Gravity's Time

C. S. Unnikrishnan

• Publisher: Jenny Stanford Publishing
• Year: 2022
• ISBN:
  9781000522761
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Astronomy & Astrophysics

This book is unique and exceptional in dealing with the notion of physical time rigorously, both logically and empirically. The central theme is the intimate relation between physical time and cosmic gravity. It establishes and explains, in an accessible manner, the one crucial physical fact that has been missed in the development of modern physics—that the enormous gravity of the matter and energy in the Universe is the controller and cause of the relativistic time. The material in the book is accurate and free of the ambiguities in the discussion of time and its modifications (dilation), synchronization of clocks, and simultaneity. The contents go beyond the current theories of relativity that fail to incorporate the cosmic gravity in their structure. The discussion of clocks in satellite navigational systems (like the GPS) is the most complete and accurate. The book offers several new insights, and it is the only available treatise on the complete physical truth about time. The contents are addressed to a wide range of readers, from general readers and students to experienced researchers, and will alsoappeal well to philosophers and historians of physics. This book has the enabling quality to deal with difficult questions about physical time, with unprecedented clarity and without paradoxes.

Chapter 1 Time

We explore the concept of Time with a desire to grasp it...

Then we realize that we can’t take even our baby steps on this road because we do not have the ingredients to make ‘time’. Our abstract time should be the distilled essence of our experienced time, as it is the case of all other physical quantities. And what do we see when we search our experience for the definition and meaning of time? Words that characterize time are ‘Evolution’, ‘Change’, ‘Order’, ‘Memory’, etc. But, all these notions dissolve away outside our consciousness, in the empty physical space. Pure emptiness cannot change. It cannot evolve, and it has no order or memory. Empty space does not have time. All our analyses of time finally focus on the evolution of the physical states of matter. Dynamics of matter suggests the concept of time, in its elementary nature. Motion, growth and decay, changes of all kinds, are what seed and reinforce our notion and experience of time. The seat of all these is matter and its energy distributed in space. The manifestation of time is only through the medium of matter.

We may at least pretend, with our vast experience, that we understand space and matter because we can imagine space without time or matter, and matter itself is our daily experience (the act of ‘imagining’ requires the gray matter called the mind, but we may ignore that for the time being due to our necessity to start somewhere). Time as we know is inseparable from our notions of matter. However hard we try, there is no viable notion of time in space devoid of all matter. We should not be surprised or despaired – Newton had tried to reach to the self of time, by defining it as a self-evident element of nature, but even he could not go beyond a theological soliloquy. This attempt was just a repetition of what he tried for defining absolute space. However, realizing the need to define tangible concepts of space and time that were fundamental to the dynamics he was developing, he defined usable space and time as ‘relative’, from the material reference markers and the evolution of matter.

The inseparable relation between matter and time may suggest, but not establish, a relation between gravity and time, because there is no matter without gravity. All matter, whether it is in a form tangible to the senses or in the form of energy of various kinds, generates, and also responds to, gravity. However, the relation between gravity and time is subtle, and hidden in the very core of physics. Theoretical developments like the General Theory of Relativity brought out this connection to some extent, but the actual roots go very deep. Today, ‘keeping time’ means much more in life than ever. Without our direct awareness, the deep and subtle relation between matter, gravity, and time is guiding and affecting the course of our lives, as manifested in daily navigation, banking, travel, safety, etc.

Thus, we realize that to understand time in a way we can use it in our lives with definite mastery and control, we need to understand it physically. The physical understanding of time enriches its psychological and intuitive understanding, revealing the harmony of our total empirical experience. Even the many layers of the philosophical understanding of time come within our grasp with the correct physical understanding of time. After all, marking and measuring time have been one of the most discussed tasks assigned by civilizations and human society to physicists and natural philosophers.

1.1 Space

We need to discuss the concept of ‘space’ and understand it before we can explore the nature of time. Though time is very different from space, in experience, time is realized and felt in space. Time is measured in space, with material devices occupying space.

We feel that we understand space better than time. Perhaps that is right, because space is an extension of ourselves. In fact, it is extension itself, and therefore space extends with our imagination to infinities without facing conceptual problems. Our visual reach covers both near and far; as near as our bodies and as far as the stars. However, our familiarity of space is limited to three dimensions. All discussions on a larger number of spatial directions have remained as speculations, without even any indirect evidence for their plausibility. Thus, space in real physics today has the same number of dimensions as matter itself and extended matter is the guide for our notions of space. In fact, if one thinks how we came to the conclusion that space is of three dimensions, the only reasonable answer is that we know only the dimensions of matter, and both the notion and the dimensions of space are the extrapolations of the properties of matter.

Newton attempted a description of ideal space, as an entity that was prior to matter, perhaps because he was convinced of its existence. Newton’s approach for a definition of space and time is similar to Aristotle’s approach in Physics: Book IV, the earliest of such an attempt explicitly in the context of the physics of motion (Aristotle, 1991). However, Newton made much progress compared to Aristotle. The real advance was in trying to distinguish between the ‘relative’ and the ‘absolute’, as we will see. Aristotle, as well as Galileo much later, acknowledged motion as sensible only relative to other things, whereas Newton recognized that all motion cannot be reduced to a single category.

In spite of Newton’s general statement in his Principia Mathernatica that the terms ‘space’, ‘time’ and ‘motion’ are well known to all, he put down formal definitions for the fundamental notions of space and time as the most essential a priori elements for the description of dynamics (Newton, 1846). In doing so, he clearly distinguished between the ‘relative’ and ‘absolute’ nature of motion, a division that has lasted to this day, dividing physical theories as well as philosophies sharply. He even provided an experimental proof for the reality of the ‘absolute space’, which remained unchallenged till two centuries later. Let us briefly examine the relevant aspects of Newtonian space and time.

Figure 1.1 Newton’s Principia (1686), the basis of the theory of dynamics.

Newton’s concepts of categories of space and time are defined and described in detail in the first ‘scholium’ of Book 1 of his Principia (Fig. 1.1), after definitions, and before the ‘axioms’ on the laws of motion.

SCHOLIUM

Hitherto I have laid down the definitions of such words as are less known, and explained the sense in which I would have them to be understood in the following discourse. I do not define time, space, place and motion, as being well known to all. Only I must observe, that the vulgar conceive those quantities under no other notions but from the relation they bear to sensible objects. And thence arise certain prejudices, for the removing of which, it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common. I. Absolute, true, and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year.

II. Absolute space, in its own nature, without regard to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces; which our senses determine by its position to bodies; and which is vulgarly taken for immovable space; such is the dimension of a subterraneous, an aereal, or celestial space, determined by its position in respect of the earth. Absolute and relative space, are the same in figure and magnitude; but they do not remain always numerically the same. For if the earth, for instance, moves, a space of our air, which relatively and in respect of the earth remains always the same, will at one time be one part of the absolute space into which the air passes; at another time it will be another part of the same, and so absolutely understood, it will be perpetually mutable...

But we may distinguish rest and motion, absolute and relative, one from the other by their properties, causes and effects. It is a property of rest, that bodies really at rest do rest in respect to one another. And therefore as it is possible, that in the remote regions of the fixed stars, or perhaps far beyond them, there may be some body absolutely at rest; but impossible to know, from the position of bodies to one another in our regions whether any of these do keep the same position to that remote body; it follows that absolute rest cannot be determined from the position of bodies in our regions.

Newton then prescribes how to distinguish empirically between absolute and relative motion, motion relative to the absolute space and relative to other bodies. His ‘water and pail’ experiment has been discussed and debated by physicists and philosophers over the next three centuries, without consensus. We do not need to discuss these details. It will suffice to realize that Newton’s distinction between absolute and relative space was the appearance and experience of the centrifugal force only when bodies rotate with respect to the ‘absolute space’. Two centuries later, the philosopher-physicist Ernst Mach expressed his remarkable criticism of Newton’s dependence on the insensible and metaphysical absolute space, as the basis for the physical explanation of the centrifugal and inertial forces (Mach, 1919). Mach suggested that some physical interaction with the stars, nebulae and the rest of the matter in the Universe must be the cause for the inertial forces. It is an empirical fact that such forces appear when the rotation is relative to the celestial frame of distant motionless stars. However, with very little matter seen and known then, the gravitational interaction (or any known interaction) could not be explicitly invoked as the reason. This was because the law of gravity was well measured and characterized, and the potentials and forces due to the matter visible and known then would have been too small to be taken seriously as the source of large inertial forces, despite the strong clue that such forces were ‘inertial’, proportional to the mass, just as gravity was. During the discussion of Newton’s notions of space and the inertial forces, Mach wrote in his ‘Science of Mechanics’ something deep and significant about time as well:

When we say a thing A changes with the time, we mean simply that the conditions that determine a thing A depend on the conditions that determine another thing. The vibrations of a pendulum take place in time when its excursion depends on the position of the earth. Since, however, in the observation of the pendulum, we are not under the necessity of taking into account its dependence on the position of the earth, but may compare it with any other thing (the conditions of which of course also depend on the position of the earth), the illusory notion easily arises that all the things with which we compare it are unessential. Time, accordingly, appears to be some particular and independent thing, on the progress of which the position of the pendulum depends, while the things that we resort to for comparison and choose at random appear to play a wholly collateral part. But we must not forget that all things in the world are connected with one another and depend on one another...

Note the particularly important point about the apparition of time as an independent entity, ‘on the progress of which the position of the pendulum depends’ when factually it is the motion of the pendulum, or any other equivalent, that we call the passage of time. We will discuss this later, in great detail.

It is a subtle, but important point that Mach’s criticism of the Newtonian concept of empty ‘absolute space’ as an existential basis for dynamics is applicable to the Newtonian concept of the ‘absolute time’ in empty space as well. The two cannot be separated because, while the notion of space is tightly linked to matter and its extension, the notion of time is linked to the evolution of the physical states of matter. Finally, as we shall learn, the evolution of matter and time itself are modified by the gravity of matter and energy in a universal way, as only gravity can do.

It is very important to realize that even today, we do not understand the origin of inertia and the commonplace and ubiquitous inertial forces. Therefore, the deep questions raised by the discussions by Newton and Mach remain unanswered even after Einstein’s apparent success with his General Theory of Relativity. Isn’t it surprising, and somewhat unbelievable, that the real force that presses us to the seat in an aircraft that is taking off, or the crazy forces we feel in a turn-twist roller coaster at an amusement park do not have a proper explanation in physics, even after centuries of refinements and advance in the theory of motion and dynamics? Which of the known forces of nature appear as the inertial forces? For me, it was a troubling surprise and a sure indication that our theories were incomplete. However, these are precisely the questions for which we will soon find definite and lasting answers.

1.2 Matter

Though the reason for physics is ‘matter’ and its ‘dynamics’, modern theoretical physics tries to treat space and time as more fundamental than matter. However, any rigorous approach shows that matter is the anchor for time. Time, in all cases imaginable, is the changes in the physical states of matter; time has no existence separate from matter. Time is localized with matter. All of theoretical dynamics, where we assume a ‘flowing time’ to describe the motion in space, is a comparison of one motion of matter with another, with one of them abstracted as time. Therefore, there is nothing physical called space-time, separate from matter and its physical states; space is where matter is, and time is contained within, and not outside space in a separate dimension. We will pursue this important observation further, in more detail.

Matter is the greatest puzzle faced by the ‘matter with awareness’, the ‘conscious us’. The origin of space and time is of secondary importance to the origin of matter. The reason is that the only tangible reality that we sense is matter. The many qualia that we experience, based on which we form our intuitions of the external world, are all through the physical states of sensible matter. That is why scriptures of learned civilizations hypothesized on the origin of matter as prior to even the notion of God. The primary preoccupation and effort of physics have been always in understanding the ultimate structure and elementary units of matter, in the hope of understanding its presumably simple origins. There are two aspects of matter that are relevant at the core of our discussions. One is that all matter is source of gravity, without exception. This is very different from other interactions because there is a lot of bulk matter with no electromagnetic interaction – we label such matter as electrically ‘neutral’. Only the matter with residual electric charge has the electromagnetic interaction. But, all matter has gravity. Matter mass is the charge of gravity. There is no ‘gravitationally neutral’ matter.

The second aspect of matter that is relevant for our discussion is the equivalence of mass and energy, discovered for the electromagnetic energy by Lorentz, and established in general by Einstein. Thus, energy is also matter and it is an equal source of gravity. This equivalence finally provided us a way of consistently speculating a possible origin of matter from ‘nothing’. If the matter with positive energy is created with an equivalent amount of compensating negative energy of mutual in...

Table of contents

• Cover Page
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• List of Figures
• List of Tables
• Preface
• Acknowledgments
• 1 Time
• 2 Gravity
• 3 Time and Motion
• 4 Our Universe and Cosmic Gravity
• 5 Gravity's Time
• 6 Interlude on Simultaneity and the One-Way Speed of Light
• 7 The Moving Clocks of Navigational Satellite Systems
• 8 The Dissemination of Standard Time
• 9 Gravity’s Time in Quantum Mechanics
• 10 Apparent Arrows of the Corporeal Time
• 11 The Last Ticks
• Bibliography
• Index