December 21, 2005

objective reality in quantum mechanics

here's my physics/philosophy term paper if anyone is interested

The Collapse of a Subjective Reality

The different interpretations of quantum mechanics create an uncertainty as to whether reality is objective or subjective. This uncertainty should not be considered a lack of knowledge but rather a difference of opinion about correctness. A subjective interpretation of quantum mechanics forces reality to be defined by experience and interaction. At first thought, it seems as if reality is directly related through experience; however, this suggests that reality depends on consciousness. Unarguably, one’s own personal reality depends on experience, but reality as it applies to the universe must be independent of the consciousness of its constituents. Some of the consequences of a purely subjective reality will be discussed later. In this light, reality must have at least some objectiveness, and the objective nature of reality must be verifiable in the subatomic world.

An objective reality is independent of observation. Perception and consciousness do not define an objective reality. In an objective reality, there are brute facts, truths not requiring any outside framework, which govern reality. The goal of most theories is to uncover the brute facts underlying reality. Quantum mechanics, however, seems to question whether or not there are brute facts about the position and momentum of a quantum object.

The most accepted interpretation of quantum mechanics is the Copenhagen interpretation, which was largely developed by Bohr and Heisenberg. Under the Copenhagen interpretation, the collapse of the wave function creates an indeterminism that is explained by a fundamental lack of knowledge about the system. This fundamental lack of knowledge can lead to some strange philosophical implications that border on mysticism. If a mystical approach to reality sounds far fetched, don’t worry; there are other options besides the Copenhagen interpretation.

The probabilistic nature of quantum mechanics does not force quantum mechanics into a state of indeterminism or subjectivity. The propagation of the wave function, as long as no measurements are made, is deterministic. As a result, the probabilistic nature of the wave function can be verified by any number of observers and is therefore objective. The famous two-slit experiment demonstrates the objective nature of the wave function. When attempting to simultaneously measure a quantum object's position and momentum, the objective nature of quantum mechanics becomes questionable. The Heisenberg Uncertainty Principle dictates that the position and momentum of a quantum particle cannot be simultaneously known. This uncertainty implies that the position and momentum of a quantum particle are subject to how the observer performs measurements. Some physicists argue that the subjective nature of performing a quantum measurement results from a loss of objective reality. Quantum mechanics tells us all that there is and nothing more.

If reality at the atomic level loses objectivity, it seems as if reality at the macroscopic level must also lose objectivity. The shift from the microscopic world to the macroscopic world presents no evidence to claim that the microscopic and macroscopic world are discontinuous from each other. A non-objective macroscopic reality is counterintuitive to mankind’s everyday experience. The counterintuitive nature of a theory, however, is not a valid basis to judge a theory. Einstein’s theory of general relativity is counterintuitive to mankind’s everyday experience, yet it holds merit among most physicists. The problem with a non-objective interpretation of the uncertainty principle is that there is no relationship between quantum mechanics and reality. More specifically, an observer is needed to determine reality.

The mathematical formalism of quantum mechanics seems to be incomplete. When Einstein, Podolsky, and Rosen questioned the completeness of quantum mechanics in their paper entitled “Can Quantum-Mechanical Description of Physical Reality be Considered Complete?”1, Bohr responded by saying that quantum mechanics “is based on a coherent mathematical formalism covering automatically any procedure of measurement.”2 Heisenberg, however, admits that the observer must intervene for quantum mechanics to be complete, but Heisenberg argues that the discontinuity in the collapse of the wave function “is . . . a consequence of the transition from the possible to the actual.”3 Heisenberg’s argument contradicts Bohr’s statement that quantum mechanics’ formalism is complete because, as Heisenberg said, it is not possible to derive the collapse of the wave function from Schrödinger’s equation.4

The incompleteness of quantum mechanics’ formalism plays a key part in the Copenhagen interpretation, namely that the observer is required to determine reality. A saving quality of theories is the ability to exchange the interpretational framework of a theory without changing the theory's observable predictions. In this light, a different interpretation of quantum mechanics can imply an objective reality which does not depend on the observer. As will be shown, an objective reality is much more concrete and precise than a reality determined by the observer.

The probabilistic nature of quantum mechanics can be explained by a fundamental lack of knowledge or by the statistical nature of the problem being solved.5 The Copenhagen interpretation purports that a fundamental lack of knowledge explains the probabilistic nature of quantum mechanics. The non-objective nature of this interpretation forces reality into the hands of the observer. The consequences of the Copenhagen interpretation will be discussed later. For now, the statistical nature of quantum mechanics will be discussed.

Planck’s black body radiation theory, Einstein’s photoelectric effect, and Bohr’s theory of spectral emissions all started off as statistical problems.6 The fact that these statistical problems can be solved in a statistical manner (the wave function) suggests that the probabilistic nature of quantum mechanics is explained by the statistical nature of the problems being solved. In this light, the wave function is more of a property of the system rather than a property of the quantum object. If we again consider a two slit experiment and compare the interference patterns of two different objects projected towards two slits, we can see that the wave function depends on the system and not the object. For instance, a neutron and an electron, when incident upon two slits, both produce qualitatively very similar interference patterns, yet the physical properties of the objects are vastly different.7 The nature of the wave function has little to do with the properties of a quantum object.

A probabilistic nature does not devoid a theory of objectiveness. For example, thermodynamics explains macroscopic thermal properties by expected behavior and probabilities.8 The objectiveness of temperature, heat density, and other thermodynamic measurements are rarely questioned. Certainly, the heat density of the sun does not depend on an observer. The detectable properties of quantum objects are also explained by behavior and probabilities. When incident upon two slits, an electron produces an interference pattern which is explained by probability and is objective. The Heisenberg uncertainty principle, the source of the Copenhagen interpretation’s loss of objective reality, is itself objective.

During interactions with the macroscopic world, a quantum object loses its probabilistic nature. The loss of a quantum object’s probabilistic nature is often referred to as the collapse of the wave function. Quantum mechanics does not explain why and when the wave function collapses. The Copenhagen interpretation considers the macroscopic world to be unexplainable by quantum mechanics.9 This conclusion seems illogical. The macroscopic world is composed of an enormous quantity of quantum objects. To further explore the connection between the macroscopic world and the quantum world, I will examine Schrödinger’s cat-in-a-box thought experiment.

Schrödinger’s famous cat-in-a-box thought experiment demonstrates that reality is not determined by observation. In the experiment, the quantum world is represented by radiation emitted by a radioactive substance, and the macroscopic world is represented by the cat. Through a series of interactions, quantum processes control the outcome of the macroscopic world. A purely subjective interpretation would dictate that the radioactive decay event has no reality until it is observed. Before the cat is observed, the cat is in a superposition of being alive and dead. Only after the cat has been observed does the state of the cat become reality. A superposition of being alive and dead is not possible. To amend this impossibility, the Copenhagen interpretation argues that a quantum object cannot interact directly with the macroscopic world. In this case, part of the interaction process must destroy the quantum mechanical nature of the system. However, a formal explanation for the destruction of the quantum nature does not exist in quantum mechanics. If quantum mechanics underlies classical mechanics, then it must explain quantum interactions with the macroscopic world. Since there is no destruction mechanism in quantum mechanics, one cannot conclude that a quantum object cannot directly interact with the macroscopic world. One could conclude that quantum mechanics is incomplete.

John von Neumann attempted to bridge the gap between quantum mechanics and classical mechanics. Von Neumann eventually concluded that human consciousness collapses the wave function.10 If von Neumann’s conclusion is accepted, then the paradox of the cat being both alive and dead must be answered. Although von Neumann’s hypothesis provides a connection between the quantum world and the macroscopic world, the paradoxical consequences of such a link suggest that a subjective connection is incorrect.

Karl Popper, a long time critic of the Copenhagen interpretation, believes that the collapse of the wave function is a property of the probabilistic nature of quantum mechanics.11 Popper argues that a given quantum mechanical experiment possesses a certain objective probability distribution and that once a measurement takes place, the probability distribution changes because the specifications of the experiment have changed. Without performing a measurement, the experimenter does not know any new information about the probability distribution and therefore the wave function does not collapse. Suppose an experimenter detects the position of a quantum object. Once the experimenter makes the observation, the probability distribution has been reduced to a single point with unity probability.

To further investigate Popper’s reasoning, I will discuss a modified two slit experiment. Suppose there are two screens, and two slits are carved in each screen. Screen number one is positioned several centimeters directly behind screen number two. An electron emitter is placed directly in front of screen number one, and an electron detector is placed behind screen number two. Also suppose two electron detectors are positioned so that they detect which slit the electron travels through in the first screen. Between the electron emitter and screen number one, an electron travels with a certain probability wave. Once the electron is detected in a slit of screen number one, the probability wave changes. Popper would argue that this results from the probability distribution being determined at that point. After the detection at screen number one, the probability distribution changes because of new information, but it does not discontinuously disappear or collapse. The new probability distribution travels through the slits on screen number two and produces an interference pattern on the detector behind screen number two. The probability distribution does not lose objectivity at any point throughout the experiment. Popper’s conclusion strongly suggests that statistical properties and their formalisms, such as the wave function, are always objective.

There are other non-statistical, objective properties of quantum objects. The quantized nature of light is objective. An observer is not needed for light incident upon a photodiode to cause electrons to flow. If two electrons are emitted from a system with no spin, the emitted electrons have spins aligned in opposite directions. By measuring the spin of one of the electrons, the spin of the unmeasured electron is simultaneously known. This simultaneous knowledge is known as quantum correlation. The knowledge of the unmeasured electron’s spin is an objective fact and need not be influenced by observation.

The properties of quantum objects, such as spin and quantization, are objective. The statistical properties of quantum mechanics, such as the wave function, are also objective. The objective nature of these properties attempt to uncover the reality of our world. However, the position and momentum of a quantum object behave as if they are subject to an observer’s measuring techniques. This suggests that objective reality is lost and that there is a fundamental lack of knowledge that restricts quantum mechanics from explaining reality. If quantum mechanics cannot explain reality, namely how the observer influences measurements, quantum mechanics is not a theory of reality. Even if reality is subjective, a complete theory would explain all aspects of reality. Currently, the formalism of quantum mechanics allows multiple interpretations. A theory of reality cannot allow multiple interpretations.

The pragmatic approach of Bohr, Born, and Heisenberg created the Copenhagen interpretation. Bohr argued for the absence of reality under quantum mechanics by drawing conclusions from the structure of quantum mechanics.12 Bohr’s theory of complementarity and Heisenberg’s uncertainty principle give quantum mechanics a probabilistic nature. Bohr interpreted the probabilistic of nature quantum mechanics as a lack of knowledge of reality. Some notable physicists, including Einstein, refused to accept Bohr’s suggestion that there is no deep reality in the quantum world. For the most part, the Copenhagen interpretation continues to dominate the world of physics. Who wants to challenge the fathers of quantum mechanics? Perhaps the key reason for the success of the Copenhagen interpretation is that quantum mechanics functions without considering whether or not reality is objective; arguing over the details of a theory which makes correct predictions seems unproductive.

Physicists and philosophers, who believe that objective reality is lost in quantum mechanics, sometimes conclude that reality is subjective. Gary Zukav’s “The Dance of the Wu-Li masters” and Fritjof Capra’s “The Tao of Phyiscs” are two works which explore the philosophical implications of a subjective reality. Some of the implications are paradoxical and far fetched, but if reality is defined by experience as a subjective interpretation of quantum mechanics purports, these bizarre implications cannot be ruled out entirely.

Zukav and Capra both argue that a fundamental lack of knowledge in quantum mechanics prevents reality from being objective. Going beyond the Copenhagen interpretation, both writers also adopt von Neumann’s view that human consciousness collapses the wave function. Under this assumption, both Zukav and Capra state that observers create reality; brute facts, if there even is such a thing, do not dictate reality. Von Neumann’s hypothesis forces consciousness to somehow collapse the wave function.13. Consciousness connects the microscopic world to the macroscopic world.

If consciousness controls the structure of physics, the world must be very manipulatable. Zukav states that “without perception, the universe continues, via the Schrödinger wave equation.”14 In effect, the universe is in a superposition of states if there is no conscious being. If reality is subjective, as von Neumann hypothesizes, Zukav’s statement cannot be disproved. However, this view places an enormous amount of power on consciousness. If one could control one’s consciousness, the boundaries of reality would be limitless.

A reality controlled by consciousness is subjective, and herein lies a problem. For example, two different people consciously observe the speed of a car. Person number one believes the car to be moving at 25mph, and person number two believes the car is moving at 30mph. If consciousness controls reality, then the car must be moving at both 25mph and 30mph, but we know this is impossible. Suppose the car is moving at 27mph. Both persons’ interpretation of the car’s speed is incorrect. The car’s speed is independent of observation. One could argue that the aforementioned example does not involve quantum objects and is therefore invalid; however, this argument can be refuted because the situation does involve a quantum interaction. The light reaching the eyes of the observers is quantum mechanical, and it is interacting with the eye. Now we must conclude that consciousness does not control reality. In a situation with two or more observers, there is no way to differentiate which consciousness, if any, controls reality.

When attempting to define reality, the probabilistic nature of quantum mechanics creates problems. There is a current trend in literature to explore von Neumann's hypothesis that reality is defined by consciousness. The predicted consequences of such a reality can be disproved as was demonstrated in the aforementioned car example. The Copenhagen interpretation does not define reality as subjective but purports a loss of objective reality. Objective reality is lost because of a fundamental lack of knowledge. A fundamental lack of knowledge of reality suggests that quantum mechanics is not a theory of reality. However, the probabilistic nature of quantum mechanics is objective, just as the probabilistic nature of thermodynamics is objective. In this light, their is no fundamental lack of knowledge; the uncertainty of quantum mechanics is a result of a probabilistic nature, which is objective. Furthermore, if quantum mechanics is a theory of reality, the uncertainty principle of quantum mechanics cannot be explained by a fundamental lack of knowledge, and reality does not lose its objectiveness.

Posted by mrpibb at December 21, 2005 1:02 PM | TrackBack
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A++++

Posted by: jen at January 2, 2006 10:07 AM
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