Of Bootstraps and Bohm
It seems to be a feature of our cognitive makeup to seek underlying organising unities behind regularities we find. This probably has a link to something like Leibniz’s Principle of Sufficient Reason: there must be a reason why things are as they are.
However, as Hagedorn points out, we seem to be driven to see the big picture too (the whole):While SU(3) symmetry and the quark concept aim at satisfying some obviously deep-rooted desire of our mind, to reduce everything to “elements”, there is another, equally deep-rooted need in us to see the world an unity, as an entity in which the “elements” are no longer selfcontained, isolated objects but where everything depends on everything, where the whole is more than the sum of its parts and where even the “elements” become real only through their relation to the whole ([6], p. 106).
Hagedorn claims that these (just our old atomist versus One inclinations again?) are not in contradiction, as analysis and synthesis might be, but are complementary (in Bohr’s sense). We might then call this ‘Hagedorn Duality’. Neither gives a complete picture alone. Yet physics is often divided into two opposing camps as we have seen in the Weinberg-Anderson debate and others. Hagedorn calls them “quarkists” and “bootstrappers”. These represent two different ways of ‘getting to the bottom of things’: the first by finding the lego, the second by finding the relational structure (preferably a unique, self-consistent one).
The bootstrap approach Hagedorn refers to is worth delving into since it represents another way of doing physics that ‘might’ have been our present physics (see, e.g., [4])—indeed, it corresponds most closely to Anaxagoras’ theory. The bootstrap principle characterised Geoffrey Chew’s S-matrix approach to particle physics, and was based on the notion of ‘particle democracy’ (equal rights for particles: this was developed in the 60s...).
The approach was developed to understand hadrons (which quantum field theory was then struggling with), and supposed that there was an infinite spectrum of particles (laid along a ‘Regge trajectory,’ with ever rising masses), but, crucially, no one was more fundamental than any other, thus bypassing a standard particle physicist’s question: which particles are fundamental and which are composite? One could in fact view the particles as either fundamental (part of a composite system) or composite themselves.It is principles that do the work in this approach: one imposes on the S-matrix the conditions of crossing, Lorentz invariance, and analyticity. This approach morphed (via dual resonance models) into string theory, which originally started with the same ‘uniqueness’ mindset, but then faced the landscape problem of course, which transferred uniqueness to an entire multiverse. Hence, the principles are fundamental. This is in some way like Anaxagoras’ approach (ontologically speaking that is, with particles neither composite nor fundamental), but methodologically it is a top-layer fundamentalism. Indeed, this ties in somewhat to the mathematical links mentioned in the previous section, for the bootstrap approach is not based on equations of motion, but on the S-matrix and principles of invariance. In this way of carving approaches, it is more like Weinberg’s imperialism than the Anderson-style complexity approach, particle-democracy notwithstanding.
One might object that history shows that quantum chromodynamics was the ‘winning’ theory, and this is precisely in like with the reductionist-fundamentalist mindset: three cheers for micro-imperialism! However, Chew’s approach offered a genuine alternative, that was able to make accurate predictions and solve puzzles that orthodox quantum field theory couldn’t cope with at the time. There are other more obviously top-level yet nonetheless fundamentalist approaches.
There are other similar approaches that invert the usual fundamentalisms, and these, not surprisingly, tend to be monistic.
Attempts to geometrize physics (e.g. John Wheeler’s geometrodynamics, or even Einstein’s unified field theory) are of this kind: from pure geometry one tries to extract the particulate nature of the world as we find it (with discreteness, charge, mass, and so on, all falling out of the spacetime metric, or metric and topology). What is doing the work, in grounding the way the world is, and in grounding explanations, is the geometry as a whole. This is an example of fundamentalism in which the layer is not at the bottom, but at the top of the hierarchy. David Bohm explicitly draws attention to this feature, stating that Einstein’s unified field theory showed “in a concrete way how consistency with the theory of relativity may be achieved by deriving the particle concept as an abstraction from an unbroken and undivided totality of existence” ([3], p. 221). Likewise, the notion of inertia, understood in Machian terms, inverts the usual micro-reductive approach, with a body’s local inertia determined globally by the masses of all of the other bodies in the universe.Finally, Bohm himself [3] too had an alternative, the ‘implicate order,’ in which the higher-level was more fundamental. The level of particle physics was part of the ‘explicate order’: the world of appearance, which is as it is due to our measurements. The implicate order, underlying it, has something like the structure of Leibniz’s monads (and is more like Anaxagoras’ approach): each region of spacetime, and each particle, reflects the whole universe, and so one can answer puzzles such as why all elementary particles have the same properties—recall that Wheeler famously answered this question, “why are electrons the same?”, by postulating a single electron zig-zagging backwards and forwards through spacetime. The local includes the global: “whatever part, element, or aspect we may abstract in thought, this still enfolds the whole” ([3], p. 172). But there is a sense, as with Chew’s approach, in which this has kinship with Parmenides:
The entire universe has to be understood as a single, undivided whole, in which analysis into separately and independently existent parts has no fundamental status ([3], p.
221).Bohm had personal reasons for following this ‘wholeness’ view, since he believed that how we conceptualise the fundamental nature of reality has a bearing on how we relate to the world and one another. Viewing the world as so many independent, separate entities leads to an independent, separate existence, with all that entails in terms of (social) divisions. Adopting a mentality of one unified system eliminates divisions and establishes us as part of the same whole.
This approach, like the others we have mentioned, is part of a persisting tendency to make what is fundamental different from what we see and are immersed in. It must be bigger, or smaller, or more abstract, or more logical, or more something. It is the relationship of Plato’s cave and its contents as compared to the shadows these contents cast. It is the veil of Maya. However, we chose to define “fundamentality” going forward, we cannot fail to recognise that it will simply be the next chapter in this age old story.