Max Planck made many contributions to theoretical physics, but his fame rests primarily on his role as originator of quantum theories. This theory revolutionized our understanding of atomic and subatomic processes, just as Albert Einstein’s theory of relativity revolutionized our understanding of space and time. Together they constitute the fundamental theories of 20th-century physics. Both have forced humankind to revise some of the most cherished philosophical beliefs, and both have led to industrial and military applications that affect every aspect of modern life. Quantum physics is believed to be the fundamental theory underlying our understanding of the physical Universe. At the same time, on a basic level, quantum physics is predicting bizarre things about how matter works that are completely at odds with how things seem to work in the real world.
Planck was interested in both the humanities and the natural sciences and seriously considered philology. Besides this, his two other strong passions were music and mountain climbing. His new focus on thermodynamics allowed him to ascend to the highest peak of his scientific creativity.
Max Planck was deeply interested in – even obsessed with – the second law of thermodynamics. According to this law (in one of its many versions), no process is possible in which the only result is the transfer of heat from a colder to a hotter body. By the way, Planck first applied in his doctoral thesis (1878, University of Munich) the concept of “entropy,” introduced earlier by Rudolf Clausius, to solve specific physical problems.
Entropy is a measure of a system’s thermal energy per unit temperature that is unavailable for doing useful work. With the help of the concept of entropy, the law can be reformulated to a state that the entropy of an isolated system always increases or remains constant.
There is a debate about the second law centered on the statistical (or probabilistic) interpretation originally proposed by Ludwig Boltzmann. According to his molecular-mechanical interpretation, the entropy of a system is the collective result of molecular motions. The second law is valid only in a statistical sense.
Planck’s belief in the absolute validity of the second law made him reject not only Boltzmann’s statistical version of thermodynamics but also doubt the atomic hypothesis on which it rested. Planck concluded that the atomic conception of matter was irreconcilably opposed to the law of entropy increase.
From the perspective of Planck and his contemporaries, it was natural to seek an explanation of the entropy law in Maxwell’s electrodynamics. After all, Maxwell’s theory was fundamental and was supposed to govern the behavior of the microscopic oscillators that produced the heat radiation emitted by black bodies. But, electrodynamics, Boltzmann showed, provides no more an “arrow of time” than mechanics. Planck had to find another way of justifying irreversibility.
Ultraviolet catastrophe
The ratio of the radiant capacity of a heated body to its absorption capacity does not depend on the nature of the body. It is the same for all bodies and is a function of temperature and frequency of radiation. This is how Gustav Kirchhoff formulated the law of thermal radiation, failing only to find a mathematical expression for this function. The physicist Ludwig Boltzmann concluded that the energy of radiation is proportional to the fourth power of the absolute temperature. Then Wilhelm Wien, Boltzmann’s equally famous compatriot, proved that the maximum intensity in the spectrum was shifted to the range of short waves. However, the calculations of the English scientist John Rayleigh soon led to a paradoxical result: a heated body, regardless of temperature, must emit infinitely more energy in the ultraviolet region of the spectrum. This conclusion contradicted all notions of classical physics. It went down in the history of science as the “ultraviolet catastrophe”.
This was the “data bank” that Planck had at his disposal when he began his own research. He realized that to find a way out of the situation, he needed something “unknown”. It was necessary to derive such a formula that would clearly express the dependence of energy distribution in the spectrum of radiation on temperature and wavelength (frequency).
Planck was not interested in producing an empirically correct law but in establishing a rigorous derivation of it. In this way, he believed, he would be able to justify the entropy law. Guided by Boltzmann’s kinetic theory of gases, Planck formulated a “principle of elementary disorder” that did not rely either on mechanics or electrodynamics. More interestingly, this first version of the famous Planck radiation law also agreed perfectly with the experimental spectrum in the lower-frequency infrared region. Although it included a constant b that Planck believed was fundamental, the subsequent shift from b to h was more than merely a relabelling. Planck’s derivation did not use energy quantization, and neither did it rely on Boltzmann’s probabilistic interpretation of entropy.
Max Planck put forward his theory of the quantized nature of the energy of electromagnetic waves, which gave rise to future quantum theories.
It is a form of energy that can propagate in a vacuum or material medium and shows wave-like and particle-like properties. Radio waves, microwaves, infrared, visible light, UV-rays, X-rays, gamma rays are electromagnetic radiation.
According to the temperature, all objects emit electromagnetic radiation. Objects having low temperature emit radio or microwaves (low-frequency waves), while objects having high temperature emit visible or ultraviolet light or even higher frequency radiations.
A black body is an idealized object that can absorb all electromagnetic radiation that comes into contact. After this, it starts emitting thermal radiation in a continuous spectrum according to its temperature. The radiation which a black body emits is called black body radiation. Stars almost behave like a black body.
The intensity of the radiation varies according to the wavelength and temperature of the object. At a given temperature, the intensity of light varies according to wavelength. This phenomenon was not explained by classical theory or Maxwell’s equation. Hence, Max Planck put forward his theory of quantization of energy or Planck’s quantum theory of radiation to explain this phenomenon.
Although “quantization” may seem to be an unfamiliar concept, we encounter it frequently in quantum mechanics (hence the name). For example, US money is integral multiples of pennies. Similarly, musical instruments like a piano or a trumpet can produce only specific musical notes, such as C or F sharp. Because these instruments cannot create a continuous range of frequencies, their frequencies are quantized. It is also similar to going up and down a hill using discrete stair steps rather than moving up and down a continuous slope. Your potential energy takes on discrete values as you move from step to step. Even electrical charge is quantized: an ion may have a charge of −1 or −2, but not −1.33 electron charges.
Planck managed to come up with a complex algebraic formula that accurately described the radiation of short waves. Soon Planck received the results of experiments with long waves. Based on the old formula, he derived a new one for them, then combined both and obtained a universal radiation law. Planck presented the results of his work at the Berlin Physical Society on October 19, 1900. Most of his colleagues, however, could not immediately appreciate the significance of the discovery.
Something had gone wrong, and Planck had to return to his desk to reconsider why the apparently fundamental derivation produced an incorrect result. The problem, it seemed to him, lay in the definition of the oscillator’s entropy. Planck immersed himself into work. He concluded that radiation consists of individual groups of atoms rather than a constant flux, as science believed.
On December 14, 1900, four weeks after presenting the first formula in the same hall of the Berlin Physical Society, Max Planck presented his hypothesis to the audience. He introduced a new constant, “h,” now called Planck’s constant, and the discrete portions of energy were called quanta. The value h (Planck called it the action quantum) is a fundamental constant. It is included in all basic formulas of theoretical physics and chemistry. Its numerical value is unimaginably small. Just as there can be no speed in the world greater than the speed of light, so there can be no “action” less than the Planck “quantum of action”.
Quantum theory did not owe its origin to any failure of classical physics but rather to Planck’s profound insight into thermodynamics. Specialists in thermodynamics focused on the relationship between the laws of mechanics and the two fundamental laws of heat – the principle of energy conservation and the second law of thermodynamics. This discussion looked at the status of statistical-molecular physics and therefore examined the fundamental question of whether all matter is composed of atoms. Although the two discussions had much in common, it was the latter in particular from which quantum theory emerged.
The author of the quantum theory himself was unaware of the importance of his discovery. For him, the quantum was a means to confirm the formula. The emission and absorption of energy by atoms and molecules did not occur continuously, as thought, but discretely – in certain “portions,” or quanta. This was the quintessence of Planck’s idea. It undermined the tenets of classical physics at their very core.
Planck’s Quantum Theory in brief
Planck’s quantum theory explains the emission and absorption of radiation. Planck’s quantum theory postulates are as follows – matter radiates energy or absorbs energy in discrete quantities discontinuously in the form of small packets or bundles. The smallest bundle or packet of energy is known as quantum. In the case of light, a quantum of light is known as a photon.
The energy of the quantum absorbed or emitted is directly proportional to the frequency of the radiation. So, the energy of the radiation is expressed in terms of frequency as follows- A body or matter can radiate energy or absorb energy in whole-number multiples of a quantum as nhv, where n is a positive integer. So, energy can be absorbed or radiated as hv, 2hv, 3hv, 4hv, etc., not in the form of 1.5hv, 2.5hv, etc.
Planck’s quantization of energy is described by his famous equation: E=hν
Planck’s work in thermodynamics led to the formulations of his quantum theory. To explain the colors of hot glowing matter, he proposed that energy is radiated in very minute and discrete quantized amounts of packets rather than in a continuous unbroken wave. Planck called the packets of energy quanta, and he was able to determine that the energy of each quantum is equal to the frequency of the radiation multiplied by a universal constant that he derived, now known as Planck’s constant. This number, expressed in terms of erg-seconds, measures the energy of an individual quantum. An erg is the amount of energy needed to raise a milligram of mass by a distance of 1 centimeter. Planck’s constant, expressed by the variable h in equations, is approximately 6.63 x 10(E-27) erg-second. Planck’s constant has become one of the basic constants of physics. It is used to describe the behavior of particles and waves at the atomic scale.
Quantum physics was born that way
Quantum theory was initially met with reluctance. Some considered it unrealistic, and others did not need it. Einstein first adopted it and later described it as follows: “It was Planck’s law of radiation that gave the first precise definition of the absolute magnitudes of atoms. It convincingly showed that there is a kind of atomistic structure of energy governed by a universal constant in addition to the atomistic structure of matter. This discovery became the basis for all researchers in twentieth-century physics. Without it, it would have been impossible to establish a valid theory of molecules and atoms and the energy processes governing their transformations. It shattered the framework of classical mechanics and electrodynamics and set a challenge: to find a new cognitive basis for all physics.
Later, after developing mathematical laws describing quantum behavior, the field previously called “quantum theories” or “quantum physics” became known as “quantum mechanics”.
According to John L. Heilbron, one could say that Planck’s second most important discovery was that of Albert Einstein. This is, of course, some artistic exaggeration, but there is some truth in the historian of science’s statement. Planck was indeed one of the first to appreciate Einstein’s writings and supported his young colleague’s career advancement. Planck was also instrumental in popularizing the term “theory” to describe Einstein’s famous work and introduced the term Relativitätstheorie (“theory of relativity”) into widespread use.
Throughout his distinguished career as a physicist and statesman of science, Planck maintained that the ultimate goal of science was a unified world picture built on absolute and universal laws of science. He firmly believed that such laws existed and reflected the inner mechanisms of nature, an objective reality where human thoughts and passions had no place. The second law of thermodynamics was always his favorite example of how a law of physics could be progressively freed from anthropomorphic associations and turned into a purely objective and universal law.
