I thoroughly enjoyed Kumar’s book. He traces the scientific discoveries leading to quantum theory and the relationships of the scientists with a focus on the Einstein-Bohr debate over the theory’s meaning. I found Kumar’s explanations of complex theories accessible and helpful. I remember in high school and college in the 1960’s always hearing about this strange quantum world that didn’t quite exist unless someone looked at it. Kumar really helps make sense of it. My notes below summarize the science that paved the way for quantum theory, the Einstein Bohr rivalry and the various takes on the Copenhagen interpretation.
Kumar’s history begins with Max Planck’s discovery of the quantum and his eponymous constant. Working to derive a formula to predict the spectral distribution of blackbody radiation in 1900, Planck found that only whole increments of energy worked. At a time when the atom was not a widely accepted theory, this confronted Planck’s belief in the continuous nature of energy and matter. He dodged the issue by saying that only the exchange of energy was quantized, not energy itself.
Along came Einstein who accepted atoms as discrete matter and sources of discrete energy. After reading Planck’s paper Einstein challenged the prevailing wave theory of light, proclaiming light is made up of quanta. Einstein employed his quantum theory of electromagnetic radiation to explain the photoelectric effect in which light precipitates the release of electrons from metals. This was in 1905. Even in 1922 when Einstein was awarded the Noble Prize for his equation explaining the photoelectric effect, the underlying principle of light as quanta was still not widely accepted. Newton had held that light was composed of particles, but Thomas Young’s famous two slit experiment in 1801 showed light to be a wave. After overcoming the implied disrespect to Newton, scientists finally accepted light as a wave and held onto that view as tenaciously as they had held onto the particle view before. Also in Einstein’s Annus Mirabilis he explained Brownian motion with atomic theory gaining the atom much wider acceptance. And in his spare time that year he formulated the special theory of relativity and the famous E=MC2.
In 1913 Niels Bohr conceptualized the quantum atom. Recognizing that J. J. Thomson’s plum pudding model of the atom was inherently unstable Bohr assigned electrons to special orbits in which they could not continuously emit radiation and lose energy. Each orbit had a specific energy level. When an electron moved from one orbit to another an exact amount of energy (quantum) was exchanged which resulted in unique spectral patterns. Amazingly there was no in between. An electron left one orbit and appeared in another instantaneously. The Franck-Hertz experiment in 1914 confirmed that the energy released or absorbed was exactly the difference between the energy levels of the orbits. In 1922 Bohr refined his atomic model with the concept of electron shells. This allowed him to predict the chemical similarities of elements in the periodic table.
Einstein was thrilled with Bohr’s quantum atom as he felt it proved his theory of light-quanta. In 1916, finding time after his ground shattering theory of general relativity was announced in 1915, Einstein theorized that spontaneous emission occurred when an electron jumped to a lower energy orbit. The rub was that in his theory electrons made these jumps at random. His theory employed probabilities to determine the frequency of these jumps. Einstein, now as later, was uncomfortable with chance in physics theories. Einstein’s light-quantum, later to be renamed the photon, was proven in an 1923 experiment by American Arthur Compton who firing x-rays at graphite recorded changed wavelengths in the reflected scattered x-rays. Only a particle would behave this way. Furthermore he found the recoiling electrons that the x-rays had bounced off of. Then a French prince, Louis de Broglie, setting the stage for quantum mechanics, postulated that if a wave could have the values of a particle, why not the reverse? Ascribing wave characteristics to electrons explained perfectly the available orbits for electrons in an atom. Only those orbits that could accommodate whole or half wave lengths were physically possible. Sure enough subsequent experiments showed that electrons diffracted just like light. Wave particle duality was now established for energy and matter.
In 1925 Wolfgang Pauli building on a paper by Edmund Stoner developed the exclusion principle. Stoner determined the number of possible energy states of electrons orbiting an atom. But the three quantum numbers denoting angular momentum, shape of orbit and orientation of orbit only allowed for half of the possible energy states. Pauli developed a fourth quantum number which would later be explained as spin. This quantum spin had two states, up or down, doubling the number of allowable electrons. It also explained the heretofore mysterious splitting of spectral lines known as the Zeeman Effect. The exclusion principle stated that no two electrons in an atom could have the same set of quantum numbers thus limiting the number of electrons.
Werner Heisenberg solved a remaining problem of the quantum atom model. Even though it now explained the frequency of spectral lines, it did not explain the different intensities. Heisenberg decided to discard anything not observable, even that electrons occupied orbits. He needed the help of Max Born who collaborated with one his students, an excellent mathematician named Pascual Jordan, to get the math to support the physical theory. This new quantum mechanics employed a strange form of matrix mathematics in which A times B does not equal B times A, but it successfully calculated spectral line intensities. In England, Cambridge student P. A. M. Dirac also developed a mathematical proof working from a draft of Heisenberg’s paper.
In 1926 Edwin Schrödinger developed a wave function for de Broglie’s electrons which eliminated the incomprehensible electron jumps. It also supported calculations that achieved the same predictive results as Heisenberg’s matrix mechanics. The rub was picturing what the wave represented. Schrödinger claimed it was a cloud of charge that could smoothly and continuously move from one orbit to another. He denied that electrons were particles at all while Heisenberg, committed to particles, opposed the wave theory, putting the two at odds.
Heisenberg trying to settle his dispute with Schrödinger developed the uncertainty principle. This stated that quantum mechanics could not determine both the position and momentum of a particle, specifically an electron. Heisenberg, working as Bohr’s assistant, toyed with the idea that the photon itself that measured the electron interfered with the observation. Heisenberg refused to imply any behavior to an electron that could not be measured. There was no assuming what happened to an electron between two measurements, thus no path at all was held to have been traveled. Basically Heisenberg was saying classical concepts of wave, particle, position, momentum and trajectory had no meaning in the quantum world until observed.
Bohr believed that uncertainty was fundamental to the quantum nature of wave-particle duality. Bohr felt the electron was both a wave and a particle, but that no experiment could measure both at the same time. He called his principle complementarity. Bohr held that observer and observed could not be separated. The way the quantum world was observed determined what was seen. Be it wave or particle, both observations were true depending on the way it was observed. Causality and regular patterns had no meaning. The only prediction quantum mechanics could make was one of probability. No experiment could ever return the deterministic clockwork cosmos of Newton to the quantum world. There was no reality at the quantum level outside of observation. This view became known as the Copenhagen interpretation.
Einstein, while accepting that quantum mechanics was a correct and important theory, did not accept this interpretation. Einstein believed the quantum world was deterministic (“God doesn’t play dice.”) and most importantly real. It was there even when nobody was looking. The stage was set for a lifelong series of challenges to this interpretation by Einstein directed at Bohr, the Copenhagen Interpretation’s champion. At the conferences in Solvay in 1927 and 1930 Einstein offered thought experiments to show quantum mechanics was an incomplete description of reality. Bohr would parry and nothing would be resolved.
After the Nazi’s assumed power in Germany In 1933 Einstein moved to Princeton. Bohr would be able to continue in Copenhagen until the Nazi’s declared martial law in Denmark in 1943. Many Physicists in Germany were Jewish or had Jewish connections. They were leaving and scattering around the world. Despite the turmoil of the 1930’s and 40’s, Einstein and Bohr carried on their quantum chess match. Einstein in 1935 published a paper with help from Princeton assistants known as the EPR paper. This thought experiment proposed measuring the momentum and position of one of a pair of entangled particles to determine the momentum and position of the other. The point was to prove the existence of the other particle independent of direct observation of it. The Copenhagen interpretation denied reality independent of observation. Key to Einstein’s argument was the concept of locality, that nothing faster than the speed of light could affect the other particle. Bohr conceded this but claimed the particles were entwined and thus one system, that a measurement of one was a measurement of both.
Einstein reached out to the sympathetic Schrödinger who came up with his famous cat in a box thought experiment. A tiny radioactive substance is placed in the box. When it decays it will trigger a Geiger counter that will trigger the release of a vial of poison killing the cat. Since the event is not observed, does it happen? In the Copenhagen interpretation of quantum mechanics only a probability wave of the event exists. Schrödinger was trying to appeal to common sense in support of Einstein believing in reality that the cat was either actually dead or still alive. But Copenhagen purists would still say that the cat was both dead and alive until the wave was collapsed by observation. The debate would dominate the minds of Bohr and Einstein over the ensuing years. Bohr last visited Einstein in Princeton in 1954. Einstein died the next year at 76. Bohr died in 1962 at 77. The night before his death Bohr had drawn on his blackboard Einstein’s light box, a thought experiment Einstein proposed at the 1930 Solvay conference in an attempt to prove quantum mechanics an incomplete theory. Over 30 years later Bohr was still refining his argument.
In 1964 John Stewart Bell put forth a theorem to test whether any local hidden variables could be used to explain the behavior of the entangled particles in the EPR thought experiment. Subsequent tests of the theorem supported non-locality between entangled particles and paved the way for today’s experiments with quantum level teleportation. But even though what Einstein called “spooky action at a distance” was proven to exist, his underlying belief that the quantum world also existed even when not measured was not disproven. In 1957 Hugh Everett III found a neat way around the problem with his many worlds interpretation. In this theory all quantum states actually exist simultaneously, obviating the probability wave. This resolved one objection to the Copenhagen Interpretation: Who observed the big bang to collapse the probability wave? God, of course, is one answer. Another issue for quantum mechanics is determining the dividing line between the quantum world and the classical world where reality is the norm.
Despite the overwhelming acceptance of the Copenhagen interpretation in the mid-twentieth century, today while quantum mechanics itself is universally accepted, many physicists don’t believe it is a complete theory. The Copenhagen interpretation has lost its luster. Nobel laurate Murray Gell-Mann said ”Niels Bohr brain-washed a whole generation of physicists into believing that the problem had been solved.” At a 1999 quantum mechanics conference at Cambridge University, of 90 physicists polled, only four accepted the Copenhagen interpretation, thirty believed the modern version of the many worlds theory and most were undecided. Famed British physicist Roger Penrose said “I would, myself, strongly side with Einstein in his belief in a submicroscopic reality, and with his conviction that present-day quantum mechanics is fundamentally incomplete.” So maybe somewhere in the great beyond Einstein is finally winning his argument with Bohr.