3.4.7 What is “Free Space?”

An Æther By Any Other Name…

Permeability and permittivity work together in another important way that was not appreciated by Maxwell and his contemporaries. The square root of the ratio of permeability to permittivity is a resistance-like quantity called the free-space impedance of the fields: Z_o = √(μ_0/ε₀) = 376.7 ohms. The free-space impedance provides the ratio of the electric field (|E|) to the magnetic field (|H|) for an isolated electromagnetic wave propagating in free space: Z_o = |E|/|H|. It’s like Ohm’s Law, but for fields. This condition also requires that the electric and magnetic fields convey the same energy. An electromagnetic wave carries equal amounts of electric and magnetic energy at the speed of light. If an interaction upsets this balance, the field impedance changes from the default value of the medium, and some of the energy will slow down and may change direction. Since fields always propagate at the speed of light, this has fascinating implications for understanding how fields and energy work together, to be further addressed in Book III. For now, though, let’s answer the question: what is free space?

Renaissance physicists dispelled the Aristotelian plenum and the “horror vacui” in experiments that demonstrated essentially all physical matter could be removed from within an enclosure. Without the medium of air to propagate sound waves, bells “rung” in a vacuum remained silent, and yet light – increasingly regarded as a wave motion – continued its wave propagation. The existence of waves implies a medium. In addition, Faraday’s lines-of-force suggested seemingly “free space” was rife with tensions, pressures, and other properties of physical media. This evidence reinforced the idea of a medium, dubbed “the æther,” as the seat of these physical properties. Later experimental evidence, to be discussed in Book II, cast doubt on the reality of the æther. And yet, modern physicists still ascribe physical properties to “the vacuum,” implicitly confirming that the supposed nothingness has very real and measurable characteristics.

Historian of electromagnetism, Edmund Whittaker (1873–1956), observed in the introduction to his classic text, A History of Theories of Æther and Electricity:

A word might be said about the title Æther and Electricity. As everyone knows, the æther played a great part in the physics of the nineteenth century ; but in the first decade of the twentieth, chiefly as a result of the failure of attempts to observe the earth’s motion relative to the æther, and the acceptance of the principle that such attempts must always fail, the word ‘æther’ fell out of favour, and it became customary to refer to the interplanetary spaces as ‘vacuous’; the vacuum being conceived as mere emptiness, having no properties except that of propagating electromagnetic waves. But with the development of quantum electrodynamics, the vacuum has come to be regarded as the seat of the ‘zero-point’ oscillations of the electromagnetic field, of the ‘zero-point’ fluctuations of electric charge and current, and of a ‘polarisation’ corresponding to a dielectric constant different from unity. It seems absurd to retain the name ‘vacuum’ for an entity so rich in physical properties, and the historical word ‘æther’ may fitly be retained [[i]].

Figure 3.31: A 1933 portrait of Edmund Whittaker (1873–1956) [[iii]], left, and bust reputed to be of Parmenides (~515 BC) [[iv]].

“Free space” is a convenient alternative to “æther” that sidesteps the absurdity of pretending that nothing, a “vacuum,” is something with physical properties. Whether describing a vacuum or merely an unobstructed path through air, free space captures the concept that there is nevertheless something positive there with the property of supporting and conveying electromagnetic waves. “Out of nothing, nothing comes,” declared Parmenides (~515 BC) [[ii]]. In other words, you cannot get something from nothing. We should embrace this ancient wisdom.

Next time: 3.4.8 Maxwell's Methods and Views: The Profound Meaning Behind His Math.

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References

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[i] Whittaker, Edmund, History of the Theories of Æther and Electricity, vol. 1, New York: Thomas Nelson & Sons, 1951, p. v.

[ii] Barnes, Jonathan, Early Greek Philosophy, New York: Viking Penguin, 1987, pp. 132-133.

[iii] A 1933 portrait of Whittaker by Arthur Trevor Haddon titled Sir Edmund Taylor Whittaker. See: https://en.wikipedia.org/wiki/E._T._Whittaker#/media/File:Edmund_Taylor_Whitakker_by_Arthur_Trevor_Haddon.jpg

[iv] Head from a (1^st century?) herm discovered at an excavation in Velia in 1966. The body of the herm had been discovered in 1962, with the inscription “Parmenides the son of Pyres the natural philosopher.” It is unlikely that the sculptor knew what Parmenides looked like, and it is believed that this portrait is actually based on the bust of the Epicurean philosopher Metrodorus. See: https://infogalactic.com/info/File:Parmenides.jpg