Leibniz and Entanglement

By Michael F. Duggan

My doctorate is in American History with minors in Modern European History and Western Philosophy (mostly in the philosophy of science), so if you are a physicist and this seems like a dumb or commonplace idea, please just scroll through to the next essay.

One of my favorite thinkers is Wilhelm Gottfried Leibniz (1646-1716). A bona fide polymath, he is on my shortlist for the “smartest person who ever lived” (for me, the smartest people are those who posit an original, plausible, non-theistic cosmological model relative to the most advanced models of the day). In addition to his cosmological model, Leibniz made contributions in biology, computation, diplomacy, ethics, geology, history, the law, library science, logic, mathematics, philosophy, political theory, psychology and theology, as well as other areas. He famously invented calculus independently of Isaac Newton, and while Leibniz had the better notation, Newton had better lawyers. He wrote in at least 6 language and may have had understanding in as many as 12.1

Leibniz outlined his cosmological model in a short work written near the end of his life called The Monadology.2 It was not published during his lifetime. Where the Newtonian model is commonsensical and demonstrable, Leibniz’s outline is cryptic, rationalistic (as opposed to empirical), counterintuitive, and largely untestable. Interestingly, modern developments in physics (special and general relativity and quantum mechanics) showed that, although the model of Newtonian mechanics is useful as a heuristic instrument in predicting things like ballistic trajectories and orbital decay, it is not a an accurate representation of the true nature of the physical world. By contrast, Leibniz’s model dovetails with the ideas and models of modern physics and has been embraced by some prominent physicists.3 Thus, although the Newtonian cosmos was killed off by Einstein more than a century ago, the cosmology of Leibniz lives on as a productive model. The Monadology is also one of my favorite books.

On the night of April 25, 2022, I decided to read before going to bed and chose The Monadology. There are many fascinating ideas in this book and Leibniz presents them successively as short sections, as if working up from basic provisions to describe an overall outline or basis for the cosmos, to include consciousness. It reads as of he is merely transcribing something that he has already worked out in his head, inventing the rules of a functional universe as if he was God. Each section is like a brick in a building or like the monads (atoms) that make up his world. In section 17, for example, he beautifully and succinctly describes why consciousness cannot be accounted for or reduced to mechanical processes. His idea (a version of panpsychism) is that consciousness is an irreducible characteristic intrinsic to monads. This idea is one of the few remaining thorns in the side of the modern emergence (evolutionary) view of consciousness. This time I skipped ahead to sections 61 and 62.

In these sections, Leibniz describes the interconnectedness of all things in the universe and their instantaneous affect on one another, as instantaneous action at a distance. This struck me as conceptually identical to the modern idea of quantum entanglement, the “spooky action at a distance” that vexed Einstein and is a fly-in-the-ointment to the classical elegance and simplicity of his Special Relativity.

In the Einsteinian universe of special and general relativity, action is limited to the speed of light (with the possible exception of the expansion of space itself during the inflationary period).4 But Leibniz saw space as an abstraction of relationships of objects to one another as well a plenum of physical objects.

But Leibniz saw space as an abstraction of relationships of objects to one another as well a plenum of physical objects.5 He does not appear to have considered space itself (as opposed to objects in it) in Einstein’s terms as a realm with physical qualities, dictates, and limitations. Leibniz’s concept of space as abstraction knows none of the limitations of physical space.

Therefore, if we posit an underlying abstract universe that is an infinite mathematical matrix (as Leibniz does), then instantaneous action at a distance would be permissible. Given that Leibniz’s model does not preclude or prohibit Einsteinian space, then perhaps “spooky action at a distance” is a manifestation or function of this primal, mathematical realm on its physical overlay (as Pythagoras and Plato (and Max Tegmark?6) might believe). It would be the prior mathematical matrix overriding the limitations of the physical cosmos. As such Leibniz appears to be positing a robust idealist model in which abstractions exist actively in the world outside of of minds and beyond the relationships and ratios of known physical laws.

I do not know by what means or mechanism the abstract Leibnizian world would assert itself on the physical Einsteinian universe, but then nobody has described or explained the mechanism by which multiple universes peel off from each other during probabilistic events in the multiverse implied by the ideas of Hugh Everett.7 And yet his ideas are widely and increasingly embraced.8

I sent this idea in an unsolicited email to two prominent physicists and received no reply, so it is most likely a dumb idea with no future—an incongruous intermixing of two fundamentally distinct realms by a non-physicist, a meddling amateur—or else an idea that others have already hit upon in a different form. Anyway, there it is.

Postscript July 7, 2022
A few weeks after posting the essay above, I searched “quantum entanglement” and “Leibniz” on the Internet. One of the things that came up was a wonderful article from 2021 by Professor Ludmilar Ivancheva of Bulgaria titled “Leibniz’s Monadology and its insights concerning quantum Mechanics.”9 This article is an overview, an intellectual history, of the many areas in which Leibniz’s ideas either presage, inform, or find modern analog in modern physics. Turns out I was scooped by many years and in a multiplicity of areas that I had not even considered (e.g. the “holographic and fractal nature of reality;”). Although I should have known better, at least I have the satisfaction of having come up with an idea on my own, even if many others had hit on it long before.

Note

  1. https://history.stackexchange.com/questions/45824/how-many-languages-did-leibniz-speak
  2. See G.W. Leibniz’s Monadology, An Edition for Students, Nicholas Rescher, ed. (University of Pittsburgh Press, 1991).
  3. For example, see Lee Smolin, The Life of the Cosmos (Oxford University Press, 1997).
  4. Regarding inflation generally, see Alan H. Guth, The Inflationary Universe (Reading, MA: Addison-Wesley Publishing Company, Inc., 1997).
  5. Leibniz “also believed in the plenum. But he maintained that space is merely a system of relations.” See Bertrand Russell, A History of Western Philosophy (New York, NY: Simon and Schuster, 1945) 70. For a more in-depth discussion of the complexities of Leibniz’s concepts of space, see Benson Mates, The Philosophy of Leibniz (Oxford University Press, 1986) 227-240.
  6. The physical world seems to run on finely-tuned mathematical relationships. See Max Tegmark, Our Mathematical Universe (New York, NY: Alfred A. Knopf, 2014). See also Martin Reese, Just Six Numbers (New York, NY: Basic Books, 2001). Perhaps this fine tuning is the result of the cosmological natural selection suggested by Lee Smolin in The Life of the Cosmos and elsewhere. But these relationships allow the physical world to work the way it does. My idea is that a greater mathematical realm would allow a process not permitted by the limits of the physical world.
  7. Hugh Everett, III, “Relative State Formulation of Quantum Mechanics,” (Review of Modern Physics, v. 29, no. 3. July 1, 1957), 454-462.
  8. Tegmark, 228-29.
  9. Papers pf BAS Humanities and Social Science, Vol. 8, 2021, No. 2, https://www.papersofbas.eu/images/Papers_2021-2/Ivancheva.pdf.