July 19, 2003

IN HIS inaugural lecture at the University of Cambridge in 1871, James Clerk Maxwell expressed the prevalent mood of the scientific society in following words: “In a few years, all the great physical constants will have been approximately estimated, and . . . the only occupation which will then be left to the men of science will be to carry these measurements to another place of decimals.” Only three decades later, the first cracks had already started to appear in this soothing picture of ultimate determinism as initially postulated by the 18th century French mathematician, Pierre Simon Laplace.

With the same passion for a deterministic description of nature in mind, science had made enormous progress using classical mechanics and electrodynamics. By 1871, the basic equations provided by classical mechanics and electrodynamics could describe most physical systems, at least the ones that were observed in everyday life. There were a few inconsistencies, but it was generally believed that major issues had been ironed out. As it turned out however, this quest for understanding the “reality” that nature poses was, not surprisingly, filled with great obstacles and increased obscurity.

As man probed deeper and struggled to understand further, these inconsistencies became widespread and started to challenge the fundamentals of modern physics. By the early 20th century, these dilemmas had become major embarrassments for physics and tormented the most brilliant minds. Apparently, even though the macroscopic world could be studied with classical mechanics, these rules failed once it came to the understanding of microscopic particles, such as atoms, photons and electrons. Since these particles constituted of macroscopic matter, the implications were of course, deep, to say the least.

On another level, our knowledge of the macroscopic world itself was challenged. At high velocities or extreme gravitational fields classical mechanics failed once again to agree with empirical data. The key data in question had to do with heavenly bodies where these extremities were normally observed. Albert Einstein overcame this impasse with his beautiful insight when he single handedly formulated Special and General Relativity.

However, as far as the tinniest particles of the universe were concerned, another set of rules had to be developed to understand nature fully.

Quantum Mechanics, thus took shape to answer this challenge. What is so unique about quantum mechanics is that it was not the brainchild of just one scientist. Undoubtedly, the quantum effects of the particle world were so unnerving and so anti intuitive that it took decades of trial and error, postulations, arguments and theories by such brilliants minds as Max Planck, Albert Einstein, Erwin Schrödinger, Louis De Broglie, Max Born and Werner Heisenberg to formalize quantum mechanics. Everyone contributed a piece to solve the giant puzzle.

Despite the immense insight from these people, certain interpretive glitches remained and have been continuously argued over to date. But the most important outcome of this turbulent childhood was that the mathematical foundations of quantum mechanics were laid down. It was now at least possible to study physical phenomena using the language of mathematics.

In other words, physicists had learnt the limitations on describing physical systems but “why” it was the way it was remained a riddle for years to come. This apparently naive yet pragmatic approach of focusing on the formulation and building a workable model for quantum mechanics first while ignoring the interpretive issues and their implications bore tremendous success. It is surprising to note that, although, some of these issues have yet to be resolved even at the start of the 21st century, the number of things that have been made possible through quantum mechanics is truly astonishing. These include everyday things, such as semi conductors in computer chips to lasers in compact disc players, magnetic resonance imaging in hospitals and much more.

Given its puzzling demeanour, deciding on a point to explain quantum mechanics is an essentially difficult task. In the simplest sense, quantum mechanics seeks to describe the behaviour of physical entities at the microscopic level of electrons and photons.

What is astounding about quantum mechanics is perhaps twofold. On one hand, the dawn of the quantum era drew the curtain on man’s dream of scientific determinism. It postulated an indeterminism that was inherent in nature itself, thus dashing all attempts to describe any physical entity beyond a certain degree of accuracy.

More stirring, however, is the fact that despite providing explanations and perfectly acceptable solutions to many of the 20th century’s chronic scientific problems, quantum mechanics had no fundamental principles. It does not explain the reason behind why one observes what one does, rather it describes statistically what one does observe and yet unmistakably agrees with empirical evidence.

William Shakespeare once said, “In nature’s book of infinite secrecy a little can I read.” Personally, nothing seems to fit better for quantum mechanics.

David Griffiths of Reeds College and author of the first quantum mechanics textbook most physics students come across, makes a fine distinction between what we can or cannot do with quantum mechanics. He claims that no discourse can tell you what quantum mechanics means but only what it does, and that too mathematically.

The mathematics, however, is complex enough that it cannot be the subject of an article in Popular Science. This article instead, endeavours to show an appreciation for the place quantum mechanics takes in modern physics. By focusing on the problems that physics faced towards the end of the 19th century, we can better understand the development of quantum mechanics. This would later give us a chance to also study the different interpretations that evolved to explain the fundamental roots of the quantum behaviour. One hopes to leave the reader with a flavour for quantum mechanics and perhaps, a motivation for a deeper study into the subject.

The first spark of the quantum revolution can be easily credited to Max Planck. Among the biggest problems classical physics faced towards the end of the 19th century, one had to do with the inability to calculate the apparent spectrum of glowing bodies. Traditional equations gave results which implied such absurdities as the “ultraviolet catastrophe” — in layman’s terms; it suggested that a hot cup of coffee would radiate enough energy to blind you. In a 1900 paper, Planck solved this problem using a pure mathematical trick when he divided energies into packets or “quanta.” Despite the fact that the equations fit in perfectly with empirical data, Planck distanced himself from the idea of quantized energy because his revolutionary insight was not backed by any fundamental theory.

In 1905, Einstein took Planck’s idea to the next level, proving its success. In a monumental paper for which he was honoured with the Nobel Prize (Photoelectric effect), he showed that energy could only be carried in packets of energy, which he called photons.

By 1911, Ernest Rutherford had convinced the world of the solar system like arrangement of the electrons and the nucleus inside the atom. According to the established electromagnetic theory, an accelerating charge gives off energy. And if the orbiting electron scenario was really true, then no one could explain why the hydrogen atom was stable when the electron should theoretically gradually lose energy and spiral into the nucleus. Physics faced another embarrassment.

Neil Bohr came up with a solution in 1913 when he proposed that the angular momentum of electrons was itself quantized, and thus would limit these electrons to certain orbits only. A change from a higher orbit to a lower orbit would give off a discrete amount of energy and vice versa. Since an electron in the inner most orbit could give off no more energy and thus could not lower itself further, there was no possibility of an unstable hydrogen atom.

Despite these sporadic revelations, physicists still did not have a single rule that would unite and explain these results. In his doctoral thesis in 1923, Louis de Broglie produced an answer so elegant and yet so baffling that the examining committee had to seek external advice on whether to accept his paper. He proposed that to explain the discretization (or quantization) of energy, electrons and other particles can be thought of as standing waves, like those created when a guitar string is plucked, that can only occur with certain frequencies.

The idea that electrons were mere particles was so ingrained that Broglie’s idea was truly a shock for many. Erwin Schrödinger nonetheless, successfully produced a wave equation for these electrons in 1925. These wave equations of the electrons, yet again, fit in perfectly with empirical data and emerged to explain an enormous amount of measurements, ranging from the chemical properties to the spectrums of higher order elements. But what exact quantity did this wave function describe? That remains the central puzzle and the point of the most conflict in quantum mechanics to date.

Max Born’s beautiful insight was his interpretation of the wave function, the wave function f(x,t) should be taken as the probability of finding the electron at point x and at time t. Thus, the probability of finding an electron at a certain location in an experiment depended on the amplitude of its wave function there. At around the same time, the German physicist Werner Heisenberg, came out with his now famous “Uncertainty Principle” that showed that it was impossible to determine the exact characteristics of a physical state, for instance, it was impossible to measure with absolute precision both the momentum and the position of an electron because the act of measurement would invariably disturb the system. Thus, a particle could only be said to have a certain combination of momenta and position with a certain probability.

To summarize, the new picture visualized electrons as neither waves nor particles, but both. The wave function represented the limitations of the “Heisenberg Principle” in finding the position of the particle with certainty (or probability = 1). Meanwhile, the amplitude at every point on the wave was the probability of observing the particle at that point.

These developments strongly suggested an inherent randomness built into the laws of nature, a point that continued to haunt Einstein for the greater part of his life. He actively disagreed with these postulations. Refusing to accept the fallibility of a perfectly predictive universe, he made his reservations public at many occasions: “I can’t believe that God plays dice.”

While Einstein believed that quantum mechanics lacked a fundamental portion, Bohr, however, had more belief in the beauty and completeness of quantum mechanics. The two giants competed academically to prove the other wrong for years. In one of their witty, yet insightful debates, Bohr is known to have rebutted Einstein by remarking: “quit telling God what to do.” Later as we shall see, Bohr was eventually proven to be correct.

Translated into everyday terminology, classical physics would have the observer as objective and passive. Physical events happen independently of whether there is an observer or not. This is known as objective reality, an apple falls off irrespective of whether anyone watches it or not.

In the quantum regime the observer is neither objective nor passive. As the uncertainty principle states, a possibility dictates whether a particle will be found at a certain location. But when the observer interferes with the system, this act of observation changes the physical system irrevocably and brings the state into one of the many possibilities that depend on the original wave function. This is known as subjective reality, in other words, using the same analogy, although not perfectly suitable, the apple is there because we disturbed the system such that it would be found there.

That settled, for most, the issue of the indeterminacy in the description of any physical state and idea of associating observable possibilities with probabilities. However, these developments offered answers only to what happens when an observation is made. The search is still on for an equation to describe how the particle got to where it was observed.

The interpretation game for quantum mechanics has been strewn with more conflict and indeterminism than perhaps, its predictions itself. Numerous interpretations were forwarded, did their time and then, either passed the baton to more comprehensive theories or simply died out. The transactional and the pilot wave theories remain the least popular of them all. This article briefly mentions two strong theories that competed aggressively for the explanation. A more recent but extremely plausible interpretation commonly referred to as the many worlds postulate is also mentioned together with its bizarre implications.

Two schools of thought existed during quantum theory’s infancy: the realists, headed by Einstein himself, postulated that quantum mechanics was inherently incomplete and could not account for certain hidden variables without which it was impossible to talk about the pre observation time. Thus the probabilistic description was an epistemic interpretation of our lack of knowledge of the values to these variables.

The second interpretation and by far the most widely accepted came to be known as the orthodox view or the Copenhagen interpretation. Pragmatically, Bohr asserted that a measurement is what forces a quantum system to adopt a definite state. It is a circular definition, but if one accepts it and does not question the process of measurement itself, then all else follows. The observation creates the reality after it collapses the wave function so that only a sharp amplitude occurs at the location where the particle is observed. In this view, the first point at which it becomes possible to talk about the electron really doing anything at all is when it is detected.

One reason for the Copenhagen interpretation’s success was that it provided a strikingly successful recipe for doing calculations that accurately described the outcomes of experiments without having to worry about interpretations. Between the theories vying for an explanation, the hidden variables theory was excluded in 1982. CERN’s theorist, John S. Bell suggested an experiment that would reveal the presence of these hidden variables. Once the experiment was performed, it was clear that quantum mechanics was here to stay and it was indeed a probabilistic, yet complete description of nature.

The most recent of the interpretations, the many worlds or the relative state interpretation, was first proposed by a Princeton graduate student Hugh Everett III in 1957. The “many-worlds” requires our universe to be a tiny facet of a larger multiverse, a highly structured continuum containing many universes. This theory was only recently formalized by Oxford physicist and author of The Fabric of Reality, David Deutsch.

According to this theory, all possibilities (on the wave function) for an electron exist in different universes, but we only see the possibility that the electron picks for the universe we exist in. The consequences of such a reality are indeed mind boggling. An exaggerated yet possible description of these universes could be: “A universe must exist for every physical possibility. There are Earths where the Nazis prevailed in the Second World War, where Marilyn Monroe married Einstein, and where the dinosaurs survived and evolved into intelligent beings who read” — New Scientist.

Confused? Quantum Mechanics and its implications are surely a mouthful, specially since its effects do not correlate with our everyday experiences. But it’s not just us; this indeterminacy is equally disturbing for scientists and philosophers alike. Richard Feynman, the late Nobel laureate, the famed theoretician and one of the most adored figures in science, might have had some words for our consolation. In 1965, speaking on the issue of the comprehension of quantum mechanics, he said: “it could safely be said that nobody understands quantum mechanics, and if you think you understand it, you’re wrong.”

Truth is that quantum mechanics has countered many queries that had stood from a century ago. Its role in the prediction of anti matter, understanding radioactivity, explaining superconductivity and describing interactions, such as those between light and matter has been without doubt, rewarding. Typical of every scientific breakthrough, however, it raises a few problems because it is a package deal.

We should not be put down by our inability to answer these questions. The fact alone that we are more inquisitive now than ever before is proof enough that we are heading in the right direction. On a lighter note, here’s to hoping that there exists a part of us in an alternate universe where we have already understood “it” all.

The writer is a young scholar at the National University of Singapore

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