einstein

These packets or bundles of energy came only in fixed amounts, determined by Planck’s constant, rather than being divisible or having a
continuous range of values.
Planck considered his constant a mere calculational contrivance that explained the process of emitting or absorbing light but did not apply to the
fundamental nature of light itself. Nevertheless, the declaration he made to the Berlin Physical Society in December 1900 was momentous: “We
therefore regard—and this is the most essential point of the entire calculation—energy to be composed of a very definite number of equal finite
packages.” 12
Einstein quickly realized that quantum theory could undermine classical physics. “All of this was quite clear to me shortly after the appearance of
Planck’s fundamental work,” he wrote later. “All of my attempts to adapt the theoretical foundation of physics to this knowledge failed completely. It
was as if the ground had been pulled out from under us, with no firm foundation to be seen anywhere.” 13
In addition to the problem of explaining what Planck’s constant was really all about, there was another curiosity about radiation that needed to be
explained. It was called the photoelectric effect, and it occurs when light shining on a metal surface causes electrons to be knocked loose and
emitted. In the letter he wrote to Mari right after he learned of her pregnancy in May 1901, Einstein enthused over a “beautiful piece” by Philipp
Lenard that explored this topic.
Lenard’s experiments found something unexpected. When he increased the frequency of the light—moving from infrared heat and red light up in
frequency to violet and ultraviolet—the emitted electrons sped out with much more energy. Then, he increased the intensity of the light by using a
carbon arc light that could be made brighter by a factor of 1,000. The brighter, more intense light had a lot more energy, so it seemed logical that
the electrons emitted would have more energy and speed away faster. But that did not occur. More intense light produced more electrons, but the
energy of each remained the same. This was something that the wave theory of light did not explain.
Einstein had been pondering the work of Planck and Lenard for four years. In his final paper of 1904, “On the General Molecular Theory of Heat,”
he discussed how the average energy of a system of molecules fluctuates. He then applied this to a volume filled with radiation, and found that
experimental results were comparable. His concluding phrase was, “I believe that this agreement must not be ascribed to chance.” 14 As he wrote to
his friend Conrad Habicht just after finishing that 1904 paper, “I have now found in a most simple way the relation between the size of elementary
quanta of matter and the wavelengths of radiation.” He was thus primed, so it seems, to form a theory that the radiation field was made up of
quanta. 15
In his 1905 light quanta paper, published a year later, he did just that. He took the mathematical quirk that Planck had discovered, interpreted it
literally, related it to Lenard’s photoelectric results, and analyzed light as if it really was made up of pointlike particles—light quanta, he called them
—rather than being a continuous wave.
Einstein began his paper by describing the great distinction between theories based on particles (such as the kinetic theory of gases) and
theories that involve continuous functions (such as the electromagnetic fields of the wave theory of light). “There exists a profound formal difference
between the theories that physicists have formed about gases and other ponderable bodies, and Maxwell’s theory of electromagnetic processes in
so-called empty space,” he noted. “While we consider the state of a body to be completely determined by the positions and velocities of a very
large, yet finite, number of atoms and electrons, we make use of continuous spatial functions to describe the electromagnetic state of a given
volume.” 16
Before he made his case for a particle theory of light, he emphasized that this would not make it necessary to scrap the wave theory, which would
continue to be useful as well. “The wave theory of light, which operates with continuous spatial functions, has worked well in the representation of
purely optical phenomena and will probably never be replaced by another theory.”
His way of accommodating both a wave theory and a particle theory was to suggest, in a “heuristic” way, that our observation of waves involve
statistical averages of the positions of what could be countless particles. “It should be kept in mind,” he said, “that the optical observations refer to
time averages rather than instantaneous values.”
Then came what may be the most revolutionary sentence that Einstein ever wrote. It suggests that light is made up of discrete particles or
packets of energy: “According to the assumption to be considered here, when a light ray is propagated from a point, the energy is not continuously
distributed over an increasing space but consists of a finite number of energy quanta which are localized at points in space and which can be
produced and absorbed only as complete units.”
Einstein explored this hypothesis by determining whether a volume of blackbody radiation, which he was now assuming consisted of discrete
quanta, might in fact behave like a volume of gas, which he knew consisted of discrete particles. First, he looked at the formulas that showed how
the entropy of a gas changes when its volume changes. Then he compared this to how the entropy of blackbody radiation changes as its volume
changes. He found that the entropy of the radiation “varies with volume according to the same law as the entropy of an ideal gas.”
He did a calculation using Boltzmann’s statistical formulas for entropy. The statistical mechanics that described a dilute gas of particles was
mathematically the same as that for blackbody radiation. This led Einstein to declare that the radiation “behaves thermodynamically as if it
consisted of mutually independent energy quanta.” It also provided a way to calculate the energy of a “particle” of light at a particular frequency,
which turned out to be in accord with what Planck had found. 17
Einstein went on to show how the existence of these light quanta could explain what he graciously called Lenard’s “pioneering work” on the
photoelectric effect. If light came in discrete quanta, then the energy of each one was determined simply by the frequency of the light multiplied by
Planck’s constant. If we assume, Einstein suggested, “that a light quantum transfers its entire energy to a single electron,” then it follows that light of
a higher frequency would cause the electrons to emit with more energy. On the other hand, increasing the intensity of the light (but not the frequency)
would simply mean that more electrons would be emitted, but the energy of each would be the same.
That was precisely what Lenard had found. With a trace of humility or tentativeness, along with a desire to show that his conclusions had been
deduced theoretically rather than induced entirely from experimental data, Einstein declared of his paper’s premise that light consists of tiny quanta:
“As far as I can see, our conception does not conflict with the properties of the photoelectric effect observed by Mr. Lenard.”
By blowing on Planck’s embers, Einstein had turned them into a flame that would consume classical physics. What precisely did Einstein
produce that made his 1905 paper a discontinuous—one is tempted to say quantum—leap beyond the work of Planck?
In effect, as Einstein noted in a paper the following year, his role was that he figured out the physical significance of what Planck had
discovered. 18 For Planck, a reluctant revolutionary, the quantum was a mathematical contrivance that explained how energy was emitted and
absorbed when it interacted with matter. But he did not see that it related to a physical reality that was inherent in the nature of light and the
electromagnetic field itself. “One can interpret Planck’s 1900 paper to mean only that the quantum hypothesis is used as a mathematical
convenience introduced in order to calculate a statistical distribution, not as a new physical assumption,” write science historians Gerald Holton
and Steven Brush. 19
Einstein, on the other hand, considered the light quantum to be a feature of reality: a perplexing, pesky, mysterious, and sometimes maddening