miércoles, 10 de abril de 2002

Imaginary Time, or How to Force the Universe to Make Sense

Imaginary Time,

Or How To Force The Universe To Make Sense.

Throughout the Centuries humans have always tried to find a way to force the Universe to make sense by trying to find answers to questions that seemingly come unbidden to them. Humans have asked themselves the same questions over and over again: What is the origin of everything? Why are things the way they are? Why are we here? And, even if it sounds silly, they have also asked themselves: What time is it? And, what is it, time? And throughout History, the answers provided are always debatable and controversial.

Why should this be true?

One may presume that, by definition, such questions have no precise answer. As a matter of fact, when one analyzes these questions from a philosophical stance, it is clear that these questions unavoidably lead to paradoxes because it is very difficult to adequately ascertain the reality of things, for starters. But the origin of science, and indeed, of all epistemological endeavors of the Human Race is founded on desperately seeking answers to those kinds of questions.

For a long period of History, mankind’s only tools in the search of answers were reason and supposition. For example, the ancient Greeks were able to find the underlying concepts that constitute the basis of every mathematical language. By applying these concepts, they discovered the “rules” for many of the relationships represented in Geometry. This was accomplished by the use of pure reason.

Many Centuries later, the world was fortunate enough to produce people like Copernicus, Galilei, and Newton, who provided us with new tools in the search for answers. First, Copernicus took a more radical approach at searching for answers when he discovered that repeated calculations of measurements and facts did not agree with the established notion of how the Universe works. He tentatively suggested that perhaps the Sun was the center of our planetary system, but decided that challenging the conventional knowledge at the time would be against his own welfare. Some time later, Galilei was able to make a leap of imagination and use a telescope to look at the sky. His observations agreed very closely with Copernicus’ calculations, and Galilei was foolishly brave enough to go mano-a-mano with the Inquisition and propose a new way of explaining the Cosmos. A few decades later, Newton made use of reason and supposition, engaged in extensive calculation of measurements and facts, and performed precise observations to come to some conclusions about the nature of the Universe. Apparently, motion could be explained mathematically. And, since gravitational force seemed to apply equally both to an apple and to the Moon, Newton decided that physical laws should be equally applicable anywhere in the Universe.

That was the start of the modern scientific approach at finding the answer to everything.

Around the Nineteenth Century, most scientists believed that everything about the Universe had been explained, and that only two or three snags remained to be smoothed out. Therefore, Einstein saw fit to find the explanation to these snags. Working out the math during his spare time while working as a Patents Clerk, Einstein wrote a couple of scientific papers that proposed solutions for the Brownian movement observed in particles suspended on a colloidal suspension, and a clever explanation of the effect observed when shining light on certain metals. Although these snags were treated as oddities by the establishment and even Einstein had a desultory-seeming approach to explaining them, they had world-shaking consequences: not only one of these papers got Einstein a Nobel Prize, but also forced a revision of the way in which scientists thought the Universe was actually constructed. Coupled with the ideas introduced by Einstein, a new mathematical model of atomic composition came to be known as Quantum Mechanics. We will come back to Quantum Mechanics a bit later in this essay.

Meanwhile, Einstein had developed his Special - and later on, his General - Theory of Relativity. This theory pretty much did away with Newton’s concept of a linear Universe, and gave us instead a vision of a Cosmos with dimples caused by gravitational force, which came to be regarded as a “Negative” force. Or, simply stated, Gravity is the negative effect of Matter. In this new view of the Universe, time was not a constant thing, but instead was relative to the observer. Thus, the “Relativity” part of the Theory. Time became a continuum with matter, as it were, or seen another way, an extra dimension of reality.

Around that time a few radical scientists were bandying about a new idea. Most of the other well-respected, well-established scientists (such as Einstein himself) thought the idea preposterous, objectionable, and untenable. This idea asked the question, “what if the Universe originated from a tiny, non-dimensional point in space that somehow exploded and resulted in everything that actually exists today?” This came about because this guy, Hubble, discovered that those blurry objects in the sky were not objects in our galaxy, but actually galaxies themselves. Even more than that: by measuring the Doppler-effect shift to the red of the galaxy’s light, Hubble and associates discovered that these galaxies were all moving away from us. Fast. And in direct relationship with their distance. By direct deduction, people clearly saw that if everything is moving away from everything else, then it must have all come from the same point, at some time in the past. All this matter must have been created in a huge explosion, because otherwise the level of activity present in the Universe would not exist.

Einstein - who ever after, and until his death, was searching for a way to unify all the known forces acting on matter into a single explanation of how everything worked - thought the idea of a humongous explosion creating everything was an aberration because it would create a singularity in space-time. Because at such point all the current laws of physics break down and nothing makes sense any more, Einstein rejected this concept. Analogous to this concept - now regularly being referred to as the Big Bang Theory - was the idea of a Black Hole. A Black Hole is what happens when a sufficiently massive star dies and its gravitational force collapses the matter into itself, creating such a concentration of matter that the gravitational field resulting from it is so strong that nothing will escape it, not even light. It is ironic that Einstein was so disinclined to accept these ideas when they were in fact the intellectual offshoots of his own Relativity Theory.

The debate that actually raged for many years concerning the Big Bang Theory was thankfully put to rest when some guy named Robert Dicke came up with the notion that if the Big Bang was true, then it must have produced a big flash of light which should still be detectable even today, as a faint glow of radio waves. And wouldn’t you know it? Penzias and Wilson found that glow in the radio spectrum. Its fancy name is Cosmic Microwave Background Radiation, and it is so faint that it is only a few degrees above the absolute zero.

So, there. All the history of science geared toward this point in time: we finally had a new way of understanding the Universe that very nearly explained how it all works. But not quite. Even today there still are a few snags to be explained away. For example, what happens inside a Black Hole? And how to prove even such a thing exists? And how to explain away singularities in order to avoid finding ourselves in a place where no laws of physics apply and nothing makes sense?

Enter Stephen William Hawking.

Known to the general public mostly because he suffers from ALS and can only speak through the use of a computer, to the more informed segment of the public he has been the spokesperson for really complex and complicated scientific concepts in the last couple of decades. Like Carl Sagan before him, Hawking believes that people are not interested in science because scientists do very little to communicate clearly and invent all kinds of lingo to restrict access to ideas and concepts to a select few people. Because Hawking needed money at one point in his life, and because he wanted to communicate to the general public the more exciting modern concepts about the Universe, he wrote the successful and accessible “A Brief History of Time”. In it, he explains his ideas about the meaning of it all. A later book titled “Black Holes and Baby Universes” is an explanation of his personal history and how it affected his ideas. Through these books one can understand why Stephen Hawking has managed to find explanations for the most unlikely concepts.

First, his physical impediments make him aware of how much other people’s cooperation is necessary to accomplish anything. This is made clear in his work on Black Holes and No-Boundary Theory where, in association with Penrose and Hartle, Hawking proposes concepts that challenge the present comprehension of how the Universe really works. Hawking seems unafraid to compile discoveries and theories of other scientists into his work without fear of being called inauthentic or not original. For example, along with his associates Hawking was able to prove mathematically Wheeler’s No-Hair Theorem, which states that there can only be two possible attributes in any particle sucked into a black hole. It is through these associations that he has managed to put forward concepts that make the rest of the scientific community scramble to catch up with him.

Second, Hawking goes to great lengths in his books to explain to all of us why some concepts in science are neither intuitive nor common sense. Knowing that mathematical constructs and models do not necessarily represent anything in the present real world, Hawking manages to conjure propositions that seem to solve many of the present mysteries in science, even if these propositions sound far-fetched.

Now, this is the part of the essay where we go back to talk a little bit about Quantum Mechanics.

Quantum physics deals with the infinitely small world of atoms and the particles that make up atoms, and the forces that affect them. But most of the concepts used to explain these interactions are so far removed from daily life experiences that it is difficult to find analogies to exemplify them, and so at times it may sound silly or dumb to explain these matters. For instance, central to the concept of Quantum Mechanics is the Uncertainty Principle first proposed by Heisenberg. This principle says that because atomic particles are so tiny, one cannot measure them precisely. One can learn their velocity, or one can learn their position in space, but not both at the same time. Why, you may ask? Because the very act of measuring it changes the energy level of the particle. If you measure its position, you change its velocity. If you measure its velocity, you change its position. This means that in fact, a particle can probably exist within a range of possibilities, and unless it is measured it actually exists in ALL of those possibilities.

Ideas like this one make understanding Quantum physics very difficult, even for scientists. Even Einstein said, “...no one understands Quantum Mechanics”. Maybe that is why Einstein wanted to find what has been commonly referred as Unified Field Theory, or Theory of Everything. At one point in the past, scientists did not know that electricity and magnetism were facets of the force we know presently as electromagnetism. Then, when it was discovered that the atoms are made up of smaller bits and pieces held together by something called Strong Nuclear force, and that those bits and pieces are in turn made up of tinier particles held together by the Weak Nuclear force, the dream of finding a simple set of generalized rules that underlie all forces was born. These simple laws should explain how gravity, electromagnetism, and strong and weak nuclear interactions are but different facets of the same thing. Einstein seemed to have believed this thing was a force of some kind. Modern thinking points more toward an actual thing: the Super string theory. At the present time there is very little proof that this string thing actually works out, so we will not discuss it here.

Now, Hawking seems to have been born to think exactly in those terms so contrary to conventional thinking. After all, he was the one to require that if both Einstein’s Relativity and the Big Bang were correct, then the Universe must have started in a singularity. He also was central to the development of the idea that nothing escapes a black hole’s gravitational field once it falls past the event horizon.

What I personally find most amazing and remarkable about Hawking is that he has the courage to change his mind and unabashedly recants publicly by announcing his intentions of working on finding ways to disprove his own propositions. And he has to work hard at it, since most of his propositions and theories always seem absolutely irrefutable! He had to spend years doing mathematical calculations to show that black holes actually emit X-ray radiation and heat. In doing so, he seems to have broken faith with Relativity, because his calculations require that some virtual particles accelerate to speeds faster than light. One would think that this is impossible, but X-ray telescopes have indeed detected huge emanations from the center of galaxies and stellar clusters, which seem to indicate that Hawking was correct in changing his mind about the nature of Black Holes.

But the main reason why I wrote this essay is because I personally disagree with Professor Hawking. I believe that we experience the reality of the Cosmos through our senses, which in turn is analyzed by our reason. Thus, the perception of the Universe may very well have nothing to do at all with the reality of the Universe. In fact, we apprehend the Universe in precisely these mathematical and logical physical laws because we must. The Universe is the way it is because of the way we are. This is called the Anthropic Principle, and it is anathema to Stephen Hawking, but central to my personal beliefs. Instead, Hawking believes that the Cosmos is the way it is, and that we may very well break through in our understanding of it. He believes that everything is already determined because everything follows physical laws, and thus the results can be predicted. However, he admits that everything might as well not be determined, since we can never know what exactly is determined. But in another one of his amazing theory reversals, Hawking has come very close to converting me to his deterministic view of the Cosmos.

While studying the ways in which the universal constants and physical laws could be saved from a singularity, Stephen Hawking and Jim Hartle proposed the No-Boundary Theory mentioned before. Simplified to a ridiculous point so I can understand it, this theory proposes that the Universe has no beginning or ending, and that there are no singularities. Starting with Feynman’s idea of “sum over histories”, where a particle follows all possible paths to its current state instead of following a single track, and mixing it with the Einstein’s concept of a Universe curved because of the space-time continuum, Hawking proposes that the history of the Universe is like a sphere, where the Big Bang marks the north pole, therefore avoiding any breakdowns in the laws of physics. In order to arrive at this conclusion, one must actually perform the sum of the particles’ histories to find them at a specific point in space. And to do this, one must resort to a mathematical device called “Imaginary time”. Even Hawking has admitted his misgivings about using this term, since it seems to denote a mere fanciful imagining, when in reality is a dead-serious mathematical entity.

Let us consider for a moment what mathematicians call “imaginary”. The product of the same two whole numbers is always a real number, as in 2 x 2 = 4 and -2 x -2 also = 4. If one imagines this numbers on a straight line, then one can visualize the zero in the middle, and whole numbers stretching to both sides eternally. Now, we know that the square root of four is 2 and -2. But what is the square root of -1? Nothing in our life experience can relate to this concept. So this is called an imaginary number, denoted by i. All we can do to visualize the reality of these numbers is to think that these i’s exist perpendicularly to real numbers. Therefore, when Hawking and Hartle calculated the sum over histories, they had to resort to defining time with imaginary numbers. Regular time, the time we know, could not yield a singularity-free model of the Universe. Instead, if some of the possible histories the Universe might have gone through in its evolution were to happen perpendicularly with real time, then there is no need to find an “edge” to the Universe. Thus, a No-Boundary Theory.

So far, Hawking leads the way, step by step, closer to a Unified Field Theory. With this No-Boundary Theory, he has advanced enormously on the way to prove that humans may very well discover the meaning of it all. We may really be destined to know the mind of God!

While the philosophical implications of this new way of viewing the Cosmos are even more difficult to fathom than the scientific ones, one thing is certain: Stephen Hawking has found a way to force the Universe to make sense once again, and has almost convinced me that everything is real, and everything makes sense.

A note on the listed resources:

This essay can be said to have been many years in the making. These ideas are representative of my personal philosophy and the many things learned throughout all the years I have been interested in Astronomy in general, and the Meaning Of It All in particular. This is why no specific page references have been given, since most of the ideas presented in this essay are virtually a concatenation of many other sources not listed. The sources actually listed were used for spelling and some factual referencing only, and therefore no direct quotes were used, except for Einstein’s “... no one...”, for which I found no specific source.

1Stephen Hawking’s Universe, “Black Holes and Beyond”, Thirteen/WNET/Uden Associates/David Filkin Enterprises co-production in association with BBC TV, 1997.

2Stephen Hawking’s Universe, “An Answer to Everything”, Thirteen/WNET/Uden Associates/David Filkin Enterprises co-production in association with BBC TV, 1997.

3Eric Chaisson and Steve McMillan, Astronomy Today, “Part 1 Astronomy and the Universe Ch. 2 The Copernican Revolution”, “Part 3 Stars and stellar evolution Ch. 22 Neutron stars and Black holes”, “Part 4 Galaxies and cosmology Ch. 26 Cosmology”, “Part 4 Galaxies and cosmology Ch. 27 The early universe”, ed. A. Reeves, Prentice-Hall 2002.

4Stephen Hawking, Black Holes and Baby Universes, Bantam1993.


6“Stephen William Hawking”, Microsoft Encarta Online Encyclopedia, Microsoft Corporation 2000.

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