Early Quantum Mechanics

1. 19th Century problems

By the end of the 19th century, scientists had built up an extensive knowledge of how light and matter behaves, but this was almost entirely empirical.

The relationship between the wavelength of blackbody radiation and its temperature was not understood. No one knew how spectral lines were produced, and no one knew how light could travel through space as either a particle or a wave, since there is no aether.

The nature of matter remained just as elusive. No one knew why different elements have properties that appear periodic, and no one knew what causes fluorescence and radiation, or the identity of the particles that radioactive elements produce.

In the 1900s, all of these problems were found to be related to quantum mechanics, a new set of physical laws that seems to only apply to the microscopic world. Quantum mechanics shows that extremely small objects behave in a way that completely defies common sense, and has revolutionised our understanding of the universe.

Those that first witnessed this behaviour found it deeply disturbing, and some of the effects of quantum mechanics still seem surprising. The most visual example of this may be superfluidity, which allows liquids to climb vertical walls and escape their containers. The philosophical implications of quantum mechanics are so vast that they are still not fully understood.

Despite its strangeness, the unique predictions of quantum mechanics have never been proven false. In fact, the theory has been used to explain a wide variety of phenomena, including the behaviour of all known subatomic particles, and all forces but gravity.

It has also been used in chemistry and biology to explain, among other things, how our brain interprets different smells, and how photosynthesis works. Almost all modern technology relies on the laws of quantum mechanics to work, including transistors, microchips, and lasers.

2. Quanta

2.1 The Planck relation

The first problem to be solved was that of blackbody radiation. In 1900, German physicists Heinrich Rubens and Ferdinand Kurlbaum showed that Wien's law - which states that the peak wavelength of a blackbody is only dependent upon its temperature - does not apply to infrared light[1][2].

This problem was almost solved by British physicists John William Strutt, better known as Lord Rayleigh, and James Hopwood Jeans in 1905[3]. Rayleigh and Jeans did this by treating light as if it was made of waves. However, their theory did not work for ultraviolet light.

Ultraviolet light has a smaller wavelength than optical light. This means that it has a higher frequency, because more waves can travel across the same distance if they have shorter wavelengths.

In 1901, Wien's colleague, German physicist Max Planck, had already shown that he could describe the behaviour of some types of radiation if he assumed that objects absorb and emit light that has an energy proportional to the light's frequency[4].

Planck showed that the energies absorbed and emitted by blackbodies are 'quantised'. This means that only certain energies are allowed.

Planck showed that blackbody radiation is emitted in quanta, 'packets' of energy that depend on frequency, ν, and proportionality constant, h, which is known as Planck's constant. The only allowed energies, E, are found using:

E = h ν.

This means that energies of E = ¼hν or E = h2ν, for example, are not allowed.

Planck's theory seemed to work, but it was not thought to be a true description of nature until it was explained by German-Swiss-American physicist Albert Einstein in 1905.

Einstein showed that all electromagnetic radiation is divided into quanta, or 'particles' of light', which became known as photons.

Einstein stated that:

"when a light ray is spreading from a point, the energy is not distributed continuously over ever-increasing spaces, but consists of a finite number of energy quanta that are localized in points in space, move without dividing, and can be absorbed or generated only as a whole"[5].

2.2 The photoelectric effect

Einstein's theory explained the photoelectric effect, which German physicist Heinrich Hertz had discovered in 1887[6]. Hertz found that particles, later identified as electrons, are released from matter if it absorbs ultraviolet light.

In 1902, German physicist Philipp Lenard had shown that the energies of these electrons depend on the frequency, not the intensity of the light[7]. This could not be explained using Maxwell's theory of light. Einstein showed that electrons are only released when particular frequencies, corresponding to multiples of Planck's constant, are reached.

Diagram of the photoelectric effect, showing photons colliding with a metal, and electrons being emitted.
Diagram of the photoelectric effect on an atomic level, showing photons knocking electrons from atoms.

The photoelectric effect, photons are depicted in red and electrons in blue. Image credit: Wolfmankurd/CC-SA & modified by Helen Klus, original image by Dirk Hünniger/CC-SA.

The photoelectric effect would later be understood in terms of Danish physicist Niels Bohr's theory of the atom[8]. This shows that an electron absorbs energy from the photon and, if it gains enough energy, this will cause it to be expelled from the atom. The energy required to emit electrons from metals is known as the work function.

3. The double-slit experiment on photons

In 1909, British physicist Geoffrey Ingram Taylor showed that single photons can also act like waves. Taylor showed that even very low light sources, equivalent to "a standard candle burning at a distance slightly exceeding a mile" showed evidence of diffraction[9]. It appeared that single photons could display properties of both waves and particles.

Scientists then considered what would happen if Thomas Young's double-slit experiment was conducted using a succession of single photons[10]. If photons are waves, then an interference pattern should form. If photons are particles, however, then an interference pattern shouldn't form, as the photons must travel through either one slit or the other, and would have nothing to interfere with.

Diagram of the double-slit experiment with particles. Particles move through one of the two slits one at a time, forming two groups.

The double-slit experiment with particles. Image credit: inductiveload/Public domain.

Diagram of the double-slit experiment with waves. Waves move through both slits at once, causing an interference pattern, and producing more than two peaks.

The double-slit experiment with waves. Image credit: inductiveload/Public domain.

When this experiment was performed, what looked like a random distribution soon turned into an interference pattern. This implies that the photons split when going through the two slits, and reformed to be detected as single particles on the other side.

Credit: Leiden University, via stevenb990.

In order to see if this is what happened, later experiments placed a particle detector at each slit. But when this was done, an interference pattern didn't form; photons appear to behave as particles when equipment is used to detect particles, and as waves when equipment is used to detect waves.

The same results were found even when the detectors were placed on the other side of the slits, implying that the photon somehow 'knew' the detector would be there[11][12].

The wave-particle duality of light would later be extended to matter, and described by German physicist Werner Heisenberg's uncertainty principle and Austrian physicist Erwin Schrödinger's quantum wave equation.

4. References

  1. Rubens, H. and Kurlbaum, F., 1900, Sber. Preuss. Akad. Wiss., pp.929.

  2. Planck, M., 1900, 'On the theory of the energy distribution law of the normal spectrum', Verh. Deut. Phys. Ges, 2, pp.237-245.

  3. Baggott, J. E., 2004, 'Beyond Measure: Modern Physics, Philosophy, and the Meaning of Quantum Theory', Oxford University Press.

  4. Planck, M., 1901, 'On the law of the energy distribution in the normal spectrum', Annalen der Physik, 4, pp.90-100.

  5. Einstein, A., 1905, 'Concerning an Heuristic Point of View Toward the Emission and Transformation of Light', Annalen der Physik, 17, pp.132-148.

  6. Hertz, H., 1887, 'Ueber einen Einfluss des ultravioletten Lichtes auf die electrische Entladung' ('On the influence of ultraviolet light upon the electric discharges'), Annalen der Physik, 267, pp.983-1000.

  7. Lenard, P., 1902, 'Ueber die lichtelektrische Wirkung' ('About the photoelectric effect'), Annalen der Physik, 313, pp.149-198.

  8. Bohr, N., 1913, 'On the constitution of atoms and molecules', The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 26, pp.1-25.

  9. Taylor, G. I., 1909, 'Interference fringes with feeble light', Proceedings of the Cambridge Philosophical Society, 15, pp.114-115.

  10. Bohr, N., 1949, 'Discussion with Einstein on epistemological problems in atomic physics' in 'Albert Einstein: Philosopher-Scientist', Schilpp, P. A. (ed), The Library of Living Philosophers, Evanston.

  11. Kocsis, S., et al, 2011, 'Observing the average trajectories of single photons in a two-slit interferometer', Science, 332, pp.1170-1173.

  12. Manning, A. G., Khakimov, R. I., Dall, R. G., and Truscott, A. G., 2015, 'Wheeler's delayed-choice gedanken experiment with a single atom', Nature Physics, 11, pp.539–542.

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