time

  


Why Time is Absolute and Relative

But Never Universal


By Vincent Sauvé



Abstract

The author elaborates upon a materialist view of the absolute and relative nature of time in a simple and (hopefully) clear manner for what has always been a complicated subject.  Albert Einstein's relativity of time is defended against those who think of time as a universal absolute that extends beyond its proper frame--the inertial frame. The inertial frame is clarified and elaborated upon to show why the scale of time is naturally, through Newton's Laws of Motion, in congruence to this frame. The conclusion of this paper is that the supposed paradoxes or absurdities of Einstein's relativity theory are really the result of a false conception of time.


Introduction

Many argue against Einstein's relativity theory because they cannot conceive how time can be anything other than universal (1).  Great confusion and error abound both by those who defend Einstein's relativity and those who attack it; so much so that it is easy to be discouraged from trying to clarify matters, yet I believe it is important to make whatever attempts possible.


The Concept of Time

First of all, a clear understanding of the concept of time (2) is necessary. Time is reckoned by noting the intervals that occur by the motion of material things. Historically, this has meant how many times the sun is at its highest point in the sky (days), the moon at the same phase (month), and the passing of the seasons (year). Recognition of the passage of time is always in relation to something material. The more uniform the material motion the more accurate we can be in our measurements and divisions of time. I also agree with this view of the measurement of time, by A. Einstein:

The measurement of time is effected by means of clocks. A clock is a thing which automatically passes in succession through a (practically) equal series of events (period). The number of periods (clock-time) elapsed serves as a measure of time. The meaning of this definition is at once clear if the event occurs in the immediate vicinity of the clock in space; for all observers then observe the same clock-time simultaneously with the event (by means of the eye) independently of their position. Until the theory of relativity was propounded it was assumed that the conception of simultaneity had an absolute objective meaning also for events separated in space.


This assumption was demolished by the discovery of the law of propagation of light. For if the velocity of light in empty space is to be a quantity that is independent of the choice (or, respectively, of the state of motion) of the inertial system to which it is referred, no absolute meaning can be assigned to the conception of the simultaneity of events that occur at points separated by a distance in space.  Rather, a special time must be allocated to every inertial system. If no co-ordinate system (inertial system) is used as a basis of reference there is no sense in asserting that events at different points in space occur simultaneously.  It is in consequence of this that space and time are welded together into a uniform four-dimensional continuum. (Einstein, 1992)



The Concept of Space

It is also important to know that in the evolution of concepts, the word space first of all applies to matter in the sense of that which extends spatially.  L. Feuerbach makes an interesting and succinct statement about space and time in an argument against the philosophical idealism of Hegel:

"In reality, exactly the opposite holds good, ...it is not things that presuppose space and time, but space and time that presupposes things, for space or extension presupposes something that extends, and time, movement, for time is indeed only a concept derived from movement, presupposes something that moves. Everything is spatial and temporal...." (Lenin, 1981)


So, if we can agree with the materialistic view that time is solidly linked to the motions of matter, is there any sense in speaking of universal motion (time)? How about universal rest which is the other side of the coin to universal motion?  A favorite quote of mine on this subject is the following:

All rest, all equilibrium, is only relative, only has meaning in relation to one or another definite form of motion....A motionless state of matter therefore proves to be one of the most empty and nonsensical of ideas--a "delirious fantasy" of the purest water. In order to arrive at such an idea, it is necessary to conceive as absolute rest the relative mechanical equilibrium in which a body on earth may find itself, and then to extend this absolute rest over the whole universe....This conception is nonsensical, because it transfers as absolute to the entire universe a state which by its nature is relative and which therefore can never be simultaneously applied except to a part of matter. (Engels, 1976)


Let us note how the following statement by Einstein merges into this, specifically, the absolute and relative nature of motion (and light):

The law of the constant velocity of light in empty space, which has been confirmed by the development of electro-dynamics and optics, and the equal legitimacy of all inertial systems (special principle of relativity), which was proved in a particularly incisive manner by Michelson's famous experiment, between them made it necessary, to begin with, that the concept of time should be made relative, each inertial system being given its own special time. ...According to the special theory of relativity, spatial co-ordinates and time still have an absolute character in so far as they are directly measurable by stationary clocks and bodies.  But they are relative in so far as they depend on the state of motion of the selected inertial system. (Einstein, 1934)


Light, like everything else that moves, is both absolute (denoted by c) and relative. Every material thing can also he said to have an absolute character, providing we choose the appropriate reference frame to consider with.  So that Einstein, when he says in his second postulate that "Any ray of light moves in the 'resting' coordinate system with the definite velocity c, which is independent of whether the ray was emitted by a resting or by a moving body" he is saying, that when time is measured within such system, that there is a constant to this system.  This is a specific absolute, not a universal absolute.  A "moving" system is the same as a "resting" system from the perspective of those doing the measuring within the system.  "It is essential to have time defined by means of clocks at rest in the resting system, and the time now defined being appropriate to the resting system we call 'the time of the resting system.' " (Einstein, 1905)

That motion, and hence light and time, is both absolute and relative is only natural, it is the nature of things.  Moreover, what is referred to as universal time is merely Greenwich time calculated from midnight at the Greenwich (England) meridian, an arbitrary designation that is quite useful in our modern world, but unknown a few centuries ago.

Yet why should other sentient beings on other worlds care about our arbitrary standard unit of time, presuming that they may become aware of us someday? Their day and night, and hence, their divisions of time will certainly be different than ours.

But, is there not a universal commonality--if we accept the cosmological principle, as I believe we should--that the laws of nature should be the same everywhere in the universe? Specifically, what if there are two identical atomic clocks, one on planet A, and one on planet B, with a day/night cycle very much different from each other. In this case, one can claim a limited type of universal time, by having each observer of the clocks count a certain number of atomic vibrations or cycles. The clock keeper from planet A can agree with the clock keeper on planet B that, for example, one hundred atomic cycles will be the accepted universal standard of time.  But obviously this is a limited form of universal time in that there is to be no relative motion between the two clocks.  When relative motion is introduced the signals sent will change. Actually, the signal itself does not change, but how it is received does.

An example of signaling the pace of time using mechanics, and then extending the situation to electrodynamics, will illustrate the similarities and problems:

Consider these two clocks to be no longer on these planets, but now in deep interstellar space at a constant distance from each other. These clocks have a gun attached to each. They also have a target attached safely nearby.  After every standard unit of time passes, clock A triggers a gunshot aimed at the target on clock B.  The observer (or machine/computer) at clock B records the impact and notes the constant arrival of a bullet (assuming the cartridges have exact loads of powder and that other factors remain the same). Now then, if one of the clocks, say clock A, is to produce an acceleration away from clock B, the observer at clock B would correctly conclude that clock A is accelerating away from clock B by his recording of the time of arrival of bullet impacts.  Or, he incorrectly concludes that clock A is no longer constant, that its time is slowing.

The same is true when light is used as a means of communication rather than a bullet.

...for every reference system in which the laws of mechanics are valid, the laws of electrodynamics and optics are also valid. (Einstein, 1905)

But, note that we do not see a change in velocity of photons from objects that approach or move away from us because that light first interacts with the atoms that are in our atmosphere and/or in our lens, etc., which are at rest relative to us (3). Though, measurements will reveal the increase or decrease in energy through the interacting medium.  And unlike the situation with light, the clock observer in the above mentioned example can conclude which interpretation is correct by measuring the velocity of the bullet.


The Inertial Reference Frame

To further elucidate matters it is also very important that we clearly understand the significance of the inertial reference frame (or system), what it is and what it isn't.

An inertial system is not equivalent to that of the “fixed stars”, as is the Machian notion, although a system (or body) can be inertial with respect to the average velocity of the background stars.

The problem of formulating physical laws for every CS [coordinate system] was solved by the so-called general relativity theory; the previous theory, applying only to inertial systems, is called the special relativity theory.  (Einstein and Infeld, pp. 212-3)

An inertial system is one in which

...the laws of classical mechanics are valid for the observer inside the elevator [in free-fall].   All bodies behave in the way expected by the law of inertia. (Einstein and Infeld, p. 215)

An inertial system does not need to be a room in free-fall. It can also be a satellite in orbit or a spacecraft with its thrusters off, whether it is accelerating relative to a massive body or not. It can also be a room decelerating up after being launched away from the surface of a massive body. All that is required to be inertial is to be free-moving so that all entities within its CS are under the same influence.  Very high velocities can also be imagined for an inertial system by simply imagining our inertial coordinate system (we'll use Einstein's example of an elevator) free-falling straight down to a very massive, very dense object such as a Neutron star (or orbiting this star at close range).  Also, it is not a subjective matter having to do with a human observer.  Replace the human observer by a machine that measures the motions within the inertial system and the results will be identical.

What is the universal fact to be witnessed by all observers who are part of an inertial frame, of which there are an innumerable number, (as well as relative velocities) in our universe? It is that all things that are at rest in that system will stay that way and that things that are set in motion will continue that motion in a straight line with a constant speed unless acted upon by external forces (Newton's first law of motion). An inertial frame is a frame of reference in which bodies are not accelerated from the perspective of within the system. Yet, the whole inertial frame of reference will be accelerated relative to something else. The important point here is that gravity accelerates all material things (including light) equally together, so that an inertial observer will notice that all things move equally and together within his system (or rather, stay in place relative to him), even though his entire system will be accelerating relative to something else. His space-time region has the characteristic of being flat (Euclidean) and isotropic. Any experiment, for example, whether he measures the space (extension, distance), and the time of impact of a bullet fired from a gun, or a beam of light from one wall of his "elevator" to the other wall, will have constant results regardless of direction. For him, (when considering only that which is part of his inertial system) his sense of motion or rest is an absolute one, and therefore, also his definition of time.

The ultimate scale of time is therefore based on our concept of universal laws of nature.  This was already recognized last century, long before the advent of modern ultra-precise time-keeping, in particular by Thomson and Tait in their treatise Natural Philosophy (1890).  In discussing the law of inertia they argued that it could be stated in the form:  the times during which any particular body not compelled by force to alter the speeds of its motions passes through equal spaces are equal; and in this form, they said, the law expresses our convention for measuring time. It is easily seen that this implies a unique time-scale except for the arbitrary choice of time unit and time zero. (Whitrow, 1973, p. 404).

The laws of motion inform us that the unique time-scale should naturally be firmly welded to the inertial reference frame.

The first law of motion, by stating under what circumstances the velocity of a moving body remains constant, supplies us with a method of defining equal intervals of time.  (Maxwell, 1952)


(A brief description of regions where spacetime curvature results will be useful before I continue.  Spacetime curvature is experienced when the coordinate system experiences the effects of gravity, or, equivalently, acceleration in the sense of what results from a rocket thruster. It is very important to know the difference between free-fall acceleration, and rocket produced acceleration. These two kinds of acceleration are not the same. For example, an observer in an elevator with a rocket engine attached but turned off and left to free-fall will experience Euclidean spacetime geometry in the motions of his little enclosed world. But as soon as he fires his rocket thruster spacetime curvature results; the strength of which depends on the thrust of his engines. All things set in motion (relative to the elevators coordinate system, of course) now will have curved paths, whether it is an object tossed in the elevator compartment or a light beam initiated from the compartment. Furthermore, the velocity of this light will be altered, depending if the light is directed "uphill" or "downhill" relative to the artificially produced gravitational field.)

Inertial regions are also known as Galilean regions:

...there are finite regions, where, with respect to a suitably chosen space of reference, material particles move freely without acceleration, and in which the laws of the special theory of relativity,… hold with remarkable accuracy. Such regions we shall call 'Galilean regions.' (Einstein, 1974, pp. 58-9) 


A system of co-ordinates of which the state of motion is such that the law of inertia holds relative to it is called a 'Galilean system of co-ordinates'. (O.E.D., 1991)


These Galilean (inertial) regions should not he considered to be very large:

We can therefore always regard an infinitesimally small region of the space-time continuum as Galilean.  For such an infinitely small region there will be an inertial system ... relatively to which we are to regard the laws of the special theory of relativity as valid.... Space-time regions of finite extent are, in general, not Galilean, so that a gravitational field cannot be done away with by any choice of co-ordinates in a finite region. (Einstein, 1974, pp. 63-4)

The reader will find an excellent illustration of why these Galilean regions are small in Taylor and Wheeler's Spacetime Physics, pp. 5-10.


Conclusion

Regardless of Einstein's faults; his many errors and ambiguous statements in the expounding of his theory of relativity, (and translation problems?) it is not correct to fault him for introducing the relativity of simultaneity (the relativity of time) as a solution for problems in physics as many authors have done.  The absolute and relative nature of time (motion/light) is difficult to grasp for anybody, particularly when our textbooks and our professors are not perfectly clear (often times because they don't grasp it well). I have to agree with the following comment from the authors of Spacetime Physics, even if I don't agree with everything they wrote in their textbook:

The problem of understanding relativity is no longer one of learning but one of intuition--a practiced way of seeing.  When seen with this intuition, a remarkable number of otherwise incomprehensible experimental results are revealed to be perfectly natural.

I think of those who have not yet learned this practiced way of seeing as having three-dimensional thinking. This three-dimensional thinking is wide-spread and has given us the interpretation of increased mass with increased velocity (4), the contraction of lengths as a dynamical phenomenon rather than a kinematic phenomenon (5), and asymmetrical time dilation (6). One needs to develop four-dimensional thinking to realize that (just as absolute motion is contained within relative motion) there are no paradoxes when absolute time is understood to be contained within relative time. It is my hope that this paper will help.

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References

Capek, M., 1973, author of the article "Time" in Dictionary of the History of Ideas: Studies of Selected Pivotal Ideas, Philip P. Wiener, editor in chief, (Charles Scribner's Sons, New York). pp. 389-398.

Einstein, A., 1905, "On the Electrodynamics of Moving Bodies," translated from Annalen der Physik by Arthur Miller in the Appendix of his book, Albert Einstein's Special Theory of Relativity, (Addison-Wesley Publishing Company, Inc., Advanced Book Program, Reading, MA, 1981).

Einstein, A., 1934, Essays In Science, (The Wisdom Library, A division of Philosophical Library, New York, NY) pp. 48-9. This is an abridged edition and authorized English translation from the volume 'Mein Weltbild' (The World as I See It).

Einstein, A., and Infeld, L., 1938, The Evolution of Physics, (A Clarion Book, published by Simon and Schuster, New York, NY).

Einstein, A., 1974, The Meaning of Relativity, (Princeton University Press, Princeton, NJ, fifth edition).

Einstein, A., 1992, Fadiman, C., general editor, "Albert Einstein On Space-Time," The Treasury of the Encyclopedia Britannica, (Viking Penguin, a division of Penguin Books USA Inc., New York, NY), pp. 371-383.

Engels, F., 1976, Anti-Duhring (Peking, 1976), pp. 74-5.

Lenin, V. I., 1981, "Philosophical Notebooks," Collected Works, Vol. 38, p. 70 (Moscow, 1981).

Maxwell, J. C., 1952, Matter and Motion, (Dover Publications Inc., New York, NY), p. 31.

Oxford English Dictionary (O.E.D.), 1991, under Galilean transformations see 1920, R.W. Lawson's translation of Einstein's Relativity for the quote.

Taylor, E. F., and Wheeler, J. A., 1966, Spacetime Physics, (W.H. Freeman and Company, New York).

Whitrow, G. J., 1973, author of the article "Time and Measurement" in Dictionary of the History of Ideas: Studies of Selected Pivotal Ideas, Philip P. Wiener, editor in chief, (Charles Scribner's Sons, New York), pp. 398-406.


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Notes

(1)   I was actually moved to write this paper by reading the latest example of this view of universal time in Wen-Xiu Li's paper, "On the Relativity of Lengths and Times," Apeiron Vol. 2, No. 1, January 1995, pp. 16-9.

(2)   It makes no sense to conceive of the concept of time as arising in any other way than through our observations of matter in motion. Time is not something a God brought forth with the imaginary 6,000-10,000 year old creation of the universe that is the biblical, or the equally imaginary 13.8 billion year age Big Bang model of the universe. Legitimate science, as opposed to the "science" that panders to the Western religious tradition of a God who created us and/or everything else, does not presume that our universe has an age when it was created (from nothing, in many popular speculations). We should recognize (even if it is difficult to comprehend) that our universe is infinite in time and space. The question of how our universe got here is not a legitimate question for the scientist any more than the question is for the creationist who nevertheless seldom worries about the same question in regards to his Creator.  All points of view, religious, and scientific, inevitably involve an infinite in time; either an infinite God or an infinite universe, and sometimes both. To argue, as some will, that God created time with his (or her) Creation, leaves open the question: Did time exist for God? If not, then the thoughts of past, present, and future don't exist for this God either. Likewise, this God gave no time to think about his Creation. For a look into how the Big Bang cosmology has become the religious sophisticates version of creation, see my "Is Big Bang cosmology good science, or 'creation science'?", 1994, in: Challenges in Modem Physics, Proceedings of the Pacific Division AAAS Meeting, San Francisco State University, June 20-24. Email me for a copy.

(3)  For articles on the phenomenon of light "extinguishing" see "The Unavailability of 'Old' Light," by John B. Schaefer, Am. J. Phys., Vol. 57, No. 3, March 1989, p. 200;  "Experimental Evidence for the Second Postulate of Special Relativity," by J.C. Fox, in Am. J. Phys., Vol. 30, No. 4, April 1962, pp. 297-300; "Speed of Light," by Carl E. Ockert, in Am. J. Phys., Vol. 36, No. 2, February 1968, pp. 158-161.

(4)  Please see Lev Okun's "The Concept of Mass," Physics Today, June 1989, pp. 31-6, excerpts:

In the modern language of relativity theory there is only one mass, the Newtonian mass m, which does not vary with velocity; hence the famous formula E=mc² has to be taken with a large grain of salt. ... The notion of the dependence of mass on velocity was introduced by Lorentz in 1899 and then developed by him and others in the years preceding Einstein's formulation of special relativity in 1905, as well as in later years. The basis of this notion is again the application of the nonrelativistic formula p=mv in the relativistic region, where (as we know now) this formula is not valid.


Also see Okun's reply in the Letters column, "Putting to Rest Mass Misconceptions," Physics Today, May 1990, pp. 13-4, 115, 117. And, Carl G. Adler's paper "Does mass really depend on velocity, dad?" Am. J. Phys., August 1987.

(5)  We see the phenomenon of contraction and time dilation as real (because they will be "observed") yet, illusionary.  It is a problem of kinematics, not dynamics. See page 21 in Abraham Pais' book 'Subtle is the Lord...': The Science and the Life of Albert Einstein, (Oxford University Press, 1982).

(6)  See Mendel Sachs, 1985, "On Einstein's Later View of the Twin Paradox," Foundations of Physics, Vol. 15, No. 9, pp. 977-980. His abstract reads: "It is shown that Einstein abandoned his earlier view that there are material consequences, such as asymmetrical aging, implied by the space-time transformation of relativity theory."

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This paper was made Internet available January 15, 2000.

Edited April 5, 2014

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