Discover How We Came to Know the Cosmos

Chapter 8. Origin of Quantum Mechanics

18th December 2017 by Dr Helen Klus

8.1 19th Century problems with physics

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, which means it was based on observations without a theoretical explanation.

The relationship between the colour of a blackbody and its temperature was not understood. No one knew how spectral lines were formed, and no one knew how light could travel through space as either a particle or a wave, since it had been shown that there’s no such thing as the 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 seemed 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.

8.2 The discovery of quanta

8.2.1 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 only depends on its temperature - does not apply to infrared light.[1,2]

This problem was almost solved in 1905 by British physicists John William Strutt, better known as Lord Rayleigh, and James Hopwood Jeans.[3] Rayleigh and Jeans did this by treating light as if it is 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 a proportionality constant (h), which is known as Planck’s constant. The only allowed energies (E) are found using:

E = hν (8.1)

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]

8.2.2 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, and Einstein showed that electrons are only released when particular frequencies, corresponding to multiples of Planck’s constant, are reached:

Energy of photon = Work function + Kinetic energy of electron (8.2)
hν = Φ + 1/2mv2 (8.3)

Here, m is mass, v is velocity, and Φ is the work function. This is the energy required to emit electrons from matter, and varies depending on the material.

Diagram of the photoelectric effect, showing photons colliding with a metal, and electrons being emitted.

Figure 8.1
Image credit

The photoelectric effect.

The photoelectric effect would later be understood in terms of Danish physicist Niels Bohr’s theory of the atom[8] (discussed in Chapter 10). 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.

8.3 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 placed almost 2 km away, 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 a single photon must travel through either one slit or the other, and would have nothing to interfere with.

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.

In order to see if this is what happened, later experiments placed a particle detector at each slit. However, 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 (discussed in Chapter 15), and described by German physicist Werner Heisenberg’s uncertainty principle (discussed in Chapter 16) and Austrian physicist Erwin Schrödinger’s quantum wave equation (discussed in Chapter 17).

8.4 References

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

  2. Planck, M., Verh. Deut. Phys. Ges 1900, 2, 237–245.

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

  4. Planck, M., Annalen der Physik 1901, 4, 90–100.

  5. Einstein, A., American Journal of Physics 1965 (1905), 33, 367.

  6. Hertz, H., Annalen der Physik 1887, 267, 983–1000.

  7. Lenard, P., Annalen der Physik 1902, 313, 149–198.

  8. Bohr, N., The London Edinburgh and Dublin Philosophical Magazine and Journal of Science 1913, 26, 1–25.

  9. Taylor, G. I., Proceedings of the Cambridge Philosophical Society 1909, 15, 114–115.

  10. Bohr, N. in Albert Einstein: Philosopher-Scientist, (Ed.: Schilpp, P. A.), The Library of Living Philosophers, Evanston, 1949.

  11. Kocsis, S., Braverman, B., Ravets, S., Stevens, M. J., Mirin, R. P., Shalm, L. K., Steinberg, A. M., Science 2011, 332, 1170–1173.

  12. Manning, A. G., Khakimov, R. I., Dall, R. G., Truscott, A. G., Nature Physics 2015, 11, 539–542.

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How We Came to Know the Cosmos: Light & Matter

I Pre 20th Century theories

1. Atoms and Waves

2. Reflection, Refraction, and Diffraction

3. Newton's theory of Light

4. Measuring the Speed of Light

5. 19th Century Wave Theories

6. 19th Century Particle Theories

7. Spectral Lines

II Quantum Mechanics

8. Origin of Quantum Mechanics

9. Development of Atomic theory

10. Quantum Model of the Atom

11. Sommerfeld's Atom

12. Quantum Spin

13. Superconductors and Superfluids

14. Nuclear Physics

15. De Broglie's Matter Waves

16. Heisenberg's Uncertainty Principle

17. Schrödinger's Wave Equation

18. Quantum Entanglement

19. Schrödinger's Cat

20. Quantum Mechanics and Parallel Worlds

III Quantum field theories

21. The Field Concept in Physics

22. The Electromagnetic Force

23. The Strong Nuclear Force

24. The Weak Nuclear Force

25. Quantum Gravity

IV Theories of the mind

26. Mind-Body Dualism

27. Empiricism and Epistemology

28. Materialism and Conscious Matter

29. Material theories of the Mind

30. Material theories of the Mind vs. Descartes

31. The Mind and Quantum Mechanics

32. The Limitations of Science

V List of symbols

33. List of symbols

34. Image Copyright