Could Kuhn’s “Scientific Revolution” concept be applied to the wave–particle duality’s history? I

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In this present essay I discuss:

  • what is the nature of light and the discussions developed in such journey;
  • the importance of studying both philosophy and history of science;
  • how the works of Thomas Kuhn were essential to a better understanding of how a community of scientists structures itself;
  • how some aspects of a scientific revolution can be applied to the wave-particle duality historical period.

1. What is light?

“We know to tell many fictions like to truths, and we know, when we will, to speak what is true.” Hesiod

Let us say you wake up on a bright Saturday morning and out of the blue decide it is a good day to go out and ask people random questions about scientific things. You think valuable sampling is necessary, so in order to achieve high numbers and considerable diverse background, you choose O’Connel Street for a start. There are loads of people there who do not speak English, or even think anything else is better than have to face a cheerful Irish person disturbing their shopping stroll. Regardless, you proceed with your plan to discover what they thinks is the phenomenon of light and how it is linked to the notion of atom.

Probably some of them will recall basic physics and chemistry school lessons, and answer that “light is a wave, atoms are the tiniest constituent of matter, no connection between them two”, “light is composed of particles, so is the atom”, “light allow us to see the world around us and atoms are what we are made made of”, or they perhaps even go further and chat over stars, galaxies and the universe (I might be wishful thinking).

Point is, the commonest notion of the atom is based on an idea proposed more than twenty three centuries ago. In order to understand how our notion of the world might be reduced to invisible things, it is necessary to walk down a tenuous journey taking into account the evolution of human knowledge development and what “science”, along with its parts, means. Same goes to the understanding of light, a controversial subject central to our most basic human trait, present in everyday life without further questioning and wonder.

Kuhn already stated that Planck’s atomic quantum theory indeed was a scientific revolution, and the main objective of this essay is to find out if the changes on the concept of light (particle or wave?) during the years can also be classified as scientific revolutions.

First, it is utter necessary to address two interconnected areas of science: history and philosophy. Philosophers of science investigate the logical structure of scientific theories and the historical dynamics of their development, modifications, and even replacement. In a period posterior to World War II, most philosophers of science were logical positivists who believed that science involved two stages, going from empirical research to logical analysis of the results.

The study of history of science is relatively new compared to history itself: it started first in the United States in the 1950’s and later spread worldwide. Before the creation of such career path, practically everything we knew about science development resulted from researches and writings of historians who chose to specialize in science, and scientists who saw history as a by product of pedagogy (Kuhn, 1977).

For many years the pattern of presenting history of science to students was done through opening chapters in books, treatises and monographs, and usually was not mandatory to teach it. Consequentialy, many educators lacked interest and will to engage their pupils into deep tangled webs. This approach, or absence of it, can shine reasonably if we take into account the fact that we do not have any way of knowing what those scientists were thinking when they produced a certain piece of work. As I intend to explain further, neither does the own scientists which find themselves lost in other’s conclusions from previous scientific revolutions.

In history, the finished product of a research disguises the nature of the work that produced it (Kuhn, 1977), and even the thoughts and actions of people behind it. Both philosophy of science and history of science came to change because of the works Thomas Kuhn, Karl Popper, Imre Lakatos, and Paul Feyerabend developed in the 1940s and further.

Second, in order to categorize an event as a scientific revolution, we need to clarify what this means. This is going to be presented and explained later on. Regarding atomicity and light, most of what we know is well defined and was already well studied by specialists and those who know better, but it is important to address some moments in the history of science.

We came a long way since the start of splitting knowledge into segments. It all begun with astronomy, statics and optics, during the Hellenistic period, and such parts of physical sciences had their own vocabularies and techniques (exclusive to practitioners). From the fifth century B.C. onwards, we added mathematics and harmonics to the cluster of classical sciences, being the first a lingua franca adopted by the group and its defining factor of differentiation.

Not only Greece and the Mediterranean contributed to the cluster’s development, as we were taught at an early age, but Islam itself. Pinpointed in history 9 centuries after, it undergone a similar growth, specially in optics and algebra. The transitions of geometry to algebra, circular to noncircular orbits in astronomy, the new theory of vision, the first acceptable solution to the problem of refraction, and a completely new theory of colours were some of many others new chapters on the book of classical sciences written over Islamic studies (in contrast to European universities, Islamic universities were majority established and funded not by the state, but privately).

The frequent need for observations and experiments peeked astonishingly in the seventeenth century, as depicted in many treatises that reserve long chapters for the Enlightenment, and gave birth to a new experimental movement named after Francis Bacon: the Baconian inductive method of reasoning. Famous followers of this method were Gilbert, Boyle and Hooke, great performing experimentalists who rarely aimed to demonstrate what was already known.

Though one can, in principle, deduce the ability of flames to burn flesh, it is more conclusive to place one’s hand in the fire, but no one is going to do it just to prove a point. If Baconianism little contributed to new developments in classical sciences, it did give rise, nonetheless, to a large number of new scientific fields.

A remarkable specific trait of seventeenth century’s scientists as Galileo, Kepler, Lagrange, Descartes, and Newton was their easiness in changing study areas, going from mathematics to astronomy and statics, to optics and the study of motion. According to Kuhn (1977), while

“(T)he corpuscularism which underlies much seventeenth-century experimentation seldom demanded the performance (…) of any individual experiment, Newton’s prism experiment would have been no more effective than its traditional predecessors in transforming the theory of colours if (he) had not had access to the newly discovered law of refraction”

This shows a contrast in relation to previous nontraditional experiments responsible for revealing effects such as interference, diffraction and polarization. During the Scientific Revolution, transformations endured by the classical sciences were more related to new ways of looking at old phenomena rather than a series of unanticipated experimental discoveries.

Perhaps with the exception of his contemporaries Huygens and Mariotte, Newton set an incredible double mark, rarely seen in the eighteenth century and ahead: while his Principia lies within the tradition of the natural sciences, Opticks is unequivocally Baconian (Kuhn, 1977).

Optics was not a new field, being composed of theories and experiments (as documented on Boyle’s Experimental History of Colours), Newton, the last magician, then had the responsibility of juxtaposing and improving what was already known, but under a broader light. Before him, in the early seventeenth century, there were many philosophers of science seeking to replace Aristotelian concepts and, as a consequence, a new area of natural science arose: mechanical philosophy.

Based primarily on the works of Gassendi (a mixture of Christianity and Epicurean atomism in the void) and Descartes, light was of corpuscular nature, and this is how Newton portrayed it in his works. Refraction and reflection’s geometric nature could have only been explained if one assumed light is indeed a corpuscle, going against what Huygens preached. For him, light was a wave, as seen in Traité de la lumière when he discuss the intricacies of the phenomena of the double refraction of crystals and the atmosphere’s refraction.

Huygens’ works on wave theory were far from finished, but they opened up the road to Young’s and Fresnel’s studies on transverse vibrations and interference. Such conflict character regarding the nature of light prepared the stage to two different lines of thought: on one side sat the wave theory and on the other sat the corpuscular theory.

The fact Newton was much more famous than Huygens may have had an impact on how scientists favoured him for a while. Newton’s legacy and favouritsm lasted more than one hundred years. Practically all scientists at that time believed in the existence of ether (echoing Descartes), something indispensable to Huygens’ wave propagation, and witnessed a wide range of experiments showing the wave nature of light. Young’s single-slit experiment showed diffraction and interference patterns like those exhibited by energy waves, and after Young’s experiment, the bar started to weight towards Huygens’ theory (Buchwald, 1989).

A change of scenario in the nineteenth century was a consequence of the newly developed Maxwell’s theory of electromagnetism. Huygens, along with Rømer, proposed 22000 km/s for the velocity of light, which — due to the technological apparatus at the time — was a fair estimative. In 1862, Foucault obtained a value of 298,000 km/s, while Fizeau found 315,000 km/s. The value Maxwell calculated was somewhere in between the two. Such number appeared as a certain constant in Maxwell’s equations. This constant was deduced from the coefficient of aberration and the received value of the radius of the earth’s orbit, which was a result of applied mathematics to laboratory experiments’ values on electricity and magnetism.

Indeed, Maxwell’s equations showed wave-like solutions, and he proceed to calculate its velocity. He was probably surprised when his calculations linked to a number that happened to be close to the speed of light. In his 1864 paper, A dynamical theory of the electromagnetic field, he concluded that “the agreement of the results seems to show that light and magnetism area affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws”.

The world did not know what to do with Maxwell’s calculations for a while. It was so new that only twenty years after his publication, Hertz would come out with the radio waves. Technology is hardly hand in hand with the scientific development of an era, partially because, as Kuhn was going to formulate later in the twentieth century, theories take a time to settle down and scientists spend a considerable moment engaging in puzzle solving before encountering — if so — incongruities.

While physicists were dealing well with the wave behaviour of light, chemists were busy formulating and improving a better atomic theory for matter. Lavoisier, Dalton, and Proust kept their minds occupied with new laws such as conservation of mass, proportions, indivisibility. In the meantime, Mendeleev and Avogadro contributed to the creation of the Periodic Table and completed the basic atomic theory. But some things were about to change by the end of the nineteenth century.

Thompson discovered the electron in 1897, transforming the way scientists faced electricity: it would no longer be considered a fluid but a ray of ordered particles. Such discovery was a problem for classical electrodynamics because the theory was based on the notion of fluidity, so Maxwell’s fields (continuous wave-like entities) had to be re-thought.

Not only Maxwell’s theory called for a revision, but Planck brought up new studies in respect to radiation. After observing the spectrum emitted by a glowing object (hot objects glow, and hotter objects glow brighter than cooler ones), he published Über eine Verbesserung der Wienschen Spektralgleichung in 1900, a paper responsible for changing and shaking the structures at the time.

In it he expatiated about an ad hoc mathematical assumption of quantized energy of the oscillators that emit radiation (Kragh, 1999), a necessary move since there was no way of matching the equipartition theorem to the electromagnetic emission — the famous black body problem. We know that, when in equilibrium with light, a hot object absorbs just as much light as it emits, but if the object is black, then its thermal light emission is maximized since it absorbs all the light that hits it.

Prior to Planck’s work, it was a consensus that the energy of a body could take on any value (it was a continuous variable). Instead, Planck arrived at the conclusion that the light’s frequency emitted by the black body depended on the emitted oscillator’s frequency (a result from his equations of motion for light) and the energy increased linearly with frequency, multiply by a constant named after him (Planck, 1901).

There are an integer number of oscillators in thermal equilibrium with the electromagnetic field once they cease to exchange quanta. A quantum of light is formed when the oscillators give their entire energy to the electromagnetic field, and a quantum of light is absorbed when the oscillators are excited by the electromagnetic field. Planck’s theory is an atomic theory of the light and a quantized theory of the electromagnetic field, and while it seemed reasonable, not many physicists were happy with it — including Planck himself.

Einstein, after working alongside Planck in the quantized energy model, extended the thought to an old problem concerning the emission of electrons off a metal after light shone on it. He discusses, on the celebrated 1905’ work Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt, how the previous observation that the energy of those ejected electrons depended only on the frequency of the incoming light — not its intensity — could be mathematically explained by Planck’s energy quanta.

Like seen before, electromagnetic radiation, such as visible light, was considered to behave as a wave. That is why frequency and wavelength are terms used to describe radiation. Intensity is a light’s quality to which we attribute the relation of energy transferred in a given time, but this did not work when in terms of energy for the photoelectric effect. An increase in the light source’s intensity causes more photoelectrons to be emitted with the same kinetic energy, instead of the same number of photoelectrons to be emitted with higher kinetic energy. Einstein solved this issue by saying that light itself is quantized.

The energy of light is not transferred continuously like in a classical wave, but only in small packets of energy — in other words, quanta. These quantum of light were later named as photons. From this event on, Bohr was able to quantize the atom as an extension to Rutherford’s model, and we saw the birth of a completely new area of physics which is still producing loads of subareas and specialties.

We have seen de Broglie associate a wavelength characteristic to all matter. We have seen Heisenberg’s uncertainty principle dictate every single aspect of doubt in respect to the quantum world. We have reached a satisfactory explanation to the wave-particle duality thanks to the works of de Broglie and Bohm — also known as the Bohmian Mechanics — and we realized we are able to change the way the world is just by interacting with it. As we force a wave function to collapse, or as we see light as a connection between two fields, we can reach the conclusion that everything depends on the question we ask and the problem we are trying to solve.

You can continue reading this essay here :)

Science, education, and economics.

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