Hulchul: The Common Ingredient of Motion and Time Author, Sohan Jain, proposes the following in the book: Instants of Motion, Instants of Time and Time Outage: Just as time has instants of time, motion has instants of motion, too. Instants of time and motion can be divided into three classes: pure instants of time, pure instants of motion, and composite instants of time and motion. The sequences of the three types of instants are interspersed into a single sequence of their occurrences. A body does not experience time during pure instants of motion, a phenomenon we will call time outage -the cause of time dilation. Time outage is not continuous; it is intermittent. Internal and external motion of a body and their inheritance: Each body has, generally, two kinds of motions: internal motion and external motion. A body goes, wherever its outer bodies go. An inner body inherits external motion of its outer bodies. An outer body inherits internal motion of its inner bodies. Photons and light do not inherit motion; may be, this is why their motions are independent of their sources. Prime ticks, the building blocks of time and any motion: Motion of a common body is not continuous; it is intermittent. Any kind of motion is perceived to be made of discrete, indivisible tiny movements, called prime ticks (p-ticks). P-ticks are to motion what elementary particles are to matter or what photons are to light. There is time only because there is motion. Prime ticks are events and imply motion. Events have concurrency, which implies time. Total concurrency hulchul, a universal constant: Concurrency events of external and internal p-ticks of a body are precisely the instants of motion and time. The sum of the two is called the total concurrency hulchul (c-hulchul). Total c-hulchul is the same for all bodies. The proposed theory possibly explains: Why a particle accelerator works. Why atoms have compartmentalized internal st

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Hulchul: The Common Ingredient of Motion and Time

By Sohan Jain

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Copyright � 2012 Sohan Jain
All right reserved.
ISBN: 978-1-4685-6298-9

Preface...........................................................................xiIntroduction......................................................................xvChapter 1 Prime Ticks: The Building Blocks of Motion and Time.....................1Chapter 2 Theory of Concurrency of Events.........................................45Chapter 3 Prime Hulchul, XP-Hulchul and Concurrency Hulchul.......................65Chapter 4 Estimation of Composite Concurrency Hulchul.............................105Chapter 5 (Conclusions And Summary)...............................................139Lists of Notation And Figures.....................................................153List of Hulchul Related Concepts..................................................158Glossary..........................................................................165Bibliography......................................................................187Indexes...........................................................................189

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...

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