Essays, Analyses and Meditations

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The Curse of Gravity

  • My first obsession was Gravity. My biggest obsession is still Gravity. We need to "hold" objects otherwise they fall. We invented pockets, tables and bookcases because otherwise objects would fall. We unconsciously spend our life fighting gravity, trying to exorcise the curse of gravity. We all fail. As a child, i asked the question: "why do objects fall"? As an adult, i still don't know the answer. I know what Newton and Einsteain found out. I can even follow and understand the mathematical foundations of their theories. Nonetheless, my repulsion for gravity has inspired a great deal of my life.
  • It sounds totally unrelated, but it turned out to be a piece of the same puzzle. I was always fascinated by Zeno's paradoxes. Zeno showed that, if there is an infinite number of points between two any points (in space and time), then nothing can happen. An arrow will never reach the other side because it first has to reach half way, and one fourth of the way, and one eight of the way, and so on forever. The fastest runner will never pass a turtle if the turtle gets a headstart because by the time the runner reaches the initial position of the turtle, the turtle has already moved ahead, and by the time the runner reaches the new position of the turtle, the turtle has moved further ahead, and so on forever. Zeno's reasoning is obviously correct. Generations of mathematicians have tried to concoct convoluted proofs that Zeno was wrong, but i always felt that Zeno was fundamentally right. If space and time are made of an infinite number of infinitely small points (if any segment, no matter how small, can still be divided in two), then nothing can happen. The whole universe is impossible.
  • Albert Einstein's General Relativity is a relatively simple idea. There is spacetime, which is a continuum of infinitely small points. There are masses that are unevenly distributed over this continuum. Each mass is also energy. Masses warp spacetime. All masses would simply move in a straight line at a constant speed if spacetime were "flat". Because it is warped by masses, masses move in all sorts of convoluted trajectories. The route of each mass through spacetime is determined by all the other masses of the universe. The actual details of the route depend on the observer. Everything is relative to the observer. Each observer is witness to a somewhat different history of the universe.
  • In my opinion, the ultimate meaning of Relativity lies in the relationship between an observer and her own mass-energy.
  • Reality is different for each observer, and it happens all the time, whether observers exist or not.
  • The only cognitive limit for an observer is the speed of light: an observer can only perceive that portion of spacetime that can be reached by light during the observer's lifetime. Light has a special role in the unfolding of reality. Sometimes i feel that light is all that exists.
  • Note that the observer exists only insofar as there are irregularities in the universe. If mass were distributed uniformly across the universe, there would be no history of the universe and no observer to observe it.
  • Quantum Theory provides an alternative way to look at nature. There is a limit to how small things can be, to how close things can be, to how small a chunk of energy they can exchange, and so forth. These limits are expressed as multiples of the Planck constant. There is also a limit to how small a piece of space can be. "Points" are not infinitely small: there is a finite number of points in any given segment of space. In other words, everything is discrete, not continuous (digital, not analogue). Spacetime is a (four-dimensional) grid, not a jelly. In this "discrete" world the law of causality is not quite what it used to be. An action can have many consequences. There is an equation, Schroedinger's equation, that predicts the set of possible consequences (which is actually a wave of sorts). Each is likely to occur with a certain probability. Schroedinger's equation can predict all possible histories of the universe given the current state of the universe, but cannot predict which one will actually take place for real. Once we observe that one of those possible consequences has indeed happened, it turns out to be one of the possibilities predicted by Schroedinger's equation. But we know that this is "the one" (out of all the ones contemplated by Schroedinger's equation) only "after the fact".
  • Schroedinger's equation does not predict reality. Reality happens only when someone observes the universe. If nobody observed the universe, maybe there would be no "reality". It appears that the observer creates reality. Once an observer has "collapsed" the wave of probabilities into a specific event, all observers observe the same event. Reality is the same for each observer, and it happens only when an observer checks it out. There is, however, a limit to how much of reality an observer can "collapse" into reality: the Heisenberg principle states that some entities cannot be measured when some other entities are measured.
  • In my opinion, the ultimate meaning of Qauntum Theory lies in the relationship between an observer and her own observations (which then become reality for her and everybody else).
  • The cognitive limit for an observer is represented by the "wave": the observer cannot know reality until it is actually observed, and Heisenberg's principle (not the observer's lifetime) limits what can be observed.
  • Relativity and Quantum theories are clearly very different descriptions of the universe. They provide different models of the universe (one is continuous and the other is discrete) and different roles for the observer (one creates reality only for herself, the other creates reality for everybody). More importantly, Relativity Theory does not put any limit to the knowledge of the observer. A community of eternal observers could potentially "learn" the entire universe. Quantum Theory puts a limit to what the observers can know, no matter how long the observers live.
  • When i focus on the two theories, i see a difference mainly in the "level" at which they operate. Relativity Theory is about the universe, about the dimensions of existence. Quantum Theory is about the human world of objects, about the world of "sizes".
  • My favorite metaphor to describe the two theories is of an observer causing ripples in an ocean. Relativistic spacetime is the equivalent of an ocean, and quantum values are the equivalent of the ripples caused by an object moving through the ocean of spacetime. Relativity is the theory about the ocean, and Quantum Theory is the theory about the ripples. Relativity describes the continuous ocean, while Quantum Theory describes a discrete world of ripples. Quantum Theory describes the ripples caused by the observer while she moves through spacetime. Einstein's equation describe how spacetime is warped because of matter from the viewpoint of an observer. Schroedinger's equation describe the ripples caused by such observer moving through spacetime.
  • The spacetime in which we live (the "ripples") has an atomic structure itself, just like matter. There are indivisible units of spacetime, atoms of space and time. It is not true that one can divide any segment in two: there is a limit to how small one can go. This removes once for all Zero's paradoxes: the universe that we inhabit is possible.
  • Gravity is a daily reminder that we are merely observers, and very imperfect observers, not creators, of reality.