Thursday, August 03, 2006

Determinism and Indeterminism in the Physical World and the Influences of Quantum Theory on the Nature of Causality


An important aspect of understanding a quantitative scientific process is evaluating the qualitative conclusions it leads to. Arguably this evaluation is subjective. It is statistically within the hypothetical sphere of reality that an individual constructs. Therefore in retrospect the nature of this procedure lacks the objective ability to be determinate due to unaccounted variables of personal ideology which drive hypothesis construction in the scientific world. This situtation brings up questions of causality and chance, determinism and the indeterminate and even explores the real extent of human free will. In the history of ideas, Natural philosophy was a discipline concerned with discerning the true identity of reality; however with the specialization of knowledge, physics and philosophy were separated. Physics retained the experimental and factual structure of developing the truth, while philosophers delved into the metaphysical and moralistic aspects that constructed our world. However the effect of one discipline on the other is irrefutable. This paper offers an analysis of the “local” effects that philosophy had on physics and vice-versa. An effort is also made to understand the ideals that led to the construction and subsequent domination of a certain natural view. Thus in some ways it is a critique of the elastic and evolving nature of reality and the conflicting attributes of varied thought mechanisms that have tried to define it.
The Greek idea of Natural philosophy was steeped in traditional mythology. Mythology dismissed as trivial by most modern scientists allowed for the assigning of defining forms to most of natural phenomenon. In essence it was the first, relatively primitive efforts at creating an understanding of the nature of nature. Therefore “the intuitive phase of myths provided for a set of terms for use in the conceptual phase of early science” (Sambursky). Even in antiquity or first impulse was to put a determinate form to the projected phenomenon which existed beyond a human realm. Constructing a working, predictable idea of the physical world may not have been the Grecian priority. Working within the Aristotelian framework there was little room for objective understanding of the manifest destiny that was a part of every natural thing. The rudimentary physics that came out of classical antiquity followed a chain of thought that had its basis in a faith axiom – the human world of senses could never perceive of the heavenly “absolute” world of the gods. Theoretical constructs of the nature of the universe were essentially devoid of actively employed scientific experiments. The need was to preserve natural science as an interpretation of the human conception of reality which could never aspire to parallel and predict the celestial world. There were two views of reality in conflict. The “teleological” which propagated by Aristotle explained that “the universe was a sum total of events that tend towards a goal in which an earlier events happens for the sake of a later” (Sambursky). The “structural”, which abided by the presupposition that everything in existence could be explained numerically and therefore, was “form”. It is important to understand the connection here between the teleological ideologies of the Aristotelians to the Laplacian world view of the Newtonian era. Laplace postulated using Newton’s laws that “by following Newton’s method men would be able to predict every event in a whole range of phenomenon” (Sambursky) The connecting value here is the belief that a causal explanation for a future event can be derived from an occurrence in the present. The Greeks, who lacked the advanced degree of mathematical expertise that the Newtonians did, had propagated (in the 5th and 6th century B.C.) for a similar world view where events occurring in one time frame were causally connected to the ones that would occur in another. A logical deduction of this premise is the idea that one could always decipher the future from the present. Even though the scientific communities of the Newton-Laplacian era, allowed for a seemingly Grecian concept of reality drive their scientific ventures, they differed in an important aspect. Mechanical Determinism, which was the greatest product of this era, was lacking in Grecian thought. Therefore it can be argued that the Greeks even though believing “nature does nothing in vain” confined themselves to understanding the effects of nature and not its form. Causality was restricted to phenomenon that was easily observable and even though conjectures were available about the nature of reality, it was widely accepted that nature was, for all human purposes, indeterminable by sensory data. (Cushing, Boorstin)
Sensory data was the foundation of the Cartesian world view (introduced in the16th century) which postulated a mechanistic reality. However even within the confines of this concept of reality there were two schools of thought – the empiricists and the rationalists. The empiricists believed that the human “mind was a blank page” on which experience created ideas, while the rationalists were of the belief that even the first experiences were acquired through “innate pre-existing ideas” in the mind (Sambursky). In the context of this paper, the point of ideological friction was between the factual and the conceptual. Therefore reality emerged as a fusion of these two instruments or rival methodological tools of description. It is interesting to note the existence of the same conflict in modern physics. Philosophically Einstein could not accept the quantum mechanical world view due to its innate lack of determinism. Due to the lack of irrefutable facts during the earlier days of quantum theory, its critics were often conceptualists that found the non-locality of effective force and the existence of a statistical probability when describing a natural event to be a theoretical improbability. Einstein believed in a “rational causal world that could be comprehended in terms of an objective reality”, while Pauli (in his earlier days) was of the opinion that “there was no point discussing quantities that cannot in principle be observed” (Cushing) It would seem obvious to ideologically group Pauli and Einstein. However a closer inspection reveals the contradicting nature of their refutation of quantum mechanics. Einstein disfavored quantum mechanics because it departed from the classical mechanical idea of determinism (“[God] is not rolling the die”) (Cushing). Pauli’s argument rests on the lack of a factual framework that can used to construct a workable physical law. In essence Pauli’s skepticism was derived from the lack of experimental data that would justify quantum mechanics. Thus Einstein appears to be conceptual and Pauli factual. It can be argued Pauli’s lack of interest in the progression of the Quantum ideology could have led to his “conceptual” disregard for the area .Thus he didn’t assume it prudent to focus the efforts of the scientific community towards the development of experimental methods which would provide for more concrete facts.
Even though the methodological developments in doing science coupled with advanced instrumentation allowed for the availability of precise data, it was the philosophically revolutionary ideas of the Quantum theory which made it controversial. The theory of relativity asserted for a correction to the classical framework and was revisionist and unifying in nature. Einstein made “the greatest demands on the ability of abstract thought (but) still fulfilled the traditional requirements of science” (Sambursky). In his efforts to create an epistemological foundation to the world of physics, Einstein modified classical physics to adhere to Maxwell’s equations. In the relativistic world the traditional axiom that divided the physical universe into “subject” and “object” were prominent. Frames of observation for the observer were discussed in his thought experiments with gravity and inertia, however the effect that the observation had on the state of the phenomenon was never considered. Philosophically this can be attributed to the formulation of causality in physics. It has now been recognized that the theory of relativity was the epitome of the classical world view. The foundational principle of Newtonian mechanics, causality, formed the core ideology of relativity. (Sambursky, Bohm, Carnap)
David Hume, the skeptical genius, pointed out a major flaw in the extrapolation process of causality. According to him it was impossible to know that certain laws of cause and effect would always apply. In essence, just because the sun has risen everyday till today, does not lead us to the logical conclusion that it will rise tomorrow. Even though Hume’s teachings were motivational for the relativistic theory, the point here is that he postulated for a break in the continuity of physical law. Thus he brought in statistical reality into the domain of what was actual existent truth. It should be noted that Hume even though instrumental in propagating skepticism about the necessity of causality was in no way directly related to the development of the philosophical structures of Quantum mechanics. However his ideas were influential to scientists like Heisenberg and Bohr that finally constructed the plane of statistical reality (Sambursky, Carnap)
Statistical reality created an order of answers that could never be definite. The classical physical world relied heavily on the causality axiom where, “Causal relations (meant) predictability” (Carnap) However work done by Bohr, Plank and Heisenberg created instances in the microsphere where causality would give answers that failed to account for all variables and essentially lacked the tools to define a system that was innately indeterministic. Heisenberg’s uncertainty principle has a simple numerical form – Δp Δx > ħ/2. Here p is the momentum, x the position of a particle and ħ = h /2Π. Ideologically this relationship along with the “collapse of the wave function” (talked about later) was the most revolutionary idea in the development of Quantum mechanics and created the final separation between classical physics. Heisenberg’s principle denied the need for determinism by predicting the impossibility of correctly evaluating the nature of both the position and the velocity of an electron simultaneously. The argument was linked to the interference caused by the deliverance of a certain amount of energy due to the light quanta that was essential to observe the electron. This relationship transcends into all forms of measurements. Philosophically the claim was that nature was inherently indeterminate. In essence an answer could only statistically predict the outcome of a measurement. For the first time in the western scientific school , it was hypothesized that the lack of precision data was not due to a lack of advancement in instrumentation or experimental methods , but due to “the indeterminacy relationships...which operate throughout the whole of natural law”(Bohm).Thus according to proponents of the quantum theory “there existed a fundamental limitation ...at the quantum mechanical level...such that we are unable to obtain the data needed to specify completely initial values...”(Bohm) this made causality a philosophical and pragmatic impossibility. Due to the lack of causality the mechanical universe which had been the dominant world view since the Newton-Laplacian construction, was replaced with the observer dependant statistical reality of the indeterminate universe.
The rise of indeterminism was philosophically fuelled by the work of Edwin Schrödinger. His life as a scientist was just as controversial and progressive as his personal life, in which Schrödinger preferred living with his wife and his mistress. Using De Broglie’s ideas of wave aspects of matter he came up with the Schrödinger wave equation. Historically this was another instance of mathematical and structural form being imparted to a conceptual framework that had been hypothesized earlier. This was similar to Newton’s work on Galileo’s assumptions and Maxwell’s equations using Faraday’s ideas of field theory. With the publication of the wave equation in 1925, Schrödinger created a mathematical tool that could be employed to describe the area of probability of finding a particle in a specific area in space. Philosophically this reduced matter to collective sensation of waves. This revolutionary concept reduced matter to extensions of waves in space. Einstein whose theory of general relativity incorporated for this idea of matter said, “Physical objects are not in space, but these objects are spatially extended (as fields). In this way the concept 'empty space' becomes replaced by the notion of undifferentiated energy” (Einstein). This ideology was detrimental to the understanding of matter as particular. The possibility of being explainable by waves may have been scientific progression the scientific community was not prepared for. However fully understanding the nature of the Schrödinger wave equation is constructive to a more productive view about the need for this progression. It sets up the scene for probably the most controversial aspect of quantum theory – the collapse of the wave function. In an experimental setup it has been repeatedly observed that the identity of a particle remains ambiguous till it is observed. In essence the observation systematically “forces” the particle to assume a certain identity. Two phenomenons are in question here - inherently the particle lacks the subjective ability to decide which state to conform to. Thus for example, an electron does not know whether it has a spin up or a spin down (this is discussed later on) and the subsequent destruction of the wave function along with which a non-local (instantaneous) force is seen at work. Conceptually this aspect of quantum mechanics violated Einsteinian relativity. As postulated in the theory of special relativity, the speed of light is the highest velocity for propagation of any electromagnetic signal, thus locality (finite speed of propagation) had to be preserved. Therefore (for example) the moment an electron was observed to be spin up; the corresponding electron had to be spindown (for more details look up the EPR paradox).The idea that somehow these two particles were communicating with each other, instantaneously was propagated by quantum theory. Einstein was opposed to this idea of physical reality since it violated one of the fundamental principles of relativity. However, the fundamental concepts and physical existence of non-locality at the quantum level have been experimentally consistent for close to seventy years now.
Non-locality is probably the most counterintuitive concept in quantum mechanics. To most early twentieth century physicists it was a philosophical impossibility especially due to one of the central postulates of special relativity. The transmission of a cause at a distance which produced at effect, instantaneously sounded characteristically like Newton’s propositions of the instantaneous propagation of gravity. Philosophically non-locality resembled an ideological problem to the einsteinian world view which held the speed of light as the upper constant of velocity. The propagation of non-locality would in some ways allow for the existence of some inherent ability of particles to send signals to each other about their information. Without a medium of transmission and experimentally unobservable phenomenon of this signaling a majority of the physicists of the post-einsteinian era found this phenomenon conceptually hard to accept. While writing this paper an important assumption has been made. The Copenhagen interpretation of quantum mechanics has been considered to be the valid understanding of quantum theory. It should be noted that there are other interpretations of quantum theory and constructive criticism about the Copenhagen interpretation abound, however that is beyond the scope of this paper. This point is brought up since in the Bohm Interpretation (an attempt at maintaining the classical integrity of deterministic analysis), a non-local hidden variable theory is postulated, which is elemental in explaining the instantaneous effects seen. Attempts at creating a theory based on “local realism” (that Einstein was pushing for) are rendered pointless after the work of John Bell and the subsequent publication of the Bell Theorem in the 1960s which predict that “any theory accounting for violations in Bell’s inequality must be non-local” (Cushing).
Along with the concept of non-locality it is important to mention the “observer effect”. Ideologically this places immense importance on methodology and relates to the rather vital aspect of human free will. As observed in atomic experiments, the statistical probability of finding the information about a certain attribute of a particle is reduced to a singular identity when observed. The best example of this is the Schrödinger's Cat thought experiment (refer to Cushing, pg.311- 312). However epistemologically it can be argued even in this situation that on opening the box and finding a dead cat and doing an autopsy it could be predicted that the cat had died a few days ago , thus removing any effect that the observer actually had on the final conclusion of the cat’s “state”. The effects of observation on a certain system become inherently important to the final outcome of the experiment, but unlike classical physics it is impossible to gauge the actual effect an observer is going to have on the final result. The emphasis here is on the innate inability to predict the effect of observation in the quantum world. In light of this a moral and philosophical issue is raised. According to the philosopher Reichenbach “ if physics had retained the classical position of strict determinism, we could not meaningfully speak of making a choice, uttering a preference, making a rational decision, being held responsible for out acts...”(Carnap). The ideological reflection here is on the Laplacian world view of a pre-determined future and past and its predictability, an evaluation of a “temporal cross section of the world” (Carnap). The quantum mechanical world view provides factors other than the ones controllable by human understanding, saying essentially that the natural world inherently lacks a sense of determinism. This provides for a situation (philosophically) where an individual is subjected to empowerment that is created due to the lack of a pre-decided structure to the universe. In retrospective the lack of an accurate final conclusion in the indeterminate quantum world reduces this ephemeral sense of “control” to slightly more than a random selection of reality. In conclusion, the lack of a certainty in the final outcome ensures that whether it is the calculated macro effects of classical physics or the random micro effects of quantum physics, the effect of free will on the character of reality is similar. In both instances “Man can predict the results of his actions not with certainty but with some degree of probability” (Carnap).
Probability is the idea that differentiates the two major views of the world: classical and quantum. An understanding of this concept requires a closer inspection of causality. After the evolution of quantum mechanics the very form of causality had to be modified in order to account for the phenomenal and theoretical arguments of Bohr and Heisenberg. Thus the system of cause and effect is split into – mechanical causality and statistical causality. In classical physical theory a system is described “in terms of its state” (Cushing). Certain variables are assigned to ensure that the time evolution of them will help to predict the values of the future. In most of classical physics state variables are also the “observable physical quantities” (Cushing). Therefore as defined, the classical view of the world postulates for a system which is changed from present to future by a set of variables and “the agency responsible for this event-by-event causal structure” (Cushing) does not propagate faster than light. As opposed to this in quantum mechanics, the wave function (state-vector) of a system is not “itself directly observable” (Cushing). Therefore the Schrödinger equation governance of the time evolution of this state vector instead of displaying definite values for positions and momentum , presents one with probabilities of “various allowed outcomes(eigenvalues)”(Cushing). Thus in the Copenhagen interpretation of Quantum mechanics, there is no “event-by-event causality and particles do not follow well defined space time trajectories” (Cushing). In conclusion, the classical world view of mechanistic causality is replaced by the quantum world view of statistical causality. Thus the concrete existence of causality in Quantum mechanical analysis is justified by Max Born’s statement that, “statistical elements are thoroughly strict statements and the probabilities are by no means indefinite since they are determined by the formalism of quantum theory” (Cassirer)
The formative change in the world view from deterministic to indeterministic has arguable been the greatest revolution in physical thought in the history of ideas. Even though quantum physics has sought to abandon the more mechanical causal structure of the universe, many of its governing principles are still drawn from classical physics. Philosophically the influence of Aristotle, Kant, Mach, and Hume (to name a few) cannot be disregarded when constructing a realistic picture of the evolution of physical thought. Often the motivational idea behind searching for a rationalization of the world view has been a search for “the ultimate reality”(Sambursky). Ideologically, as a race, that has been our destination and each generation correspondingly has tried to reconstruct a better picture than its predecessor. Going from a world view fuelled by mythological stories of ambiguous actions to a mechanically predisposed universe to finally the inherent indeterminable nature of the universe there has been a constant conceptual synthesis of phenomena to theoretical practice. Interestingly sometimes progression has ideologically lead us to re-investigate certain ideas. For instance , “if the speed of transmission signals is assumed to be infinite, not finite, the classical picture of absolute space and time and the discarded concept of an absolute simultaneity of events is restored” (Sambursky). It is important to realize that even though the Newtonian world view advocated for an infinite idea of space, they never thought it would be mortally possible to investigate the nature of it. With the advent of modern philosophy and physics the prominent world view has experienced a heightened respect for human ability and recognized that understanding the fundamental nature of reality, space and time are within our abilities.
The change in the nature of causality marks a prominent paradigm shift in the understanding of the universe. Accommodating for a probabilistic answer frame has evolved causality from an absolute idea of the universe, to one that is numerically more accurate in its interpretation, though seemingly less definite. The development of statistical reality and its implications on a universal scale are undoubtedly conceptually significant when understanding the epistemological construct of reality. Even as acceptance of our observation of the innate randomness in nature has increased, the idea has been subtly differentiated from the fact that nature itself does not display a pattern at the quantum level. This theory even though concrete in structure leaves room for conjecture, regarding the nature of variables that could be affecting it , but are still to be experimentally ratified.
The greatest philosophical effect of Quantum mechanics has been the revision of the understanding of phenomenon. The duality of the “objective phenomenon” and the observer is a constant in the world view proposed by quantum mechanics. To understand the effects of quantum theory on the world consciousness it is important to return to probably its most holistic thinker – Niels Bohr. According to him describing human experience using the principles of quantum theory lead to the conclusion that there is “a wholeness” (Sambursky) in the physical world that cannot be partially observed. Thus human consciousness cannot divide a phenomenon into segments without affecting it in some way. The rather vague line between the subject and the object of “physical phenomenon” (Sambursky) is omnipresent in the physical world. To understand the division between a phenomenon and the observer is slowly becoming impossible, as the consciousness of the affected person is constantly merging into the actual experience. This rather dynamical system is susceptible to variations at any given instant that along with being unpredictable, define the actual position of humans in the physical world.
Bibliography

“Philosophical Concepts in Physics: The Historical Relation between Philosophy and Scientific Theories” (Paperback), James T. Cushing, Cambridge University Press (January 29, 1998)

“Physics and Philosophy: The Revolution in Modern Science” (Great Minds Series) , Werner Heisenberg, Harper, New York, (May 1958)

“Physical thought from the Presocratics to the Quantum physicists: An anthology”, Shmuel Sambursky, PICA Press, New York, 1976

“Philosophical Foundations of Physics” (Hardcover), Rudolf Carnap , Basic Books; 1st edition (1966)

“Determinism and Indeterminism in Modern Physics: historical and systematic studies of the problem of causality”, Ernst Cassirer, (Translated by) O. Theodor Benfey, New Haven: Yale University Press, 1956

“Causality and Chance in Modern Physics”, David Bohm (foreword by Louis De Broglie), Routledge and Kegan Paul Limited, London, 1959

“Physicists in Conflict – from antiquity to the new millennium”, Neil A. Porter, Taylor & Francis; 1 edition (June 1998)

“The Character of Physical Law”, Richard Feynman, Modern Library (November 8, 1994)