By the Numbers ĖDavid Bohm

In one lifetime, David Bohm succeeded in becoming successful, tortured, and one of the most controversial physicists of the modern era. Instead of a strictly mathematical treatment of quantum physics, Bohm sought to philosophically tie all elements of the universe into one phenomenon, instead of a sum of probabilistic ones. His political and philosophical insights and principles were both his hammer of thunder as well as his Achillesí heel. However, in his seventy four years, he caused many theorists to stop, cock their heads, and wonder what the shape of Quantum Mechanics would have been had he been born just twenty years earlier.

Biography

David Bohm was born on December 20th, 1917 in Wilkes-Barre, Pennsylvania. He was the son of an Austrian immigrant. His father, Samuel had married into a furniture dealing family and produced two sons, David and Bobby with his wife Frieda. David was essentially the product of an arranged marriage, and grew up in quite tumultuous surroundings. His mother had some mental abnormalities brought on by immigration to the U.S. that became an ever-present reality during Davidís formative years. His father and mother constantly fought, but remained married. As a preschooler, his greatest influence was his grandmother, but he quickly became very close to his mother after her death.

His earliest scientific influences were the Amazing Stories science fiction comic books. From a very young age, David saw these not only for their entertainment value, but also as a source of scientific inspiration. Samuel Bohm labeled his sonís interests as "scientism" and classified them as unbecoming of a developing boy. Unfortunately for David, he was born devoid of all coordination, and this only hampered his interests in athletics. Samuel was able to find a manly son in Bobby, but David always lived under the umbrella of being unaccepted. In fact, as a youth David formed his pattern of being awkward and withdrawn and always had problems fitting in.

In trying to impress and gain favor with his father, David was always trying to invent something practical and innovative. None of his inventions made the open market, but he had many things on paper. One of which was a "Drip-less Pitcher," a beverage receptacle with a long, flat spout and an extension that served to disturb the surface tension of the receiving liquid. Also on his list were a wing tip and a two-cycle compression diesel engine.

After the depression struck in 1929, Davidís surroundings were irreversibly altered. The economy of the coal-mining Wilkes-Barre was shattered. New York began to heat their homes and buildings with inexpensive petroleum, and with the international lack of capitol came the decreased demand for coal. Many mines in the region closed, and the fathers of Davidís classmates were out of work. It is said that the Depression was what had initially spurred Bohm to contemplate on social justice, society, and the political systems of this country. (Peat, p. 22)

As high school student, Bohm was particularly strong in the arena of mathematics. It is ironic that so much of his trademark work would come out of his rejection of math in favor of philosophical approaches. One of his former teachers, Mayer Tope said, "You can teach something in mathematics for many years, toiling away at it until you believe that there is no other way of doing it." But then, along came David Bohm, formulating creative and unique solutions to time-tested problems. "That was the sort of thing he did. Doing the impossible attracted him." (Peat, p.22) When he graduated, he had found two passions, physics and politics. His friends labeled him as an introvert, unless either of those subjects was brought up, and then he quickly transformed to animated and intense.

Even though Davidís father was somewhat of a pragmatist, with a business he dreamed of passing down to his sons, he supported his first born and paid for his schooling at Penn State. As a student in the top echelon of high school, David had many options for college. He chose Penn State for its proximity and laid back atmosphere. He could not envision a competitive environment as one that would promote creativity.

What he found at Penn State was a practical school that focused on agriculture and engineering, with little original research. Fortunately, with the companionship of his high school friend Mort Weiss, a EE major, he undertook many independent studies that gave him ample opportunities for intellectual growth. In college, he clung to a love of nature, viewed trees as inherently wild creatures, and wanted to understand the fourth dimension. He wasnít very active; instead he was calm and did not date. David was active in the ROTC, but his awkwardness was always noticed by his drill instructors. Through his ample independent study, Bohm developed Ph.D. skills in his undergraduate degree. In fact, he often corrected proofs and errors in textbooks. (Peat, p.31)

Much of his senior year was spent thinking. During this time, he received many prizes and honors, however was unable to be accepted into graduate school. The primary reason for this was probably because of his Jewish ethnicity. He had the options of SUNY-Rochester (The physics chair was Jewish) or Caltech, but without the offer of an assistantship. At the last minute, he was given $600 from Penn State to apply to graduate school. He picked up and moved.

Unfortunately, what he found was an intense course load that focused on the completion of problem sets and massive quarterly exams. Bohm found this restrictive for his personal growth and discoveries. While in the E & M course of W.R. Smythe, Bohm acquired the reputation of being the first student to successfully solve every problem in Smytheís trademark textbook. More than once, Smythe would present Bohmís solution to a problem to the class and remark on his studentís novelty. (Peat, p.34) By the end of his first year, his only source of pleasure was through his private study of the works of hallmark physicists such as Paul Dirac and Arthur Eddington.

His second year only provided Bohm with further frustration. As he began research he was only given purely mathematical questions to solve, not things to do theoretically. While Bohm did have many talents in mathematics, that science was not the one that he found the most elegant or applicable. Bohm believed that a bond that could only be understood through a combination of philosophy and science tied the universe together. One of his friends identified J. Robert Oppenheimer to David as someone who might share in Davidís approach to science. The next step was to approach the famous physicist. Apparently, Bohm made a good first impression as Oppenheimer arranged a small assistantship for him for the upcoming school year. Thus, his years at Caltech are officially listed as Ď1939 ó.Ď

Once at Berkeley, Bohm found that the environment there exceeded his expectations. He loved the school for both its superior students and its atmosphere conducive to individual exploration. However, it was at Berkeley that his trouble began.

In 1936, J. Robert Oppenheimer had a love affair with Jean Tatlock, a relationship that would lead to his love affair with Communism. From here, began an epic misunderstanding. People began to think that instead of just preaching Communism, that Oppenheimer was actually beginning to establish a Communist Cell at Berkeley. Bohm saw Oppenheimer not only as an advisor and professor, but also as a father. This explains how Bohm himself began involved with Communism.

However, Bohm was in fact not a Communist who sought to overthrow the Government, but someone who was an analyzer and believer in political systems other than those in place in this country. Bohm was a member of the Communist Party in California for only 9 months in 1942. He said that he found the meetings boring, and paid little attention to the goings on there. As a dialectic philosopher, Bohm was attracted to the teachings of Marx, Lenin, and Engels as a new social organization that could cease the suffering and hatred of the human race. Also, as WWII raged in Europe, Marxism was a symbol for Jews in America as the first to stand against European Fascism.

After the war, and into the beginning of the McCarthy era, it was believed that the atomic formula for creating atomic weapons had been leaked to Stalin in Russia. As the leader of the Manhattan Project and an open, practicing Communist, Oppenheimer was the first sought for the breach. What he offered to the Congressional Committee, helped to cast the heat off of him, but his full disclosure released the names of every student and friend he had ever known. Of course Bohmís name was one of the ones towards the top. This would eventually lead to Bohm becoming one of the prime suspects in the "gift" to the Soviets.

While Oppenheimer and other physicists were assembling the bombs at Los Alamos, Bohm continued to drive forward on his Ph.D. work. He specialized in the area of plasmas. Like his political and physical views, Bohm viewed plasmas as all one piece. Much of his work gained useful insight through Bohmís friendships with British physicists, notably Maurice Wilkes, working at Berkeley during the war. In fact, their departure caused Bohm significant despair that only escalated with his persecution by the House Committee on Un-American Activities.

One of Bohmís initial questions was the problem of quantum electrodynamics. Under the assumptions of the then practiced theory, when the energy of an electron surrounded by its own electromagnetic field was calculated, it was found to be infinite. This conclusion even extended to the vacuum of space. Bohm postulated that if the wave function were "re-normalized" at each step of the calculation, then the arrived energy would be finite. Oppenheimer told him that this was a pointless pursuit, and a referee of his paper criticized the idea, harshly. However, the referee was Pauli (who later told him that he shouldnít have taken the comments so personally), and this one paper laid the foundation for what would eventually become the field. His paper did draw the attention of John Wheeler, a former assistant to Einstein and a Princeton Faculty member. Wheeler saw to a generous offer being extended to Bohm, and the physicist followed his mentor, Oppenheimer there in 1947. (Peat, p. 72)

At Princeton, he quickly took on many graduate students and continued his own research. As he strove to completely understand Quantum Theory, he maintained his philosophical approach to the science. This culminated in publishing Quantum Theory in 1951, and the subsequent reformulation of his theory the next year.

In 1949, Bohm was subpoenaed to testify before the HCUA. Instead of following in the full-disclosure steps of Oppenheimer, Bohm remained silent, repeatedly invoking his First and Fifth Amendment rights. Eventually, he was sought after as a spy, and arrested in New Jersey on December 5th, 1949 for contempt of Congress. By the time the smoke had cleared, Bohm was acquitted on all charges, but the damage to his reputation was irreversible. He was sacked from Princeton, and unable to find work anywhere in the U.S. In 1952 he accepted a position as a Professor at Sao Paulo, Brazil.

Shortly after he left the U.S., his new theory was published. He entered into many dialogues with all the notables, including Einstein, Bohr, Oppenheimer, etc. It is ironic to note how immediately after the political controversy was settled, Bohm began a scientific one. Never in his life was Bohm satisfied to once swim with the current.

After his exile in Brazil (and a confiscation of his U.S. Passport), Bohm took a position in Israel. It was here that he met his wife, Saral Woolfson, a British medical volunteer living in Israel. He served for two years at the Technion at Hafia. In 1957 Bohm moved to the UK. He held a research fellowship at Bristol University until 1961, when he was made Professor of Theoretical Physics at Birkbeck College London. He retired in 1987.

From England, Bohm continued dialogues with old friends and steadfastly debated his new theory. He had conversations with the Dalai Lama, and also published with the Indian Mystic, Krishnamurti in the 1970ís. All of these things again reflect the concrete connection between philosophy and science for Bohm.

Eventually he would be reinstated as a U.S. citizen, and held many important seminars across the country. This no doubt brought some closure for this depressed and tortured man. His life was a long cycle of looking for a father figure, and eventually being betrayed and forsaken. This began with Samuel Bohm, continued with J. Robert Oppenheimer, and even faced him after the death of Krishnamurti. However, Bohm personified unbridled philosophical and scientific brilliance, and was too concerned with greater problems and questions as to be stubborn or unforgiving to those who would suffer him injustice.

On October 24th, 1992 David Bohm died of heart failure in London, England. This came just immediately before the publication of his theory in Undivided Universe, and its warm and welcome reception as viable, albeit controversial, Quantum Theory.

Work

In 1957, Bohm published one of his first comprehensive treatises on his new interpretation. By this time, he had debated it with the Quantum community, and was ready to showcase his philosophy with Causality and Chance in Modern Physics.

In Chapter 6, section 4 (Bohm CCMP p. 111), Bohm offers: "A Specific Example of an Alternative Interpretation of the Quantum Theory." Here, Bohm explains the position of the electron and slit diffraction and how his approach relates to and includes the mathematics of Schrödinger and Bohr. Bohm begins by restating the accepted classification of matter under Wave-Particle Duality. He cites evidence of dualityís inadequacy as the fact that neither approach can fully actualize the "full richness of properties demonstrated by matter in this domain." (CCMP, p. 111) To Bohm, the elementary weakness lies with both theories being regarded as mutually exclusive. Why couldnít one tie them together to jointly explain what was observed? Prof. Bohm states that what he is proposing in this chapter will not be groundbreaking or invoke any new principles, but that it is readily available for application.

The first postulate isolates the existence of a special field associated with each fundamental particle of physics existing in a small region of space. Bohm makes the same size approximation of the particle being the size of a mathematical point within the larger body. So, now the point is implied as the particle. Next, with each particle following it is a wave. The atomic body/particle is not found without this wave. The wave is characterized as an oscillation within the field, characterized by Schrödingerís Y wave function. Bohmís approach removes Y as a mathematical symbol that predicts quantitative probabilities, and uses it as an equation to describe, a real, physical field. This field reaches beyond the gravitational forces of the electromagnetic field to exist on the quantum, atomic level.

Next, assume that the Y field and the body/particle are interconnected in the sense that the Y field exerts a new kind of "quantum mechanical" force on the body, a force that belongs specifically to atoms, so to explain why it doesnít influence matter in any larger domain. To coordinate with Newton, Bohm identifies a reciprocal force exerted by the body unto the field, but that it is negligible in the present, quantum domain.

From here, more generalizations on the field are made so to say that it may act in any of various ways, but that its character permeates so as to always attract the particle into the region where |Y | is the greatest. Further assumption is the resistance of this tendency by random motions of the body, motions analogous to Brownian motion. However, if the forces that would tend towards maximization were the only ones that were present, then the particle would find itself at precisely one location on all locations in all bodies. This is known to be physically inaccurate of anything, so then where does the explanation stem from? The next step is to search for the source of forces that would give rise to the observed drift.

In order to explain the context of the atomís physical behavior, that is the random motions undergone by the body as dictated within Y, Bohm identifies the actions as random fluctuations within the field itself. To successfully explain this, he cites examples with large body scaling. The first are the fluctuations that occur in electromagnetic fields. In general, they have complicated and irregular fluctuations, not the beautiful, oscillatory nature described by the equations. Next he turns to turbulence in hydrodynamic fluids. Present here are fluctuations that are macroscopic enough to be seen by the naked eye, and will average out to the point as being able to be effectively described by a set of fixed equations. From this base, Bohm makes the supposition that the Y field is undergoing random fluctuations about an average that satisfies Schrödingerís equation and that theses fluctuations communicate themselves to the body. Or, in turning back to Brownian motion, the fluctuations could be embedded at the sub-quantum level. But this begins to diverge from the original question; solely assuming the presence of fluctuating forces can make progress in the discussion.

Once admitting the existence of the fluctuations, it can then be observed that they produce a tendency for the particle to wander over its entire available space. The ďquantum forceĒ which pulls the body into the places where the Y is at its maximum, opposes this. In the end, the particleís motion and displacement will have a mean distribution, favoring where Y is the most intense, but providing the possibility of moving where the Y is relatively weak.

This approach can be justified by examining Brownian motion itself. For a rather similar behavior of a particle in a gravitational field is observed under the principles of Brownian motion. The random, Brownian motion will pull the particle into all parts of the container, but is opposed by the gravitational force that pulls it towards the bottom. The distribution is probabilistically typical and described by the function P=e-mgz/kT. Then, through reasonable physical assumptions concerning the "quantum force" and the random, reactive motions at the sub-quantum level, harks the arrival of Bohrís probability density, |Y|2.

At the initial examination, this may seem insignificant. However, the key difference for the field of quantum mechanics is in the process. After making a few reasonable assumptions and coordinating the theory with proven and observed ideas (i.e. Brownian Motion) the theory arrives at Bohrís distribution. "Standard" quantum mechanics would begin at Bohrís distribution as an unconditional, yet unexplainable quality of matter. The validity of Bohmís process stems out of all random motions being assigned and brought from the sub-quantum level, so as to directly correlate them with the matter itself, which can simultaneously exhibit both wave and particle characteristics.

To further, and more specifically explore the wave-particle duality, Bohm next turns to the double slit diffraction experiment. (Figure 1, p. 114) 

(Ibid, p. 114) At the outset, each particle has the same momentum, and thus the same wave function (De Broglie Principle). The traveling, projected wave will be in the form of a plane wave perpendicular to the slit. Now, turning back to the afore mentioned idea that each particle has with it a distinct wave body, remember the random motion of the particle as it travels through space. Therefore, it follows an irregular path out from its place of projection, and arrives at a certain point on the screen. After significant projection, the density of distribution of points will be proportional to |Y|2. This "gravitation" towards the maximum is due to the quantum force that commands the action of the particles.

When slit B is closed, the dynamics of the experiment entirely change. From this point, the wave pattern will cease to be distributed. An altogether new pattern is projected. (Figure 2, p. 115)

Therefore, the closing of one slit will completely affect the behavior of the electrons passing through the other. This interference is because of the disturbance of the "quantum force" felt by a particle as it moves between the slit and the screen. The presence of this force serves to explain how the closing of one slit would affect the particles passing through the other.

By citing the "quantum force," some explanation to the origination of the wave-particle duality may be understood. Within the Copenhagen interpretation, the duality may not be comprehended, only observed. All that can be done with the slit-interference experiment is to watch electrons speed from the projector to the slit, and by an invisible hand, interfere on the screen. A question of Why? cannot even be raised. By invoking the complementarity principle, the wave model will explain the tie between statistical interference, and the particle model will explain how individual spots are received on the screen. Absent is the explanation that ties it all together, and gives both a quantitative and qualitative answer. Here is a thorough and reasonable account that asserts the importance of change in the formulation of quantum theory.

The Undivided Universe, Bohmís (with B.J. Hiley) last work before his sudden death in 1992, Prof. Bohm provides an exposition for his extension of [his, Hileyís, and other dissidentsí] approach beyond the domain of current quantum theory (UU, p. 345). Immediately, Bohm states how the simple difficulty of exploring theory through experimentation applies to his new approach. He says: "there is such a wealth of possibilities and such a dearth of experimental clues." (UU, p. 345)

The first example is the equations for a trajectory of a particle. (UU, p. 345) They are:

(1)

(2)

Next, Bohm adds an "arbitrary forces" term, F and "arbitrary additions," l .

+ F

+ l .

Importantly, he dictates that any such changes could exhibit fundamental changes in the theory. Carefully, he uses words to keep the door open on his new science with saying that the additions may be chosen to negligibly change any current results, but could possibly have serious ramifications in new discoveries.

Other innovations proposed are to change the Schrödinger equation into a non-linear form with additional terms that would relate it to particle positions. He carefully reiterates the importance of applicability specifically to new discoveries. Here he would have rn be regarded as the actual position of the nth particle in the following equation:

.

From this would follow that the overall wave function would collapse towards the particle positions, so in a large system, the empty wave packets would disappear. Unfortunately, he then speaks the harsh truth of no experimentation means no implementation.

Shortly after this, Bohm raises the bar on his discussion and addresses a contradiction of his ideas with: "Our proposed ontological explanation of the quantum theory has, as we have seen, also led to a certain paradox. For it implies nonlocality and this would seem to contradict relativity which is regarded as a theory that is equally fundamental to quantum theory." (UU, p. 347) Bohm moves rapidly on this idea and proposes a deeper theory of the individual quantum process that is not relativistically invariant. He elucidates with: "In this theory there is a preferred coordinate frame in which the instantaneous transmission of impulses is in principle possible, so that there is no contradiction with nonlocality for individual quantum processes." (UU, p. 347) What Bohm says here is that underlying the level where relativity is valid, there exists a subrelativistic (just as subquantum) level in which it is not valid even though relativity is [approximately] quantified in the same statistical manner as if it were large scale.

The subrelativistic level is one that is essential for Bohmís further postulates, including possibly the existence of another quantum dimension. For example, he states that at base, a subrelativistic level would go beyond existing quantum theory. However, there are inherent problems, such that in order for the sublevel to be anything significant and experimentally determinable, it would have to extend far beyond quantum theory, and in a completely thorough manner. He reconsiders the probabilistic nature of the current theoretical school by discussing its description of the elementary trajectory of a particle.

To begin with, a particle follows a random trajectory, but one which is modified by an osmotic velocity jointly with the influences of the quantum potential. For the motion of atoms at the Brownian level, random trajectories are thought of as approximations to the actual paths of the atoms where the randomness fails at very short differences. So, at the length where exists the cutoff to Brownian motion, the trajectories are forcibly described by the mean free path, below which causal laws dominate.

Since the mean free path is applied to things from diffusion and conductivity of heat, then it is plausible to argue for the existence of the same cutoff level of mean free path for the atomic level. Where in systems, below the cutoff the trajectories are casual, in atoms below the cutoff, the sub quantum effects are subrelativistic. The correlation between system description and system prediction breakdown is evidence enough for the consideration.

In Bohmís further philosophizing, the next logical progression from the quantum sublevel would be another atomic dimension. In analogy, it would be just as the atom in its role of the building block of matter. Here, he exuberantly premises: "We do not as yet know what this dimension is, but it seems reasonable to propose that it could be on the order of the Planck length, where, in any case, we can expect that our current ideas of space-time and quantum theory might well break down." (UU, p. 348)

Perhaps Bohm sounds righteous or egotistical in his statement of "breaking down" established, tested, and accepted theory. However, after reading some of Bohmís exquisite rhetoric in his deep probing of quantum mechanics, any sensible being would strive for the universal tie that must bind the Universe together on all its levels.

References
Bohm, David. Causality and Chance in Modern PhysicsNew York. Harper Bros.
1957.
Bohm, David & Hiley, B. J. The Undivided UniverseLondon.Routledge.1993. Hiley, B.J. NCUACS PROGRESS REPORT 21. http://www.bath.ac.uk/ncuacs/prgrts/prgrep21.htm (accessed May 2002).

Peat, F. David. Infinite Potential: The Life and Times of David BohmReading, MA. Addison-Wesley Publishing Company, Inc. 1997.