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Hulchul: The Common Ingredient of Motion and Time
By Sohan Jain
AuthorHouse
Copyright © 2012 Sohan Jain
All right reserved.
ISBN: 978-1-4685-6298-9
Chapter One
Prime Ticks: The Building Blocks of Motion and Time
1.1 What Is Hulchul?
We believe that motion and time are two sides of the same coin; the coin, here, is hulchul. What is hulchul? Literarily, hulchul is a common Hindi word, an abstract noun that means movement, commotion, hustle-bustle, agitation, any activity attracting one's attention, with a wide variety of its connotations. Of its two syllables, "hul" means shaking and "chul" means moving; both syllables rhyme with the word "null." Some examples of sentences using the word hulchul:
• Are you having a party? I see some hulchul in your house.
• He had hulchul in his heart after he saw the woman of his dreams again.
• There is a lot of political hulchul before a major election.
• There is some hulchul here mostly on Friday evenings; otherwise, it is a quiet shopping center.
• We had a couple of earthquakes in the last year; Mother Nature is having some hulchul, too.
All hulchuls in the above sentences imply some kind of motion directly or indirectly—all are complex motions. This does not mean hulchul implies only complex motion—it includes any kind of motion, simple or complex.
1.2 Instants of Time and Instants of Motion
Goal: Our goal in this book is to explore for an intrinsic, deeper relation between motion and time in the light of time dilation. Further, to establish a mathematical theory of motion and time to demonstrate: Just as time is a sequence of instants of time, similarly, motion is a sequence of instants of motion; instants of motion are the smallest movements, indivisible any further. Hulchul is just a set of these small movements we will call prime ticks. The two sequences of instants of motion and time are interspersed into a common sequence; that is, the common sequence is a mix of instants of motion and instants of time. Alternatively, the common sequence is a mix of three types of instants: Pure instants of motion, pure instants of time, and composite instants; a composite instant is both an instant of motion and an instant of time. We believe:
The instants, making the common sequence, are the common ingredient of motion and time; further, a body does not experience any time during pure instants of motion—a phenomenon we will call time outage; time dilation is the same as a time outage; the way a time outage is arrived at, explains why there is time dilation.
1.3 Bodies, Motion, and Time—A Different Perspective
1.3.1 Motion and Time
Motion: For the purpose of this research, hulchul refers to any kind of motion that may be translational, rotational, vibrating, oscillating, etc. or a mix of them. Here, motion and time are two views of the same physical concept we will call hulchul; we will define hulchul, with a mathematical precision later. For the moment, to keep it simple, we will assume motion of a body as a sequence of small movements, indivisible any further, of the body.
Motion is not continuous. Motion is like a movie—a sequence of individual picture frames; individual picture frames, here, are the instants of motion.
Time: One common use of time is to measure the speed of a moving body. The Theory of Relativity elevated this relationship between motion and time to another level called Time Dilation: The time for a body slows downs as the body moves; the slowdown of time increases as the speed of the body increases. One of the objectives of this research is to go a step further and to introduce the notion of Time Outage as alluded to earlier.
1.3.2 Inner and Outer Bodies, and Their Relationship
If b1 is a constituent part of a body b, then we will call b1 an inner body of b, and b an outer body of b1. The inner-outer body relationship is transitive. We denote this relationship between b1 and b as: b1 b. The inner-outer body relationship is one of the fundamentals of the notion of hulchul.
The inner-outer body relationship between two bodies is not necessarily permanent or continuous: A spaceship on the surface of the Earth, ready for launch to orbit Mars, is an inner body of the Earth but after the spaceship begins orbiting Mars, it is an inner body of Mars. The inner-outer body relationship between two bodies may be continuous or intermittent. The preceding observation adds complexity to hulchul; hulchul deals with the inner-outer body relationship extensively. For example: Earth is an inner body of the solar system; compared to this, a double star and its planets have a more complex inner-outer body relationship. The inner-outer body relationship between an electron and two atoms sharing the electron is more complex than an atom having an electron permanently. Hulchul theory, by conception and design, is intended to handle this kind of complexity.
Lineal Bodies and Non-Lineal Bodies: Two bodies will be called lineal bodies if exactly one of the two bodies is an inner body of the other body. If two bodies are not lineal, then they will be called non-lineal bodies. Two or more lineal bodies can be viewed as one body embedded into another body serially (not in parallel). The notion of lineal and non-lineal bodies is central to hulchul. Later, we will extend this notion to the small, indivisible movements of bodies, too. For example, in Figure 1.3.2, movements t1 and t3 are lineal; movements t1 and t2 are non-lineal.
Naming Convention for Inner-Outer Bodies: As much as possible, we will use the following names in the following order for bodies in a chain of inner-outer bodies:
... b2 [subset] b1 [subset] b0 [subset] b [subset] B [subset] B0 [subset] B1 [subset] B2 ...
1.3.3 Inheritance of Motion
We will assume the following characteristic of a body and its motion: A body goes wherever any of its outer bodies goes; in addition to this, the inner body may move independently, too. We will define this characteristic in this way: An inner body inherits the motion of its outer body. For example: Passengers on a moving train go wherever the train goes. The passengers and train go wherever the Earth goes.
Passengers, train, and the Earth go wherever the solar system goes, and so on. In each case, additionally, an inner body may also move independently of its outer bodies.
1.3.4 About Bodies—Their Four Types
For the purpose of this research, all bodies, in general, are the same and we will treat them generally the same way. However, we will divide the bodies into the following four categories:
The U Body—We will call the universe as a whole the U body. To keep it simple, we will assume that all bodies are inner bodies of U and U has no outer body.
Elementary Bodies—We will define an elementary body as one having no inner body. Elementary particles are elementary bodies (on the assumption that an elementary particle has no inner body).
Phantom Bodies—We will define a phantom body as a body that does not inherit the motion of its outer bodies; another characteristic of a phantom body is that it does not have any outer bodies except the U body. We will assume photons and light are examples of phantom bodies.
We believe it is the first characteristic of a phantom body as to why the speed of the source of light does not add to the speed of light. In fact, the source of light is not even an outer body of light. The two characteristics of phantom bodies are complementary of each other.
Strictly speaking, the above implied behavior of light and photons is correct when they are moving in a vacuum; when they interact with matter, they are in a more complex state.
We will discuss this more under Proposition #3.
Common Bodies—Any body, other than the U body, an elementary body or a phantom body, will be called a common body. Examples: atom, car, animal, heart, brain, planet, star, galaxy.
1.3.5 Outer Body as a Frame of Reference
For the purpose of this research, for the motion of a body b, we will use mostly an outer body B of b as a frame of reference. The outer body B can be turned into a practical frame of reference, for example, by firmly attaching a coordinate system to B so the frame of reference goes wherever the outer body B goes and it does not move in B. The body b goes wherever the frame of reference and the body B go; aside from this, the body b can have its own independent motion with reference to B.
1.3.6 Internal, External and Composite Motion
Internal and External Motion: We will divide motion of a body b into two broad categories: external motion and internal motion. The external motion of b is with reference to an outer body B of b whereas the internal motion of b is the collective motion of all inner bodies of b with reference to b. Internal motion and external motion are two views of the same motion. If a body b moves in a body B, then the underlying motion is the external motion of b and a part of the internal motion of B. The internal motion of a body is as critical as the external motion is to the notion of hulchul.
Composite Motion of a Body: Internal motion and external motion of a body are not necessarily mutually exclusive. A body b can have internal motion and external motion concurrently. We will call this composite motion of the body b. For example: a ship is moving and, at the same time, a number of other activities, involving motion, are going on inside the ship; some of the motion caused by these activities may be intermittently concurrent with the motion of the ship as a whole. Therefore, the ship may have: 1) both internal and external motion concurrently during some instants of time, 2) only internal motion during some other instants of time and 3) only external motion during the remaining instants of time.
1.3.7 Extended and Absolute External Motion of a Body
Suppose b [subset] B [subset] B1 [subset] B2. Suppose b moves in B, and B moves in B1. Then b moves in B1 and this will be called an extended external motion of b in B1. If B1 also moves in B2, then b has an extended external motion in B2. Extended external motion of b in U will be called an absolute motion of b. We will create a formal mathematical framework for extended and absolute motion of a body in Chapter 3. (Internal motion of a body is always absolute.)
1.3.8 An Observation to Understand Motion and the Absolute Nature of Motion
Look at a book lying on a table. The book appears to be at rest but it is not. Internally, trillions of atoms and their constituent parts are frantically jostling with each other—we will call this the internal motion of the book. On the other hand, if we move the book on the table, we will call this an external motion of the book relative to the table. Instead, if we move the table, the book again has external motion though in a different frame of reference—the room. If we move neither the book nor the table, the book still has external motion for so many other reasons such as: the Earth is rotating about its axis and it is also moving around the Sun; the Sun is rotating about its axis and it is also moving in our galaxy; the galaxy itself is spinning; and so on until we come to the U body.
Therefore, the book has absolute motion in the U body aside from several relative motions. It has two kinds of motions: internal motion and external motion. In fact, the same can be said about any body such as: an electron, photon, atom, car, animal, heart, brain, planet, star, galaxy or the U body, though an electron and photon can have only external motion and the U body can have only internal motion.
Absolute Motion: We can talk about the motion of the Earth in the solar system, and motion of the Earth in the Milky Way. Can we talk, in a similar way, about the motion of Earth in the U body, at least, in the sense of a mathematical abstraction? Absolute motion of a body b can be thought of as the total motion of the body b relative to all outer bodies of b, which is the same as the motion of b in the U body.
Question: In view of the inheritance of internal motion by outer bodies and external motion by inner bodies, it appears that an outer body has more internal motion than any of its inner bodies has, and an inner body has more external motion than any of its outer bodies has. That is, internal motion increases outer-body-ward and external motion increases inner-body-ward. In that case, is the sum of internal motion and external motion the same for all bodies?
In fact, we will show that this is true if we measure the motion in a certain way—to be called concurrency; we will establish this in Chapter 3. We will also show that concurrency of external motion behaves like motion and concurrency of internal motion behaves like time.
1.3.9 Interchangeability of Internal and External Motion
A thought experiment: Let us do a thought experiment. Suppose we have a system of four point particles P1, P2, P3 and P4. We will call this a point system PS4. In Figure 1.3.9A, some or all four point particles move slightly in different directions, some of them may not even move at all. This causes an internal motion in the point-system PS4. Now suppose the four points again move slightly, and this time, all points move the same distance and in the same direction as shown in Figure 1.3.9A. This is a case of an external motion of the point system PS4 as a whole. As shown in Figure 1.3.9A, the four points move the same distance and in the same direction again and, finally, four points move in different directions.
Now suppose the four points undergo a little collective motion, say, 100 times; sometimes they may undergo an internal motion and sometimes an external motion. Therefore, we see that a body may sometimes experience internal motion and sometimes external motion. What we want to emphasize here is that internal motion of a body may change to external motion and vice-versa, from instant to instant, depending on whether its constituent parts, enough constituent parts making up the entire body, move the same distance and in the same direction or not.
We notice, so far, that if there is an internal motion, then there is no external motion and vice versa; but this is not necessarily to be so. Internal and external motion of a body may occur concurrently. We will call this a composite motion. A composite motion is visualized in Figure 1.3.9B where one of the point particles, P1, is replaced by another point system PS5, which consists of five point particles. PS5 is an inner body of PS4. PS5 behaves like PS4 in its own right. PS5 can experience composite motion when PS5 moves as a whole in PS4 and at the same time, PS5 has internal motion.
Question: On the assumption that electrons do move in an atom: Do the electrons in a shell/sub-shell of an atom move independently in the shell/sub-shell so a shell/sub-shell has internal motion or do they all move in sync, that is as one body, so a shell/sub-shell moves or wobbles as a whole around its nucleus? Or, is it a mix of the two kinds of motions?
1.4 Prime Ticks—The Building Blocks of Time and Motion
1.4.1 Ticks, Prime Ticks and Chained Ticks
We believe that any kind of motion of a body can be divided into tiny indivisible movements of the body; these movements are very similar for any kind of motion of any body. We will assume that motion of a body is not continuous; it is discrete.
Suppose b1 and b are two bodies such that b1 [subset] b. We may perceive the motion of b1 in b, for example, as a sequence of the repetition of the following two steps:
• Step 1: The body b1 moves in b with b as a frame of reference.
• Step 2: After the movement in Step 1, there is a change in the motion of b1 in b. The change may be: b1 has a pause, and/or its direction changes.
We will call an occurrence of the above two steps a tick of b1 in b; we will say: b1 ticks in b. Let us name this tick as t1 and denote it as t1 = t[b1, b]. We will call the body b1 the object body of t1 and body b the reference body of t1.
It is possible that there exists a body b0 such that b1 [subset] b0 [subset] b, b1 ticks in b0 and b0 ticks in b concurrently; then we will call the tick of b1 in b a chained tick. We will represent this as: t[b1, b] = t[b1, b0] + t[b0, b] and we say: tick t[b1, b] is decomposed into two ticks t[b1, b0] and t[b0, b]. A tick may or may not be decomposed into two or more ticks. If a tick t1 cannot be decomposed in the preceding manner, then we will call t1 a prime tick or p-tick of b1 in b. A tick is either a prime tick or a chained tick; the term "tick" is just a common name for prime ticks and chained ticks. (Technically, we can also say, prime ticks and chained ticks are sub-classes of the class ticks.)
(Continues...)
Excerpted from Hulchul: The Common Ingredient of Motion and Time by Sohan Jain Copyright © 2012 by Sohan Jain. Excerpted by permission of AuthorHouse. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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