The Need for a Quantum Theory of Light and Matter

Karma Dorjee. November 11, 2014 10:55 PM. 1676

Written by: Tenzin Rabga. Date : 27 July, 2013

There is no quantum world. There is only an abstract physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature…
[1]” – Niels Bohr

 

As Niels Bohr, one of the greatest physicists to have lived in the twentieth century, puts it, the relation between the observer and the observed lies at the heart of quantum mechanics. The uncertainty principle as formulated by Werner Heisenberg, puts a fundamental limit to the certainty with which we can ‘know’ about certain aspects of a system. For example, if we ‘know’ the momentum of a particle very precisely, the measurement of the particles’ position will be greatly compromised. This is not because of the lack of a better technology, but it arises by the virtue of the fact that when we quantitatively measure any aspect of the particle (could be momentum, position or energy), we interact with the particle. The act of observation changes the state that the particle was initially in. This is not so obvious on the scale of the ‘ordinary world’ (the quotation marks imply that scales are relative[2]). The scale of the ordinary world refers to the world in which Newtonian mechanics accurately provides us with an understanding of the physical world around us, a very deterministic picture of the world. When we see an object, the light bounces off the object, enters our eyes and forms an image on our retina, which we identify as an object with a certain shape and color. On this scale of events we neglect the interaction of light with the object being observed. Light as shown by Albert Einstein in his paper on the Photoelectric Effect and experimentally verified by R.A. Millikan, can be described as composed of massless particles now known as ‘photons’. These particles have momentum as by the virtue of their frequencies and hence are able to interact with other particles. Photoelectric Effect shows how it interacts with electrons in the metallic plates, knocking them out of their orbitals. This effect is negligible on the classical scales. However on the ‘quantum scales’ of the molecular and the atomic and even the subatomic levels, this effect cannot be neglected. If we use a form of radiation to measure the particles’ position, we are essentially shooting photons at it and observing where the photons bounce off from and where they pass through untouched. That gives us a sense of the particles’ locality. However, throwing a photon at it, imparts momentum on it, like hitting a billiard ball with another. Therefore the more precise our measurement of the particles’ position, our measurement of the particles’ momentum is bound to be greatly imprecise. All along this discussion it should be kept in mind that these arguments deal with the work of physicists, as Bohr expounds, as not to describe how nature is but what they can say about it.

 

Having elaborated on the quote at the beginning of this page, the mood should have been set for further discussion about the need for a new picture of the physical world. Till the late nineteenth century, Newtonian mechanics enjoyed dominance in the physics community as an accurate model of predicting not only the motions of the objects around us in the immediate surrounding but also of the planets in the heavens above. It was shortly after Einstein’s papers on Special and General Relativity that the Newtonian assumption of an absolute time and space were disposed. This had tremendous ramifications on the laws of physics that govern the motion of the planets and motions at speeds close to the absolute limit of the speed of light.

 

Alongside these developments, physicists were doing researches on the fundamental structure of the matter around us. J.J. Thomson in 1897 showed that there exists, negatively charged elementary particles in matter (assumed to be made up of indivisible building blocks called atoms). Followed by the discovery of a heavy, positively charged nucleus by Ernest Rutherford, the planetary model of the atom as seen in Fig 1.was developed. This model depicts atoms as made up of a heavy, positively charged and very highly compact nucleus with electrons orbiting around it. However classical mechanics and electrodynamics does not allow such an atom to exist. Such an atom with electrons revolving the nucleus in orbits predicts emission of energy in the form of radiations. This means the electron will slowly spiral into the nucleus and cause the atom to collapse according to the principle of energy conservation.

 

In addition to his groundbreaking work on the theories of relativity, Einstein also produced the paper on the Photoelectric Effect in 1905 and R.A. Millikan’s experiment showed exactly the kind of effects Einstein predicted. Light in the classical picture, is described as a wave. The experimental findings of the Photoelectric Effect are inconsistent with this description. They comply with Einstein’s depiction of light as composed of massless photons that carry energy by the virtue of their frequency. This suggests that the energy carried by light is quantized or discrete and not continuous. It comes in packets of these photons unlike the continuous picture that classical physics paints.

 

Another experimental result that had bizarre implications for the atomic models was the discrete energy levels of the electrons in the atoms. When a gas of atoms is heated to very high temperatures, every element emits a characteristic set of lines of color at different wavelengths. This discreteness observed in the emissions suggests that the electrons in the atoms can only jump from certain energy levels to others[3]. This means that the electrons can only be in certain energy levels. This cannot be explained by classical mechanics, which allows for the existence of continuous energy levels.

 

All these experimental findings shook the very foundations of Classical physics. It called for a reevaluation of assumptions, formulation of new models and a new way of describing the phenomena that were being observed. This led to the development of Quantum Mechanics. It builds upon the idea of indeterminacy of our measurements. It paints a random and probabilistic picture of the natural phenomena. Which many of the physicists including Einstein found very difficult to reconcile with, as is expressed by his famous quotation ‘Quantum mechanics is certainly imposing,’ Einstein said. ‘The theory says a lot, but it does not really bring us any closer to the secrets of the Old One. I, at any rate, am convinced that He does not play dice[4]’. This probabilistic model of the atomic world astounded many great thinkers in the early twentieth century and still continues to do so.

 

As in Bohr’s own words, ‘Anyone who is not shocked by quantum theory has not understood it.[5]’ To illustrate the non-intuitiveness and the bizarreness of this theory, let’s assume we have a simple set up for a double slit interference experiment. We shine light through these slits and observe interference patterns, which are characteristic of waves. However now let’s imagine we make the light very feeble such that only one photon is emitted at a time. The immediate question one might ask is through which slit did the photon pass. From the screen we see that the interference patterns, however vague they might be, indicate that the photon passed through both the slits. However if we block one of the slits with a detector, we observe that the photon passes through only one of them. Hence the photon doesn’t travel through both of the slits according to this observation. Therefore to sum up this experiment, the photon neither passes through only one of the slits, nor through both of them, nor through none of them. Considering all of these as four distinct states (passing through either one of them, passing through both at the same time, and not passing through at all), quantum mechanics explains that the photon is in a superposition of all these states. In other words, all these are equally viable states for the photon to be in with certain probabilities. When we measure the system, we force this superposition to collapse into one to the four states, which means, it is now in one of the four states and not in any of the other three states. This is one of the non-intuitive implications of quantum mechanics and lies at the heart of its’ explanation of the physical phenomena as a superposition of such states.

 

To further muddle up the boundaries between particles and waves, Louis de Broglie in his doctoral thesis in 1924, introduced this idea of matter waves. Drawing from Einstein’s work on the Photoelectric Effect, he showed that electrons have waves associated with their momentum. This has been generalized to incorporate all forms of matter and experimentally confirmed by the electron diffraction experiments done by Davisson and Germer[6]. Matter waves imply that what are normally considered to be particles (electrons, molecules, any form of matter) can exhibit wave like behavior, in this case, interference patterns.

 

Quantum mechanics considers these bizarre ideas and attempts to build a model of the subatomic world that explains the phenomena as we observe them. It is as many physicist find it, difficult to reconcile with, chiefly because it depicts the phenomena not as the deterministic dynamic of forces at play as Classical physics did, but as a probabilistic system with uncertainties and surprises. However it has been experimentally established to be the correct description of the phenomena that we observe at these levels.

 

About the author: Tenzin Rabga studied Physics at Massachusetts Institute of Technology, USA.

 

References:

1. P.A.M Dirac, The Principles of Quantum Mechanics. New York: Oxford University Press, 1958.

2. Walter Isaacson, Einstein: His Life and Universe. New York: Simon & Schuster Paperbacks, 2008.

3. Robert Eisberg and Robert Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles. John Wiley & Sons, 1985.

[1] As quoted in “The philosophy of Niels Bohr” by Aage Petersen, in the Bulletin of the Atomic Scientists Vol. 19, No. 7 (September 1963).

[2] Paul Dirac in his ‘The Principles of Quantum Mechanics’ pages 3 – 4 makes a case for this relativity of big and small and the need for the finiteness of our power to observe for there to be a well defined small.

[3] Line Spectrum is the set of lines of distinct colors (of distinct wavelengths) that is different for different elements. This is emitted when electrons are excited from their ground state to higher energy levels as in this case by heating the gas to high temperatures. When the electrons fall back to their ground state, they emit photons with certain energies that correspond to the energy difference between their ground and excited states.

[4] This is found in letter to Max Born. (Isaacson 335)

[5] Quoted in Heisenberg, Werner (1971). Physics and Beyond. New York: Harper and Row. pp. 206.

[6] Electrons were accelerated through a potential difference and directed onto a nickel crystal. A detector was placed and adjusted at various angles to measure the intensity of the electron beam. They observed a peak at around 50 degrees. This qualitatively demonstrates the validity of de Broglie’s hypothesis as it could only be explained as a result of interference of waves scattered by the lattice of the atoms in the nickel crystal. (Eisberg&Resnick 58)

 

Comments

Leave a Comment

Most Popular Articles