JERUSALEM, D.C. (David's Capital), Yom Shishi (Sixth Day - "Friday"), 23 Nisan, 5759 (April 9, 1999) [Day Eight in Sefirat HaOmer], Root & Branch:
This paper was originally presented at the Second International Conference on Jews in a Changing World, held in Riga, Latvia on August 25-27, 1997.
The only one of its kind where Eastern European Jews discuss their past, present, and future ethical, cultural, social, and intellectual challenges, the conference was sponsored by the Memorial Foundation for Jewish Culture of New York and the Soros Foundation of Latvia.
The Chief Rabbi of Riga and Latvia, Natan Barkan, was its Honorary President. Professors Herman Branover and Ruvin Ferber co-chaired the conference and co-edited its Proceedings, published by SHAMIR in English and Russian.
THE CONCEPT OF ABSOLUTE TIME IN SCIENCE AND JEWISH THOUGHT
Both contemporary physics and traditional Jewish thought recognize two types of time:
1) absolute or unified world time;
2) relative or local time.
Using Moshe Carmeli's equations, cosmological time is read backwards, approaching the initial moment of Creation. The closer we mentally approach the point of temporal origin, however, the longer the time intervals become.
Insight into Louis de Broglie's Great Law of Nature reveals that a perfectly free elementary particle must be, in essence, itself a perfect or ideal clock. This insight may provide a missing link between the geometric concept of the space-time continuum and the arithmetic concept of time.
Maimonides disagrees with the Midrash that time had existed before the Creation. Hasidic philosophy also upholds that time was created with the rest of the universe by G-d.
Hasidism defines two types of time:
1) 'absolute, permanently flowing' (etsem hemshekh ha'zman);
2) 'measurable and estimable' (zman ha'nimdad veha'meshuar).
There is a special cycle in the Hasidic system called ratso v'shov, which comprises a dual process of 'escape and return.' In physics this corresponds with the periodically recurrent process needed to measure time, i.e. with a finite 'to-and-fro' cycle which occurs by means of some restoring force.
The concept of time is full of mystery. We intuitively feel that time cannot be stopped, we all exist in time, and everything is subject to time. It seems obvious that because we live in time, it is the prime measure of existence.
Humans seem to have been interested in time ever since they started thinking about life, but there has never been so much literature published on the subject as there is now. Dozens of books appear annually on the nature and philosophy of time, from the standpoint of mathematics, physics, biology, and other natural sciences. Some of them arouse enormous interest. "A Brief History of Time" by the well-known British astrophysicist Stephen Hawkings, for example, instantly became a best seller.
Can time be accelerated or slowed down? Was time created at the moment of Genesis, or has it always existed? Is it possible to travel in time (into the past or future)? Is time one and the same throughout the universe? How can we explain the unidirectional character of the time arrow directed from the past to the future?
Merely enumerating these questions reveals that time is a category not only of physics -- or, more precisely, metaphysics -- but of mental perception in general. Issues concerning the essence of time cannot be the exclusive prerogative of science. The category of absolute time as a Supreme Being that cannot be reduced to any other value is consonant with the idea of the Divine in its broadest sense.
This essay consists of two parts. Part One deals with the changing conceptions in physics regarding what is time. Part Two compares some Torah-based opinions on the essence of time with certain principles of physics today.
WHAT IS TIME: CHANGING CONCEPTS IN PHYSICS
In pre-relativistic physics, the predominant concept of time was that of Sir Isaac Newton, who wrote, "Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external." Newton comprehended time as absolute and external to nature.
The twentieth century revolution in understanding the phenomenon of time is usually connected with Hermann Minkowski's mathematical description of the world as a space-time continuum. Minkowski came out with his idea in 1907 and based it on the Theory of Special Relativity, or SRT, formulated by Albert Einstein in 1905.
SRT postulates the existence of systems of reference, by which one understands a system of coordinates serving to indicate the position in space, as well as clocks fixed in this system serving to indicate time. Such clocks have to be perfect, or ideal. That is, two of them, if combined, have to produce absolutely equal time intervals.
Special kinds of systems of reference exist in which a freely moving body proceeds with constant velocity. Such reference systems are called inertial. In particular, an observer with attached clocks constitutes a rest or proper inertial system of reference.
The question arises whether readings of the clocks will be the same from the point of view of an observer at rest as from that of an observer moving with respect to the clocks.
Let us suppose, for example, that one clock is placed on a train traveling past the platform. As a result of the postulate of the constancy of the velocity of light in vacuum (about 300,000 km/sec), the time intervals read on the clock at rest on the platform will be shorter than those read on the clock in a train traveling past the platform -- from the point of view of an observer on the platform.
The difference in time will be substantial only in the hypothetical case where the velocity of the train is not negligibly small with respect to that of light. Strictly speaking, to observe the effect of the time dilatation, it is necessary to have at least two clocks on the platform. The readings should be compared at the moments when a similar clock on a moving train passes them.
The time dilatation effect is mathematically expressed by a simple formula: Dt = Dt¢/Ö(1-v2/c2 ) relating a time interval Dt¢ in the proper reference system (the observer's rest system) with a time interval Dt read from a clock moving with respect to the above-mentioned system at the velocity of v.
This effect has become a routine reality in the physics of fast particles in accelerators; in other words, it is a well-established fact. Indeed, the above time dilatation formula follows as a special case from the Lorentz transformations relating time and space coordinates in such a way that when passing from one reference system to another, time is not transformed per se, but only in combination with space coordinates. Thus, time is no longer considered absolute because its measurable magnitude depends on the conditions of measurements.
The Special Theory of Relativity apparently robs time of its independence, relegating it as an integral part of a four-dimensional space-time continuum. Putting it most simply: Newton's time is absolute, whereas Einstein's SRT time is relative.
Does this mean that there is no absolute time at all? An affirmative reply to this question conflicts with our intuitive perception of time. The first chapter of the second volume of the theoretical physics textbook by Lev Landau and Eugene Lifshits used in universities around the world presents Einstein's Theory of Special Relativity. The final chapter of the same volume entitled "Relativistic Cosmology," however, states: "The homogeneity and isotropy of space mean that we can choose a world time so that at each moment the metric of space is the same at all points and in all directions."
Thus, the current view of physics is that local time, which seems different if viewed by a passenger in a moving train or by an observer on the platform, co-exists with a certain unified world time! The branch of physics that deals with this type of time is called cosmology. So even physicists are not always logically consistent! Sometimes they refer to one physics-relativistic mechanics; and sometimes, to another physics-cosmology, representing the scope of General Relativity Theory (GRT). Thus, a certain dissonance has arisen.
While we are ready to agree that the duration of time interval Dt from the viewpoint of an observer in different reference systems can vary, we still do not want to abandon the concept of time as an absolute physical and metaphysical category ruling all life. It is also difficult to agree with the idea of space and time sharing equal roles. Obviously, one can be at rest in space with respect to a chosen reference system, but not in time, whose mysterious "absolute course" remains a permanent challenge to our daily lives.
In fact, it is within the framework of the physical study of the universe, i.e., of Relativistic Cosmology, that the concept of cosmic unified time functioning, in essence, as absolute time has regained meaning.
MOSHE CARMELI'S EQUATIONS IN WHICH TIME IS READ BACKWARDS
In 1995 Moshe Carmeli, an Israeli physicist working in Beersheba, obtained equations that are similar to the Lorentz-Einstein's Special Relativity Theory equations, but refer to Cosmological Special Relativity, relating physical quantities (space coordinates and velocities) in different time T. These simple and very beautiful equations involve a unified world, or cosmological time T, whereas a constant expansion rate of our universe, or Hubble's time (To » 18 billion years), plays the role of the constant light velocity c, T2/To2 replacing v2/c2 in Lorentz transformation formulae.
The equations are derived on the basis of the principle of Cosmological Relativity. According to the latter, all physical laws (and natural laws in general) should be valid at any cosmic time.
Most interestingly, in Carmeli's equations time T is read backwards with respect to the present moment of time, which is just a cosmic or world time moment. Carmeli does not call it absolute, adhering to the term 'cosmological time,' but it should be understood that this time is unified for all space. And if we read it 'backwards' from the present moment of time, an extremely interesting phenomenon occurs. The contraction of all lengths (those of entities and distances between entities) is the same as in Einstein's theory, but not because of the relative velocity of reference systems, but because of the backward 'motion' in time.
In fact, since, according to Relativistic Cosmology, the universe was created 15-18 billion years ago from a singular initial point, it is clear that all distances between entities in the past were shorter. All this is described by simple equations of a well-known, 'Lorentzian' form. Certainly, not only cosmic time (present also in Relativistic Cosmology, as we have mentioned) arises in these equations. Here the initial moment of Creation emerges.
Undoubtedly, this moment denotes an utterly defi-nite temporal origin. It is noteworthy that it may seem that we could mentally approach this moment moving backwards in time. But it turns out that time intervals themselves are elongated when approaching the special point of temporal origin.
In the very remote past -- for instance, when cosmic time was 90 percent closer to the initial moment of the Creation of the universe -- the interval between two instants of time equal to one second today increases tenfold. This means that an interval of one second today would have lasted 10 seconds then (from the point of view of today's observer). Therefore, we are unable to reach the singular point of temporal origin even mentally, since this would take infinite time.
QUANTUM PHYSICS AND TIME: ACCORDING TO DE BROGLIE'S GREAT LAW OF NATURE IS A FREE ELEMENTARY PARTICLE IN ITSELF AN IDEAL CLOCK?
What has quantum physics introduced to the concept of time? We shall dwell on one aspect only. This aspect is connected with the basic notion of quantum (or wave) mechanics, namely, with the 'matter waves' predicted by Louis de Broglie on the basis of his great hypothesis:
"One may therefore assume that, as a result of a great law of nature every bit of energy of proper mass 'mo' is intrinsically related to a periodic phenomenon of frequency 'no' in such a way that hno = moc2, no being, evidently, measured in the system attached to a bit of energy. This hypothesis is the basis of our system: it is valid, like all hypotheses, as much as are valid the consequences which one can deduce from it.
Since the importance of the well-known consequences cannot be overestimated (quantum mechanics is entirely based on them), any effort to obtain some insight into the 'great law of nature' cited by de Broglie is worth a try. Such an attempt was made by Ruvin Ferber, one of the authors of the present paper. His arguments are as follows.
According to the principles of Einstein's Special Theory of Relativity, an inertial reference system, which includes an ideal clock mentioned above, may be attached to any massive free entity serving as the origin of the system of reference. But here we are dealing with an obvious contradiction. Such a rigid linking between a clock and an entity, i.e., of two entities inevitably involves interaction and, thus, is in conflict with the principal postulate of SRT related to a freely moving entity that does not by definition interact with anything.
Specifically, what about an elementary particle? There can be only one answer: Such a perfectly free elementary particle that is not connected with others must be, in essence, itself a perfect or ideal clock!
Since an ideal clock is actually an ideal periodic process with the frequency, say, 'no', and since the only intrinsic feature of any massive particle is its proper mass 'mo', it seems natural to assume that the period of the ideal proper clock of a particle counting its proper time periods to = 1/no, should be unambiguously defined by the mass 'mo'.
Assuming that the frequency 'no' is proportional to the proper mass 'mo', the proportionality factor, from dimension consideration, equals c2/h. Thus, de Broglie's relation no = moc2/h, where 'h' is Planck's constant, necessarily arises. Here the clock ideality for all elementary particles of the same kind is determined by the Indistinguishability Principle known in quantum physics.
According to this principle, de Broglie's frequency no of any fundamental particles of the same type is absolutely independent of their position in space or of their pre-history.
Now let us watch de Broglie's periodic phenomenon from the standpoint of a different reference system, say, moving at the velocity of 'v'. We already know that according to SRT requirements, local time in the reference system of a particle satisfies Lorentz's transformations, i.e., it is not invariant. What is then conserved under such a transformation?
It was suggested that such a fundamental invariant is an ordered sequence of integers 1, 2, 3, n, enumerating de Broglie's periods to and progressing with time course.
This can be presented as an arithmetic concept of time or, equivalently, as a physical realization of the sequence of natural numbers -- a basic object of arithmetic which persistently defies any definition.
According to a statement of Leopold Kroneker, it is the Almighty Himself Who created natural numbers, while all other numbers are invented by man. Thus, the search for an 'absolute' time conserved in any reference systems leads to the idea of actual realization of natural numbers. The 'great law of nature' behind de Broglie's periodic phenomenon may appear to be a missing link between the geometric concept of the space-time continuum and the arithmetic concept of time.
It is noteworthy that Einstein did not at all claim that only the time measured by a particular clock, i.e., local time, existed. He wrote in his article "Physik und Realitaet" in 1936 that there are two kinds of objective time. There is local objective time related to a succession of experiments in time or clock readings, i.e., to a closed system of periodical events; and there is a unified objective time for all space. According to Einstein, thanks to the latter notion, the idea of local time expands, becoming the idea of time in physics.
TRADITIONAL TORAH-BASED OPINIONS ON THE ESSENCE OF TIME AND THEIR PARALLELS WITH CERTAIN PRINCIPLES IN CONTEMPORARY SCIENCE
In our discussion of the concept of time in Jewish thought we shall look at two aspects of the rich Torah-based literature on the subject:
1) The connection between time and Creation, including the concept of absolute time measured from the initial moment of Genesis;
2) The two types of time: local time measured by clocks, and the time flow that makes our universe evolve.
In Midrash Rabba Genesis there is a hermeneutic exchange of opinions among the Talmudic Sages Rabbi Yehuda ben Shimon, Rabbi Abbahu, and Rabbi Pinhas on the meaning of the first appearance of the statement "And it was evening" in Genesis 1:5.
Rabbi Yehuda ben Rabbi Shimon said, "It is not written, 'Let there be evening' but 'And it was evening.' Hence we know that temporal order existed before that."
Rabbi Abbahu said, "This proves that He created and destroyed worlds until He created ours and declared, 'This one pleases Me; the others did not please Me.'"
Rabbi Pinhas said, "The proof of Rabbi Abbahu's reasoning is that 'G-d saw everything that He had created, and, behold it was very good' (Genesis, 1:31). 'This one pleases me; the others did not please Me.'"
In other words, according to the above midrash, time had existed previous to the Creation of our world, and moreover, other worlds had been created before the Creation of our universe.
It is interesting to compare Rabbi Abbahu's interpretation that other worlds had been created before our present world was created with the Anthropic Principle of present-day cosmology. According to the Anthropic Principle, if any of the basic physical constants of our universe, such as light velocity, Planck's constant, or the gravitational constant was changed in the slightest -- say, by a hundredth of a percent -- then all the properties of the universe would change to such an extent that it would contain no life forms (human or otherwise).
Thus, the Anthropic Principle asserts that human existence in this world means that it was created for humans to live here. Strong and weak anthropic principles are discussed in works on physics and cosmology -- not in religious literature.
DID TIME EXIST BEFORE THE CREATION OF THE UNIVERSE?
In the Talmudic tradition of debate, in the twelfth century (about 900 years after Rabbis Yehuda, Abbahu, and Pinhas handed down the Midrash quoted above) Maimonides --the ultimate authority in Jewish law and tradition for all generations -- criticized them.
In his fascinating philosophical work "The Guide to the Perplexed", Maimonides maintains that it is absolutely incorrect to think that time had already existed before Creation. The existence of time before the Creation would have required a motion of spheres to determine this time interval. The spheres themselves, however, Maimonides says could have been created only in the process of Creation.
Maimonides identifies Rabbi Yehuda ben Shimon's opinion with Aristotle's concept of the eternity of matter. According to Aristotle, the universe was not created but evolved from eternal matter.
Creation is the second most important postulate of the Torah after the postulate of G-d's unity, Maimonides teaches us. We find complete agreement between Maimonides and the idea of the big bang as the initial moment in a standard cosmological model. According to both Maimonides and the Big Bang Theory, time appeared simultaneously with the appearance of our universe.
THE TWO KINDS OF TIME: LOCAL AND FLOWING
Regarding the concept of two kinds of time, there are precise indications of this in Torah-based literature. In particular, Hasidic philosophy states that there are two kinds of time -- 'absolute, permanently flowing' (etsem hemshekh ha'zman) and 'measurable and estimable' (zman ha'nimdad veha'meshuar). These two kinds of time should be differentiated.
The reference system of lasting, permanently flowing time is related to the Absolute: This is the one in which G-d, the Creator, exists. In this system His independent existence is absolute. But there exists also another reference system that is just connected with each individual human being.
In this system human temporal existence takes place, along with one's perception of the world. In such a system the Creator is perceived as 'Nothing'-consonant with the universe having been created from Nothing. 'Nothing' is the Absolute that is not humanly perceived; it is absent from the human proper coordinate system, and not involved in the humanly perceived world.
There is a special cycle in this system comprised of the dual-process of 'escape and return,' (ratso and shov). In physics this corresponds with the periodically recurrent process needed to measure time, i.e., with a finite 'to-and-fro' cycle which occurs by means of some restoring force. The process of escaping implies the aspiration to reach the Absolute, to comprehend the Almighty, and to merge with Him.
In the final limit, it implies the departure of the soul from the body, i.e., transformation back into Nothing in the material sense. The opposite process to escaping is that of returning to the physical world in which we live. According to a Hasidic concept, each individual as well as the Absolute possess the proper, permanently recurrent ratso-shov cycle. It is the ratso-shov cycle inherent to the Absolute that creates a certain scale, a world-wide pulse determining the flow of absolute, universal time.
In conclusion, we present an opinion which the Lubavitcher Rebbe expressed to Herman Branover on the well-known 'twin paradox' of Special Relativity Theory, concerning how human biological age is determined.
The paradox goes as follows: The clock of a twin traveling in a rocket is slower than the clock of his twin brother remaining on Earth. After 25 years have passed on his clock and the twin-traveler finally returns to Earth, 50 years might have passed on the clock of his twin brother who remained on the Earth. (The difference in the two clocks depends on the relative velocity of the rocket). Thus, the twin brother who stayed on the Earth will be about 25 years older than his returning sibling!
This paradox formally corresponds to the equations of Special Relativity Theory. Basing his opinion on his vast study of Torah, the Lubavitcher Rebbe, however, concludes that human biological age is determined by permanently flowing time, and not by local measurable time. The reference system of the former is related to the Absolute, and it is on this basis that the solution to the paradox should be sought.
We are grateful to Tomas Turan of Budapest who advised Ruvin Ferber on the ideas quoted from the Midrash. .
Maimonides, Guide to the Perplexed, Part Two, Chapter 30
ABOUT PROFESSOR HERMAN BRANOVER
Prof. Herman Branover is a member of the International Council of the Root & Branch Association.
Prof. Branover is Director of the Liquid Metal MHD Laboratories at Ben-Gurion University of the Negev and Founder of SHAMIR: The Israel Association of Religious Professionals from the Former Soviet Union.
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