Is Einstein's Theory of Relativity a Classical Theory?

What Makes a Theory Classical or Modern?

The Special Theory of Relativity is usually considered the archetype of Modern Physics – a typical, physics (as opposed to science history) text book, definition of Modern Physics is everything from Special Relativity and the Planck/Bohr theories of Quantum mechanics onwards.

However, there are many characteristics of “classical physics,” which allow for a more meaningful description than a simple textbook classification scheme. These aspects of classical physics include the use of “World Pictures” - either “Mechanical” (explaining the ether and charges as mechanical processes. Eg. Maxwell’s etheric vortices) or “Electromagnetic” (explaining inertia and other mechanical processes as effects of electromagnetism. Eg Larmor’s Electronic Theory of Matter.)[6], a reliance on empirical, experimental data to drive the detailed development of theory (eg Lorentz’s evolving theories of the electromagnetism.[1, 4, 5]) an incremental approach from a phenomenological explanation of a single experiment outwards towards an overall theory of the universe (again Lorentz’s electromagnetism and also the work of McCormmach’s Jacob [1, 2, 4-6]), a sense that classical physics is the physics of “pre WWI” physicsists, like Jacob and Cunningham – people who even once they were aware of relativity were unable or unwilling to understand it in the way Einstein intended it, and a relatively unimportant role played by observers in the processes of the universe [2, 4]. Although none of these characteristics can obviously be considered either necessary or sufficient, let alone both, several provide insight into what aspects of relativity can be considered classical physics. I will consider the special theory of relativity in the light of each of these aspects of classical physics, in order to show that while the results of special relativity are indistinguishable from similar classical results, the structure, basis and import of the theory are thoroughly modern.

In the era of Newton, and then the industrial revolution there was a movement to explain all things in terms of mechanics. This was known as the Mechanical World Picture. For example, Newton’s own corpuscular theory of light – which explained effects like refraction in terms of the motion of particles of light. Then, in the era of Maxwells’ equations, mechanical explanations of the ether were required – ranging from explicit microscopic machine pictures to Maxwell’s later very abstract “action”-based ideas [1].

Around the beginning of the Twentieth Century with the advent of widespread electrification theorists like Lorentz, Poincare, Larmor, Cunningham and Wein developed various Electro-Magnetic World Pictures, which attempted to explain mechanics in terms electromagnetism and charged particles. Electro-Magnetic World Pictures were considered quite successful in their day [5].

In 1905, (classical) physicists felt that EM was approaching “correctness” - a little more tinkering and Lorentz’s theory of the electron would be correct. Lorentz’s theory was a dynamical (force based) theory that “explained” “effects” such as the unobservable ether and the electron mass variation with velocity in terms of length contraction, apparent times and the interactions of electrons and the ether [5].

While working on his 1905 black body radiation paper, Einstein came to realise that light was discrete and could not be trusted to exactly obey Maxwell’s equations when dealing with effects on the scales of the electrons involved in the electromagnetic theories. Based on this observation, there was no way that a world picture based on Maxwell’s equations could be right – the basis on which they were building their theory was fundamentally flawed [5].

Einstein made an unprecedented move in the development of his theory. He abandoned all attempts to explain what stuff was made of. He was content to let matter, energy and fields exist without worrying about what they were for now. He instead developed a theory of how they moved (a kinetic theory) instead [5].

The theory of relativity was more a theory that specified the form the laws of physics would have to take in order that any future coherent investigation of a theory matter would be possible. In this way, the postulates of Einstein’s theory of relativity are dramatically different from the classical “world picture” based theories of his contemporaries, despite their generally identical predictions [5].

As discussed above, the classical theories that were Relativity’s “competition” were built incrementally – for example, Lorentz was engaged in a “physics of desperation” continually patching his Electromagnetic world picture with additional ad hoc postulates in order to explain each new experimental result, while carrying along the baggage of the last two centuries of physics – Newton’s Laws of velocity addition and the Ether. When, in 1907, when Kaufman published electron mass results that disagreed with the observationally indistinguishable theories of Lorentz and Einstein, Lorentz was unable to continue modifying his theory to match the results; He had reached the end of his “latin” and conceded that he would not be able to make an electron based theory work. By working in the classical fashion of constructing a theory that explained one experiment then extending it to further experiments little by little, Lorentz’s position was weaker than Einstein’s [1,5].

Einstein’s unique approach to his research into relativity extended beyond the rejection of all world pictures. By beginning with just two axioms of broad scope and unassailable foundation [3], Einstein had built his theory in the reverse fashion. As his theory encompassed the entire universe from the start, Einstein considered it impossible for him to be fundamentally incorrect on any specific result derived from his theory. Thus Einstein knew (and stated) Kauffmann’s results were incorrect [5].

Einstein’s rejection of empirical results is inherent in his thought experiments – by basing his reasoning on gedanken-experiments that could probably never be carried out (certainly not in 1905). [3] Einstein was creating a precedent that other modern physicists followed: There were many calculations carried out in quantum mechanics and quantum field theory that were not “real” as researchers worked up to the real calculations. In much the same way today’s string theorists are writing down their theories based on criteria other than matching experimental data.

Einstein and Lorentz had essentially opposite approaches to developing theories that combined electromagnetism and motion – Lorentz took Newton’s Laws and Maxwell’s equations and added further and further ad hoc assumptions to them to create a theory that matched, at least, the current experimental results [1,5]. Einstein instead threw away the entire theoretical framework of the last two centuries and, based on a few postulates – designed to eliminate paradoxes in his thought experiments – rebuilt all of physics [1, 3, 5]. In a sense, this approach is the forbear of Schrödinger’s and Heisenberg’s when they too abandoned the old quantum mechanics and laid down a new foundation of postulates on which the new quantum mechanics was built.

Those Physicists who in 1905 read “On the Electrodynamics of Moving Bodies” for the most part failed to see the revolutionary nature of what Einstein had done. Those with a strong belief in either the ether or an Electro-Magnetic world Picture, like Jacob and Cunningham respectively, as far as they understood the mathematics, took it to be vindicating their views [2, 4]. For example,

“The absence, as far as experiment can detect, of any phenomena arising from the earth’s motion relative to the electromagnetic aether has been fully accounted for by Lorentz and Einstein, provided the hypothesis of electromagnetism as the ultimate basis of matter to be accepted, so that the only available means of estimating distances between two points is the time of propagation of effects between the bodies, such propagation taking place in accordance with equations of electron theory.”[6]

Cunningham equates Einstein and Lorentz as having the same theory of the ether, the same as his theory, from his mentor, Larmor. Cunningham was able to show that the observational and mathematical results of special relativity were identical to the results that he got from the Lorentz transformations and the electronic theory of matter. In that sense we can say the results of special relativity were classical, even though they were based on the very modern structure that Einstein laid down, they were still the same classical results that Lorentz had found, and Cunningham had confirmed [1, 4, 5].

In Newton’s original theory of mechanics, space and time were absolutes, considered by Newton to be defined by God. When events happened, they happened in absolute space, and absolute time; the role of the observer was incidental. In the early theories of Maxwell, the ether became the fundamental frame where everything was defined. In this sense, there was the original idea that Physicists would be able to find this frame, or be able to find our velocity relative to it, by detecting the etheric wind [6]. When the attempts to detect this wind all returned no results, theorists like Lorentz and Poincare came up with their theories of matter that took the role of the observer backwards. Not only was the ether an absolute frame in which things really happened, but in their theories, the observer was not only unable to find the absolute frame, but also unable to make correct measurements in his frame [1, 5]. Observers would only be able to perceive the so-called apparent time, and their rulers would shrink and bend in the etheric wind.

Einstein’s theory finally brought observation to the forefront; time and space now became the property of the individual observer [1, 3, 5]. There was no fundamental frame. Everyone measured a real time, and a real position for every event. Observers moving at different speeds still didn’t agree on this values, but because of the postulates of the theory, everyone still sees the ‘same Physics’, especially everyone sees the same causality. Farther along the scale of modernity is quantum mechanics, which is undoubtedly a theory of modern physics, not classical physics. In Quantum Mechanics, the observer is an intrinsic part of his own experiment; the act of observing the result is what causes the result to appear. Moreover, there can’t be an absolute observer, always observing every particle, else nothing would ever be able to move (a sort of universal Quantum Zeno Effect).

Thus, we can see that the predictions of Einstein’s theory did not distinguish it from Lorentz’s theories in the first decade of the Twentieth Century, making the results classical in a sense. However, the way Einstein set up his theory – rejecting world pictures, throwing out the baggage of old theories to start with the simplest sufficient postulates, ignoring empiricism and radically changing the status of the observer within science, differed so drastically from his contemporaries it is hard to deny that the reasoning and postulates of relativity are definitively modern. By extension, it also must be accepted that Einstein’s interpretation of the results and meaning of relativity are modern too. Moreover, the fact that the “classical physicists” of Einstein’s day (with important exceptions) failed to grasp the modern aspects of relativity theory explicitly demonstrates the non-classical nature of these aspects.

References

[1] Galison, Peter. Einstein’s Clock’s, Poincare’s Maps (New York: Norton, 2003)

[2] McCormmach, Russell. Night Thoughts of a Classical Physicist (Cambridge: Harvard University Press, 1991).

[3] Albert Einstein, "On the Electrodynamics of Moving Bodies," in A. I. Miller (ed.), Albert Einstein's Special Theory of Relativity, pp. 392-415.

[4] Andrew Warwick, "Cambridge Mathematics and Cavendish Physics: Cunningham, Campbell and Einstein's Relativity 1905-1911: Part I: The Uses of Theory," Studies in History and Philosophy of Science 23 (1992): 625-656.

[5] Arthur I. Miller, Albert Einstein's Special Theory of Relativity: Emergence (1905) and Early Interpretation 1905-1911 (Reading: Addison Wesley, 1981), pp. 143-183

[6] Cunningham, E. “The Principle of Relativity in Electrodynamics and an Extension Thereof”, Proceedings of the London Mathematical Society 8 (1910): 77-98