# Relating the One with the Many

0. Review and Context: This post is the last one in this mini-series on the subject of the one vs. many (as understood in the context of physics). The earlier posts in this series have been, in the chronological and logical order, these:

1. Introducing a very foundational issue of physics (and of maths) [^]
2. The One vs. the Many [^]
3. Some of the implications of the “Many Objects” idea… [^]
4. Some of the implications of the “One Object” idea… [^]

In the second post in this series, we had seen how a single object can be split up into many objects (or the many objects seen as parts of a single object). Now, in this post, we note some more observations about relating the One with the Many.

The description below begins with a discussion of how the One Object may be separated into Many Objects. However, note that the maths involved here is perfectly symmetrical, and therefore, the ensuing discussion for the separation of the one object into many objects also just as well applies for putting many objects together into one object, i.e., integration.

In the second and third posts, we handled the perceived multiplicity of objects via a spatial separation according to the varying measures of the same property. A few remarks on the process of separation (or, symmetrically, on the process of integration) are now in order.

1. The extents of spatial separation depends on what property you choose on the basis of which to effect the separation:

To begin with, note that the exact extents of any spatial separations would vary depending on what property you choose for measuring them.

To take a very “layman-like” example, suppose you take a cotton-seed, i.e. the one with a soft ball of fine cotton fibres emanating from a hard center, as shown here [^]. Suppose if you use the property of reflectivity (or, the ability to be seen in a bright light against a darker background), then for the cotton-seed, the width of the overall seed might come out to be, say, 5 cm. That is to say, the spatial extent ascribable to this object would be 5 cm. However, if you choose some other physical property, then the same object may end up registering quite a different size. For instance, if you use the property: “ability to be lifted using prongs” as the true measure for the width for the seed, then its size may very well come out as just about 1–2 cm, because the soft ball of the fibres would have got crushed to a smaller volume in the act of lifting.

In short: Different properties can easily imply different extensions for the same distinguished (or separated)“object,” i.e., for the same distinguished part of the physical universe.

2. The One Object may be separated into Many Objects on a basis other than that of the spatial separation:

Spatial attributes are fundamental, but they don’t always provide the best principle to organize a theory of physics.

The separation of the single universe-object into many of its parts need not proceed on the basis of only the “physical” space.

It would be possible to separate the universe on the basis of certain basis-functions which are defined over every spatial part of the universe. For instance, the Fourier analysis gives rise to a separation of a property-function into many complex-valued frequencies (viz. pairs of spatial undulations).

If the separation is done on the basis of such abstract functions, and not on the basis of the spatial extents, then the problem of the empty regions vaporizes away immediately. There always is some or the other “frequency”, with some or the other amplitude and phase, present at literally every point in the physical universe—including in the regions of the so-called “empty” space.

However, do note that the Fourier separation is a mathematical principle. Its correspondence to the physical universe must pass through the usual, required, epistemological hoops. … Here is one instance:

Question: If infinity cannot metaphysically exist (simply because it is a mathematical concept and no mathematical concept physically exists), then how is it that an infinite series may potentially be required for splitting up the given function (viz. the one which specifies the variations the given property of the physical universe)?

Answer: An infinite Fourier series cannot indeed be used by way of a direct physical description; however, a truncated (finite) Fourier series may be.

Here, we are basically relying on the same trick as we saw earlier in this mini-series of posts: We can claim that what the truncated Fourier series represents is the actual reality, and that that function which requires an infinite series is merely a depiction, an idealization, an abstraction.

3. When to use which description—the One Object or the Many Objects:

Despite the enormous advantages of the second approach (of the One Object idea) in the fundamental theoretical physics, in classical physics as well as in our “day-to-day” life, we often speak of the physical reality using the cruder first approach (the one involving the Many Objects idea). This we do—and it’s perfectly OK to do so—mainly because of the involved context.

The Many Objects description of physics is closer to the perceptual level. Hence, its more direct, even simpler, in a way. Now, note a very important consideration:

The precision to used in a description (or a theory) is determined by its purpose.

The purpose for a description may be lofty, such as achieving fullest possible consistency of conceptual interrelations. Or it may be mundane, referring to what needs to be understood in order to get the practical things done in the day-to-day life. The range of integrations to be performed for the day-to-day usage is limited, very limited in fact. A cruder description could do for this purpose. The Many Objects idea is conceptually more economical to use here. [As a polemical remark on the side, observe that while Ayn Rand highlighted the value of purpose, neither Occam nor the later philosophers/physicists following him ever even thought of that idea: purpose.]

However, as the scope of the physical knowledge increases, the requirements of the long-range consistency mandate that it is the second approach (the one involving the One Object idea) which we must adopt as being a better representative of the actual reality, as being more fundamental.

Where does the switch-over occur?

I think that it occurs at a level of those physics problems in which the energetics program (initiated by Leibnitz), i.e., the Lagrangian approach, makes it easier to solve them, compared to the earlier, Newtonian approach. This answer basically says that any time you use the ideas such as fields, and energy, you must make the switch-over, because in the very act of using such ideas, implicitly, you are using the One Object idea anyway. Which means, EM theory, and yes, also thermodynamics.

And of course, by the time you begin tackling QM, the second approach becomes simply indispensable.

A personal side remark: I should have known better. I should have adopted the second approach earlier in my life. It would have spared me a lot of agonizing over the riddles of quantum physics, a lot of running in loops over the same territory (like a dog chasing his own tail). … But it’s OK. I am glad that at least by now, I know better. (And, engineers anyway don’t get taught the Lagrangian mechanics to the extent physicists do.)

A few days ago, Roger Schlafly had written a nice and brief post at his blog saying that there is a place for non-locality in physics. He had touched on that issue more from a common-sense and “practical” viewpoint of covering these two physics approaches [^].

Now, given the above write-up, you know that a stronger statement, in fact, can be made:

As soon as you enter the realm of the EM fields and the further development, the non-local (or the global or the One Object) theories are the only way to go.

A Song I Like:

[When I was a school-boy, I used to very much like this song. I would hum [no, can’t call it singing] with my friends. I don’t know why. OK. At least, don’t ask me why. Not any more, anyway 😉 .]

(Hindi) “thokar main hai meri saaraa zamaanaa”
Singer: Kishore Kumar
Music: R. D. Burman
Lyrics: Rajinder Krishan

OK. I am glad I have brought to a completion a series of posts that I initiated. Happened for the first time!

I have not been able to find time to actually write anything on my promised position paper on QM. … Have been thinking about how to present certain ideas better, but not making much progress… If you must ask: these involve entangled vs. product states—and why both must be possible, etc.

So, I don’t think I am going to be able to hold the mid-2017 deadline that I myself had set for me. It will take longer.

For the same reasons, may be I will be blogging less… Or, who knows, may be I will write very short general notings here and there…

Bye for now and take care…

# Some of the implications of the “One Object” idea…

0. Review and Context: This post continues with the subject of one vs. many physical objects. The earlier posts in this series have been, in the chronological and logical order, these:

1. Introducing a very foundational issue of physics (and of maths) [^]
2. The One vs. the Many [^]
3. Some of the implications of the “Many Objects” idea… [^]

In this post, we cover the implications of the second description, i.e., of the “one object” idea.

1. The observed multiplicity of objects as corresponding to certain quantitative differences in the attributes possessed by the universe-object:

In the second description, there exists one and only one object, which is the entire universe itself. This singleton object carries a myriad of attributes—literally each and everything that you ever see/touch/etc. around you (including your physical body) exists as “just” an attribute of this singleton object. In the general case, such attributes exist with quantitatively different degrees in different parts of the singleton universe-object. Those contiguous regions of the singleton object where the quantitative degrees of the given attribute fall sufficiently closer in range are treated by our perceptual faculty as separate objects.

In the general philosophy, there is a certain observation: Everything is interconnected. However, following the second description, not only are all objects interconnected, but at a deeper level, they are literally one and the same object! It’s just that each perceptually separate object has been distinguished on the basis of some quantitative measures (or amounts) of some or the other attribute or property with which that distinguished region exists.

A few consequences are noteworthy.

2. Implications for what precisely the law of causality refers to:

In the second description, what physically exists is the single physical object (that is the physical universe) and nothing else but that physical object.

The physical actor, in the primary sense of the term, therefore always is the entire universe itself, acting as a whole. The “appearance” of multiple objects—and their separate actions—is only a consequence of the universe having varying properties in different parts of or logically within itself.

Just the way the attributes carried by the universe are inhomogeneous (i.e., they differ in quantitative measures over different parts), so are the actions. The quantitative measures of actions too are inhomogeneous. In the general case, for any of the actions taken by the universe, the same action in general occurs to different degrees in different parts.

In the deepest and the most fundamental sense, since there is only one physical actor viz. the entire physical universe, what the law of causality refers to it is nothing but this physical actor, i.e., to the entire universe taken as a whole.

However, since the very nature of the singleton object includes the fact that different parts of itself exist with different attributes of differing degrees and therefore can and do act differently, the law of causality can also be seen to apply, in a secondary or derivative sense, to these distinguishable parts taken in isolation. The differing natures of the inhomogeneous parts together constitute all the causes existing in the physical universe, and the nature of the actions that this singleton object takes, to differing measures in different parts of itself, constitute all the effects.

The fact that the universe-object exists with various physical attributes or properties, leads to different concepts with which the universe-object can be studied.

3. The idea of space as derived from the physical universe:

One most prominent, general and fundamental property which may be used for distinguishing different parts of the universe-object is the fact that the distinguishable parts, taken by themselves, are spatially extended, and the related fact that they carry the attribute of being located where they are.

Locations and extensions are given in the sensory perceptual evidence. Thus, extensions and locations are directly perceived. They in part form the perceptual basis for the concept of space.

Space is an abstract, mathematical concept. Using this higher level concept, we are able to ascribe places even to those combinations of spatial relations where there is no concrete object existing.

4. A (mathematical) space as an abstraction based on certain attributes of the (physical) universe:

The above discussion makes it clear that the universe does not exist in space. On the other hand, space may be said to exist “in” the universe. However, here, here, the word “in” is to be taken in an abstract logical sense, not in the sense of a concrete existence. Space does exist in the universe but not concretely.

Space is an abstraction based on certain fundamental, directly perceived, spatial attributes or properties possessed by the singular universe-object. The two most fundamental of such (spatial) attributes are extensions and locations; other spatial attributes such as connectivity/topology, of being enclosed or covered or placed inside/outside, etc. are merely higher-level ideas that isolate different ways in which groups of objects with various extensions and locations exist. The extensions and locations themselves pertain to certain quantitative but directly perceived differences over different parts of the universe-object. Thus, ultimately, all spatial properties are possessed by the perceptually distinguishable parts of the singleton universe-object.

Since the concept of space is mathematical and abstract, many different ideas or imaginations may be used in formulating the concept of a space. For instance, Euclidean vs. hyperbolic space, or continuous vs. discrete space, etc. Not only that, multiple instances of a given space also are easily possible. In contrast, the idea of instances, of quantities, does not apply to the universe-object; it remains the unique, singular, concept, one which, when taken as a whole, must remain beyond any quantitative characterization.

Since there is nothing but the universe object to exist physically, the only spatially relevant statement we can make about the universe itself is this: if some part of the universe does indeed exist, then this part can be put in a quantitative relation with one of the instances of some or the other space.

The italicized part is based on the assumption that every part of the universe does carry spatial attributes. This itself is just an assumption; there is no way to directly validate it.

Note that the aforementioned statement does not imply that the physical universe can be said as being present everywhere. The universe does not exist everywhere.

To say that the physical universe is present everywhere is an epistemologically misconceived formulation. It is indicative of an intellectually sloppy, inconsistent way of connecting the two ideas: (i) physical universe (which is what actually exists, in the physical sense), and (ii) space (which is a mathematical and abstract concept).

“Everywhere” refers to a set of all possible places implied by a certain concept of space. Physical universe, on the other hand, refers what actually exists. It is possible that the procedure of constructing a concept of space includes places that have no correspondence to any part of the physical universe.

5. A space can be finite or infinite, but the physical universe is neither:

Space, being a mathematical concept, can be imagined as infinitely extended. However, the physical universe cannot be. And the reason that an infinitely extended physical universe is a nonsense idea is not because the physical universe is, or even can be known to be, finite.

The fact of the matter is, no quantitative statement can at all be made in respect of the physical universe taken as a whole.

Quantitative statements can only be made if some suitable mathematical procedure is available for making the requisite measurements. Now, any and all mathematical procedures are constructed only in reference to some or the other parts of the universe, not in reference to the entirety of the universe taken as a whole. The very nature of mathematics is like that. The epistemological procedures of differentiation and integration must first be performed before any mathematical procedure can at all be constructed or applied. (For instance, before inventing or applying even the simplest mathematical procedure of counting, you must have first performed integration of a group of similar concrete objects such as identical balls, and differentiated this group from the background of the rest of the she-bang.) But as soon as you say: “differentiate,” you already concede the idea that the entirety of the universe is not being considered in the further thought. To differentiate is to agree to selectively pick up only a part and thereby to agree to leave some other part(s). So, as soon as you perform differentiation, from that point on, you no longer are referring to all the parts at the same time. That’s why, no concrete mathematical procedure can at all be constructed which possibly can allow you to measure the universe as a whole. The very idea itself does not make sense. There can be a measure for this part of the universe or for that part. But there can be no measure for the universe taken as a whole. That’s why, its meaningless to talk of applying any quantitative attributes to the entirety of the physical universe taken as a whole—including the talk of the universe being even finite in extent.

No procedure can be said to have yielded even a finite amount as a measurement outcome, if the thing asserted as measured is taken to be the universe as a whole. As a result, no statement regarding even finitude can be made for the physical universe. (I here differ from the Objectivist position, e.g., Dr. Peikoff’s writings in OPAR; they believe that the universe is finite.)

It is true that every property shown by every actually observed part of the physical universe is finite. The inference from this statement to the conclusion that every part of the not-actually-observed but in-principle possibly existing part itself must also be finite, also is valid—within its context. However, the validity of this inference cannot be extended to the idea of a mathematical procedure that applies to all the parts of the universe at the same time. The objection is: we cannot speak of “all” parts itself unless we specify a procedure to include and exhaust every existing part—but no such procedure can ever be specified because differentiation and integration are at the base of the very conceptual level (i.e. at the base of every mathematical procedure).

The idea of an infinite physical universe [^] is flawed at a deep level. Infinity is a mathematical concept. Physical universe is what exists. The two cannot be related—there can be no mathematical procedure to relate the two.

Similarly, the idea of a finite physical universe also is flawed at a deep level.

Now, the idea that every part of the physical universe is finite, can be taken to be valid, simply because the procedure of measuring parts can at all be conducted, and such a procedure does in principle yield outcomes that are finite.

To speak of an infinite space, in contrast, also is OK. The idea here is to make a mental note to the effect that any  statements being made for some parts (possibly infinite number of parts) of this space need not have any correspondence with the spatial attributes of the actually existing physical universe-object—that the logical mapping from a part of a space to a physically existing spatial attribute would necessarily break down for every infinite part of an infinite space.

As far as physics is concerned, infinity is only a useful device for simplifying—reifying out—the complications due to certain possible variations in the boundary conditions of physics problems. When the domain is finite, changes in boundary conditions make the problem so complex that is is impossible to yield a law in the form of a differential equation. The idea of an infinite domain allows us to do precisely that. I had covered this aspect in an earlier post, here [^].

6. Implications for the gaps between perceived objects, and the issue of whether empty space plays a causal role or not:

There is no such a thing as a really “empty” part in the physical universe; the idea is a contradiction in terms.

In contrast, on the basis of our above discussion, notice that there can be empty regions of space(s), in fact even infinitely large empty regions of space(s) where literally nothing may be said to exist.

However, the ideas of emptiness or filled-ness can refer only to space, not to the physical universe.

Since there is no empty part in the universe, the issue of what causal role such an empty part can or does play, does not arise. As to the empty regions of space, since there can be no mapping from such regions to the physical universe, once again, the issue of its causal role does not arise. An empty space (or an empty part of a space) does not physically exist, period. Hence, it has no causal role to play, period.

However, if by empty space you mean such things as the region between two grey “objects” (i.e. two grey parts of the physical universe), then: that region is not, really speaking, empty; a part of what actually is the physical universe does exist there; otherwise, during their motions, the grey parts could not have come to occupy this supposedly empty regions of the space. In other words, if literally nothing were to exist in the gap between two objects, then the attribute of grayness could never possibly travel over there. But no such restriction on the movement of distinguishable objects has ever been observed, reported, or rationally conceived of, directly or indirectly. Hence, in conclusion, the gap region is not really speaking empty.

7.  The issue of the local vs. the “non-local” actions:

In the second description, since only one causal agent exists, what-ever physical action happens, it is taken by this one and the only physical universe. As a particular implication of that fact, where-ever any physical action happens, it again is to be attributed to the same physical universe.

In taking a physical action, it is easily conceivable that wherever the physical universe is actually extended, it simultaneously takes action at all those locations—and therefore, in all those abstract places which correspond to these locations.

As a consequence, it is possible that the physical universe simultaneously takes the same action, but to differing degrees, in different places. Since the actor is a singleton, since it anyway is present wherever any action occurs at all, any and all mystification arising from ascribing a cause and its effect to two separate entities simply vaporizes away. So does any and all mystification arising from ascribing a cause and its effect to two spatially separated locations. The locations may be different, but the actor remains the same.

For the above reasons, in the second description, instantaneous action-at-a-distance no longer remains a spooky idea. The reason is: there indeed is no instantaneous action at a distance, really speaking. IAD is only a loose way of saying that there is simultaneous action of, by, in, etc., the same causal (and effectual) actor that is the singleton object of the physical universe.

In fact we can go ahead and even say that in the second description, every action always is necessarily a global action (albeit with zero magnitudes in some parts of the universe); that there is no such a thing as an in-principle local action.

However, the aforementioned statement does not mean that spatially separated causes and effects cannot be observed. All that it means is that such multiple-objects-like phenomena are not primary; they are only higher-level, abstract, consequences of the more fundamental processes that are necessarily global in nature.

In the second post of this series [^], we saw how the grey regions of our illustrative example can be distinguished from each other (and from the background object) by using some critical density value as the criterion of their distinction or separation.

Since the second description involves only a single object, it necessarily requires a procedure for separating this singleton universe-object into multiple objects. There are certain interesting ideas concerning such a separation, and we will have a closer look at this very idea of separation, in the next post.

Of all the posts in this series, it is this post where I remain the most unsatisfied as far as my expression is concerned. I think a lot of simplification is called for. But in the choice between a better but very late expression and a timely but poor, awkward, expression, I have chosen the latter.

May be I will come back later and try to improve the flow and the expression of this post.

Next time,  I will also try to write something on how the two objections to the aether idea (mentioned in the last post) can be overcome.

A Song I Like:

(Marathi) “maajhee na mee raahile”
Music: Bal Parte
Singer: Lata Mangeshkar
Lyrics: Shanta Shelke

[A very minor revision done on 4th May 2017, 15:19 IST. May be, I will effect some more revisions later on.]

# 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.]

# The One vs. the Many

This post continues from my last post. In that post, I had presented a series of diagrams depicting the states of the universe over time, and I had then asked you a simple question pertaining to the physics of it: what the series depicted, physically speaking.

I had also given an answer to that question, the one which most people would give. It would run something like this:

There are two blocks/objects/entities which are initially moving closer towards each other. Following their motions, they come closer to each other, touch each other, and then reverse the directions of their motions. Thus, there is a collision of sorts. (We deliberately didn’t go into the maths of it, e.g., such narrower, detailed or higher-level aspects such as whether the motions were uniform or whether they had accelerations/decelerations (implying forces) or not, etc.)

I had then told you that the preceding was not the only answer possible. At least one more answer that captures the physics of it, also is certainly possible. This other answer in fact leads to an entirely different kind of mathematics! I had asked you to think about such alternative(s).

In this post, let me present the alternative description.

The alternative answer is what school/early college-level text-books never present to students. Neither do the pop-sci. books. However, the alternative approach has been documented, in some or the other form, at least for centuries if not for millenia. The topic is routinely taught in the advanced UG and PG courses in physics. However, the university courses always focus on the maths of it, not the physics. The physical ideas are never explicitly discussed in them. The text-books, too, dive straight into the relevant mathematics. The refusal of physicists (and of mathematicians) to dwell on the physical bases of this alternative description is in part responsible for the endless confusion and debates surrounding such issues as quantum entanglement, action at a distance, etc.

There also is another interesting side to it. Some aspects of this kind of a thinking are also evident in the philosophical/spiritual/religious/theological thinking. I am sure that you would immediately notice the resonance to such broader ideas as we subsequently discuss the alternative approach. However, let me stress that, in this post, we focus only on the physics-related issues. Thus, if I at times just say “universe,” it is to be understood that the word pertains only to the physical universe (i.e. the sum total of the inanimate objects, and also the inanimate aspects of living beings), not to any broader, spiritual or philosophical issue.

OK. Now, on to the alternative description itself. It runs something like this:

There is only one physical object which physically exists, and it is the physical universe. The grey blocks that you see in the series of diagrams are not independent objects, really speaking. In this particular depiction, what look like two independent “objects” are, really speaking, only two spatially isolated parts of what actually is one and only one object. In fact, the “empty” or the “white” space you see in between the objects is not, really speaking, empty at all—it does not represent the literal void or the nought, so to speak. The region of space corresponding to the “empty” portions is actually occupied by a physical something. In fact, since there is only one physical object to all exist, it is that same—singleton—physical object which is present also in the apparently empty portions.

This is not to deny that the distinction between the grey and the white/“empty” parts is not real. The physically existing distinction between them—the supposed qualitative differences among them—arises only because of some quantitative differences in some property/properties of the universe-object. In other words, the universe does not exist uniformly across all its parts. There are non-uniformities within it, some quantitative differences existing over different parts of itself. Notice, up to this point, we are talking of parts and variations within the universe. Both these words: “parts” and “within” are to be taken in the broadest possible sense, as in  the sense of“logical parts” and “logically within”.

However, one set of physical attributes that the universe carries pertains to the spatial characteristics such as extension and location. A suitable concept of space can therefore be abstracted from these physically existing characteristics. With the concept of space at hand, the physical universe can then be put into an abstract correspondence with a suitable choice of a space.

Thus, what this approach naturally suggests is the idea that we could use a mathematical field-function—i.e. a function of the coordinates of a chosen space—in order to describe the quantitative variations in the properties of the physical universe. For instance, assuming a $1D$ universe, it could be a function that looks something like what the following diagram shows.

Here, the function shows that a certain property (like mass density) exists with a zero measure in the regions of the supposedly empty space, whereas it exists with a finite measure, say with density of $\rho_{g}$ in the grey regions. Notice that if the formalism of a field-function (or a function of a space) is followed, then the property that captures the variations is necessarily a density. Just the way the mass density is the density of mass, similarly, you can have a density of any suitable quantity that is spread over space.

Now, simply because the density function (shown in blue) goes to zero in certain regions, we cannot therefore claim that nothing exists in those regions. The reason is: we can always construct another function that has some non-zero values everywhere, and yet it shows sufficiently sharp differences between different regions.

For instance, we could say that the graph has $\rho_{0} \neq 0$ value in the “empty” region, whereas it has a $\rho_{g}$ value in the interior of the grey regions.

Notice that in the above paragraph, we have subtly introduced two new ideas: (i) some non-zero value, say $\rho_{0}$, as being assigned even to the “empty” region—thereby assigning a “something”, a matter of positive existence, to the “empty”-ness; and (ii) the interface between the grey and the white regions is now asserted to be only “sufficiently” sharp—which means, the function does not take a totally sharp jump from $\rho_{0}$ to $\rho_{g}$ at a single point $x_i$ which identifies the location of the interface. Notice that if the function were to have such a totally sharp jump at a single point, it would not in fact even be a proper function, because there would be an infinity of density values between and including $\rho_{0}$ and $\rho_{g}$ existing at the same point $x_i$. Since the density would not have a unique value at $x_i$, it won’t be a function.

However, we can always replace the infinitely sharp interface of zero thickness by a sufficiently sharp (and not infinitely sharp) interface of a sufficiently small but finite thickness.

Essentially, what this trick does is to introduce three types of spatial regions, instead of two: (i) the region of the “empty” space, (ii) the region of the interface (iii) the interior, grey, region.

Of course, what we want are only two regions, not three. After all, we need to make a distinction only between the grey and the white regions. Not an issue. We can always club the interface region with either of the remaining two. Here is the mathematical procedure to do it.

Introduce yet another quantitative measure, viz., $\rho_{c}$, called the critical density. Using it, we can in fact divide the interface dispense region into further two parts: one which has $\rho < \rho_c$ and another one which has $\rho \geq \rho_c$. This procedure does give us a point-thick locus for the distinction between the grey and the white regions, and yet, the actual changes in the density always remain fully smooth (i.e. density can remain an infinitely differentiable function).

All in all, the property-variation at the interface looks like this:

Indeed, our previous solution of clubbing the interface region into the grey region is nothing but having $\rho_c = \rho_0$, whereas clubbing the interface in the “empty” space region is tantamount to having $\rho_c = \rho_g$.

In any case, we do have a sharp demarcation of regions, and yet, the density remains a continuous function.

We can now claim that such is what the physical reality is actually like; that the depiction presented in the original series of diagrams, consisting of infinitely sharp interfaces, cannot be taken as the reference standard because that depiction itself was just that: a mere depiction, which means: an idealized description. The actual reality never was like that. Our ultimate standard ought to be reality itself. There is no reason why reality should not actually be like what our latter description shows.

This argument does hold. Mankind has never been able to think of a single solid argument against having the latter kind of a description.

Even Euclid had no argument for the infinitely sharp interfaces his geometry implies. Euclid accepted the point, the line and the plane as the already given entities, as axioms. He did not bother himself with locating their meaning in some more fundamental geometrical or mathematical objects or methods.

What can be granted to Euclid can be granted to us. He had some axioms. We don’t believe them. So we will have our own axioms. As part of our axioms, interfaces are only finitely sharp.

Notice that the perceptual evidence remains the same. The difference between the two descriptions pertains to the question of what is it that we regard as object(s), primarily. The considerations of the sharpness or the thickness of the interface is only a detail, in the overall scheme.

In the first description, the grey regions are treated as objects in their own right. And there are many such objects.

In the second description, the grey regions are treated not as objects in their own right, but merely as distinguishable (and therefore different) parts of a single object that is the universe. Thus, there is only one object.

So, we now have two alternative descriptions. Which one is correct? And what precisely should we regard as an object anyway? … That, indeed, is a big question! 🙂

More on that question, and the consequences of the answers, in the next post in this series…. In it, I will touch upon the implications of the two descriptions for such things as (a) causality, (b) the issue of the aether—whether it exists and if yes, what its meaning is, (c) and the issue of the local vs. non-local descriptions (and implications therefore, in turn, for such issues as quantum entanglement), etc. Stay tuned.

A Song I Like:

(Hindi) “kitni akeli kitni tanha see lagi…”
Singer: Lata Mangeshkar
Music: Sachin Dev Burman
Lyrics: Majrooh Sultanpuri

[May be one editing pass, later? May be. …]