Some of the implications of the “Many Objects” idea…

0. Context and Review:

This post continues from the last one. In the last post, we saw that the same perceptual evidence (involving two moving grey regions) can be conceptually captured using two entirely different, fundamental, physics ideas.

In the first description, the perceived grey regions are treated as physical objects in their own right.

In the second description, the perceived grey regions are treated not as physical objects in their own right, but merely as distinguishable (and therefore different) parts of the singleton object that is the universe (the latter being taken in its entirety).

We will now try to look at some of the implications that the two descriptions naturally lead to.

1. The “Many Objects” Viewpoint Always Implies an In-Principle Empty Background Object:

To repeat, in the first description, the grey regions are treated as objects in their own right. This is the “Many Objects” viewpoint. The universe is fundamentally presumed to contain many objects.

But what if there is one and only one grey block in the perceptual field? Wouldn’t such a universe then contain only that one grey object?

Not quite.

The fact of the matter is, even in this case, there implicitly are two objects in the universe: (i) the grey object and (ii) the background or the white object.

As an aside: Do see here Ayn Rand’s example (in ITOE, 2nd Edition) of how a uniform blue expanse of the sky by itself would not even be perceived as an object, but how, once you introduce a single speck of dust, the perceptual contrast that it introduces would allow perceptions of both the speck and the blue sky to proceed. Of course, this point is of only technical importance. Looking at the real world while following the first description, there are zillions of objects evidently present anyway.

Leaving aside the theoretically extreme case of a single grey region, and thus focusing on the main general ideas: the main trouble following this “Many Objects” description is twofold:

(i) It is hard to come to realize that something exists even in the regions that are “empty space.”

(ii) Methodologically, it is not clear as to precisely how one proceeds from the zillions of concrete objects to the singleton object that is the universe.  Observe that the concrete objects here are physical objects. Hence, one would look for a conceptual common denominator (CCD) that is narrower than just the fact that all these concrete objects do exist. One would look for something more physical by way of the CCD, but it is not clear what it could possibly be.

2. Implications of the “Many Objects” Viewpoint for Causality:

In the first description, there are two blocks and they collide. Let’s try to trace the consequences of such a description for causality:

With the supposition that there are two blocks, one is drawn into a temptation of thinking along the following lines:

the first block pushes on the second block—and the second block pushes on the first.

Following this line of thought, the first block can be taken as being responsible for altering the motion of the second block (and the second, of the first). Therefore, a certain conclusion seems inevitable:

the motion of the first block may be regarded as the cause, and the (change in) the motion of the second block may be regarded as the effect.

In other words, in this line of thought, one entity/object (the first block) supplies, produces or enacts the cause, and another entity/object (the second block) suffers the consequences, the effects. following the considerations of symmetry and thereby abstracting a more general truth (e.g. as captured in Newton’s third law), you could also argue that that it is the second object that is the real cause, and the first object shows only effects. Then, abstracting the truth following the consideration of symmetry, you could say that

the motion (or, broadly, the nature) of each of the two blocks is a cause, and the action it produces on the other block is an effect.

But regardless of the symmetry considerations or the abstractness of the argument that it leads to, note that this entire train of thought still manages to retain a certain basic idea as it is, viz.:

the entity/actions that is the cause is necessarily different from the entity/actions that is the effect.

Such an idea, of ascribing the cause and the effect parts of a single causal event (here, the collision event) to two different object not only can arise in the many objects description, it is the most common and natural way in which the very idea of causality has come to be understood. Examples abound: the swinging bat is a cause; the ball flying away is the effect; the entities to which we ascribe the cause and the effect are entirely different objects. The same paradigm runs throughout much of physics. Also in the humanities. Consider this: “he makes me feel good.”

Every time such a separation of cause and effect occurs, logically speaking, it must first be supposed that many objects exist in the universe.

It is only on the basis of a many objects viewpoint that the objects that act as causes can be metaphysically separated, at least in an event-by-event concrete description, from the objects that suffer the corresponding effects.

3. Implications of the “Many Objects” Viewpoint, and the Idea of the “Empty” Space:

Notice that in the “many objects” description, no causal role is at all played by those parts of the universe that are “empty space.” Consider the description again:

The grey blocks move, come closer together, collide, and fly away in the opposite directions after the collision.

Notice how this entire description is anchored only to the grey blocks. Whatever action happens in this universe, it is taken by the grey blocks. The empty white space gets no metaphysical role whatsoever to play.

It is as if any metaphysical locus standi that the empty space region should otherwise have, somehow got completely sucked out of itself, and this locus standi then got transferred, in a way overly concentrated, into the grey regions.

Once this distortion is allowed to be introduced into the overall theoretical scheme, then, logically speaking, it would be simple to propagate the error throughout the theory and its implication. Just apply an epistemologically minor principle like Occam’s Razor, and the metaphysical suggestion that this entire exercise leads to is tantamount to this idea:

why not simply drop the empty space out of any physical consideration? out of all physics theory?

A Side Remark on Occam’s Principle: The first thing to say about Occam’s Principle is that it is not a very fundamental principle. The second thing to say is that it is impossible to state it using any rigorous terms. People have tried doing that for centuries, and yet, not a single soul of them feels very proud when it comes to showing results for his efforts. Just because today’s leading theoretical physics love it, vouch by it, and vigorously promote it, it still does not make Occam’s principle play a greater epistemological role than it actually does. Qua an epistemological principle, it is a very minor principle. The best contribution that it can at all aspire to is: serving as a vague, merely suggestive, guideline. Going by its actual usage in classical physics, it did not even make for a frequently used epistemological norm let alone acted as a principle that would necessarily have to be invoked for achieving logical consistency. And, as a mere guideline, it is also very easily susceptible to misuse. Compare this principle to, e.g., the requirement that the process of concept formation must always show both the essentials: differentiation and integration. Or compare it to the idea that concept-formation involves measurement-omission. Physicists promote Occam’s Principle to the high pedestal, simply because they want to slip in their own bad ideas into physics theory. No, Occam’s Razor does not directly help them. What it actually lets them do, through misapplication, is to push a wedge to dislodge some valid theoretical block from the well-integrated wall that is physics. For instance, if the empty space has no role to play in the physical description of the universe [preparation of misapplication], then, by Occam’s Principle [the wedge], why not take the idea of aether [a valid block] out of  physics theory? [which helps make physics crumble into pieces].

It is in this way that the first description—viz. the “many objects” description—indirectly but inevitably leads to a denial of any physical meaning to the idea of space.

If a fundamental physical concept like space itself is denied any physical roots, then what possibly could one still say about this concept—about its fundamental character or nature? The only plausible answers would be the following:

That space must be (a) a mathematical concept (based on the idea that fundamental ideas had better be physical, mathematical or both), and (b) an arbitrary concept (based on the idea that if there is no hard basis of the physical reality underlying this concept, then it can always be made as soft as desired, i.e. infinitely soft, i.e., arbitrary).

If the second idea (viz., the idea that space is an arbitrary human invention) is accorded the legitimacy of a rigorously established truth, then, in logic, anyone would be free to bend space any which way he liked. So, there would have to be, in logic, a proliferation in spaces. The history of the 19th and 20th centuries is nothing but a practically evident proof of precisely this logic.

Notice further that in following this approach (of the “many objects”), metaphysically speaking, the first casualty is that golden principle taught by Aristotle, viz. the idea that a literal void cannot exist, that the nothing cannot be a part of the existence. (It is known that Aristotle did teach this principle. However, it is not known if he had predecessors, esp. in the more synthetic, Indic, traditions. In any case, the principle itself is truly golden—it saves one from so many epistemological errors.)

Physics is an extraordinarily well-integrated a science. However, this does not mean that it is (or ever has been) perfectly integrated. There are (and always have been) inconsistencies in it.

The way physics got formulated—the classical physics in particular—there always was a streak of thought in it which had always carried the supposition that there existed a literal void in the region of the “gap” between objects. Thus, as far as the working physicist was concerned, a literal void could not exist, it actually did. “Just look at the emptiness of that valley out there,” (said while standing at a mountain top). Or, “look at the bleakness, at the dark emptiness out there between those two shining bright stars!” That was their “evidence.” For many physicists—and philosophers—such could be enough of an evidence to accept the premise of a physically existing emptiness, the literal naught of the philosophers.

Of course, people didn’t always think in such terms—in terms of a literal naught existing as a part of existence.

Until the end of the 19th century, at least some people also thought in terms of “aether.”

The aether was supposed to be a massless object. It was supposed that “aether” existed everywhere, including in the regions of space where there were no massive objects. Thus, the presence of aether ensured that there was no void left anywhere in the universe.

However, as soon as you think of an idea like “aether,” two questions immediately arise: (i) how can aether exist even in those places where a massive object is already present? and (ii) as to the places where there is no massive object, if all that aether does is to sit pretty and do nothing, then how is it really different from those imaginary angels pushing on the planets in the solar system?

Hard questions, these two. None could have satisfactorily answered these two questions. … In fact, as far as I know, none in the history of physics has ever even raised the first question! And therefore, the issue of whether, in the history of thought, there has been any satisfactory answer provided to it or not, cannot even arise in the first place.

It is the absence of satisfactory answers to these two questions that has really allowed Occam’s Razor to be misapplied.

By the time Einstein arrived, the scene was already ripe to throw the baby out with the water, and thus he could happily declare that thinking in terms of the aether concept was entirely uncalled for, that it was best to toss it into in the junkyard of bad ideas discarded in the march of human progress.

The “empty” space, in effect, progressively got “emptier” and “emptier” still. First, it got replaced by the classical electromagnetic “field,” and then, as space got progressively more mathematical and arbitrary, the fields themselves got replaced by just an abstract mathematical function—whether the spacetime of the relativity theory or the \Psi function of QM.

4. Implications of the “Many Objects” Viewpoint and the Supposed Mysteriousness of the Quantum Entanglement:

In the “many objects” viewpoint, the actual causal objects are many. Further, this viewpoint very naturally suggests the idea of some one object being a cause and some other object being the effect. There is one very serious implication of this separation of cause and effect into many, metaphysically separate, objects.

With that supposition, now, if two distant objects (and metaphysically separate objects always are distant) happen to show some synchronized sort of a behavior, then, a question arises: how do we connect the cause with the effect, if the effect is observed not to lag in time from the cause.

Historically, there had been some discussion on the question of “[instantaneous] action at a distance,” or IAD for short. However, it was subdued. It was only in the context of QM riddles that IAD acquired the status of a deeply troubling/unsettling issue.

5. Miscellaneous:

5.1

Let me take a bit of a digression into philosophy proper here, by introducing Ayn Rand’s ideas of causality at this point [^]. In OPAR, Dr. Peikoff has clarified the issue amply well: The identity or nature of an entity is the cause, and its actions is the effect.

Following Ayn Rand, if two grey blocks (as given in our example perceptual field) reverse their directions of motions after collision, each of the two blocks is a cause, and the reversals in the directions of the same block is the effect.

Make sure to understand the difference in what is meant by causality. In the common-sense thinking, as spelt out in section 2. of this post, if the block `A’ is the cause, then the block `B’ is the effect (and vice versa). However, according to Ayn Rand, if the block `A’ is the cause, then the actions of this same block `A’ are the effect. It is an important difference, and make sure you know it.

Thus, notice, for the time being, that in Ayn Rand’s sense of the terms, the principle of causality actually does not need a multiplicity of objects.

However, notice that the causal role of the “empty” space continues to remain curiously unanswered even after you bring Ayn Rand’s above-mentioned insights to bear on the issue.

5.2:

The only causal role that can at all be ascribed to the “empty” space, it would seem, is for it to continuously go on “monitoring” if a truly causal body—a massive object—was impinging on itself or not, and if such a body actually did that, to allow it to do so.

In other words, the causal identity of the empty space becomes entirely other-located: it summarily depends on the identity of the massive objects. But the identity of a given object pertains to what that object itself is—not to what other objects are like. Clearly, something is wrong here.


In the next post, we shall try to trace the implications that the second description (i.e. The One Object) leads to.


A Song I Like:

(Hindi) “man mera tujh ko maange, door door too bhaage…”
Singer: Suman Kalyanpur
Music: Kalyanji Anandji
Lyrics: Indivar


[PS: May be an editing pass is due…. Let me see if I can find the time to come back and do it…. Considerable revision done on 28 April 2017 12:20 PM IST though no new ideas were added; I will leave the remaining grammatical errors/awkward construction as they are. The next post should get posted within a few days’ time.]

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Why is the physical space 3-dimensional?

Why I write on this topic?

Well, it so happened that recently (about a month ago) I realized that I didn’t quite understand matrices. I mean, at least not as well as I should. … I was getting interested in the Data Science, browsing through a few books and Web sites on the topic, and soon enough realized that before going further, first, it would be better if I could systematically write down a short summary of the relevant mathematics, starting with the topic of matrices (and probability theory and regression analysis and the lot).

So, immediately, I fired TeXMaker, and started writing an “article” on matrices. But as is my habit, once I began actually typing, slowly, I also began to go meandering—pursuing just this one aside, and then just that one aside, and then just this one footnote, and then just that one end-note… The end product quickly became… unusable. Which means, it was useless. To any one. Including me.

So, after typing in a goodly amount, may be some 4–5 pages, I deleted that document, and began afresh.

This time round, I wrote only the abstract for a “future” document, and that too only in a point-by-point manner—you know, the way they specify those course syllabi? This strategy did help. In doing that, I realized that I still had quite a few issues to get straightened out well. For instance, the concept of the dual space [^][^].

After pursuing this activity very enthusiastically for something like a couple of days or so, my attention, naturally, once again got diverted to something else. And then, to something else. And then, to something else again… And soon enough, I came to even completely forget the original topic—I mean matrices. … Until in my random walk, I hit it once again, which was this week.

Once the orientation of my inspiration thus got once again aligned to “matrices” last week (I came back via eigen-values of differential operators), I now decided to first check out Prof. Zhigang Suo’s notes on Linear Algebra [^].

Yes! Zhigang’s notes are excellent! Very highly recommended! I like the way he builds topics: very carefully, and yet, very informally, with tons of common-sense examples to illustrate conceptual points. And in a very neat order. A lot of the initially stuff is accessible to even high-school students.

Now, what I wanted here was a single and concise document. So, I decided to take notes from his notes, and thereby make a shorter document that emphasized my own personal needs. Immediately thereafter, I found myself being engaged into that activity. I have already finished the first two chapters of his notes.

Then, the inevitable happened. Yes, you guessed it right: my attention (once again) got diverted.


What happened was that I ran into Prof. Scott Aaronson’s latest blog post [^], which is actually a transcript of an informal talk he gave recently. The topic of this post doesn’t really interest me, but there is an offhand (in fact a parenthetical) remark Scott makes which caught my eye and got me thinking. Let me quote here the culprit passage:

“The more general idea that I was groping toward or reinventing here is called a hidden-variable theory, of which the most famous example is Bohmian mechanics. Again, though, Bohmian mechanics has the defect that it’s only formulated for some exotic state space that the physicists care about for some reason—a space involving pointlike objects called “particles” that move around in 3 Euclidean dimensions (why 3? why not 17?).”

Hmmm, indeed… Why 3? Why not 17?

Knowing Scott, it was clear (to me) that he meant this remark not quite in the sense of a simple and straight-forward question (to be taken up for answering in detail), but more or less fully in the sense of challenging the common-sense assumption that the physical space is 3-dimensional.

One major reason why modern physicists don’t like Bohm’s theory is precisely because its physics occurs in the common-sense 3 dimensions, even though, I think, they don’t know that they hate him also because of this reason. (See my 2013 post here [^].)

But should you challenge an assumption just for the sake of challenging one? …

It’s true that modern physicists routinely do that—challenging assumptions just for the sake of challenging them.

Well, that way, this attitude is not bad by itself; it can potentially open doorways to new modes of thinking, even discoveries. But where they—the physicists and mathematicians—go wrong is: in not understanding the nature of their challenges themselves, well enough. In other words, questioning is good, but modern physicists fail to get what the question itself is, or even means (even if they themselves have posed the question out of a desire to challenge every thing and even everything). And yet—even if they don’t get even their own questions right—they do begin to blabber, all the same. Not just on arXiv but also in journal papers. The result is the epistemological jungle that is in the plain sight. The layman gets (or more accurately, is deliberately kept) confused.

Last year, I had written a post about what physicists mean by “higher-dimensional reality.” In fact, in 2013, I had also written a series of posts on the topic of space—which was more from a philosophical view, but unfortunately not yet completed. Check out my writings on space by hitting the tag “space” on my blog [^].

My last year’s post on the multi-dimensional reality [^] did address the issue of the n > 3 dimensions, but the writing in a way was geared more towards understanding what the term “dimension” itself means (to physicists).

In contrast, the aspect which now caught my attention was slightly different; it was this question:

Just how would you know if the physical space that you see around you is indeed was 3-, 4-, or 17-dimensional? What method would you use to positively assert the exact dimensionality of space? using what kind of an experiment? (Here, the experiment is to be taken in the sense of a thought experiment.)

I found an answer this question, too. Let me give you here some indication of it.


First, why, in our day-to-day life (and in most of engineering), do we take the physical space to be 3-dimensional?

The question is understood better if it is put more accurately:

What precisely do we mean when we say that the physical space is 3-dimensional? How do we validate that statement?

The answer is “simple” enough.

Mark a fixed point on the ground. Then, starting from that fixed point, walk down some distance x in the East direction, then move some distance y in the North direction, and then climb some distance z vertically straight up. Now, from that point, travel further by respectively the same distances along the three axes, but in the exactly opposite directions. (You can change the order in which you travel along the three axes, but the distance along a given axis for both the to- and the fro-travels must remain the same—it’s just that the directions have to be opposite.)

What happens if you actually do something like this in the physical reality?

You don’t have to leave your favorite arm-chair; just trace your finger along the edges of your laptop—making sure that the laptop’s screen remains at exactly 90 degrees to the plane of the keyboard.

If you actually undertake this strenuous an activity in the physical reality, you will find that, in physical reality, a “magic” happens: You come back exactly to the same point from where you had begun your journey.

That’s an important point. A very obvious point, but also, in a way, an important one. There are other crucially important points too. For instance, this observation. (Note, it is a physical observation, and not an arbitrary mathematical assumption):

No matter where you stop during the process of going in, say the East direction, you will find that you have not traveled even an inch in the North direction. Ditto, for the vertical axis. (It is to ensure this part that we keep the laptop screen at exactly 90 degrees to the keyboard.)

Thus, your x, y and z readings are completely independent of each other. No matter how hard you slog along, say the x-direction, it yields no fruit at all along the y– or z– directions.

It’s something like this: Suppose there is a girl that you really, really like. After a lot of hard-work, suppose you somehow manage to impress her. But then, at the end of it, you come to realize that all that hard work has done you no good as far as impressing her father is concerned. And then, even if you somehow manage to win her father on your side, there still remains her mother!

To say that the physical space is 3-dimensional is a positive statement, a statement of an experimentally measured fact (and not an arbitrary “geometrical” assertion which you accept only because Euclid said so). It consists of two parts:

The first part is this:

Using the travels along only 3 mutually independent directions (the position and the orientation of the coordinate frame being arbitrary), you can in principle reach any other point in the space.

If some region of space were to remain unreachable this way, if there were to be any “gaps” left in the space which you could not reach using this procedure, then it would imply either (i) that the procedure itself isn’t appropriate to establish the dimensionality of the space, or (ii) that it is, but the space itself may have more than 3 dimensions.

Assuming that the procedure itself is good enough, for a space to have more than 3 dimensions, the “unreachable region” doesn’t have to be a volume. The “gaps” in question may be limited to just isolated points here and there. In fact, logically speaking, there needs to be just one single (isolated) point which remains in principle unreachable by the procedure. Find just one such a point—and the dimensionality of the space would come in question. (Think: The Aunt! (The assumption here is that aunts aren’t gentlemen [^].))

Now what we do find in practice is that any point in the actual physical space indeed is in principle reachable via the above-mentioned procedure (of altering x, y and z values). It is in part for this reason that we say that the actual physical space is 3-D.

The second part is this:

We have to also prove, via observations, that fewer than 3 dimensions do fall short. (I told you: there was the mother!) Staircases and lifts (Americans call them elevators) are necessary in real life.

Putting it all together:

If n =3 does cover all the points in space, and if n > 3 isn’t necessary to reach every point in space, and if n < 3 falls short, then the inevitable conclusion is: n = 3 indeed is the exact dimensionality of the physical space.

QED?

Well, both yes and no.

Yes, because that’s what we have always observed.

No, because all physics knowledge has a certain definite scope and a definite context—it is “bounded” by the inductive context of the physical observations.

For fundamental physics theories, we often don’t exactly know the bounds. That’s OK. The most typical way in which the bounds get discovered is by “lying” to ourselves that no such bounds exist, and then experimentally discovering a new phenomena or a new range in which the current theory fails, and a new theory—which merely extends and subsumes the current theory—is validated.

Applied to our current problem, we can say that we know that the physical space is exactly three-dimensional—within the context of our present knowledge. However, it also is true that we don’t know what exactly the conceptual or “logical” boundaries of this physical conclusion are. One way to find them is to lie to ourselves that there are no such bounds, and continue investigating nature, and hope to find a phenomenon or something that helps find these bounds.

If tomorrow we discover a principle which implies that a certain region of space (or even just one single isolated point in it) remains in principle unreachable using just three dimensions, then we would have to abandon the idea that n = 3, that the physical space is 3-dimensional.

Thus far, not a single soul has been able to do that—Einstein, Minkowski or Poincare included.

No one has spelt out a single physically established principle using which a spatial gap (a region unreachable by the linear combination procedure) may become possible, even if only in principle.

So, it is 3, not 17.

QED.


All the same, it is not ridiculous to think whether there can be 4 or more number of dimensions—I mean for the physical space alone, not counting time. I could explain how. However, I have got too tired typing this post, and so, I am going to just jot down some indicative essentials.

Essentially, the argument rests on the idea that a physical “travel” (rigorously: a physical displacement of a physical object) isn’t the only physical process that may be used in establishing the dimensionality of the physical space.

Any other physical process, if it is sufficiently fundamental and sufficiently “capable,” could in principle be used. The requirements, I think, would be: (i) that the process must be able to generate certain physical effects which involve some changes in their spatial measurements, (ii) that it must be capable of producing any amount of a spatial change, and (iii) that it must allow fixing of an origin.

There would be the other usual requirements such as reproducibility etc., though the homogeneity wouldn’t be a requirement. Also observe Ayn Rand’s “some-but-any” principle [^] at work here.

So long as such requirements are met (I thought of it on the fly, but I think I got it fairly well), the physically occurring process (and not some mathematically dreamt up procedure) is a valid candidate to establish the physically existing dimensionality of the space “out there.”

Here is a hypothetical example.

Suppose that there are three knobs, each with a pointer and a scale. Keeping the three knobs at three positions results in a certain point (and only that point) getting mysteriously lit up. Changing the knob positions then means changing which exact point is lit-up—this one or that one. In a way, it means: “moving” the lit-up point from here to there. Then, if to each point in space there exists a unique “permutation” of the three knob readings (and here, by “permutation,” we mean that the order of the readings at the three knobs is important), then the process of turning the knobs qualifies for establishing the dimensionality of the space.

Notice, this hypothetical process does produce a physical effect that involves changes in the spatial measurements, but it does not involve a physical displacement of a physical object. (It’s something like sending two laser beams in the night sky, and being able to focus the point of intersection of the two “rays” at any point in the physical space.)

No one has been able to find any such process which even if only in principle (or in just thought experiments) could go towards establishing a 4-, 2-, or any other number for the dimensionality of the physical space.


I don’t know if my above answer was already known to physicists or not. I think the situation is going to be like this:

If I say that this answer is new, then I am sure that at some “opportune” moment in future, some American is simply going to pop up from nowhere at a forum or so, and write something which implies (or more likely, merely hints) that “everybody knew” it.

But if I say that the answer is old and well-known, and then if some layman comes to me and asks me how come the physicists keep talking as if it can’t be proved whether the space we inhabit is 3-dimensional or not, I would be at a loss to explain it to him—I don’t know a good explanation or a reference that spells out the “well known” solution that “everybody knew already.”

In my (very) limited reading, I haven’t found the point made above; so it could be a new insight. Assuming it is new, what could be the reason that despite its simplicity, physicists didn’t get it so far?

Answer to that question, in essential terms (I’ve really got too tired today) is this:

They define the very idea of space itself via spanning; they don’t first define the concept of space independently of any operation such as spanning, and only then see whether the space is closed under a given spanning operation or not.

In other words, effectively, what they do is to assign the concept of dimensionality to the spanning operation, and not to the space itself.

It is for this reason that discussions on the dimensionality of space remain confused and confusing.


Food for thought:

What does a 2.5-dimensional space mean? Hint: Lookup any book on fractals.

Why didn’t we consider such a procedure here? (We in fact don’t admit it as a proper procedure) Hint: We required that it must be possible to conduct the process in the physical reality—which means: the process must come to a completion—which means: it can’t be an infinite (indefinitely long or interminable) process—which means, it can’t be merely mathematical.

[Now you know why I hate mathematicians. They are the “gap” in our ability to convince someone else. You can convince laymen, engineers and programmers. (You can even convince the girl, the father and the mother.) But mathematicians? Oh God!…]


A Song I Like:

(English) “When she was just seventeen, you know what I mean…”
Band: Beatles


 

[May be an editing pass tomorrow? Too tired today.]

[E&OE]

Shaken, because of a stir

We have demonstrably been shaken here on earth, because of a stir in the cosmos.

The measured peak strain was 10^{-21} [^].

For comparison: In our college lab, we typically measure strains of magnitude like 10^{-3} or at the most 10^{-4}. (Google search on “yield strain of mild steel” does not throw up any directly relevant page, but it does tell you that the yield strength of mild steel is 450 MPa, and all mechanical (civil/metallurgical/aero/etc.) engineers know that Young’s modulus for mild steel is 210 GPa. … You get the idea. …)


Einstein got it wrong twice, but at least eventually, he did correct himself.

But other physicists (and popular science writers, and blog-writers), even after getting a full century to think over the issue, still continue to commit blunders. They continue using terms like “distortions of spacetime.” As if, space and time themselves repeatedly “bent” (or, to use a euphemism, got “distorted”) together, to convey the force through “vacuum.”

It’s not a waving of the “spacetime” through a vaccum, stupid! It’s just the splashing of the aether!!


The Indian credit is, at the most, 1.3%.

If it could be taken as 3.7%, then the number of India’s science Nobels would also have to increase dramatically. Har Gobind Singh Khorana, for instance, would have to be included. The IAS-/MPSC-/scientist-bureaucrats “serving” during my childhood-days had made sure to include Khorana’s name in our school-time science text-books, even though Khorana had been born only in (the latter-day) Pakistan, and even if he himself had publicly given up on both Pakistan and India—which, even as children, we knew! Further, from whatever I recall of me and all my classmates (from two different schools), we the (then) children (and, later, teen-agers) were neither inspired nor discouraged even just a tiny bit by either Khorana’s mention or his only too willing renunciation of the Indian citizenship. The whole thing seemed too remote to us. …

Overall, Khorana’s back-ground would be a matter of pride etc. only to those bureaucrats and possibly Delhi intellectuals (and also to politicians, of course, but to a far lesser extent than is routinely supposed). Not to others.

Something similar seems to be happening now. (Something very similar did happen with the moon orbiter; check out the page 1 headlines in the government gazettes like Times of India and Indian Express.)

Conclusion: Some nut-heads continue to run the show from Delhi even today—even under the BJP.

Anyway, the reason I said “at most” 1.3 % is because, even though I lack a knowledge of the field, I do know that there’s a difference between 1976, and, say, 1987. This fact by itself sets a natural upper bound on the strength of the Indian contribution.

BTW, I don’t want to take anything away from Prof. Dhurandhar (and from what I have informally gathered here in Pune, he is a respectable professor doing some good work), but reading through the media reports (about how he was discouraged 30 years ago, and how he has now been vindicated today etc.) made me wonder: Did Dhurandhar go without a job for years because of his intellectual convictions—the way I have been made to go, before, during and after my PhD?

As far as I am concerned, the matter ends there.

At least it should—I mean, this post should end right here. But, OK, let me make an exception, and note a bit about one more point.


The experimental result has thrown the Nobel bookies out of business for this year—at least to a great part.

It is certain that Kip Thorne will get the 2016 Physics Nobel. There is no uncertainty on that count.

It is also nearly as certain that he will only co-win the prize—there will be others to share the credit (and obviously deservingly so). The only question remaining is, will it be just one more person or will it be two more (Nobel rules allow only max 3, I suppose), what will be their prize proportions, and who those other person(s) will be (apart from Thorne). So, as far as the bettors and the bookies are concerned, they are not entirely out of the pleasure and the business, yet.

Anyway, my point here was twofold: (i) The 2016 Physics Nobel will not be given for any other discovery, and (ii) Kip Thorne will be one of the (richly deserving) recipients.


[E&OE]

 

What do physicists mean by “multidimensional” physical reality?

Update on 2015.09.07, 07 AM: I have effected a few corrections. In particular, I have made it explicit that the third quantity isn’t the strength of an independently existing third property, but merely a quantity that is registered when the two independent quantities are both being varied. Sorry about that. If the need be, I will simplify this discussion further and write another blog post clarifying such points, some time later.


The last time, I said that I am falling short on time these days. This shortfall, generally speaking, continues. However, it just so happens that I’ve essentially finished a unit each for both the UG courses by today. Therefore, I do have a bit of a breather for this week-end (only); I don’t have to dig into texts for lecture preparations this evening. (Also, it turns out that despite the accreditation-related overtime work, we aren’t working on Sundays, though that’s what I had mentioned the last time round). All in all, I can slip in a small note, and the title question seems right.


We often hear that the physical reality, according to physicists, is not the 3-dimensional reality that we perceive. Instead, it is supposed to be some n-dimensional entity. For instance, we are told that space and time are not independent; that they form a 4-dimensional continuum. (One idea which then gets suggested is that space and time are physically inter-convertible—like iron and gold, for instance. (You mean to say you had never thought of it, before?)) But that’s only for the starters. There are string theorists who say that physical universe is 10-, n-, or \infty-dimensional.

What do physicists mean when they say that reality is n-dimensional where n >3? Let’s try to understand their viewpoint with a simple example. … This being a brief post, we will not pursue all the relevant threads, even if important. … All that I want to touch upon here is just one simple—but often missed—point, via just one, simple, illustration.


Take a straight line, say of infinite length. Take a point on this line. Suppose that you can associate a physical object with this point. The object itself may have a finite extent. For example, the object may be extended over a small segment of this line. In such a case, we will associate, say the mid-point of the segment with this object.

Suppose this straight line, together with the 1-dimensionally spread-out object, defines a universe. That is a supposition; just accept that.

The 1-dimensional object, being physical, carries some physical properties (or attributes), denoted as p_1, p_2, p_3, \cdots. For example, for the usual 3-dimensional universe, each object may have some extent (which we have already seen above), as well as some mass (and therefore density), color, transmissivity, velocity, spinning rate, etc. Also, position from a chosen origin.

Since we live in a 3-dimensional universe, we have to apply some appropriate limiting processes to make sense of this 1-dimensional universe. This task is actually demanding, but for the sake of the mathematical simplicity of the resulting model, we will continue with a 1-dimensional universe.

So, coming back to the object and its properties, each property it possesses exists in a certain finite amount.

Suppose that the strength of each property depends on the position of the object in the universe. Thus, when the object is at the origin (any arbitrary point on the line chosen as the reference point), the property p_1 exists with the strength s_1(0), the property p_2 exists with the strength s_2(0), etc. In short the ith property p_i exists with a strength s_i(x) where x is the position of the object in the universe (as measured from the arbitrarily selected origin.) Suppose the physicist knows (or chooses to consider) n number of such properties.

For each of these n number of properties, you could plot a graph of its strength at various positions in the universe.

To the physicist, what is important and interesting is not the fact that the object itself is only 1-dimensionally spread; it is: how the quantitative measures s_i(x)s of these properties p_is vary with the position x. In other words, whether or not there is any co-variation that a given ith property has with another kth property, or not, and if yes, what is the nature of this co-variation.

If the variation in the ith property has no relation (or functional dependence) to the kth property, then the physicist declares these two properties to be independent of each other. (If they are dependent on each other, the physicist simply retains only one of these two properties in his basic or fundamental model of the universe; he declares the other as the derived quantity.)

Assuming that a set of some n chosen properties such that they are independent of each other, his next quest is to find the nature of their functional dependence on position x.

To this end, he considers two arbitrarily selected points, x_1 and x_2. Suppose that his initial model has only three properties: p_1, p_2 and p_3. Suppose he experimentally measures their strengths at various positions x_1, x_2, x_3, x_4, \cdots.

While doing this experimentation, suppose he has the freedom to vary only one property at a time, keeping all others constant. Or, vary two properties simultaneously, while keeping all others constant. Etc. In short, he can vary combinations of properties.

By way of an analogy, you can think of a small box carrying a few on-off buttons and some readout boxes on it. Suppose that this box is mounted on a horizontal beam. You can freely move it in between two fixed points x = x_1 and x = x_2. The `on-off’ buttons can be switched on or off independent of each other.

Suppose you put the first button b_1 in the `on’ position and keep the the rest of the buttons in the `off’ position. Then, suppose you move the box from the point x_1 to the point x_2. The box is designed such that, if you do this particular trial, you will get a readout of how the property p_1 varied between the two points; its strength at various positions s_1(x) will be shown in a readout box b_1. (During this particular trial, the other buttons are kept switched off, and so, the other readout boxes register zero).

Similarly, you can put another button b_2 into the `on’ position and the rest in the `off’ position, and you get another readout in the readout box b_2.

Suppose you systematize your observations with the following notation: (i) when only the button b_1 is switched on (and all the other buttons are switched off), the property p_1 is seen to exist with s_1(x_1) units at the position x = x_1 and s_1(x_2) units at x = x_2; this readout is available in the box b_1. (ii) When only the button b_2 is switched on (and all the other buttons are switched off), the property p_2 exists with s_2(x_1) units at x = x_1 and s_2(x_2) units at x = x_2; this readout is available in the box b_2. So on and so forth.

Next, consider what happens when more than one switch is put in the `on’ position.

Suppose that the box carries only two switches, and both are put in the `on’ position. The reading for this combination is given in a third box: b_{(1+2)}; it refers to the variation that the box registers while moving on the horizontal beam. Let’s call the strengths registered in the third box, at x_1 and x_2 positions, as s_{(1+2)}(x_1) and s_{(1+2)}(x_2), respectively; these refer to the (1+2) combination (i.e. both the switches 1 and 2 put in the `on’ position simultaneously).

Next, suppose that after his experimentation, the physicist discovers that the following relation holds:

[s_{(1+2)}(x_2) - s_{(1+2)}(x_1)]^2 = [s_1(x_2) - s_1(x_1)]^2 + [s_2(x_2) - s_2(x_1)]^2

(Remember the Pythogorean theorem? It’s useful here!) Suppose he finds the above equation holds no matter what the specific values of x_1 and x_2 may be (i.e. whatever be the distances of the two arbitrarily selected points from the same origin).

In this case, the physicist declares that this universe is a 2-dimensional vector space, with respect to these p_1 and p_2 properties taken as the bases.

Why? Why does he call it a 2-dimensional universe? Why doesn’t he continue calling it a 1-dimensional universe?

Because, he can take a 2-dimensional graph paper by way of an abstract representation of how the quantities of the properties (or attributes) vary, plot these quantities s_1 and s_2 along the two Cartesian axes, and then use them to determine the third quantity s_{(1+2)} from them. (In fact, he can use any two of these strengths to find out the third one.)

In particular, he happily and blithely ignores the fact that the object of which p_i are mere properties (or attributes), actually is spread (or extended) over only a single dimension, viz., the x-axis.

He still insists on calling this universe a 2-dimensional universe.

That’s all there is to this n-dimensional nonsense. Really.


But what about the n-dimensional space, you ask?

Well, the physicist just regards the extension and the position themselves to form the set of the physical properties p_i under discussion! The physicist regards distance as a property, even if he is going to measure the strengths or magnitudes of the properties (i.e. distances, really speaking) only in reference to x (i.e. positions)!!

But doesn’t that involve at least one kind of a circularity, you ask?

The answer is embedded right in the question.

Understand this part, and the entire mystification of physics based on the “multi-dimensional” whatever vaporizes away.

But don’t rely on the popular science paperbacks to tell you this simple truth, though!


Hopefully, the description above is not too dumbed down, and further, hopefully, it doesn’t have too significant an error. (It would be easy for me (or for that matter any one else) to commit an error—even a conceptual error—on this topic. So, if you spot something, please do point it out to me, and I will correct the description accordingly. On my part, I will come back sometime next week, and read this post afresh, and then decide whether what I wrote makes sense or not.)


A Song I Like:

For this time round, I am going to list a song even if I don’t actually evaluate it to be a very great song.

In fact, in violation of the time-honored traditions of this blog, what I am going to do is to list the video of a song. It’s the video of a 25+ years old song that I found I liked, when I checked it out recently. As to the song, well, it has only a nostalgia value to me. In fact, even the video, for the most part, has only a nostalgia value to me. The song is this:

(Hindi) “may se naa minaa se na saaki se…”
Music: Rajesh Roshan
Singers: Sadhana Sargam and Mohammad Aziz
Lyrics: Farooq Qaisar

Well, those were the technical details (regarding this song). To really quickly locate the song (and the video), forget the lyrics mentioned above. Instead, just google “aap ke aa jaane se,” and hit the first video link that the search throws up. (Yes, it’s the same song.)

As I said, I like this video mainly for its nostalgic value (to me). It instantaneously takes me back to the 1987–88 times. The other reasons are: the utter natural ease with which both the actors perform the dance here (esp. Neelam!). They both in fact look like they are authentically enjoying their dancing. Watch Neelam’s steps, in particular. She was reputed to be a good dancer, and you might think that this song must have been a cake-walk for her. Well, check out her thin (canvas-like) shoes, and the kind of rough ground in the mountains and in the fields over which she seems so effortlessly to take those steps. Govinda, in comparison, must have had it a bit easier (with his thicker, leather shoes), but in any case, in actuality, it must have been some pretty good hard work for both of them—it’s just that the hard work doesn’t show in the song. … Further, I also like the relative simplicity of the picturization. And, the catchy rhythm. Also, the absence, here, of those gaudy gestures which by now are so routine in Hindi film songs (and in fact were there even in the times of this song, and in fact also for about a decade or more earlier). I mean: those pelvic thrusts, that passing off of a thousand of people doing their PT exercises on a new, sprawling suburban street in Mumbai/Gurgaon/Lutyens’ Delhi as an instance of dance, etc.

… I don’t know if you end up liking this song or not. To me, however, it unmistakably takes me to the times when I was a freshly minted MTech from IIT Madras, was doing some good (also satisfying) work in NDT, had just recently bought a bike (the Yamaha RX 100), and was looking forward to life in general with far more enthusiasm (and in retrospect, even naivete) than I can manage to even fake these days. So, there.

[As I said, drop a line if there are mistakes in the main post. Main mistake (or omission) corrected. As I said, drop a line if there are further mistakes in the main post. And, excuse me for some time, esp. the next week-end, esp. the next Saturday late night (IST). I may not find any time the next Sunday, because I would once again be in the middle of teaching a couple of new units over the next 2–3 weeks.]

[E&OE]

Some Interesting Reading (October 2013)

Concerning our series of posts on the concept of space, I have jotted down my thoughts on paper, but not yet made any progress on creating the diagrams to go with them. (Plain laziness.) Hence, the delay in posting it.

In the meanwhile, here are a few links to some reading that I found interesting over the past few days (in no particular order).

1. R. J. Lipton of GeorgiaTech on how “Teaching helps research” [^]

2. Ricardo Heras, “Individualism: The legacy of great physicists,” arXiv:1310.7326 [physics.pop-ph] [^]. Heras is a first year graduate student at University College, London. Check out the Fermi quote at the end of this paper. (And, also, the quote by Max Planck at the opening.)

3. Roger Schlafly puts in one place all the links to his blog posts updating his book “How Einstein Ruined Physics,” [^].

4. Tony Rothman, “Lost in Einstein’s shadows” [^]

5. Physics World, 25th Anniversary Issue, available for free downloads [^] (HT to QuantumFrontiers [^]). This special issue has the magazine’s lists of 5 images, 5 discoveries, 5 questions, 5 spin-offs, and 5 people, that mattered over the last 25 years.

6. Paul G. Kwiat, on what he calls it “interaction-free measurement” [^]. You think it’s mysterious? (LOL!)

And, in place of the usual “A Song I Like” section, yet another link!:

7. Tom Swanson, a physicist himself, offers physicists a horoscope [^]

[E&OE]

The “electric universe” belongs to the third+ world…

The two regular readers of this blog would have noticed a couple of oddities concerning this blog, viz. that (i) it does not receive as many as hits as it should, and (ii) it is mostly devoid of any real blog comments.

At this blog, we have always believed that the first is not a fault of our own making, and that the second … well… the second, you know, also is not because of anything of our own making.

We were, therefore, so taken in by sheer surprise by a real blog comment coming in here today—wait, make it two—and those too, coming in from someone seemingly well-versed with physics, and that too, right in the real-time while we were still updating our last post, that we had already begun fondly toying with the idea of making a separate post just for answering these very valuable queries. And that’s when the third comment arrived. Three comments. In a single day. All real. … It should not be too difficult to see why we immediately decided that honoring our inner voice calling us for a further exercise of our posting labours right today was entirely in order.

We are pleased to thusly present the present blog-post to your monitor.

[Steps aside for a moment and clears the throat before resuming further.]

1. The electric universe

The questioner asks for my say on the “electric universe,” and supplies links; see the first three comments by “Absolute_O_Zero” to my last post, starting here [^].

I pursued the links he provided to a depth of just about 1–2 sub-links, rapidly browsed through them, and here we go…

The answer is that the “electric universe” (I mean: the proper physics-related usage of this term) belongs to the third world in the scheme that I have been thinking about, or perhaps, further down.

I say “further down,” because I am not sure if there would (or even should) be a separate world to describe plasma as a separate physical object. I don’t know about plasmas except that they are some kind of ionized gases that exhibit some curiously different physical properties. My knowledge of plasmas stops there. Literally. So, I am not even sure if they would come after the fourth world of the quantum objects, or with them. And, if and as necessary, I would always be willing to split the worlds further, as you know!

But coming back to a plasma (of physics), is it usually taken to carry a classical (i.e. Maxwellian)  electromagnetic field? Or does it necessarily require a quantum electrodynamics for its description? [I honestly don’t know even just that much about plasma.]

If the former, they might benefit from an application of the concepts of the third world. If the latter, of the fourth. That is, in the current scheme.

And, even if we set this whole issue of the plasma state of the matter completely aside, I still would not be sure if there cannot be a further splitting down of the world.

… And it was to highlight this separate, as yet open, question that I decided to do this separate post. …Let me explain how.

2. Should there be another world in between the third world (EM) and the fourth world (QM)?:

The issue arises, you see, because of another conceptual riddle with an aether-based description, which may be best put as the following:

Just how many aethers do simultaneously occupy the “void?”

That is to say:

If the void/free space between the massive charged objects is already filled with the gravitational field-fluid, then it should not leave any empty space to fill it with the electromagnetic field-fluid, right? or do the aethers allow this circumstance? why or why not? and, of course, how?

I was not running away from this question when I presented you with that neat scheme of the four worlds, and began writing about aether, right from the very first post in this series. I didn’t mention this issue because I just wanted to postpone the complexity it adds to the discussion—one goes from the simple to the complex.

It was in order to simply the discussion of the “void”-related fundamental paradox that I presented the material objects as interacting either with gravity (in the second world) or with the electromagnetism (in the third world), but not both at the same time. The paradox remains that—a paradox—whether you have just one field phenomenon to explain or many of them.

Of course, this layer of the complexity of the aether theories is known to any one who has gone through their history. It is a very well known criticism. There was a time when virtually any field phenomenon—be it sound, light, heat, electricity, magnetism… even heat—was being described via reference to some or the other hypothetical fluid, i.e., [a separate] aether. There was a time in physics, I guess sometime in the 19th century, when someone, I suppose, had even remarked that the aethers had seemed to have multiplied at the rate that rabbits did.

But don’t, therefore, sneer at the 19th century physicists.

The 19th century aethers were taken as always existing in this (i.e. the concretely real) world, and there were only a finite number of them. And, it was right in the 19th century that some of the separately proposed aethers were either shown not to exist at all, and the two most important of them were integrated together into just one: E + M -> EM.

In contrast, today, our standard model has a far bigger zoo of fundamental particles to parade around, and worse: their number only increases and always refuses to come down over decades of research. … And, much, much worse.

Not only do the modern physicists believe that fundamentally different particles can come into existence out of the same pure nothingness without there being any need to provide any explanatory mechanism for (any part) of this “process”, and not only can such fundamental particles making up the physical existence also go completely out of existence (presumably to “nothingness,” again, and of course, without any acknowledged need to provide any theoretical explanation again), but also that some of them are such that they cannot even ever be observed. This description, some of them insist, is reasonable. Or else….

… Or else, there is the spectacle (ugly even to them) of infinity of universes being generated in every finite interval of time. And, no one is sure about the order of that infinity—whether it is the normal infinity, or an infinity of infinities, or an infinity of an infinity of infinities, or some still higher order “number” of them.

In comparison, the rates of reproduction of even the most red-blooded among rabbits would seem either vanishingly small or plain vanishing, wouldn’t they?

Still, the intent was not to downplay the difficulty posed by the simultaneous existence of multiple aethers, by pointing out the glass castle of the modern physics. It is a proper question to be pursued. In fact, the state of modern physics was only one reason—and a relatively minor one at that—why I thought that it best to keep this problematic issue for an appropriately later consideration.

Another, far more important reason was that, based on my grasp of the Objectivist epistemology, I felt confident that the difficulty shouldn’t be of a very great, unsurmountable kind of, fundamental importance. [I won’t tell you the specific reasons for that, because it would spoil some of my blogging—and thinking, and even rethinking—fun… But, confident, yes I was, and still am.]

But of course, this whole discussion is not so relevant to the question presently posed, because the plasma theorists never take the idea of aether seriously—or at least, completely seriously. Therefore, it is not a question that would even occur to them.

So, this question of the multiple aethers, really speaking, belongs only to places such as this blog.

As to their theories, well, inasmuch as the term “electric universe” refers to a proper theory of physics, it’s not just that they have a great theory of the plasmas of physics. One of the links provided by the questioner actually goes to a Nobel winning work related to the plasmas; the creation [is it?] of MHD i.e. magnetohydrodynamics or some such a long and unhyphenated thing [apparently competing somewhat aggressively on the hyphenations-not-necessary count with some of us Indians’ first and last names—each being a separate entry in that competition.]

Leaving aside the MHD, the “electric universe” folks also seemingly do quite a bit of cosmology based on that plasma theory.

Now, here, I am not sure if a detailed cosmological theory should have a place in this scheme of mine, which deals mainly with the broad views of the fundamental character of the physical objects i.e. world assumed in the core theory building of physics, by physicists of different historical eras, as it were.

A theory which says something new about how the plasma occupies the “void,” and affects planets/stars/solar systems/galaxies/whatnot in a new theory of cosmology that perhaps has a hard time getting enough highlighted by the top-5 American universities professors, may actually be great, but this whole “shebang” simply side-steps the main issue of the fundamental character of the physical objects. Let me show you how.

Let’s begin at some very simple questions. Suppose, I ask you: “What is, err, a plasma?”

You might say something like: “Say, take an atom, knock off an electron and make an ion out of it. Now, take very many of them in this compact…”

Me: “Stop! Stop!! Stop right there….”

“Two electrons” is good enough for me!

Take away all the other electrons, and nucleons, and chuck them aside. Suppose that the whole universe has only two electrons, each with some arbitrary initial motion. [For instance, initially, both of them are stationary, with a 1 meter distance between them.] And, now, suppose, we accelerate only one of them. … The question is: what does it do to both their motions? through what mechanism—if any—acting through that 1 m void?

In addressing this question, if you recite Maxwellian theory to me, I would ask: but does Maxwell’s aether have mass? If yes, then, how does this characteristic of the aether affect Newton’s three fundamental laws of motion? Do they undergo a change, too, as they should, in the process? And, if the aether is not massive, then… Here, you know the main paradox (of my last post) which I would point out to you. … If you recite the relativity theory to me, I would ask why an aether-based explanation is not satisfactory to you. And, how you answer the objection that the procedure of introducing an absolute nothing into a theory is both epistemologically and metaphysically unsound, nay, even mocking in an ugly way of any theory building at all?

Now, yes, here, I did keep aside the issue of whether the electrons would also feel the pull due to gravity or not: if you supply an aether-based explanation for the EM part of the electronic interaction, then where would you put the gravity aether at the same time?

But, if you are going to confuse between that “whole shebang” of the electric universe of a plasma that we have already chucked aside, and these simple questions of mine which, despite all their simplicity you still apparently cannot answer, then, probably, you don’t understand what the phrase like “character of a physical” means.

That phrase isn’t always hungry looking for an object that is a product of consciousness (i.e. a law of nature). At a more fundamental level, but still continuing to belong to the theory of physics, that phrase is hungry looking for an objects that make the physical world itself. …Ummm…

… Metaphysics trumps epistemology. … Quite a fine principle, don’t you think?

* * * * *   * * * * *   * * * * *

A Song I Like:
[BTW, remember the rules of this section of this blog. Unless otherwise explicitly noted, this section always focuses only on, say, the “aural” aspects of a song; it does not factor in the extraneous “non-aural” aspects such as the visual aesthetics of any picturization done using the song, or the plot of the movie in which it might appear, or actors, or the shirt worn by a musician on the day of its recording, or by a lightman on the day of the shooting of the song, or whether any one wore any shirts at all or not, etc. … I wanted to remind you this rule because, with a song like this one, if you see listen to the song itself (including its words), what it suggests is, say, one world. But if you watch only the video of the song without knowing the story of the movie, then it “transforms” into an entirely another world. And, if you go watch the movie, I gather that you will entirely stop making any sense of anything in any world at all! [I haven’t seen it, but still, that’s what I gather from a review at a blog[^]]  … In short, just listen to this song as you would listen a song  heard on [the usual pre-Internet] radio, and you should be doing fine. … Though, as you listen to it, you might think that it’s Lata, though it’s not… And you might think that it’s Laxmikant-Pyarelaal or Kalyanji-Anandji, but it’s not… All in all, this song somehow has the potential not just to fox you; it has one to make an earth or a troop [^] out of you! Rather like the universe of the modern physics… So, listen to a sage advice. Just listen to it on a virtual/real radio, and, may be, you will like it too… ]

(Hindi) “dil ne phir yaad kiyaa…”
Singers: Mohamed Rafi, Suman Kalyanpur, and Mukesh
Music: Sonic Omi
Lyrics: G. L. Rawal (?)

[Enough. I am not going to post for many, many days… Though, I might come back and streamline this post a bit (and think whether the updates to my last post really should go into a separate post, or not)… Too tired… Everything, later!]

[E&OE]

Coming back to the second “world”…

[Four updates added on September 24, 2013.]

0. Coming back to the second “world,” I would like to briefly note a few points concerning it. … But before coming to these points, first, in case you have joined late and so don’t know what I mean by the term “second ‘world’,” let me tell you that in brief.

1. The term “second ‘world'” means: a view of the physical world which would correspond, roughly speaking, with the Newtonian physics. In particular, it refers to a broad, objective view of the physical world as is implied by, or is implicit in, the state of physics as it existed after Galileo and Newton, but before the discovery of the laws of electromagnetism. Roughly speaking, the mid-17th century to, say, the early 19th century.

This “world” consists of uncharged bodies not only colliding with each other but also sucking up the gravity field-fluid. The first “world,” in contrast, would be this second world, minus the phenomenon of gravity. I had written about these ideas in my recent post here [^].

The first world really speaking doesn’t pose much of a conceptual problem to any one, because it is a local theory, and a relatively simpler one at that. The only kind of entities making it up are all definite objects—either discrete objects like apples and planets, or such continua that their defining properties always are defined in reference to a definite portion of that continuum, as in the classical fluid and solid mechanics. Further, all entities in this world are material (i.e. mass-possessing) ones. And, all the interactions are via a common surface between the directly touching bodies.

The second world, as I indicated in my earlier post, posed conceptual problems back then (and it continues to stump people even today—if they at all care to think about it) because gravity adds two difficult features: (i) forces acting through a “void,” and (ii) instantaneous action at a distance (IAD).

I had then sketched a possible solution involving a hypothetical, massless, gravity field-fluid.

In the follow-up post [^], I had referred you to Wang’s papers, and had asked if scientific papers like these would be enough. And, also what additional input would be necessary for you to be convinced that a hypothetical massless fluid indeed makes for a first-class object of physics.

2. The main paradox:

For convenience, let me now more or less fully reproduce, paraphrasing only a bit here and there, what I said by way of the question, right in that first post about the conceptual trouble with that kind of a “fluid.”

The first issue that arises in the second world, viz., forces being transmitted through a void, 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).

So, now, a question arises: Where do we place the field 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 that gravity is an attribute of the void, then an immediate next question is: does gravity exist in a world devoid of the material objects like apples and planets? If so, what does the field do? Forcing nothing is a contradiction in terms—the definition of force involves the change of momentum of a material object like an apple or a planet.

There cannot be a force in a field if there is nothing to force from/to. Assuming unit masses for all entities, mathematically, “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. If gravity is to be attributed to the material bodies themselves, then no mechanism is left to explain how it can act over the “void” (or “free space” or whatever).

This theoretical complication is what Newton himself should have commented upon. But, he didn’t. His shortcoming.

3. The (other) candidate solutions:

My further ‘net searches threw quite a few fascinating ideas. I will note down just a few of them (i.e. apart from Wang’s papers that I have noted earlier in this series).

First, the obligatory Wiki articles, and the references therein: Aether the Classical Element [^], Aether Theories [^], Mechanical Explanations of Gravitation [^], and, though meant for electromagnetism, if you wish to use similar ideas also for gravity, Luminiferous Aether [^]. …

BTW, the coverage of the aether-related ideas on the Internet in general, and on Wiki in particular, has improved a significantly great deal since the time not so long so—around 2004/05 times, when I was doing my PhD. At that time, most pages were amateur or even worse—crackpot! The only exceptions were a few groups like a nonlinear studies center in an Austrian university, or so. [Update on September 24, 2013: Link, here[^]]. BTW, my PhD papers had assumed an aether hypothesis, but quite different from what people meant about it. Which brings us to the next set of material.

  • The “MountainMan” collection of links [^]. Very comprehensive. (They didn’t miss Dirac’s surprisingly pro-aether viewpoint either!)
  • The “Cellular Universe” Web site, with an excellent summary of the views of the aether idea, throughout history (right in the format of a table/timeline!) [^]. You may want to spend some time exploring some related material (like that on cosmology) on this site; consult the links given in the side bar of that site.
  • There were quite a few others too, though the links already given would cover pretty much the entire territory one way or the other. … For instance, see this blog post [^]. Its presentation is good, but all those points are one or the other already covered in the links (and the sub-links) given above.

Comment: Realize that none of these solutions, IMO, fully satisfactorily resolve the main paradox which I have noted above.

For many of these aether theories, if you wish to use a simple heuristic to expedite your reading (though I wouldn’t advise you to outright dismiss any idea out of hand), just ask yourself this simple question:

If it is a continuum aether, is it massive or massless? If the former, how does the theory account for Newton’s three laws for the massive objects? Are they modified too? Must they? And, if the latter, then what specific characteristics of aether are proposed here that would go on to provide a mechanism for the gravity force?

For certain other, particles-based theories (i.e. particles of aether), always ask yourself: Is this theory philosophically satisfactory? What exists in between those aether particles? void?

Have fun.

4. “But why should I pursue it in the first place? What is the fallout?”

You may now wonder, of course, where the fun is, in all this “back-dated” enterprise.

You may perhaps say something like: “All we seem to be doing here is to dig through the errors of the other people, and, that too, of those who are long dead. There is no fun in going through the wrong theories of the ancient people [like Newton and all!], how they thought. Einstein proved them all wrong, and the 20th century—including all the finest and costliest experiments performed till date—has proved Einsten right.” And, continuing, you may then ask me: “How is your paradox relevant to solving the really important problems (or even paradoxes) facing today’s physics? Why dig up old paradoxes when new ones are available, and old ones are already resolved?”

I won’t argue a lot here. By way of my answer, I will only note down a couple of points. [Many other smart people, I am sure, would have already noted these by now, without me having to tell them about that…. But still…].

(i) The second world is important because it is the simplest toy world that still carries an important, defining feature of the standard model of the modern particle physics: viz., the division of all things (they call it “particles”) into two mutually exclusive and collectively exhaustive classes: the massive particles (i.e. the fermions) and the massless particles (i.e. the bosons). If you know how to (properly) quantize a continuum (the way I have done in my published papers and also writings on the blogs etc.), then, in solving the toy problem of the gravity-fluid, you create a platform that would be very directly useful in solving some of the really difficult conceptual riddles concerning the modern standard model. … I won’t name them. You should know what those are. [LOL! Why? Because you were concerned with the modern standard model, that’s why!]

(ii) If you can resolve the main paradox, by giving a logically consistent and complete (i.e. fully satisfactory) aether-based description even if only for the second world, then, that accomplishment, by itself, would mean that you had overcome the greatest hurdle in resolving the most difficult paradoxes related to the relativity theory as well. They would go out the door in one go. Web pages like, e.g., this excellent set [^], would be taken down, though the Web sites themselves (including that Web site) will still continue to thrive—by focusing on other, better, more authentic problems of physics. Why?

Because, this way, you would be able to give an “engineer’s” description for the physical world, a description that, at its most fundamental level, requires only a 3D Euclidean geometry for space, and a basically separate scalar for time. (Time would no longer be a “dimension” in the theory; it would be just a parameter, really speaking.)

Imagine what kind of a simplification in the conceptual structure of physics that would represent.

… And, yes, if you wished, you would still be free to play with the “spacetime” continuum, manifolds, their contortions… all those concepts as well, though you wouldn’t have to use them. You may find reasons (perhaps even good reasons) to continue using them for mathematical convenience in (some, not all) applications, that’s all. [For instance, you may find some convenience in error analysis of some numerical analysis code, or in presenting a more concise deductive formulation.] But not in the basic physics theory.

[Update on September 24, 2013:

This update on September 24, 2013, over.]

Of course, your intermediate step would still consist of first resolving a similar riddle for the third world (that of EM) as well. Yet, the nature of the issues is such that if you can resolve the paradox even if only in the second world, then that by itself would be a great step forward. You see, the paradox concerning the third world (i.e. the one concerning the EM field) is only mathematically a bit more complicated—conceptually, not so much, though some conceptual advancements would still be necessary, too (other than what I have already explicitly noted or hinted at).

3. One more reason why you can give it try. It’s because… the paradox—at least that in the second world—most certainly is resolvable.

And, how do I know that?

…[Suppresses laughter] …

Time to run through the description of the main paradox, again? See the main point 2. above. (… It could be put in a better, more precise way, but what I have already noted down seems to be enough. At least to me, and at least for a blog-post, and at least for the time being. It puts the issue directly enough. … So, there!)

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Updates on September 24, 2013:

Update 1. Why the classical fluid mechanics belongs to the first world:

In the classical fluid mechanics, there also is a flux of mass (in addition to that of momentum) which, at the first sight, seems unlike the first world, because with the solid colliding balls of the first world, there is a transfer of only momentum, not of mass.

However, we can still regard the classical fluid as belonging to the first world, because mass of the fluid is a property defined for both the parts of the material continuum sharing their common surface, and both these defining parts are definite material objects.

The classical fluid is nothing but just a limiting case, obtained by applying a mathematical homogenization (or “squishing” i.e. “continuum-ization”) procedure to a collection of what otherwise are only discrete material objects occupying a defining volume in the first world. For instance, a grosser-scale volume of air is taken as the classical fluid material, even though the reference volume itself is made up of a large number of tiny, discrete, gas “molecules” which themselves can be taken as the usual solid objects of the first world; ditto, for water and other liquids.

Left as an exercise for you: Figure out why also friction (e.g. Newton’s law of friction) does not pose any deep conceptual issue in the first world.

Update 2: A link to the Austrian university which was doing research on aether-based descriptions in the mid-naughties, has been inserted inline; it was the AINS [^]. BTW, I had made a reference to Prof. Gr\”{o}ssing’s papers, in one of my PhD research papers, too.

Update 3:  The additional beneficial fallouts of a new conceptual perspective:

Another point. I wish to note a bit more on the beneficial fallouts of a new conceptual perspective such as the resolution of the main paradox concerning the second world, as noted in these blog posts.

Though the final quantitative predictions of both the mainstream theory of Newtonian gravitation and an aether-based theory may outwardly seem to remain quantitatively the same, it still is not proper to dismiss the aether-viewpoint.

A plain epistemological fact is that with a new (objectively valid) conceptual viewpoint, new progress into the as-yet-not-even-imagined territory also becomes at all possible.

The progress of physics does not always depend only on new experimental observations; crucial to the inductive process of discovery also is the advancement in the conceptual perspective. (Claiming otherwise is a direct case of MBD—the mind-body dichotomy.)

Remember, consciousness is finite, not infinite. In other words, we have limitations to how much of a further progress we can make, given an already existing level of knowledge, and, given a particular conceptual vantage point that goes with it (at least implicitly).

Due to the finitude of our consciousness, given a particular conceptual viewpoint (implicit in a particular state of knowledge), some as-yet unknown facts, even if logically not inconsistent with that older viewpoint, still become so conceptually distant as to fall out of the limited range of any possible mental grasp, and hence, out of the range of any possible application involving them—or even the more basic discoveries of those facts.

For instance, Newton’s original formulation of the laws of dynamics, which is essentially a formulation in terms of vector mechanics (though the concept of a vector had not yet been explicitly grasped in his time) does remain applicable, in principle, to every dynamical problem of the first world. Yet, a very large range of problems become tractable only via the variational/energy-based approaches (or the Lagrangian/Hamilton reformulations). [BTW, Newton was also the first person to correctly pose and solve a variational problem.] In the classical physics, the law of conservation of energy does not add anything new to the already known dynamics at its most fundamental level.  [Incidentally, I still remember how discovery of this fact had come as a shock to me!] But try to use the original Newtonian mechanics in calculations of, say, the heat of a chemical reaction!

And, my point here is deeper than that. Among two or more conceptual viewpoints explaining the same set of facts, the most fundamental among them is the most crucial—abandoning it affects the scope of any new possible discoveries the worst. Physical observation is basic to mathematics—and not vice versa. Hence, abandoning a more fundamental physics viewpoint affects the new discoveries the worst.

Thus, not only inventions of new mathematical principles, but also new physical discoveries themselves become at all possible only when you actively adopt a new conceptual perspective—even if its initial scope seemingly refers to the same old set of facts.

As an example of this latter fact right in our present context, see the ease with which Wang’s paper suggests the possibility that the exponent “2” in the inverse-square law may not be a constant—and the ease with which you can understand it, too! Otherwise, precisely due to the much-prized mathematical “tightness” of the Poisson-Laplace equation—and, if you want, you can also throw in here any supposed beauty of the harmonic analysis, the beauty of its symmetry, et cetera—the very idea of a variable exponent in a law verified in as many separate instances as Newton’s Law of Universal Gravitation, would look wacky and crackpot to any one—especially if the paper were not written using LaTeX! …

When Dirac in fact made a similar suggestion concerning the possible variability of the universal “constants” of physics, he was rightly held in high regard and admiration for that idea. Understandably so. Abandoning aether, it would take a genius to think of varying just that part of, say, the “spacetime” (i.e. without using even the hyphenation mark [whether using LaTeX or not]). Since most physicists by then had abandoned that idea of the aether, the suggestion did look awesome to many of them. From their viewpoint, it would take not just a normal genius but, say a genius^genius, to conceive of so “bold” and such “daring” an idea.

Well, there is some boldness and daring in here, but it’s not in the detail of suggesting the possible variability of what we take as universal constants—I mean to say, it’s not an issue limited to making a variable out of a constant; it does not concern an apparently marvellous piece of a mathematical thought. Instead, the boldness and daring is in trying to keep a more fundamental physics hypothesis, that of aether, in the physics theory, despite its denials by the authorities of the day. Once you put aether back into the physics theory (or never fully abandon it as probably was the case with Dirac—at least privately to his own mind), it then looks a plain and relatively simpler consequence of that theory.

Now, you can always put such a consequence in precise mathematical terms, which, taken out of context, is guaranteed to look unbelievably awesome. [Morally lesser professors at the world’s leading universities have always employed this trick.] Further, once the concrete suggestion comes out, you can always go back into the woodwork (or near your blackboard), deduce—in part using the new suggestion—and then, come out of the woodwork and say that it was already deducible even from the plain old mathematics, and use that claim both to make the new advancement look lesser, and to continue justifying your dogma. [Morally lesser professors at the world’s leading universities are known to employ also this trick.]

…And, this variability of the supposed universal constants was just an example. .

.. New conceptual perspectives, even if based on the same set of observational referents, enable new discoveries that would otherwise remain out of the reach of the human mind that uses only an existing conceptual framework which contains some unresolved “merely philosophical” paradoxes. Every fundamentally new field of mathematics—i.e., if it is authentically new (and not just a deductive avatar of an existing one) has, in fact, depended precisely on such conceptual advancements coming from physics (or the “physical” thinking).

The Objectivist epistemology even has terms for such things: the DC [not that one!], the CCD [and now you believe me, don’t you?], the rule of fundamentality, and all that. … OK. More, later.

Update 4: Added the usual section about a song I like.

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A Song I Like:

(Marathi) “hari bhajanaaviN kaaL ghaalavu nako re…”
Singer [of the version I like]: Dashrath Pujari
Music [of the version I like]: Dashrath Pujari (?)
Lyrics: Sant Sohirobaanaath

[PS: Just a stray thought…. Should I have put these updates in a separate post? … May be I will… I will think about that later on… For the time being, enough is enough!]

[E&OE]