bonus of active time-traveling agents of chaos like the Deadpool clan and Cable), some Star Trek episodes, (possibly) 12 Monkeys, Sliders, that one Red Dwarf episode where the crew met female versions of themselves and Dave got pregnant, and the feature-length Fullmetal Alchemist where the Elric Brothers went to that steampunk-looking Earth that didn’t have any state alchemists. I actually don’t remember the plot of that one, as I think Brotherhood washed out most of what I recall from the original series. Also, needless to say, Chrono Trigger.

Contrast the branching-worlds approach with the single-timeline worlds found in Futurama (nb: several tropes were explored in this show), Dr. Who, Back to the Future, most other time-travelling Star Trek episodes, &c. For a first pass at the trope distinction, if the Grandfather Paradox introduces a fatal inconsistency, you have a single-timeline universe. Otherwise, you have a multiverse.

The Temporal Event Horizon

If time travel were technologically possible (and recall that according to the assumptions of this exercise, it is), there exist two hard barriers to when chrononauts might arise. The first occurs some short time after the birth of the universe, prior to boson/fermion differentiation. Obviously, time travel is impossible before the space-time continuum even resolves.

At the other end is the heat death of the universe. In order to power a device, one must first collect energy. In our time of abundance, we are Newcastle, and the coal is all around us. Think of an ordinary trip to the grocery store: a short drive and a little walking, and you’ve got all the energy you need to keep a typical human powered for weeks. A few electron volts of expenditure yields millions of electron volts of potential energy. But we live now in a universe with highly concentrated pockets of matter-energy. Our spacetime coordinates are loaded with rich deposits of negentropy. The far future is not expected to be like this. Present astronomical readings show that our universe is expanding at an increasing rate. Eventually, energy gathering forays will require more expenditure than can be returned. Instead of a five minute drive to the supermarket for the fortnight’s groceries, you’ll have to travel a full week to get to the Piggly Wiggly. The foraging costs more energy than it returns.

Heat death comes in a few flavors. Hard-line heat death occurs when 1 eV of expenditure returns exactly 1 eV of available energy. This is cold stasis. Nothing can feed, nothing can reproduce. Beyond that, utter decay is inevitable. Call this universal heat death (UHD). The threshold we’re interested in occurs well before this. Time travel will require some expenditure of energy, including R&D costs. Time travel heat death is therefore the theoretical limit at which net energy collection can just cover the creation of a device with enough left over for a voyage. Beyond this point, no entity on a monotonic timeline can develop time travel de novo. Call this the temporal event horizon (TEH).

Portable Entropy

Recall that information transmission results in the state change of some… some stuff. In the human brain, chemical reactions store neural pathway patterns. Media storage devices use atomic arrangements to modify magnetic patterns, or light refraction, or whatever else is convenient. Player pianos have holes in rolls of paper to reproduce a musician’s performance. Flipping a one to a zero is an information change. This flipping requires the expenditure of some of the universe’s entropy reserves. Recall also that the Second Law of Thermodynamics insists that entropy in a closed system increases as a function of time. This brings us to an organizationally and economically important question: does the time travel proposed by Oz in his tweet imply that chrononauts draw on the negentropy of their destination, or can they carry their own reserves with them. In other words, is the total system governing the Second Law of Thermodynamics fourth or fifth dimensional? If it’s fourth dimensional, then it’s just as advertised: no bottled negentropy can be carried past UHD. Chrononauts must use the energy they have on hand to project duplicates or holograms into the past to influence the timeline. If, contrarily, available spacetime is fifth dimensional, then the limits of the universe care about the integral of the available entropy, and packets of energy can be transferred along brane manifolds.

Why is this organizationally important? I’m glad you asked. Because in a 4d universe, the TEH is a limiting barrier on the coordinates of a time traveling organization. If ancient energy cannot be brought forward, the best you can do is scavenge from a dying universe. In a 5d universe, not even proper heat death should stop anyone from establishing a stronghold even well after every photon has fled every other. And when rival organizations compete under these circumstances, an advantage on information makes the whole difference between victory and being utterly erased from existence. In a 4d universe, he who dwells closest to the TEH enjoys the information advantage. In a 5d universe (bear in mind that I mean highest accessible dimension here), there is no theoretical upper limit on the temporal location of a temporal enclave.

Therefore, a 4d universe will tend towards a single time-travel hegemon. A 5d universe could possibly have multiple agencies, though it would require strong anonymity protections.

To see why an equilibrium of multiple temporal sovereigns is untenable in a 4d universe, all we must do is imagine even slightly heterogeneous preferences (we don’t even need imperfect information, though it doesn’t change the outcome) among representative agents. If P1 covets even a little bit of P2’s resources, he has all of space and time to completely wipe P2 from existence, forever. Think of it like pruning a branch from the fractal tree. All you have to do is pilot your ship through the nebula of your rival’s home star system before it forms, and it’s as good as The Golden Throne issuing an exterminatus order against a Necron planet (copyright Games Workshop). The only possibility for more than one time agency to exist in this case is if players had utility functions that contained very large terms for others’ total utility. While this arrangement is theoretically possible, it is unlikely to evolve naturally and would require a great deal of trust between agents who may have large incentives to conceal their intentions. Ordinary game theoretical selection would tend to produce a single winner, with rivals ruthlessly eliminated from the timeline.

Forward Induction

Knowing that any dominant time travel society would tend towards the utter elimination of upstarts, we can conclude one of the following:

1. The universe as she operates has at least five accessible dimensions for time travel, and energy can be moved along these manifolds to and from secure enclaves beyond the TEH barrier.
2. The universe has no more than four dimensions accessible to time travelers and
   1. Humanity is the ultimate hegemon, having already eradicated rival societies from timespace (note that this is consistent with radio observations of a derelict universe; this can be considered a strong filter)
   2. Humanity is an orphan species, of no great interest to the actual time hegemon
   3. Humanity understands the game theoretical nature of time travel and on the cusp of developing the appropriate technology, realizes the implications of continuing in a crowded universe and abandons the project. Note that this would require considerable coordination and is therefore unlikely, considering the enormous benefits of time travel.
3. Time travel is fantasy bullshit.

Now, number 1 is an empirical question. Radio astronomers have some evidence that the visible universe has some four-dimensional curvature to it, which at least raises the probability that the higher dimensions claimed by a unified string theory are possible, but these observations imply nothing about the ability to pass information, let alone negentropy between fifth (or higher) dimensional locations.

2.1 is a pretty good outcome for the species, I guess. However, it contains a dire catch. Since the monopoly on time travel is so vital to protecting the interests of the time sovereign, almost all of its excess resources would be devoted to protecting its privileged position. This implies efforts to get as close as possible to the TEH without slipping over the edge, and towards monitoring the timeline for rivals and eliminating them. To an organization with these priorities, preventing the rise of genocidal rulers fades into utter insignificance.

2.2 implies that we’ve simply got to deal with the hand we’re dealt.

2.3 is Wilson’s Basilisk. The best way to calm a sleeping dragon is to never wake the beast in the first place.

3 contains the same implications as 2.2.

No matter how you slice it, counting on benevolent time travelers to rescue us from the mess we’ve summoned is foolish irrationality.

So say we all.