In the real world, information about past states is continually being lost—quantum wave-functions decohere, things fall into black holes—and so present initial conditions never contain enough information to reconstruct the past (except on a probabilistic basis). Because of time-symmetry, an inability to reconstruct the past is mirrored as an inability to predict the future (except on a probabilistic basis). The job of accumulating information about a future time is never complete until the moment when that future becomes the present.
Our “now” contains neither the whole of the past nor the whole of the future, or, to put it another way, “now” contains the roots of all possible pasts—but won’t tell us which particular root is ours—and contains all possible futures in the branches of its tree—but won’t tell us which of those limbs we are about to climb out on.
No psychohistorian, no matter what godlike powers he might acquire, can predict an absolute future—too much information about the future is missing in the initial conditions of the present; no historian, no matter how meticulous, can write the definitive history—too much information about the past has been irretrievably lost.
That established, the Founder went on to describe how mathematics could determine the maximum upper limit on the amount of information that the present held about the future. Once the limits were known, mathematical method was free to give its best estimates of which futures we faced and what variables controlled the probability attached to a future.
The Master began to play amusing games with his audience—“the Group of Forty-six,” long dead, plus Eron, recently dead. They were asked to pretend that every Past Event was trying to encode itself in digital form to be transmitted through time to be filed by a harried Present in its bulging storage cabinets. He made it sound like he was chatting with the past over a wire. Eron grimaced. “Hello. This is the past. Get out your decrypter and I’ll tell you what really happened back here—hope you have enough storage room.”
As more and more messages accumulated, the physical size of the information “bits” has to shrink to be accommodated. Not a problem in the magical mathematical realm of a manifold, but in the real world—Eron could hear the Founder smiling—things got hairy when the Bureaucrats of Filing were eventually faced with the archival problem of finding space inside a cubic Planck-length for, say, the history of the Emperors. Yet how have bureaucrats everywhere always solved such an information overload problem? They condense the original into a brief memo, hide the memo inside the papers on their desktop, and hand the original report to an office boy with orders to lose it. Physicists have invented a fancy name for this bureaucratic procedure—they call it decoherence.
Of course, by time-symmetry, the events of the future were also sending messages to be stored in the same bulging cabinets and getting the same treatment. “Hello. This is your future speaking. Have I got news for you. But please make room in your storage space for my message.” Those famous branchings into alternate futures (the classical emperor-in-a-coffin conundrum) weren’t branches into other worlds at all; each branch simply represented one question (“Is the emperor alive?”) that was unanswerable because the procedures of the Bureaucrats of the Present didn’t yet have a place to store the answer. A bit of information about the past must be erased to make room for every new bit of information about the future.
Definition: The information content of an event, in bits, is exactly the number of yes/no questions needed to differentiate it from all other possible events. Consequently, if information is never lost—a deterministic requirement—any message describing an event had to carry from the past to the present exactly the same number of bits as were in the original event. Was it possible for such a transmission to be lossless?
The Founder was making sport with the determinists, catching them, teasing them, tweeking their noses, and letting them go. How could Remendian ever have mistaken this cat for a mouse? The Founder waxed with exaggerated humor about the trials and tribulations of a deterministic universe in which information conservation was a fact: every event that had ever happened was still out there transmitting its own information load, clogging every possible transmission line of space-time in a simultaneous attempt to wash ashore onto the present.
Eron tried to comprehend the preposterous magnitude of such a load. A whimsical analogy crossed his mind. He imagined the communication network of Splendid Wisdom burdened with the continual lossless transmission of every message that had ever been generated on Splendid Wisdom for the last fourteen millennia! Somewhere in there would be a wandering packet carrying Thanelord Remendian’s deathless order for breakfast on the morning of...consisting of three pig embryos in buttered thyme sauce on toast. He laughed, imagining the fate of a universe whose very survival depended upon the pristine maintenance of that message!
So much had been lost.
The universe was still here.
The Founder wrote out equations that illuminated the error.
Deduction: Determinism requires a transfinite channel capacity in order to maintain the transmission of all of its lossless messages. Space must be infinitely divisible.
At that point in his essay, the Founder took off his gloves. In a mere four lines he developed the formula for the real channel capacity of space. Prominent in the formula was the Planck length. The bandwidth of the universe wasn’t great enough to deliver the past’s messages losslessly to the present. Nor the future’s messages losslessly to the past. The real universe seemed to be “printed” in an “ink” whose “particle size” could never be less than the Planck length.
The Founder proceeded to outline some of the ways in which the universe was known to lose information.
1] What drops into a black hole can’t get out again, not even under time reversal. Black holes eat information permanently. Loss of information creates more uncertainty about the past, which is the same as saying that the information consumed by a black hole increases entropy.
2] Information is stored ambiguously at the quantum level to conserve bandwidth—for instance, data about position and momentum overwrite each other in the same “registers”—playing havoc with a physicist’s ability to pin down past or future. To operate in the present the universe never needs to know a particle’s position and momentum at the same time, so it doesn’t store that information independently.
3] A physicist may predict the pattern of hits that an electron beam makes in passing through two slits, but he cannot predict where any particular electron will hit; that information involves processes that are not derivable from any initial condition. The universe minimizes its use of bandwidth with such a compression technique. A physicist can look at a particular “hit” after the fact but cannot then backtrack the path of the electron that made the hit.
4] A physicist can predict how many alpha particles will be ejected from a gram of uranium in the next jiff; but he cannot tell you when a particular uranium 238 atom will changes State to thorium 234. Worse, the wave equations that describe uranium’s radioactivity, by time-symmetry, say that uranium has the same half-life whether it is moving forward or backward in time. But we know that the atoms in the uranium 238 sample we hold in our lab have been stable for the billions of years they have existed outside the supernova that created them! Quantum mechanics will not allow us to assume that, if we reverse time, these same uranium atoms will all remain stable for the billions of years it will take them to travel back to their mother nova. Bandwidth is limited. The universe eliminates inessential information. The uranium will not be able to return through time via the same path by which it arrived because the information that described that path no longer exists. A uranium atom’s moment of death is independent of its history.