Some comments on QM and CM—Part 1: Coleman’s talk. Necessity of ontologies.

Update on 2020.12.10 16:02 IST:

I’ve corrected the descriptions in the ontologies of the Newtonian rigid bodies, Newtonian gravity, and Newtonian deformable bodies. (In particular, the idea of the continuum goes back to Newton’s shells-based argument to make a point-particle out of a sphere.) I have also added considerably to all the five pre-quantum ontologies.

Before getting going, let me briefly mention an update concerning my RSI.

0. RSI:

Good news: After taking an almost complete break from typing for may be 3–4 weeks, my RSI seems to have subsided significantly.

Bad news: It still is palpably lurking in the background. If I type a bit, I don’t get pains as such. However, certain subtle but easily identifiable early warning signs do appear. Like, a bit of soreness or stiffness at the base of thumb/fingers or at the wrist, etc.

Current course: I do not type for more than 30–40 minutes at a stretch. I force myself a break as soon as I notice that the time is up. I take rest of at least one hour before returning to the keyboard.

Let’s see.

1. Professor Coleman’s talk:

Sidney Coleman was a professor of physics at Harvard. I came to know about him through other physicists talking / writing about him. I think that so far, I’ve watched just parts of one or two video lectures of his (the ones from a course on QFT).

In these videos, I think that he was assuming that he was talking to rather sharp people. He did seem to care quite a bit about making very careful statements. Yet at the same time, he also seemed to pull it off quite effortlessly. Actually, he seemed to carry a very informal air about him—i.e., even while being in the middle of a rigorous point. Also, a certain kind of spontaneity, and an in-built sense of humour. … If you knew the background of the topic, you could expect to remain hooked to the lecture all throughout, but you wouldn’t be quite spell-bound, really speaking: his very style of presentation would make sure that you would want to remain active. … Thus I gathered that there was ample truth to how other physicists were describing him. In a way, he came across as if he were the very idea of the physicist, personified. I had actually thought of that phrase before running into how the Wiki article [^] describes him:

He’s not a Stephen Hawking; he has virtually no visibility outside. But within the community of theoretical physicists, he’s kind of a major god. He is the physicist’s physicist.

That’s why, when Prof. Peter Woit (of Columbia Uni.) highlighted a line by Coleman in a recent post at his blog [^], I immediately went ahead and downloaded the paper [^]. Actually, it’s not a paper; it’s a transcript of Coleman’s Dirac Prize lecture. [PS: If you are into watching videos, it’s on YouTube, here [^].)

The problem is not the interpretation of quantum mechanics. That’s getting things just backwards. The problem is the interpretation of classical mechanics.

Aha!

2. One little entry from my research notebook:

It was just a few days ago that I was thinking about QM and CM, and had noted something in my handwritten “journal”. The entry was made on 03 December 2020, 10:58 IST; it was noted down in a very hurriedly manner, using a pencil. Here’s a snap-shot of the same. …I usually don’t share such things (even if I am not afraid of those “handwriting” experts), but here I am making an exception—more or less on a whim:

An entry from my handwritten research notebook/logbook/journal.

Inserting some parenthetical clarifications/addition in square brackets “[ ]”, the note reads:

“You never “see” a perfect circle, a singularity, an infinitely sharp boundary. Yet you use them [such concepts] in CM [classical mechanics].

The lesson [point] is: you don’t see CM abstractions. You only perceive *some* of the objects. You never perceive a field. Ever. You only perceive its effects on a massive charged body.

And, Stat. Mech. has randomness.

[Note completed at 11:01 IST [same day]].

My notes are almost always like that. They are scribbles, not notes. Written in a very hurried way, often without taking a hard thing for a pad underneath. My notes are basically meant only for me. They are just a means to jiggle my memory so that I don’t lose hold of some point that I notice is passing through my mind rather quickly. That’s why, they are not likely to make full sense to most anyone (and often don’t give my correct position either—they are just points noted).

[Parenthetical clarifications: Yes, I went to Marathi medium schools. No, they didn’t teach the cursive in Marathi medium schools. Yes, I taught the cursive handwriting myself. In my XI standard. I used the Barge Surekha slate (which was quite a new invention back then). It took me more than one year to get used to it. Yes, my handwriting varies a lot—much more than others’. No, I usually write in ink. Enough?]

Alright. Let me explain what I meant by the above note. In doing so, I am going to add a lot of background and explanatory material too. Indeed, as it so happens, I have to split this blog post into at least two parts, this being the first.

3. Starting point of a physics theory:

The starting point of a physics theory is not any of the following:

• Illustration of simple applications, say using sketches, photographs, simulations, or interactive media
• Definition of terms used in the fundamental laws
• Statements of the fundamental laws
• Notation being used
• Governing equations
• Proofs of the governing equations
• Description of experiments that led to the theory
• Etc.

The starting point of a physics theory is:

some object(s), including their actions, posited in it.

Any theory of physics describes actions of some or the other object(s).

In physics, the laws governing some phenomena are often stated quantitatively, via some equation. Thus, the laws are stated in terms of the sizes of causes and of effects. But causes and effects do not exist as disembodied entities. They directly or indirectly refer to some or the objects that undergo lawful changes.

The identity or the nature of an object is the cause, and the actions it takes are the effects. That’s causality at the most basic level for you. (Causality is not at all restricted to an orderly progression in time. For more on causality, see my earlier post here [^].)

So, objects are, logically, starting point of a physics theory—an already developed theory.

However, the process of development of a theory doesn’t start with well defined ideas regarding what objects it posits and uses. It begins only with some loosely organized body of knowledge, and makes a phenomenology out of them. Some degree of good phenomenology must exist before the activity of theory building proper can occur.

4. Phenomenological context:

Much before a physical theory is built, there already comes to be a large body of interrelated items of observational or phenomenological knowledge. Such prior observations include those that are made before any hypothesis has ever been formulated, before any experiment is ever designed or conducted.

The knowledge may not be well integrated, and its items may not be rigorously formulated. But it is knowledge, all the same.

The body of such pre-existing knowledge includes (but is not limited to): descriptions of arrangements or configurations of various kinds of objects, miscellaneous items of condensed descriptions, rules of thumb that seem to work, observations of regularities, and even items of mere imagination (e.g. conjectures).

So, it all is a big mess. But such a mess must exist before a neat theory can at all get built. Indeed, any one who intends to build a theory must make himself well conversant with (if not an expert of) all that mess. They call this mess “phenomenological context”.

Thus, there is a lot of background material before a theory begins to get built. Due to the nature of concept formation, a theory cannot make sense except in reference to such (logically and chronologically) preceding background material.

5. The Objects-Identity-Actions form:

If you decide to condense all the background material relating to some physical phenomenon, you will soon find that it inevitably acquires this form:

There are a certain kind of objects, and when subject to certain physical conditions (say of interactions with other objects that themselves may be only loosely specified), the objects under study do something peculiar/ interesting/ outstanding/ important.

Why does your description acquire the form of: objects-their identities-their actions? That’s a deeper philosophical point than we care to look into, right now. But it’s there. It’s a metaphysical-epistemological thing, not a thing of just linguistics. You must first assume that something exists, before you can make any statement (about any thing). The ontological idea of a “physical object” is rooted in that profound statement. Let’s leave it at that.

6. Astounding variety of physical phenomena:

Now, the next “obvious” point I want to make is this:

Physical phenomena differ very widely in their very nature.

Hot or cold weather affects objects, including your sense of temperature, in a radically different manner than the sound of a temple bell does, and both radically differ from how the birds fall silent during an eclipse. Phenomena differ radically. And, physical theories are ultimately nothing but pieces of knowledge that seek to explain phenomena in a lawful, causal, manner.

Since phenomena themselves are radically different from each other, physical theories covering them also end up making use of very different kinds of objects in their respective descriptions. The objects used in a theory of motions of objects are quite different from those in light, for example.

7. Identification of ontologies is a task neglected by physicists:

Now, it’s true that often, theorists don’t explicitly identify the deepest nature of the objects that appear in the statements of their laws.

Even in the earlier times, they didn’t always explicitly identify the ontological nature of the objects; rather, they often chose to rely on analogies. For example: Not knowing what the true nature of the static electricity was really like, some 18th century physicists posited an imaginary fluid for the electricity. So, a “special kind of a fluid” was the ontological object assumed in their theory. It must be assumed to exist, they thought, before Coulomb’s inverse-square law could make any causal sense.

In modern times, mere hints is all you get to hear from physicists—if at all. And then, at least in textbook presentations, a discussion of such ideas is completely left out. And that’s for a valid reason, too: There really is not enough time at the disposal of the teacher or the student. The interested student, therefore, must refer to other books like history of science, encyclopaediae, or even good pop-sci books.

So, the point for now is: Working physicists, even theory builders among them, tend to focus on the narrow technicalities of their speciality, the narrow range of the phenomena under study. In the pursuit of precision in their statement of the laws of physics, they tend to focus on formulating quantitative laws that work satisfactorily. However, in the process, they lose the precision in the ontological sense—and they don’t even notice this fact.

They don’t even use the word “ontology,” or, God forbid, “metaphysical nature.” The best of them say “qualitative nature”. However, with the advance of the catastrophe theory, this latter term has again acquired a rather narrow, mathematically defined, meaning.

Further, the roots of the mathematical concepts being very hard to identify, physicists altogether leave the issue of explicitly identifying the ontological nature of the underlying objects they do assume to exist in their theories.

It is the task of ontology to identify, clarify and explain such ideas and issues as given below:

the basic types of objects used in a theory, their nature, the kind of actions they take, how they interact with other objects, the restrictions placed on their actions and interactions, etc.

Thus, ontology of physics identifies the broad pre-physical (or “metaphysical”) nature of the objects that are actually used in a theory of physics. Let’s take an example to make this point clear.

8. But what is the “ontological nature” of an object? An example:

The physics theory of EM assumes that there are “fields,” and it defines a field mathematically: as a function of the physical space coordinates. That’s all the statements of laws of EM make use of.

It’s the task of ontology of EM to say that there is an aether whose attribute an EM field is. It is the ontology that proceeds to explain the characteristic way in which the aether transmits forces (or energies) within itself.

Hint: The aether is not at all like how the continua of engineering sciences. The fluids and solids, as used in engineering sciences (and physics of massive continua) transmit forces across definite regions lying internally within a given continuum. The idea of the mathematical cut, and of control volumes, so as to transform a continuum into a collection of definite (bounded) objects that are in direct contact (so that the earlier techniques of Newtonian mechanics of discrete bodies can be applied to them), happens to be present in both EM and engineering fluid/solid mechanics. But there are certain crucial differences regarding the nature of what all properties the continuum exhibits too.

See my ontologies series [^] for a 2019-level explanation for the difference of the EM ontology from the Newtonian mechanics ontology! I am giving an updated list immediately below.

9. Ontologies in physics theories—a minimal list:

As of today, I think that we can say that the following is a minimal list of different ontologies required by the science of physics (excluding the relativity theory, and its relation to other physical theories including the QM). I will also give some randomly selected pointers to make their nature graspable; such description is by no means carefully stated let alone comprehensive; it’s more or less completely on the fly.

9.1. Newtonian mechanics of particles and of discrete rigid bodies:

This ontology talks of forces exchanged between two or more inertia-possessing objects via the direct contact during their collisions (i.e. only for the duration of time they are in a point- or surface-contact), but not otherwise.

It has a special object of the empty space that offers no resistance to the motion of particles or rigid bodies.

Particles are point-objects. Rigid bodies have finite sizes, but can be represented as point-masses via the idea of the centre of mass. However, their finite size comes into picture in problems like forces exchanged by finite-sized bricks in a static wall—the transmission of force occurs over a surface, not through a single point.

The key idea in tackling the rigid body is that of taking the imaginary cut, so as to make a collection of many discrete rigid bodies out of a single continuous body that has no physically separated parts. This idea began with Newton himself when he formulated the shells argument and arrived at the idea of the centre of mass. But I guess it was Cauchy who gave the procedure of the mathematical cut the definitive form in which we understand such analyses today. (However, I will have to check with Truesdell before I confirm it.) Also see the ontology of deformable bodies (sec. 9.3) below.

9.2. Newtonian theory of gravity:

The key word here is: The instantaneous transmission of force across the empty space (i.e. an instantaneous action at a distance, or IAD for short). Otherwise, this ontology continues to have the same discrete objects of the previous ontology (whether point particles or rigid bodies).

Newton himself had surmised “strings” i.e. $1D$ objects as the medium that conveys the force of gravity to planets; he did not think of any continuous and $3D$ space-filling fields. However, he then decided to refuse to take any definitive position for the existence or otherwise of these strings, for a lack of evidence. (One of the key skills in science is learning how to carefully delimit your claim. Newton showed a natural mastery of this skill when he said: “I feign no hypotheses.” He meant something different from what a modern reader might think he meant.)

9.3. Newtonian mechanics of deformable continua:

The key idea here is not that a body may be a continuum. Even the rigid body already is a kind of continuum. The key idea here is that the control volumes internal to the continuum (which are obtained by taking suitable mathematical cuts), are no longer rigid bodies, but can deform.

Deformation of a finite body is a change in its size and/or shape. If you apply limiting processes to the internal CVs, you get an infinity of point-particles that together make up the finite body. With this view, the deformable continua can be seen, using more modern terminology, as carrying a non-uniform field of displacement vectors within itself. However, notice, the idea of fields as ontologically important aspects of continua came to be explicitly recognized only after Faraday’s lines of force and their mathematization into the concept of fields at the hands of James Clerk Maxwell.

As to the deformable continua, Newton again seems to have been the first to correctly address their mechanics, when he defined an internal shear force, and used it in the definition of the internal friction (viscosity) in fluids.

9.4. Fourier-theoretical description of changes in continua:

Fourier was the first to describe the changes occurring inside a continuum, in terms of some globally acting “waves”.

These waves aren’t necessarily the familiar travelling waves (as on the surface of an ocean) or even the standing waves (as the motion of a guitar string shows). The purely spatial aspects of these waves denote static waves (as in the wavy patterns left in the sand by water at a beach, or by wind in a desert). With the passage of time, the global waves of the Fourier theory do undergo changes. Thus, the purely spatial part too changes. But these changes don’t necessarily follow the laws of travelling or standing waves. In diffusion, the changes occur via exponential decay (and not sinusoidal time factors).

The key idea here is that the causal physical agents are localized in the frequency space, and not in the physical space. The frequency spectrum could, however, be continuous.

Effectively, this description means: IAD (instantaneous action at a distance). However, unlike Newtonian gravity, this IAD is not restricted to interaction between two point-masses via a straight line of no thickness. Fourier-theoretical IAD occurs at every point (an infinity of them) inside a finite or even infinite domain. You can interpret this IAD to mean: There is a simultaneous exertion of “forces” at all points in a domain, even an infinite domain. However, such forces cannot of arbitrary sizes, because their actions are subject to the appropriate time-evolution laws imposed on them. (In detail, the matter is related to how the sine and cosine waves combine and evolve.)

9.5. Electromagnetic fields in the aether:

All the ontologies so far dealt with objects that were electrically neutral (i.e. electrically uncharged and hence electrically inactive). Once you allow the objects to be charged, the peculiar ontology behind the EM theory kicks in.

Yes, the other attributes like mass/density, and capacity to move in space, carry momentum/kinetic energy, exchange gravity forces, and undergo internal deformations all remain intact. However,  the existence of electrical charges implies the existence of electrical and magnetic fields.

The key word here is what all modern physicists hate and rebel against: The aether.

The EM ontology assumes that there is a certain unmoved and unmovable object called aether. It offers no resistance to the motion of massive objects except when they are electrically charged. Thus, it replaces the “empty” space of Newton’s descriptions. When electrically charged objects are present in the control volume under study, the aether in the domain comes to carry continuous force fields. Thus, fields are nothing but attributes of the aether.

The trick of the mathematical cut again applies, as in all continua: adjacent CV’s are supposed to “transmit” fields via the direct physical contact, with zero divergence.

Realize, the aether transmits forces without any part of it (i.e. any CV within it) undergoing any deformation. This single characteristic requires us to posit a new ontology for the EM phenomena. Not many people realized this point—which, after the hindsight of 100+ years, looks rather simple to grasp! The idea that the internal CVs must undergo deformation is what marks the so-called “mechanical” view for the aether. In contrast, the EM aether must be seen as the background object whose internal CVs need not at all undergo any displacements, let alone relative displacements (i.e. deformations), for it to be able to transmit forces.

Even Maxwell continued to think in terms of the mechanical aether. Lorentz seems to have been the first to indicate the correct approach. (However, I haven’t yet read either Whitaker or Lorentz’ original works. So, I can’t be sure if Lorentz had fully reached the transmission-without-local-deformations viewpoint. The reason for my hesitation: I know that Lorentz was thinking in terms of deformations of a charged body when he formulated the transformations that go by his name.

In any case, Lorentz was the first to realize how to ultimately connect the other attributes mentioned previously (like mass/density, accelerations under forces, etc.) with the specifically EM attribute of charge. This connection is known as Lorentz’ force law; it is the “fifth’ equation” that is required in order to make a complete system out of Maxwell’s “purely” EM equations (18 in his system, reduced to 4 by Heaviside).

9.6. Ontology of quantum mechanics:

What is the key idea here?

Well, you don’t expect a short-n-sweet description for QM, do you?

And, even if I were to give you that, would you (the physicist) understand anything? So there.

I’ve begun writing a new document that will replace the Outline document of 2019 [^]. It will have some description concerning what kind of ontology we must expect if the QM postulates are to work. However, the specifically ontological issues are going to be spread all over the planned document. But yes, I am confident that you will come to have a very good idea concerning this ontology.

10. Pre-Quantum $\neq$ “Classical”:

The list of ontologies given in the section 9. above supersedes my previous writings on the ontologies in physics [^]. (However, a lot of the points spelt out in that series, of course, continue to remain valid.)

I hope that you can now appreciate the fact that:

Clubbing everything pre-quantum into the “classical” is not a good idea. There are at least five different ontologies operative for the so-called “classical” physics.

However, I admit, even I myself am getting used to calling it “pre-quantum” physics.

All the same, remember that, in saying just “classical” physics, there are contexts in which you cannot hope to have both precision/unambiguity and generality to your statements.

In the next post, I will come to connecting the objects of the Newtonian mechanics with the concrete objects you perceive in your perceptual field. That will lay down the context for understanding the research notebook entry I just shared in this post (I mean the photograph). It will then become possible to make further comments on what Coleman indicated.

So, in the meanwhile, if you are like me, go through Coleman’s paper [^]. Otherwise, i.e. if you like videos better, then go through the video available on YouTube [^].

A song I like:

(Hindi) तुम को भी तो ऐसा ही कुछ होता होगा (“tum ko bhee to aisaa hee kuchha”)
Singers: Kishore Kumar, Lata Mangeshkar
Music: Laxmikant-Pyarelal
Lyrics: Anand Bakshi

[Another song from my high-school days. That way, this song is not much above the usual average/good songs of Hindi film music. On second/third listen, I think this song is much above average; it definitely is, IMO, very good, if you think about it. … Apart from the nostalgic value, it’s a song I like for the style of rendering. …

You know, just take any Pandit/Ustaad Utterly Boring Guy from the Indian classical music, especially one who you much admire (or perhaps are a भक्त (“bhakta”) of), and ask him to take Kishore Kumar’s place in this song. Just do that, and record the “performance” for posterity. If replaying, make sure to play that rendering on an awesome sound system too.

Then, just relax back and see if you can enjoy anything of it! (And, more or less, ditto for any Utterly Boring Gal of the Indian classical music.) …

A good quality audio is here [^]. ]

History:
— 2020.12.09 19:53 IST: Originally published.
— 2020.12.10 16:02 IST: A significant (though limited) update effected. Noted at the beginning of the post.