Strange Paths

The concept of star travel, from planetary system to planetary system, is at the same time completely familiar and completely uncharted. Familiar, as we have certainly all heard of science fiction stories set on a far galaxy, where planets are nations or provinces of an empire. The characters usually move from one planet to another during intervals of time consistent with the story. The actual travel appears just like a formality, which the future advancements of a Triumphant Physics will put within reach.

This is what I’ll call the “strategy zero” (S0) : here travel is “instantaneous” or at the very least quicker than one year, eg. comparable to the durations of terrestrial travels or manned missions to the moon or other solar system’s bodies.

The way toward stars becomes however quite unfamiliar if we consider that such Triumph of Physics could possibly not happen, and that the famous constant of Einstein c, the speed of light (3E8 m/s), represents an horizon speed which is impossible to exceed and which is even extraordinarily difficult to approach, so that we would begin to see outer space like it is seen by astronomers: a vastness compared to which that of terrestrial oceans is nothing.

It is not without reserve that our mind adapts to the true dimensions of interstellar space. The insanity of these distances is not the only reason: in a sense, one could say that the “strategy zero” is enracined in a child’s desire of space. Not of a space-distance, of a horridly naked space, speechless and fearless, but of a space-treasure, and of the worlds which roll within its vastness. All these worlds whose reach should not suffer any delay and whose discovery turns on our imagination.
Realism helping, we leave with some regret the green paradise of “strategy zero”, but we can still consider a little more “teenager” strategy, within the framework of Special Relativity, which we will name “short strategy” or SI, which promises a travel duration within a man’s lifetime.

(more…)

We can understand the paradoxes by Zeno of Elea (ca. 470 BC)¹ in two ways.

The first interpretation is that Zeno is not denying movement, but rather questioning its continuity, which is what actually leads to the paradoxes. In this sense, we can consider that Zeno is experiencing a kind of technical difficulty, and that the problem can be easily solved with calculus or as a converging sum of an infinite series. This interpretation is however short-sighted in its way of arbitrarily postulating the existence of movement, and just concentrating on the technical argument of the consistency of continuity, which is truly a mathematical problem and not a physical nor philosophical one. It shall be noted that one cannot prove that Zeno intended to contradict that the sum of an infinite series can be finite, as the mention of ‘finite time’ appearing in the report of the paradoxes² could be merely an interpretation by Aristotle.

The second interpretation is that Zeno basically denies movement, in the extraordinarily modern meaning of Parmenides, who considered change as illusory and the world as static and eternal. Zeno is not denying the appearance of movement, but rather its reality. The paradoxes thus appear at a deeper level, from the comparison between the phenomenon of movement and its disappearance implied by a thorough analysis of its model - either it being continuous (dichotomy paradox) or discontinuous (arrow paradox) -. The question becomes a purely physical question, which must be answered within a physical theory : why the experience of movement if movement appears logically impossible?

In the classical continuous model, the arrow must assume an infinite number of states in order to move from a point to another point. If such an infinite separation between two events, modelled by the absence of the successor of a real number, is equivalent or not to their physical dissociation, is a physical question, on the same level of reasoning as the ultraviolet catastrophe ideas which brought to quantum mechanics.³ If infinite divisibility is mathematically consistent, it is not necessarily physically meaningful (see also the Banach-Tarski paradox).⁴ This picture further changes with quantum mechanics as, per Heisenberg principle, a particle in a determined motion does not have a determined position. Interestingly, Zeno also gives his name to a quantum effect described by the Misra-Sudarshan theorem :⁵ if it is observed continuously whether a ‘quantum arrow’ has left the space it occupies, then it indeed never leaves this space.

In a discrete model (arrow paradox), Zeno’s argument is even stronger, and we can find a similar formulation of the argument in loop quantum gravity on the basis that time, being a pure gauge variable, is fundamentally nonexistent.⁶

1. • DICHOTOMY: Motion is impossible, because before arriving to the end, that which is moved must first arrive at the middle, and so on ad infinitum.
   • ACHILLES: The slower tortoise cannot be overtaken by the quicker Achilles, as he must first reach the point where the tortoise started, from which it has already left, and so on ad infinitum.
   • THE ARROW: An arrow shot from a bow occupies an equal space when at rest, and when in motion it always occupies such a space at any moment, the flying arrow is therefore motionless. [↩]
2. Aristotle, “Physics”, VI:9 [↩]
3. A. Einstein, “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt” (”On a Heuristic Viewpoint Concerning the Production and Transformation of Light“), Annalen Der Physik, 1905. [↩]
4. S. Banach, A. Tarski, “Sur la décomposition des ensembles de points en parties respectivement congruentes”, Fundamenta Mathematicae, 6, 244-277 (1924) [↩]
5. B. Misra, E. C. G. Sudarshan, “The Zeno’s paradox in quantum theory“, Journal of Mathematical Physics, 18, 4, 756-763 (1977) [↩]
6. J. Barbour, “The end of time“, Oxford University Press (2001) [↩]

Most theories predict that at some time in the future, matter, structures, and/or the universe will have an end. Protons could decay within about 10⁵⁰ years according to Grand Unification theories.¹ The whole universe should approach an absolute zero temperature within 10¹⁰⁰ years, even black holes having evaporated.² And time itself could have an end, in a final imploding big-crunch singularity³ or in a diverging expansion cutting the universe in smaller and smaller chunks up to each particle.⁴ If a form of intelligent life would still exist by such times (certainly not based on current biology), how could it adapt to handle such fundamental limits?

Living systems could optimize toward less redundancy and less energy consumption. However, such optimizations being finite, they would not solve the problem, unless time happens to be infinite.⁵⁶

In end-of-time singularity scenarios, life could try to slow down perceived time by thinking faster. For example, the same amount of thinking and experience of billion years of human life could happen in a second. However, the energy required would accordingly increase, and physical time would subjectively slow down but not stop. In order to make eternity fit into a finite time interval, so as to escape an end of time singularity, infinitesimally small durations should exist, but time could be discrete at Planck scales, and even if it was not, infinite amount of energy would need to be pumped in the “eternity” process, so as it cannot happen “before” the singularity. Some argue that it could happen “during” the singularity itself.⁷

So how to escape the system? Logically this should be impossible. However, the system could prove to be more deep and resourceful than we perceive it today.

My favorite dream is about an infinite “sub-time”, perfectly still into each instant of time, where life could ultimately translate itself. There is also the idea of a cyclical universe,⁸ where the same finite combinatories of experience would come up again and again, which is similar, as if the whole universe was cyclical, time included, then it would not cycle within time but within another variable, so there would be no way to make a difference within time between it being cycling or not cycling. The same would apply if we live in a multiverse, like the one modeled by the chaotic inflation theory, where any singularity is local and the multiverse is made of a non-countable infinity of inflationary domains.⁹

So this fundamental question appears to be an introductory question about the nature and meaning of time.

1. H. Georgi, S. L. Glashow, “Unity of All Elementary-Particle Forces“, Phys. Rev. Lett. 32, 438-441 (1974) [↩]
2. S. W. Hawking, “Particle creation by black holes“, Comm. Math. Phys., 43, 3, 199-220 (1975) [↩]
3. Although there is experimental evidence for an universe presently undergoing an accelerated expansion, the dark energy could still be an oscillating scalar field leading to future recollapse [↩]
4. R. R. Caldwell, M. Kamionkowski, N. N. Weinberg, “Phantom Energy and Cosmic Doomsday“, Phys. Rev. Lett. 91 (2003). [↩]
5. F. J. Dyson, “Time without end: Physics and biology in an open universe“, Rev. Mod. Phys. 51, 447 - 460 (1979) [↩]
6. K. Freese, W. H. Kinney, “The Ultimate Fate of Life in an Accelerating Universe“, Phys. Lett. B 558, 1-8 (2003) [↩]
7. F. Tipler, “The Physics of Immortality“, Anchor (1997) [↩]
8. P. J. Steinhardt, N. Turok, “A Cyclic Model of the Universe“, Science, 296, 5572, 1436 - 1439 (2002) [↩]
9. A. Linde, “Eternally Existing Self-Reproducing Chaotic Inflationary Universe“, Phys. Lett. B175, 395 (1986) [↩]