This post is a sort of a record of my as yet failed attempt to fully satisfactorily answer a certain question that had occurred to me. We will come to a more precise version of the question later in this post, but just to get going, let’s say, the question is something like this one: how many types of worlds does physics really describe?…
If the question looks odd, let me explain its meaning to you. [Suckers for the multiverse “theory”: this post is not for you. I continue to refuse to take it seriously.] The motivation behind the question is the following.
The first volume deals mainly with “mechanics, radiation and heat;” the second, with “electromagnetism and matter;” and the third, with “quantum mechanics.”
As I have argued before at iMechanica [link to be inserted], writing UG text “forces” you to be, say, integrative. If writing a text in the historical order (or reading one) forces you to think (at least implicitly) about the proper hierarchical order of concepts, writing a text for the UG students forces you to isolate the basic elements of a theory from its intricate offshoots and applications, distil the essence of the theory, and present it in as simple manner as possible.
Though I don’t believe that Feynman’s Lectures makes for a great text-book, it, nevertheless, is a great UG-level book. The book is wonderful, and like all such books, it makes you think a little “out of the box.”
Following Feynman’s book, I had sometimes wondered if the entire development of physics till date might not be divided neatly as: (i) Newtonian Physics, (ii) Electromagnetism, and (iii) Quantum Mechanics.
And, since I believed (and all physicists should believe) that physics deals with this (i.e. concretely real) material world (and not with mathematics/analysis/logic/symmetry/etc.), I also thought that if we can really divide the development of physics in the above-mentioned three broad periods or views, then there also must be an underlying statement concerning what kind of a physical world was being assumed and described by physicists.
Of course, the intent here was not to divide up the world metaphysically. Essence is epistemological, not metaphysical. So, the expression: “three kinds of worlds” was to be taken only in a loose, informal sense. Those were meant to be only three broad views of the physical world. And, a physical world, it emphatically was. Here, I was interested more in the philosophy of physics than general philosophy as such.
The temptation to do so seems to be quite “in the air” if not outright obvious.
The Newtonian “world” i.e. view is built with several distinctive elements: an “absolute” void of the space (as if a 3D, say Cartesian, grid were embedded in the world out there), an absolute and separate time, and solid objects (like planets) happily living in that void, moving about in a definite manner, capable of interacting with each other (or, literally speaking, exchanging momenta in finite intervals of time or forcing each other) mostly via direct contact. It’s a world that operates like a clock-work, or a billiards ball table.
The Maxwellian “world” may be taken to retain almost all the elements of the Newtonian world intact, and then simply add the idea of fields. The idea of a field is interesting. Most people, I think, would instinctively think of a field in terms like the following: The space between objects is not empty; it is filled with the electromagnetic fields.
The special relativity may be taken as just an implication of the Maxwellian electrodynamics, and so, though it seems to introduce complications (if not outright confusions) concerning the concepts of space and time, it still belongs right in that “classical,” Maxwellian, world.
The quantum “world” seems absolutely ridiculous in comparison. You know all its weirdities, and so, I won’t expand on them.
For quite some time, my reading seemed only to confirm this above-mentioned division into three worlds. For example, Gary Bowman even begins his book on QM [^] with an introductory chapter dwelling precisely on such a division. Before that, Munir Bhatti’s neat Amazon review [^] for Carver Mead’s book [^] had also suggested something very similar. And, these are just a couple of examples. If you go through lecture notes, blogging fora, etc., you tend to naturally reinforce the assumption of precisely such a division: mechanics of uncharged bodies, mechanics of charged bodies, and mechanics of quanta.
And so, I was thinking of presenting this division in a neat manner here on this blog, by way of preparing some material for my planned book on QM.
* * *
However, the more I went through the actual history of physics, consulted the timelines, and thought more deeply about it, the more the division began to seem artificial. Here’s how.
In the above discussion, I have spoken of the three worlds. But, really speaking, when I began to think about it on my own—as in contrast to “chewing” what others had said or indicated—I began with a different question. Here, I remembered what Leonard Peikoff had said in his book systematizing Ayn Rand’s philosophy (and, of course, what she herself had said in ITOE). Peikoff explains how our knowledge begins with specific, concrete objects. What we perceive first are only particular objects, not the “world.” The concept “existence” is only implicit in our perceptions, and its explicitly reached only at an advanced stage of development of knowledge. Applied to the realm of physics, I thought, it must be easy enough to spell out, first, the nature of the physical objects and the means and methods of their interactions, and if done right, that would take care of spelling out the nature of the three physical worlds by themselves.
I knew that QM would be the proverbial thorn, in this scheme. “Nobody understands QM,” we have been assured by our Nobel laureates. And, so, it would be difficult to succinctly spell out the nature of the physical objects that constitute the third, quantum, world, I thought. But it should be easy enough, I thought, with the first two worlds.
And, that’s when I ran into issues.
I could not convince myself that, “mechanics of uncharged bodies” and “mechanics of charged bodies” could make for a candidate description for the first two worlds. The proverbial hammer was thrown by two “things”: gravity, and electromagnetic fields.
Newton, it is widely believed, was the first to formulate the inverse-square law of gravity. Actually not. It was someone else. (Off-hand, was it Hooke?) Yet, it is correct to credit Newton with the discovery of the law of universal gravitation, because he was the first to explain the inverse-square law in reference to (i) a more basic set of laws, i.e. the three laws bearing his name today, and (ii) the methods of analysis (in particular, calculus). The mathematical proof that a spherical ball acts as if its mass is located at its center, via the ingenious argument of shells of that sphere, is due to Newton. Newton does deserve the admiration and adulation accorded him throughout history.
Yet, when it comes to presenting a good, philosophically sound view of the universe, Newton did fall short. When people asked him about the action-at-a-distance obviously implicit in his theory of gravitation, he entirely side-stepped that issue. And, the later Newtonians (who themselves were far lesser souls both intellectually and morally) made it look as if the issue does not merit any serious cognitive attention.
Yet, the fact is, the idea of a field is implicit right in Newtonian gravity. And, it throws hammer in our neat scheme. How come?
You see, take the Newtonian mechanics in its entirety—not just his laws and his applications, but also including all the later developments, e.g., the developments at the hands of the likes of the Bernoullis, Euler, Laplace and whonot, indeed, including even the development of continuum mechanics (i.e. mechanics of solids and fluids) and arguably even some heat transfer—but except for gravity, and we have (or, at least, we can have) a neat, consistent view of what kind of objects constitute this world. They all are definite in space, and exchanging forces only via the direct contact (which, incidentally, is a term that can be ostensively defined as consistent with what constitutes a physical object, in that world). Even mechanics of deformable solid bodies, and mechanics of fluids, are not exceptions: though a continuum may be taken, for mathematical convenience, to be infinite in extent, its defining properties always refer to a definite part (or volume) of that continuum; forces are always exchanged via direct contact of such parts. This characteristic of this world-view is important: it makes it a local theory. How come? If you divide a metal bar into three parts, then any momentum imparted at the leftmost end must first travel to the middle part before it can reach the rightmost part. In fact, even heat should behave this way. (That in Fourier’s theory it doesn’t, is a different story. And, BTW, such a nature of Fourier’s theory is yet another hammer thrown in the works of the building a neat, single, classical Newtonian world.)
In short, in the entirety of the Newtonian mechanics excepting for the theory of gravity, there always is a material object, or at least a definite part of a material object in reference to which all the important dynamical properties are to be defined. In particular, the property of momentum. The only way to force an object, i.e. the only way to change the momentum of an object, is for another, definite object to directly interact with it, say via collision, or at least via some exchanged at a shared boundary. On both sides of a shared surface are two material objects, each of which can be ostensibly pointed out in this material world.
The theory of gravity—even Newton’s theory of it—is the odd man out. Gravity is a form of a force, but (i) it is transmitted without a material medium and, (ii) in Newton’s theory, its action is instantaneous. The first is a more serious challenge, because it spoils the neat view otherwise built for our first world—a view of localized, definite objects exchanging momenta/energy through direct contact via a common surface (collisions or fluxes, in any case).
Now, in comparison, the electromagnetic field of the second world is much more “well-behaved.” At least the second-order changes in it don’t involve an instantaneous action at a distance. (Such changes have to be second-order because if you take the first-order changes, you have to take the two of them because there is a coupling between the two.)
So, now, a question arises: Where do we place the fields, esp., that of gravity? Is gravity an attribute of the distinct material objects (such as apples or planets), or is it an attribute of the “void” in between them.
The issue is not as simple as it might sound to you. If you say “the latter,” an immediate next question is: does gravity exist in a world devoid of the material objects like apples and planets? If so, what does it, you know, do? Forcing nothing is a contraction in terms—the definition of force involves the change of momentum of a material object like an apple or a planet.
And, if you are not still convinced (that there cannot be a force in a field if there is nothing to force from/to), then consider this. Here, there is one way which I find very convenient to think. It is to imagine as if all the objects in the universe were solid spheres of identical size, constant density, and a unit mass each. In such a world, what we call force is the same as acceleration. “Forcing” is nothing but another name for “accelerating.” Even if you hypothesize the existence of a definite, lawful, but massless physical object for the Newtonian gravitational field, i.e. one with identity, a question still remains: how do you define forces (i.e. accelerations) within this object? A massless forcing object can make sense but only when there is some mass to be accelerated.
Naturally, you have to attribute the phenomenon of gravity to the usual material objects: the stars and planets, for example. If so, you have come back to square one: You can no longer explain interactions via simple direct contacts between material bodies.
This theoretical complication is what Newton himself should have commented upon. But, he didn’t. His shortcoming.
And thus, we come to the precise version of the question which I said, at the beginning of the post, I will come to: “What is the nature of the physical objects that completely constitute physics theory? At least the physics theory, as it existed (i) after Newton but before the discovery of EM, (ii) after Cavendish, Coulomb, … Maxwell, but before Planck,” (iii) After Planck and till, say, 1935?
Now, in answer, even if you say something like: OK, here is this sun, and this earth and they not only emit light (the earth, if you include the IR thermal radiation), but also absorb a massless fluid of gravity. Every material object acts as a sink for this gravity-fluid. And, the “void” in between them is actually stuffed with that gravity-fluid. And, following the Poisson-Lapace equation (i.e. same thing as the good old inverse-square law, but put in a mathematically a bit more sophisticated form, with notions of fluxes and sources or sinks and all that), the action of absorption of the gravity-fluid produces the effect of forcing that object as per the law of gravity. All matter wants to come together, in short, not because that’s how matter wants to behave, but because the action of sucking up the fluid makes the object move towards the “center” of the void (i.e. the center of any pair of material objects). It’s rather like a pair of hungry monkeys ending up moving their faces ever closer to each other because even if not interested in kissing, they were only eating a common banana from its two ends. … And, errr… where does then that gravity-fluid finally go? Well, when all that material stuff finally comes together, like a tossed ball hitting the ground, this fluid might now begin oozing out, in a cyclical universe or something, you know—you might say that…
I won’t necessarily disagree. Cosmology is (relatively) easy to do. Being convinced that such seemingly bizarre fluid makes for a first-class object of physics is relatively harder.
And, yet, it’s not a question devoid of cognitive merit. The Newtonians (and their later-day avatars) notwithstanding.
In any case, it kills my initial neat theory of there being only those three worlds of physics. There are, now, four of them: (i) Colliding uncharged material objects; (ii) Colliding uncharged material objects sucking up (but not emitting) the gravity field-fluid; (iii) Colliding charged material objects either emitting or sucking the electromagnetic field-fluid; (iv) and, well, the quantum objects. (LOL!)
Left as an exercise for you: work out the nature of the quantum world, in this scheme. Hints: think if the attribute “charged” continues to make sense; think what precisely it means to say that particles are absorbed and emitted—e.g., is their sum-totality conserved? how?… It should be fun, even if:
(a) you may have to re-work many things, e.g., the conceptual basis of Bose’s statistics, what specific mechanics to assign to the force-carriers vs. to the emitters and absorbers;
(b) you may not be able to tell (unless you have read my papers) how to reconcile spatially discrete force-carrying massless particles (as in contrast to the all-pervading force-carrying electromagnetic field-fluid) with the impossibility of there being a literal void; and
(c) you won’t be able reconcile the simultaneous existence of the gravity field-fluid and these particles.
* * * * * * * * * * * * * * *
A Song I Like
[Heard for the first time just a couple of days ago, and instantaneously liked it!… Even if the (closest in a possibly long line of) “inspiration”(s) from “piyu bole, piya bole…” is obvious!!]
(Marathi and Hindi(!)) “Tik Tik vaajate Dokyaat…”
Music: SAY Band
Singers: Sonu Nigam and Sayali Pankaj (?)