The Greatest Story Ever Told—So Far

by Lawrence M. Krauss

  This may not sound so revolutionary, and as Faraday did with electric fields, Planck viewed his assumption as merely a formal mathematical crutch to aid in his analysis. He later stated, “Actually I did not think much about it.” Nevertheless, this proposal that light was emitted in particle-like packets is clearly difficult to reconcile with the classical picture of light as a wave. The energy carried by a wave is simply related to the magnitude of its oscillations, which can change continuously from zero. However, according to Planck, the amount of energy that could be emitted in a light wave of a given frequency had an absolute minimum. This minimum was termed an “energy quantum.”

  Planck subsequently tried to develop a classical physical understanding of these energy quanta, but failed—causing him, as he put it, “much trouble.” Still, unlike a number of his colleagues, he recognized that the universe didn’t exist to make his life easier. Referring to the physicist and astronomer Sir James Jeans, who was unwilling to give up classical notions in the face of the evidence provided by radiation, Planck stated, “I am unable to understand Jeans’s stubbornness—he is an example of a theoretician as should never be existing, the same as Hegel was for philosophy. So much the worse for the facts if they don’t fit.” (Just to be clear, in case readers are moved to write me letters, Planck cast this aspersion on Hegel, not me!)

  Planck later became friends with another physicist who had let the facts drive him toward another revolutionary idea, Albert Einstein. In 1914, when Planck had become dean at Berlin University, he established a new professorship for Einstein there. At first Planck could not accept Einstein’s remarkable proposal—made in 1905, the same year in which he proposed the Special Theory of Relativity—that not only was light emitted by matter in quantum packets, but that light beams themselves existed as bunches of these quanta—that light itself was made up of particle-like objects, which we now call photons.

  Einstein was driven to this proposal to explain a phenomenon called the photoelectric effect, discovered by Philipp Lenard in 1902—a physicist whose anti-Semitism would later play a key role in delaying Einstein’s Nobel Prize, and ensuring, curiously, if perhaps poetically, that it would be not for Einstein’s work on relativity, but rather on the photoelectric effect. In the photoelectric effect, light shining on a metal surface can knock electrons out of atoms and produce a current. However, no matter how intense the light, no electrons would be emitted if the frequency of the light was below some threshold. The moment the frequency was raised above that threshold, a photoelectric current would be generated.

  Einstein realized, correctly, that this could be explained if the light came in minimum packets of energy, with the energy proportional to the frequency of light—as Planck had postulated for light emitted by matter. In this case, only light with frequencies greater than some threshold frequency could contain quanta energetic enough to kick electrons out of atoms.

  Planck could accept the quantized emission of radiation as explaining his radiation law, but the assumption that light itself was quantum-like (i.e., particle-like) was so foreign to the common understanding of light as an electromagnetic wave that Planck balked. Only six years later, at a conference in Belgium, the Solvay Conference, which later became famous, was Einstein finally able to convince Planck that the classical picture of light had to be abandoned, and that quanta—aka photons—were real.

  Einstein was also the first to actually use a fact that he later denounced in his famous statement deriding the probabilistic essence of quantum mechanics and reality: “God does not play dice with the universe.” He showed that if atoms spontaneously (i.e., without direct cause) absorb and emit finite packets of radiation as electrons jump between discrete energy levels in atoms, then he could rederive the Planck radiation law.

  It is ironic that Einstein, who started the quantum revolution but never joined it, was also perhaps the first to use probabilistic arguments to describe the nature of matter—a strategy that the subsequent physicists who turned quantum mechanics into a full theory would place front and center. As a result, Einstein was one of the first physicists to demonstrate that God does play dice with the universe.

  To take the analogy a little further, Einstein was one of the first physicists to demonstrate that the classical notion of causation begins to break down in the quantum realm. Many people have taken exception to my proposal that the universe needed no cause but simply popped into existence from nothing. Yet this is precisely what happens with the light you are using to read this page. Electrons in hot atoms emit photons—photons that didn’t exist before they were emitted—which are emitted spontaneously and without specific cause. Why is it that we have grown at least somewhat comfortable with the idea that photons can be created from nothing without cause, but not whole universes?

  The realization that electromagnetic waves were also particles began a quantum revolution that would change everything about the way we view nature. To be a particle and a wave at the same time is impossible classically—as should be clear from the earlier discussion in this chapter—but it is possible in the quantum world. As should also be clear, this was just the beginning.

  Chapter 7

  * * *

  A UNIVERSE STRANGER THAN FICTION

  Therefore do not throw away your confidence, which has a great reward.

  —HEBREWS 10:35

  Conventional wisdom might suggest that physicists love to invent crazy esoterica to explain the universe around us, either because we have nothing better to do, or because we are particularly perverse. However, as the unveiling of the quantum world demonstrates, more often than not it is nature that drags us scientists, kicking and screaming, away from the safety of what is familiar.

  Nevertheless, to say that the pioneers who pushed us forward into the quantum world lacked confidence would be a profound misstatement. The voyage they embarked upon was without precedent and without guides. The world they were entering defied all common sense, and classical logic, and they had to be prepared at every turn for a change in the rules.

  Imagine taking a road trip to another country, where the inhabitants all speak a foreign language, and the laws are not based on experiences that compare to any you have ever had in your life. Moreover imagine the traffic signals are hidden and can change from place to place. Then you can get a sense of where the young Turks who overturned our understanding of nature in the first half of the twentieth century were heading.

  The analogy between exploring strange new quantum worlds and embarking on a trek through a new landscape may seemed strained, but exactly such a relationship between the two was paralleled in the life of none other than Werner Heisenberg, one of the founders of quantum mechanics, who once reminisced about an evening in the summer of 1925 on the island of Helgoland, a lovely oasis in the North Sea, when he realized he had discovered the theory:

  It was almost three o’clock in the morning before the final result of my computations lay before me. The energy principle had held for all the terms, and I could no longer doubt the mathematical consistency and coherence of the kind of quantum mechanics to which my calculations pointed. At first, I was deeply alarmed. I had the feeling that, through the surface of atomic phenomena, I was looking at a strangely beautiful interior and felt almost giddy at the thought that I now had to probe this wealth of mathematical structures nature had so generously spread out before me. I was far too excited to sleep, and so, as a new day dawned, I made for the southern tip of the island, where I had been longing to climb a rock jutting out into the sea. I now did so without too much trouble and waited for the sun to rise.

  Heisenberg, fresh from obtaining his PhD, had moved to the distinguished German university in Göttingen to work with Max Born to try to come up with a consistent theory of quantum mechanics (a term first used in the paper “On Quantum Mechanics” by Born in 1924). However, spring hay fever had laid Heisenberg low, and he escaped the green countryside for the sea. There, he polished off his ideas about the quantum be
havior of atoms and sent it off to Born, who submitted it for publication.

  You may be familiar with Heisenberg’s name, not least because of the famous principle associated with it. The Heisenberg uncertainty principle has gained a New Age aura, providing fuel for many a charlatan to take advantage of people for whom quantum mechanics seems to offer hope of a world where any dream, no matter how outlandish, is realizable.

  Other familiar names, Bohr, Schrödinger, Dirac, and later Feynman and Dyson, each made great leaps into the unknown. But they weren’t alone. Physics is a collaborative discipline. Too often science stories are written as if the protagonists had a sudden Aha! experience alone late at night. Heisenberg had been working on quantum mechanics for several years with his PhD supervisor, the brilliant German scientist Arnold Sommerfeld (whose students would win four Nobel Prizes, and whose postdoctoral research assistants would win three), and later with Born (who was finally recognized with a Nobel almost thirty years later), as well as a young colleague, Pascual Jordan. Every major triumph we celebrate with a name and a prize is accompanied by a legion of hardworking, often less heralded, individuals, each of whom moves forward the line of scrimmage by a little bit. Baby steps are the norm, not the exception.

  The most remarkable leaps into the unknown are often not fully appreciated, even by their developers, until much later. Thus Einstein, for example, never trusted his beautiful General Relativity enough to believe its prediction that the universe cannot be static but must be expanding or contracting—until observations demonstrated the expansion. And the world didn’t stand on its head when Heisenberg’s paper appeared. Heisenberg’s friend and contemporary the brilliant and irascible physicist Wolfgang Pauli (another future Nobel laureate assistant to Sommerfeld) thought the work to be essentially mathematical masturbation, leading Heisenberg to respond in jocular form:

  You have to allow that, in any case, we are not seeking to ruin physics out of malicious intent. When you reproach us that we are such big donkeys that we have never produced anything new in physics, it may well be true. But then, you are also an equally big jackass because you have not accomplished it either. . . . Do not think badly of me and many greetings.

  Physics doesn’t proceed in the linear fashion that textbooks recount. In real life, as in many good mystery stories, there are false leads, misperceptions, and wrong turns at every step. The story of the development of quantum mechanics is full of them. But I want to cut to the chase here, and so I will skip over Niels Bohr, whose ideas laid out the first fundamental atomic rules of the quantum world as well as the basis for much of modern chemistry. We’ll also skip Erwin Schrödinger, who was a remarkably colorful character, fathering at least three children with various mistresses, and whose wave equation is the most famous icon of quantum mechanics.

  Instead I will focus first on Heisenberg, or rather not Heisenberg himself, but instead the result that made his name famous: the Heisenberg uncertainty principle. This is often interpreted to mean that the observations of quantum systems affect their properties—which was manifest in our earlier discussions of electrons or photons passing through two slits and impinging on a screen behind them.

  Unfortunately this leads to the misimpression that somehow observers, in particular human observers, play a key role in quantum mechanics—a confusion that has been exploited by my Twitter combatant Deepak Chopra, who, in his various ramblings, somehow seems to think the universe wouldn’t exist if our consciousness weren’t here to measure and frame its properties. Happily the universe predates Chopra’s consciousness and was proceeding pretty nicely before the advent of all life on Earth.

  However, the Heisenberg uncertainty principle at its heart has nothing to do with observers at all, even though it does limit their ability to perform measurements. It is instead a fundamental property of quantum systems, and it can be derived relatively straightforwardly and mathematically, based on the wave properties of these systems.

  Consider for example a simple wavelike disturbance with a single frequency (wavelength) oscillating as it moves along the x direction:

  As I have noted, in quantum mechanics particles have a wavelike character. Thanks to Max Born we recognize that the square of the amplitude of the wave associated with a particle at any point—what we now call the wave function of the particle, following Schrödinger—determines the probability of finding the particle at that point. Because the amplitude of the oscillating wave above is more or less constant at all the peaks, such a wave, if it corresponded to the probability amplitude of finding an electron, would imply a more or less uniform probability for finding the electron anywhere along the path.

  Now consider what a disturbance would look like if it was the sum of two waves of slightly different frequencies (wavelengths), moving along the x axis:

  When we combine the two waves, the resulting disturbance will look like:

  Because of the slightly different wavelengths of the two waves, the peaks and troughs will tend to cancel out, or “negatively interfere” with each other everywhere except for the rare places where the two peaks occur at the same point (one of these locations is shown in the figure above). This is reminiscent of the wave interference phenomenon in the Young double-slit experiment I described earlier.

  If we add yet another wave of slightly different wavelength

  the resulting wave then looks like this:

  The interference washes out more of the oscillations aside from the position where the two waves line up, making the amplitude of the wave at the peak much higher there than elsewhere.

  You can imagine what would happen if I continue this process, continuing to add just the right amount of waves with slightly different frequencies to the original wave. Eventually the resulting wave amplitudes will cancel out more and more at all places except for some small region around the center of the figure, and at faraway places where all the peaks might again line up:

  The greater the number of slightly different frequencies that I add together, the narrower will be the width of the largest central peak. Now, imagine that this represents the wave function of some particle. The larger the amplitude of the central peak, the greater the probability of finding the particle somewhere within the width of that peak. But the width of that central peak is still never quite zero, so the disturbance remains spread out over some small, if increasingly narrow, region.

  Now recall that Planck and Einstein told us that, for light waves, at least, the energy of each quantum of radiation, i.e., each photon, is directly related to its frequency. Not surprisingly, a similar relation holds for the probability waves associated with massive particles, but in this case it is the momentum of the particle that is related to the frequency of the probability wave associated with the particle.

  Hence, Heisenberg’s uncertainty relation: If we want to localize a particle over a small region, i.e., have the width of the highest peak in its wave function as narrow as possible, then we must consider that the wave function is made up by adding lots of different waves of slightly different frequencies together. But this means that the momentum of the particle, which is associated with the frequency of its wave function, must be spread out somewhat. The narrower the dominant peak in space in the particle’s wave function, the greater the number of different frequencies (i.e., momenta) that must be added together to make up the final wave function. Put in a more familiar way, the more accurately we wish to determine the specific position of a particle, the greater the uncertainty in its momentum.

  As you can see, there is no restriction here related to actual observations, or consciousness, or the specific technology associated with any observation. It is an inherent property of the fact that, in the quantum world, a wave function is associated with each particle, and for particles of a fixed specific momentum, the wave function has one specific frequency.

  After discovering this relation, Heisenberg was the first to provide a heuristic picture of why this might be the case, which he posed in terms o
f a thought experiment. To measure the position of a particle you have to bounce light off the particle, and to resolve the position with great precision requires light of a wavelength small enough to resolve this position. But the smaller the wavelength, the bigger the frequency and the higher the energy associated with the quanta of that radiation. But bouncing light with a higher and higher energy off the particle clearly changes the particle’s energy and momentum. Thus, after the measurement is made, you may know the position of the particle at the time of the measurement, but the range of possible energies and momenta you have imparted to the particle by scattering light off it is now large.

  For this reason, many people confuse the Heisenberg uncertainty relation with the “observer effect,” as it has become known, in quantum mechanics. But, as the example I have given should demonstrate, inherently the Heisenberg uncertainty principle has nothing to do with observation at all. To paraphrase a friend of mine, if consciousness had anything to do with determining the results of quantum physics experiments, then in reporting the results of physics experiments we would have to discuss what the experimenter was thinking about—for example, sex—when performing the experiment. But we don’t. The supernova explosions that produced the atoms that make up your body and mine occurred quite nicely long before our consciousness existed.

  The Heisenberg uncertainty principle epitomizes in many ways the complete demise of our classical worldview of nature. Independent of any technology we might someday develop, nature puts an absolute limit on our ability to know, with any degree of certainty, both the momentum and position of any particle.