From 2100 to the End of Time


Frank J. Tipler

Frank J. Tipler is Professor of Mathematical Physics at Tulane University. He is the co-author of The Anthropic Cosmological Principle (Oxford University Press, 1986), about the significance of intelligent life in the universe, and the author of The Physics of Immortality (Doubleday, 1994) about the ultimate limits of computers, and the role computers will play in the universe. Professor Tipler was the post-doc of a post-doc of John von Neumann, the mathematician who made the first American digital computer. Tipler was also the post-doc of a post-doc of a post-doc of Albert Einstein. Finally, Tipler was the post-doc of John Wheeler, the man who named the black hole, and Wheeler was in turn the post-doc of Niels Bohr, one of the founders of quantum mechanics. Not surprisingly, Tipler's research is on discovering the mutual implications of computer theory, relativity, and quantum mechanics.

The year is 2100. AI's and human downloads have begun to explore and colonize interstellar space. The spaceships carrying the AI's and human downloads are tiny, massing no more than a kilogram. Quantum computers, which can code more bytes of information in 400 atoms than there are atoms in the entire visible universe, do not require much mass. An entire simulated city with thousands of humans and AI's can be coded in a few grams. And a tiny spaceship has a huge advantage over the ponderous rockets of today. Powered by matter- antimatter annihilation, such tiny spaceships can reach 90% of lightspeed with only a few kilograms of fuel. At such a speed, the nearest star, some four and one-half light years away, will be reached in only five years. Acceleration to 90% of lightspeed will be very fast, because the downloads and AI's will be impervious to acceleration. Humans not living in computers can take only a few gravities of acceleration, and can take that small acceleration only for a short time. Simulated humans will experience only the usual one gravity acceleration in their simulated environment. Human downloads have such a natural advantage over present-day humans in the environment of space, that it is exceedingly unlikely non-downloaded humans will ever engage in interstellar travel. The stars are to be the inheritance of our downloaded descendants, of the children of our minds rather than our bodies.

All this may sound like the most outlandish science fiction, but it is not. The above scene from the year 2100 uses only the technology allowed by the known physical laws. The quantum computer should be a practical device by 2020, according to the physicists and engineers now developing it. CERN, the prestigious European research center for particle physics, has announced it is ready to begin work designing a matter-antimatter rocket. And the readers of Wired know full well that AI's and human downloads should be a reality by 2100. We know from experience that if anything, the actual technology possessed by civilization in the future will actually be much more sophisticated than that which we project using the physical laws which we now understand. So let us continue, conservatively using only the known physical laws, with the story of our mind children as they begin their expansion into interstellar space.

After five years of travel - this is Earth time; by adjusting the spaceship computer's clock speed, the travel time experienced by the downloads could be less than a blink of an eye - the spaceship has arrived in the solar system of the nearest star. They begin to explore. They can also begin to colonize. There is a huge amount of material - meteors, asteroids, planets - present in all star systems for the downloads to construct other computers which can code other simulated cities and entire simulated worlds for the downloads and their descendants to inhabit. Our mind children can also construct new spaceships, controlled by their descendants or perhaps even backup copies of themselves, and send these newly commissioned ships out to yet more stars.

We have exponential growth. A single tiny interstellar quantum computer controlled starship can make several copies of itself in the near star system, each copy travels to yet another star system, and in turn makes several copies. At 90% lightspeed, in less than one million years, the entire Milky Way Galaxy has been explored and colonized. In another ten million years, the Local Group of Galaxies has been explored and colonized. In another 100 million years, the Virgo Cluster of Galaxies has been completely colonized. Where will this expansion end?

It will never end. Eventually, mind children will engulf the entire universe! In fact, they must eventually engulf the universe if they are to survive. In fact, the laws of physics require them to eventually engulf the entire universe and take control of the universe!

To understand why, we have to understand just a bit about the laws of physics that control the universe. Twenty-five years ago, the great English scientist Stephen Hawking made a remarkable discovery: black holes are not black; instead, they slowly but surely radiate away their energy, and thus slowly but surely they evaporate. Given time, they would completely evaporate. Nothing would be left. But although energy can escape a black hole, information - the bytes describing the matter that went to make up the black hole - cannot escape. So were a black hole to evaporate completely, the information would have to be annihilated, to disappear completely from reality.

This discovery greatly puzzled Hawking. For, great physicist that he is, he knew very well that quantum information cannot be destroyed. (This fact, that information cannot be destroyed, is the basis of the quantum computer.) Since black holes certainly exist - astronomers have seen them orbiting stars, and in the centers of galaxies - it seemed that a fundamental law of nature, the indestructibility of quantum information, would be violated, at least if the universe were to last long enough for a black hole to evaporate.

This is solution to Hawking's dilemma. The universe must not last for an unlimited time. There is one and only one type of universe which lasts for only a finite time, and that is a "closed" universe. Such a universe expands (as the actual universe is now expanding) to a maximum size, and then contracts to zero size after a finite time. It is "closed" in time. In order for no black hole to evaporate, the universe must end within 10^64 years. A very large closed universe, but closed nevertheless.

But another fundamental quantum law is a limit on the complexity of a physical system. This limit, called the Bekenstein Bound after the Israeli physicist who discovered it, says that any physical system can code at most 10^43 bytes of information times the system's mass in kilograms and its maximum size in meters. This means, for example, that a typical human can code at most 2 times 10^45 bytes, since most people weigh less than 100 kilograms, and are less than two meters tall. This Bound poses a serious problem for a closed universe, because one way to state the Second Law of Thermodynamics is as follows: the microscopic complexity of the universe can never decrease. Think about what this means when combined with the Bekenstein Bound. If the non-gravitational mass and energy of the universe is constant, then as the size of the universe goes to zero, the maximum information coded by the universe - its complexity -must go to zero, giving a direct contradiction with the Second Law. We seemed to have escaped one dilemma, only to land into another one.

There is one and only one way out. If the closed universe is a very special type in which every location in the universe can send signals back and forth an infinite number of times to every other location in the universe, then the gravitational energy due to the collapse of the universe itself will increase to infinity much faster than the size of the universe goes to zero - remember it is the product of mass and size that restricts the complexity of a physical system. In such a special case, the Bekenstein Bound on the complexity of the universe would no longer force the complexity of the universe to zero. Indeed, it would be possible for the complexity of the universe to go to infinity!

We're not out of the woods yet. The type of closed universe that has unlimited communication between all location is very special. So special, that the probability the actual universe, acting only under the action of blind and dead forces, will evolve in such a way as to allow such unlimited communication is zero. Such a universe is infinitely improbable. This means that an unlimited communication universe, if it evolves under no guidance, would violate the Second Law of Thermodynamics, because another statement of the Second Law is "physical systems evolve from less probable to more probable states". An infinitely improbable state is not a "more probable" state. Some crucial physical phenomena has been left out of the analysis.

Our downloaded descendants have been left out. Notice I emphasized that an unlimited communication universe is infinitely improbable if it evolves under no guidance. But guided physical systems routinely evolve into vastly improbable states. For example, it is a well-known fact that chaotic system can be pushed into an extremely improbable state with negligible effort. State-of-the-art jet fighters are designed to be unstable - their dynamics are chaotic - so that a negligible effort by the guiding computers can push the jet into a rapid change of direction. So the mutual consistency of the laws of physics requires that our downloaded descendants control the entire universe in the far future.

To ensure an unlimited amount of communication in the far future - something our descendants will have to do in order to control the universe - our descendants will have to act an infinite number of times between now and the end of time, and by the Second Law this will increase the complexity of the universe to infinity. But this in turn means that the computer capacity of the universe will also have to increase to infinity as the final state of the universe is approached, because to control a system - the entire universe - whose complexity is increasing without limit means that our downloaded descendants' knowledge of the system must increase without limit.

I've gone through a discussion of the physics in some detail - probably excruciatingly more detail than you would like to read! - in order to show how the laws of physics collectively force us to accept the conclusion that computer capacity in the universe will diverge to infinity, and the conclusion that our downloaded descendants will ultimately control the universe. The laws of physics require us to survive, and to increase our capacity without limit. If the laws of physics be for us, who can be against us?

One of the things our downloaded descendants can do with this diverging to infinity computer capacity is resurrect us. The Bekenstein Bound shows that any human can be perfectly simulated in a computer with 10^45 bytes of storage capacity. The entire visible universe can be perfectly simulated with 10^123 bytes of storage capacity. Large as these numbers are, they are insignificant in comparison with infinity. So they could easily simulate us - bring us back into existence, since a perfect simulation is the thing being simulated - with an insignificant part of their total computer resources. They could also simulate perfectly all possible variants of the visible universe, an endeavor which would require a mere 10 raised to the 10 raised to the 123 bytes of storage capacity. (You read correctly: the number is a DOUBLE exponent: 1 followed by 10 raised to the 123 power zeros!) Our descendants may wish to reproduce all possible variants in case they don't remember or know everything about us. No problem: they'll just simulate every possibility consistent with what they do know. Isn't it amazing what you can do with unlimited amount of hard disc space?

Now that we know where our downloaded descendants will ultimately end up - ubiquitous throughout, and in complete control of, the entire universe - let's take up their history from where we left off. As you recall, when we left them, they had just completely colonized the Virgo Cluster (100 million years from now). They will expand out from the Virgo Cluster, engulfing the entire universe just a bit after the time of maximum expansion of the universe. After that they will work to convert the entire universe into habitable space, increasing their knowledge to infinity, by the end of time knowing everything that can be known. They can have an infinity of experiences between now and the end of time, even though the universe will end in a finite time, because they can increase their computer clock speed without limit (recall that light will pass back and forth across the universe an infinity of times.) They will also increase their use of energy to infinity (remember, there is an unlimited amount of energy available from the the collapse of the universe into zero size).

So our mind children at the end of time will be omniscient (they will know everything that can be known); they will be omnipotent (they will have infinite energy, controlling all the energy resources in the universe), and they are omnipresent (they are ubiquitous throughout the universe). It is interesting that God's Name, as given in Exodus 3:14, is in the original Hebrew Ehyeh Asher Ehyeh, which translates into English as I SHALL BE WHAT I SHALL BE.

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