Author Topic: Nature of Unpredictability  (Read 1026 times)


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Nature of Unpredictability
« on: February 11, 2017, 07:47:21 pm »
A Treatise on the Nature of Unpredictability

From the heart of controversy and seemingly chaotic events comes a theory that in and of itself states one of the basic principles of contemporary quantum mechanics. Werner Heisenberg's uncertainty principle is a fundamental basis for the structure upon which the ideas and philosophies of quantum nature are established. Indeed if the effects of this principle did not hold true, our very existence may have been an impossibility. The uncertainty principle also indirectly stipulates the origin and existence of random events in nature.

Numerous occurrences in our world appear to be random. Yet when one thinks about the causes and effects of such happenings, the reasoning becomes apparent. We live in seemingly causal world, with events causing the genesis of a new events. Because the uncertainty principle has an infinitesimally small appearance in a macroscopic environment, the implications in our everyday environment are virtually eliminated. Thus the macroscopic world is, for all practical purposes, causal. Let me suggest an example of the apparently causal nature the world in which we live. Think of the lottery. An apparatus that blows light spheroids with numbers on their faces attempts to create a random drawing. Yet if every starting position, air current velocity, impurity on the surfaces of the balls, and any extraneous interference from an outside source were taken into account, one could hypothetically calculate the outcome based on sound theoretical applications and calculations. Although this is impractical, it is still possible. Highly complicated mathematics, aerodynamics, and complex, involved, theoretical techniques would be necessary, but still, it is possible. So what we think of as a random drawing, is in actuality, a series of measurable events with predictable outcomes.

The educated chemist or physicist will likely suggest that radioactive substances in our macroworld are subject to random radiational decay, calculable only by probabilities. This is true, but also in accordance to whims of the uncertainty principle. Ask yourself, what causes a radioactive substance to decay? The atomic nucleus of the radioactive material is the origin of alpha, beta, and gamma radiation. The release of radiation from an atomic nucleus is preceded by an instability, or inability of the nucleus to hold in the radiation in question. The wave function (more about this later) corresponding to the shape and structure of the atomic nucleus will change in such a way that the position and amount of energy of a nucleon will be unpredictable. If a nucleus and a pair of protons find that their corresponding wave functions describe the probabilities of their positions at a length where the binding energy between the two is too weak to hold the nucleons together, the protons may be released, or emitted as radiation. The same goes for the emission of an electron, or beta radiation.

In contrast to the law of the conservation of energy, the uncertainty principle provides for quantum fluctuations causing local discrepancies in total energy present. It has been determined that in a pure vacuum, there are subatomic particles being created and destroyed in direct defiance the law of conservation. But since the particles are almost instantaneously converted back into energy, total energy on a global scope is conserved. The uncertainty principle provides for this effect by allowing the amount of energy in a system to be unpredictable, and thus small amounts of energy can become matter for short periods of time. As long as these particles do not exist for periods over the Planck period of time, no discrepancies are detected over a relatively longer time. This brings us to the subject of particle interactions.

For a particle to interact, it must first create an intermediary particle to communicate with the other particle. If energy were conserved at all times, where would these particles come from? What if an electron of an atom in its lowest energy state needed to exchange a photon with another electron in close proximity? The aforesaid particle would have no extra energy available, and would thus be unable to produce the needed photon. But if the amount of energy available to the electron is uncertain, the electron can convert the uncertain amount of energy into the needed photon for a short period of time. If particles were allowed only to use the energy directly available to them, the necessary transmissions of intermediary particles could not be carried out at all time, and intermittent upholdings of the laws would be observed. But because of the implications of the uncertainty principle, the particles can harness the indeterminacy of the universe to uphold the laws at all times. Without this uncertainty of energy, the strong, and weak forces would not always function correctly and atoms just wouldn't stay together. No life would be possible, indeed no matter would hold together stably at all.

The general uncertainty principle states that one cannot measure both the position and momentum of a particle at the same time with relative precision. This is derived from the froth of probabilities contained in configuration space. When you observe or measure something, you collapse the wave function corresponding to that feature and, in effect, change that property because whatever you use to measure that aspect will inevitably change it and its other properties. Thus it is directly caused by the probabilistic nature of the quantum world. The basis of this principle nevertheless draws on the uncertain and unpredictable nature of the universe and is in essence a much more deeply rooted principle. The existence of purely probabilistic events in nature confirms the existence of choice and the endless possibilities of our universe. The is no predestination and endeavors to predict the future may prove futile. Indeed an entire rewriting of physics books and a new look at the world we live in must take place. Such a profound but beautifully simple principle can tell us so much about ourselves and the world that surrounds us. Few other tenets of quantum physics have the profound implications that the Heisenberg uncertainty principle has. The advent of this principle has sent us beyond Newtonian mechanics of old and taken us into a realm of infinite possibilities and new truths. There is so much the principle has done for modern physics that its importance cannot be understated.

Also contained in the uncertainty principle are the effects of measurement on a quantum scale. In classical mechanics, the viewer of an experiment is completely removed from the subject of the experiment, that is, by making measurements, the experiment is not changed. However, in modern mechanics, the viewer changes the experiment in question every time they conduct a measurement. In fact, it has been postulated that without a viewer the outcome of an experiment exists in a superposition of possible states. Only when a measurement is taken does this superposition become one or another outcome. This is called the collapse of the wave function, and explains much about the strange effects of recent experiments. Let me give an example: a well known quantum physics experiment is the double slit test. We set up a light, or electron emitter, and then an opaque panel with two small slits or holes in it. On the other side of the panel we place a photographic plate, or in the case of electrons, an array of electron detectors. When we turn on the light or electron emitter, the particles will travel through the slits and register on the detector. But when we look at the plate of, say, the photons, we see a pattern of light and dark bands. This is caused by the constructive and destructive interference caused by the light. But the strange thing is, the same happens for electrons-particles by definition. The pattern on the electron detectors is the same as on the photographic plate. Thus, the electrons must also exhibit a wave property. This phenomenon is simply called wave-particle duality and is present for all particles in accordance to the de Broglie equations. But what happens when we set up a detector on each of the slits to determine which one it went through? The detectors allow the photon to pass through, and only record which slit the particle traveled through. With this setup, the wave pattern on the photographic plate disappears! Now the pattern is that of a particle, where as before it was that of a wave. It seems that by recording where a particle was, we have determined its location, and it thus does not exist as a superposition of possible states, but as a single entity passing through a certain slit. In a direct breach with classical mechanics, the viewer has altered the experiment by simply measuring it. We can demonstrate the superposition of states by emitting only one photon at a time into the experiment. We remove the slit detectors, and proceed. After letting many photons out, one at a time, we find that the buildup on the photographic plate is the same as it was in the first experiment. So we must conclude that the photon is interfering with itself! As the photon travels to the slits, it seemingly splits into two possible states, going through one slit or the other, and since there are now two photons, the two interact and interfere destructively or constructively. The quantum indeterminacy of which path is taken leads to the wave pattern. Theory postulates that light is a particle but exists as a wave in configuration space. That is, in our world light is made of particles, photons, and only exhibits wave like characteristics because of the wave nature coming from the quantum probabilities contained in configuration space. Think of this space as a holding place for each of the possible positions of the photon. When moving, the manifestations of the same photon in configuration space interfere with each other and can create wave like properties. This is why light does not need a medium in which to travel. It is not really a wave, but particles interacting with themselves and each other, creating wave-like observables. No ūther is needed in this model, and we already know that light can easily pass through a vacuum, so this model is ideal.

A thought experiment will prove excellent to demonstrate the effect of measurement on an experimental variable. Say, for instance, we have a particle we call a quason. This quason has two qualities that we will call color and spin. The color can be either blue or red, and the spin can be either left or right. We have two devices that will measure either spin or color without effecting the trajectory of the particle. If we set up two color detectors in a row and pass a quason through the first and find it reads 'blue', then when it passes through the second detector it will also read 'blue' (this has been determined through sound physical experiment in real life). The same happens for the spin tests. Next we set up a color box, and then a spin box. A quason going through each will read out a certain choice as we assumed. But when we set up color, then spin, then color box, and pass a number of quasons through them we find that only half of the quasons measured 'blue' by the first box are also measured 'blue' by the other color box. It appears that the spin box is changing the color of exactly half the blue quasons. We can rebuild the spin box to more exact specifications and try to stop the changing of color, but we never can. The Heisenberg uncertainty principle is causing the change. The simple act of observing one property of the quason puts the other property into a superposition of possible states. After a large number of observations of this kind, one will see an outcome of exactly fifty percent one property and fifty percent the other. Only purely statistical occurrences can cause this type of behavior, and these occurrences have their origin on the quantum level.

In an attempt to describe the effects of quantum indeterminacy and the Heisenberg uncertainty principle in a plausible theory, two general theories have been proposed. The Copenhagen and Everett interpretations.

The Copenhagen theory of quantum behavior was mostly organized by Max Born. In essence, Born and his associates stipulated that each quantum event will cause a superposition of the other possible states involved with that particle. The 'virtual' particles of any given particle are theorized to be held in something called configuration space, and a 'wave function' contains the probabilities of position, momentum, spin, etc. in the configuration space. Once a particle is observed, the wave function collapses and the probabilities in configuration space disappear. The interference caused by the virtual particles creates the wave like properties of all matter. This approach remains conservative in that it does not need any duplicate worlds, but causes mathematical complications in that one needs three separate dimensions for each and every particle described in a quantum system.

The alternate approach to viewing quantum mechanics is the Everett interpretation. Although a very radical view of the world, the theory nevertheless accurately predicts all the quantum effects that the Copenhagen theory does. Sometimes called the 'many worlds' theory, the Everett interpretation provides for numerous, perhaps infinite alternate universes that each cause interference in the other worlds. Usually viewed erroneously as a branching system, the Everett theory actually states that each universe exists at a ninety degree angle to the others. Thus the paradox of Schršdinger's cat is elegantly pictured as two cats existing in separate universes, one in which he is alive, one where he is not. The thought of splitting universes every time a quantum event occurs may seem a bit too much to fathom, yet can seem trivial when compared to the three dimensions needed for each particle in the Copenhagen interpretation.

The implications set forth by quantum physics and the Heisenberg uncertainty principle have caused a major revision in the way we think of the universe, and how we conduct experiments. The universe is no longer thought of as a completely causal system, as Einstein would have liked it to be, but essentially an observer based system where observations cause a collapse of a superposition into a given state. It has even been theorized that the universe may not have really existed until sentient beings came along and measured it. By observing something we cause it. This thought has thrown metaphysics and our view of the surrounding world upside down. Once again we find that the more we know of something, the more questions we have about it.

Tom Werner 27 February 1996