INDIRECT EVIDENCE IN SUPPORT OF THE BIG BANG
The indirect body of evidence supports the postulate that the universe had a beginning; in other words that it has not had eternal existence. The most basic philosophical consequence of the Big Bang theory is its postulation of the fact that the universe did have an origin. Every piece of evidence that suggests that the universe had a beginning indirectly corroborates the Big Bang theory. Of the said evidence, I am going to address in the first three items those that are related to physics. In the last item of this chapter I will briefly outline how the theory that advocated that the universe had an origin had its counterpart in philosophy.
1. EVIDENCE FROM ENTROPY THE LAW OF ENTROPY
Entropy is a measure of the unavailable energy in a closed thermodynamic system that is also considered to be a measure of the system’s disorder. The concept of entropy follows from the application of the second law of thermodynamics. This law posits that the end of the universe is drawing near and that this process is irreversible according to the laws of physics. The fact is that heat flows irreversibly in one direction. Let us suppose that we leave a pail full of hot water in a room: the thermal energy in the mass of water will spread about the room never to return again to its source. The flow of energy in a closed system travels one way and continues until a point of balance is attained called ‘thermodynamic equilibrium,’ where the entropy is at its peak.
The existence of this irreversible process proves that the universe, like human beings, is subjected to the irreversible aging process. Both our sun and the other stars are subject to this oneway thermodynamic law. The sun increases the entropy by the continuous transfer of heat to space. Yet, this heat does not return to the sun. The law of thermodynamics postulates that the entropy is continuously increasing and the process is definitely in one direction.
PHILOSOPHICAL CONSEQUENCES OF THE LAW OF ENTROPY
A great many people conceive the data relative to entropy merely in terms of physics. But the law of entropy enables us to arrive at very significant philosophical consequences.
1-The flow of heat in the universe follows one single direction; this is irreversible (the second law of thermodynamics).
2-Under these circumstances, a day will come when a thermodynamic equilibrium will be established and we shall experience the “heat death.” This means the universe has an end.
3-Had the universe existed from eternity, the universe would, in the course of time that has elapsed, have reached the state of thermodynamic equilibrium and experienced the “heat death .” A mortal universe cannot exist from eternity.
4-Given the fact that the universe does not exist from eternity, it follows that the universe had an origin. The universe in its initiatory state (t=0) is heading from a state of low entropy to a state of high entropy. The continuous increase in entropy suggests that in the origin the universe enjoyed low entropy.
ENTROPY, PESSIMISM AND HOPE
Some philosophers at first dwelt on that portion of the law of entropy that postulated that the universe does not have a perpetual existence, ignoring the fact that it had had a beginning. Bertrand Russell spoke of his pessimism in the face of his expectations of the total annihilation of whatever existed: “All the labors of the ages, all the devotion, all the inspiration, all the noonday brightness of human genius, are destined to extinction in the vast death of the solar system…the whole temple of man’s achievement must inevitably be buried beneath the debris of a universe in ruins…” Paul Davies is puzzled at the fact that scientists and philosophers focus on the prospective annihilation of the universe toward which entropy seems to be heading, ignoring the fact that it had a beginning: “Something that runs down at a finite rate obviously cannot have existed from eternity. In other words, the universe must have come into existence a finite time ago. It is remarkable that this profound conclusion was not properly grasped by the scientists of the nineteenth century.”
The law of entropy is not entirely pessimistic. The factor that will enable man to overcome his pessimism is not the eternal existence of the universe when he is no more, but his own eternal life. There is no denying that man is weak in that respect. The power to secure himself an eternal existence is what he can hope for. The law of entropy that postulates that the universe had a beginning makes indispensable the belief in the existence of a Power outside the confines of the universe sustaining the argument of monotheistic religions that advocates that the universe had had a beginning. Those who surmise that matter is eternal and that the universe they believed to have had perpetual existence is drawing to an end will, of necessity, be despondent. But for those who feel confident that the universe had had a beginning and will come to an end and believe in the existence of God and in the truth of this message conveyed by monotheistic religions and in the almighty God, the law of entropy should not lead them to pessimism.
MEETING OF ENTROPY AND THE BIG BANG
The idea that the universe had a beginning and will have an end was suggested by the Big Bang model. The laws of thermodynamics (entropy) had been devised before; the results they reached are converging, as we see. Conclusively, the laws of thermodynamics, the astronomical observations and the formulas of the theory of relativity are mutually corroborative.
The law governing entropy, in another aspect, can also be taken for a direct evidence of the Big Bang theory. Entropy is very high in the universe, which can be accounted for only by the intense heat generated by a primordial explosion. (Entropy is measurable by the ratio of the smallest particle of light, photons, to baryons, protons and neutrons).
Despite the fact that the supernova explosion is one of the most entropic events, it is not to be compared to the entropy existing in the universe. No formation in the universe we know can account for the high quantity of entropy existing in the universe. Yet, this high entropy is compatible with the Big Bang model.
2.EVIDENCE CONCEALED IN THE EXTINCTION OF LIGHT ERROR OF THE CONCEPT OF A STATIC UNIVERSE
The star-studded universe gives us the impression of a static and immutable universe model. Aristotle was convinced that the stars were eternal and postulated that they had an inexhaustible fuel. A person looking at the sky with the naked eye at night may believe that the universe is steady, and fail to perceive the dynamism and the continuous process of evolution and destruction.
Prior to the insight into the structure of stars, materialist thinkers contended that stars had an eternal existence and that they would continue to exist forever. At present we know that the stars have a definite lifetime, that all of them (including the sun) owe their existence to their conversion of hydrogen into helium and that once their fuel is exhausted they will come to an end. Thereafter, it was believed that the newly formed stars replaced the stars that disappeared and that this process would go on till eternity. We know today, however, that this also is not true. A day will come when the stars and light will be no more.
A disappearing star is replaced now by a newly formed star. This process will continue so long as there is enough raw material. The source of this raw material is the explosions and eruptions in supernovas and other stars, just like the primordial process at the beginning of creation. These gases, condensed by the force exerted by gravitation, collapse and give rise to the formation of stars. After having spent their lifetimes, they are transformed into black holes, neutron stars, white drafts and red giants. The raw material required for the formation of stars is becoming exhausted. Once this raw material is drained, no stars will form any longer. The universe will grow dark as the stars fade out (unless a prior cataclysm ending the universe does not intervene).
PHILOSOPHICAL DEDUCTIONS FROM THE EXTINCTION OF LIGHT
According to scientific data, this process will last billions of years. Such an immense space of time may not interest the multitude, although it has much significance in philosophical terms. Let me summarize:
1-Light will vanish in the universe
2-As no life is possible without light, life upon earth cannot be eternal.
3-Considering that light in the universe is expected to end one day, light as such cannot have existed from eternity, so it must have had a beginning.
With the postulate that light (or the stars) will be extinguished after a space of time, the idea of an eternal universe is shown to be without foundation. This result is compatible with the law of entropy and the Big Bang theory.
Since the idea of the eternal existence of stars has fallen into disuse, the point at issue now is to calculate the ages of stars as precisely as possible. It is computed that the second population of stars, which are the most numerous, formed 1.5 – 5 billion years after the beginning of creation. If one adds the age of the second population of stars to this number, we can learn the age of the universe.
Computations made based on these measurements give the approximate age of the universe as 15 billion years. This result is very near the result obtained using the Hubble Constant. Stars and the light they emit belie the eternal universe model while they confirm the postulate that it had a beginning and an end.
3.EVIDENCE FROM THE AGE OF RADIOACTIVE ELEMENTS HALF-LIFETIME OF RADIOACTIVE ELEMENTS
Radioactive elements are no mystery for the high school student of our day. Radioactivity was discovered in 1896 by the French scientist Henry Becquerel. Radioactivity is the spontaneous disintegration of the nuclei of certain atoms accompanied by the emission of particles or rays. It is the release of energy by rare, heavy elements when their nuclei decay into lighter nuclei. In such disintegration not all the radioactive atoms break simultaneously apart. The effect of the radioactive matter decreases in time, because its number of atoms continuously diminishes as time goes by. The time it takes for a given portion of atoms in a radioactive substance to decompose is always the same. Therefore, the time that elapses for the decay of half of the atoms in the radioactive substances is used in calculations. This time is referred to as the “half-life” of the radioactive element and the said space of time differs according to the radioactive substance in question. The following are the half-lives of certain radioactive elements:
Radioactive Isotope Half life
Thorium 232 13.900.000.000 years
Uranium 238 4.500.000.000 years
Uranium 235 700.000.000 years
Neptunium 237 2.250.000 years
Carbon 14 5.700 years
Radium 226 1.600 years
Radon 222 3.8 days
Let us take as an example the Uranium 235 mentioned in the above list. Existing in a given quantity, Uranium 235 will be reduced to half in the course of 700 million years. The same will take place in another 700 years and will be reduced to the half of the previous quantity. This process will be repeated every 700 years. By this method one can mathematically calculate the quantity of Uranium 235 at a given date in the past. US chemist Willard Frank Libby was awarded the 1960 Nobel Prize for chemistry for his development of the radiocarbon dating technique, which has extensive applications in geology. The importance of the radioactive elements became still more marked in the world of science.
Modern observation techniques allow us to deduce the age of chemical elements from the available radioactive elements and from the calculation of the quantity of the radioactive elements formed at the end of their half-lives. In 1997, English and American astrophysicists Margaret and Geoffrey Burbidge, William Fowler and Fred Hoyle demonstrated that the elements having higher atomic weights were formed through the processes in supernovas. Their research and the work undertaken subsequently indicate that elements such as Thorium 232, Uranium 238 and Uranium 235 are the remnants of the first supernovas. The existing quantity of these elements and the mathematical data we have acquired relative to half-lives allow us to calculate the age of the first supernovas.
AGE OF THE UNIVERSE ON BASIS OF RADIOACTIVE ELEMENTS
Based on the proportions of Thorium 232, Uranium 238 and Uranium 235, European physicists Thielemann, Metzinger and Klapdor stated in 1983 that the formation of the first supernovas must have taken place in the time interval of 16.8 – 22.8 billion years. Afterward, in 1987, William Fowler tried to correct these calculations and posited that Thielemann’s calculations should be reduced to 3-9 billion years. Later Thielemann and two collaborators, Cowan and Truran, made a new calculation according to which the interval should be 12.4-14.7 billion years. This was followed by the postulate of US physicist Donald Clayton, who, having used eight different methods, computed the date of the first supernovas as somewhere between 12 – 20 billions years.
The first supernovas came about at the beginning of the creation, when matter was very dense. Therefore the approximate dates obtained from radioactive elements about the formation of the first supernovas give the approximate age of the universe. Calculations made using this technique based on the age of stars or on the Hubble constant point to the same time interval. The results of these calculations do not widely differ from one another. Certain difficulties make it impossible to make a precise calculation, yet assessments indicate that the age of the universe must be somewhere around 15 billion years. Despite the varying parameters the results reached do not widely differ. Use of the characteristics of the radioactive elements was among the calculation methods. The point at issue is no longer whether the universe is eternal or not, but the determination of the exact date when the universe was created.
4. PHILOSOPHICAL EVIDENCE ATTESTING THAT THE UNIVERSE HAD A BEGINNING PHILOSOPHICAL ARGUMENTS IN FAVOR OF THE ORIGIN OF THE UNIVERSE
At a time when astronomical and physical developments had not yet taken place, when nothing was known about the cosmic microwave background radiation, when man had not yet observed the expansion of the universe and when he was still unaware of entropy and radioactive elements, rational approaches to the idea that the universe had had a beginning were already being adopted by such philosophers as Saadia of the Judaistic creed, Bonaventure representing Christianity and Kindi standing for Islam. I will try to address this subject only briefly, for it is a subject about which volumes might be written. In following these trends of ideas it was argued that the universe and the time and motion in the universe could not be eternal. It was stressed that there should be a Cause behind the creation, a Cause outside the confines of the universe. The cogent arguments put forth can be summarized as follows:
1-Whatever begins to exist has a cause.
2-The universe has a beginning
3-Therefore the universe has a Cause for its existence.
The second point is the critical argument. Objections were especially raised to this point. The basic evidence provided by the Big Bang theory has been the scientific substantiation of this point. However, even in the absence of scientific proofs, one may have recourse to philosophical reasoning. Motion and time in the universe cannot be eternal; the beginning of time is also the beginning of the universe. Time in the universe is a measure of the motion in the universe; what is in motion is the universe itself. A universe where there is no motion is unimaginable. Given the fact that there is a beginning of time, it follows that this beginning is also the beginning of the motion in the universe and of the universe itself. This beginning entails a Cause outside the confines of the universe.
ACTUAL INFINITY AND IMAGINARY INFINITY
The study of the concept of infinity is vital for our cause. It is important that we clarify the meaning of the word “infinity” if we are to dispel confusion. The sets of numbers formulated by a mathematician like Cantor are “imaginary infinities” that have no corresponding parts in the universe. “Actual infinity” must differentiate from “imaginary infinity.” A great many people including such mathematicians as Zeno of Elea, Russell, Frege and Hawking could not help being faced with paradoxes just because they failed to make this differentiation. Mathematical paradoxes are the consequences of the failure to differentiate between “the real” and “the fictitious.” Yet, these paradoxes do have an important task, as they announce to their addressees in the following manner: “You are engaged in dealing not with the mathematics of the really existent but dallying with imaginary mathematics!” Mathematics based on infinite sets of numbers can be indulged in, no doubt, as Cantor has attempted. But this has no counterpart in the universe.
ZENO’S TORTOISE AND HARE
If we may be permitted to make a slight digression, it is my intention to briefly note the manner by which paradoxes in the history of philosophy can be solved. According to Zeno of Elea, the hare can never catch up with the tortoise. For when the hare has reached the point “X” where the tortoise had been, the tortoise will have reached the point “Y” and when the hare will be at point “Y” the tortoise will be at point “Z” and this will go on infinitely, thus the hare will never be able to catch up with the tortoise. By having recourse to such paradoxes Zeno of Elea tried to demonstrate that there could be no motion or change in the universe. But the fact is that the mathematical pattern he has contrived is in no way related to the motion in the universe. To begin with, when the hare catches up with the tortoise, it does not stop to watch the tortoise proceed. The simple mathematical formula that is the distance covered is equal to speed multiplied by time.
There are certain established distances in the universe like 10 km and 100 meters. But while dividing this length by a number, attributing infinity to the denominator is an imaginary application. In the first place, “infinity” is not a number; it merely connotes the continuous increasing. On the other hand, there is no real integer in the universe divided by “infinity;” to try to divide the integer in this way is but a figment of the imagination. All that one can deduce from the expression ‘to divide an object by infinity,’ would be the division of an object into ever bigger numbers. If we assume “infinity” to be an actual number, outside its meaning as “continuous increasing,” we cannot help but create an absurdity that does not exist in the real world. When Zeno claimed that an arrow would not be able to strike the target towards which it was heading, he divided the distance between the point of origin of the arrow and the target by infinity and claimed that, given the fact that this distance was infinite, it could never be crossed. The fact is that the division by infinity was purely imaginary and the target did not obey it. Hares will likewise catch up with and surpass the tortoise. To state that the hare stops when it catches up with the tortoise and make these stops infinitely is contrary to the actuality existing in the universe.
Another well-known paradox in mathematics is Russell’s Paradox”. In this paradox a definition of set is given; it includes the same sorts of entities but it is not a member of its own. For instance, the set of dogs includes in it all the dogs existing in the universe, but “the set of dogs” is not a member of this set. All sets satisfy this characteristic, but not in the case of “the set of all sets.” This set must include not only other members but also “the set of all sets.” But then “the set of all sets” will be its own member, which is against the definition given of a set. Frege was thrown into a panic when he heard Russell’s set-theoretic paradox related to an important chapter of mathematics. Had they modified the “imaginary definition” of their own naive invention, which does not actually exist in the universe, the paradox would have been solved. As can be seen in these examples, some mathematicians confuse their intellectual fictions with reality, approximating the figments of their imaginations to Platonic ideas.
INFINITY AS CONTINUITY
People tend to confuse the reality of the universe and their fictive projections of the universe, especially when they consider the concept of infinity. There have been mathematicians who have imagined “infinity” to be an actual number. Actually there is no such number as “infinity;” infinity suggests that we can proceed on and on without stopping. Let us take, for instance, the natural series of 0,1,2,3,4. When we say that this set of numbers extends to infinity, we are not suggesting that it has a definite target ahead; all that we state is the fact that the set proceeds on by addition of 1 every time. This is why none of these sets of numbers reaches “infinity,” they just go on and on; if we assume that this set of numbers stops somewhere, it will be contradicting the definition of the concept of “infinity.”
We ought now to differentiate the assertions of those who claim that the time in the universe was infinite in the past and will be so in the future. Those who conceive the past and the future of the universe to be like Cantor’s set of numbers will be disposed to readily accept this expression. Those who contend that the universe proceeds on to infinity will have said that time in the universe continues perpetually. In this respect for progression toward the future there have been theoreticians who used the expression of “potential infinity.” This definition changes nothing in terms of the result we have given. Yet, I do not favor using this definition, for the idea of “potential” may associate in the mind the possibility that something can develop or become actual. A process that is oriented toward infinity never comes to a standstill, as per the definition of infinity. It will never attain infinity; as a matter of fact, we cannot speak of a point representing infinity for “infinity” is not a target to be reached. It simply means a perpetual progress. Therefore the contenders who suggest that the future time of the universe is the “actual infinite” are in error. No matter where we stop in the perpetual progress, that place is not infinity.
Thus, those who maintain that the past of the universe is infinite contend that infinity has come to its term and that the age of the universe is “actual infinite.” In this sense, the definition of “infinity” means an accomplishment, an attainment outside perpetuity. This is quite different from what is meant by the infinitude of future time; this important point has been ignored by many.
CAN ONE GO BEYOND INFINITY
The notion of “passed infinity” is incompatible with the definition of infinity. Those who use the concept of “infinity” in an imaginary sense have failed to take cognizance of this. Let me summarize it:
1-Infinity means that which proceeds on and on perpetually and is never completed.
2-It is suggested that the time past is infinite.
3-In order that we may exist at this point we must have gone past the infinity (in accordance with item 2 above).
4-However, considering that infinity cannot be passed (in accordance with item 1 above) and our existence cannot be denied, time past in the universe cannot be infinite.
5-It follows that time reigning in the universe had a beginning.
If the misuse of the concept of infinite is corrected, the fact that the universe had a beginning will be evident. Let me stress once more the fact that what is wrong is not the association of imaginary elements existing in the universe with mathematics, but the correlation between “imaginary” and “reality” in the universe. I am of the opinion that paradoxes of mathematics will contribute significantly to the corrections of these errors. “So long as mathematics is the mathematics of the phenomena (reality in the universe) it cannot entail any paradoxes,” may be adopted as a motto.
If no error is made in the ontological status of mathematics (regarding whether mathematical concepts are imaginary or actual), no paradoxes will come about. In point of fact, in the advancement of sciences the correct application of mathematical formulas has an incontestable part. The mathematics that has remained on an imaginary level and fallen short of having a field of application to the reality in the universe has had no part to play in the progress achieved in scientific fields. Such mathematics has not gone further than being a mental jugglery and a source that has produced nothing else but paradoxes.
Mathematicians cannot do without imaginary considerations, but they must beware of mixing up what is imaginary with the reality of the universe. For instance, Pamela Huby, in her study of Cantor’s infinite sets, states that they have no message to convey about “actual infinite.” In addition, Abraham Robinson has announced that the said set of numbers has no counterpart in reality. Yet, it appears that not everybody has been successful in differentiating between “imaginary” and “the reality of the universe.” William Lane Craig gives a detailed account of this and makes the following summary that tries to demonstrate that the universe could not have existed from eternity:
1-An actual infinite cannot exist.
2-An infinite temporal regress of events is an actual infinite.
3-Therefore an infinite temporal regress of events cannot exist.
HILBERT’S HOTEL
When we project the Cantorian patterns related to the concept of “infinity” to the real world, we are faced with contradictions. We appreciate Cantor’s work; however, we must realize that in this universe there is no “actual infinite.” In this connection we can repeat the well-known puzzle of German mathematician Hilbert (1862-1943). Let us take up the case of Hilbert’s hotel. Let us assume that the “actual infinite” of rooms in the hotel are occupied and an “actual infinite” numbers of guests are soliciting accommodation, whereupon, we shift the person in room number 1, into room 2, 2 to 4, 3 to 6, 4 to 8 (let us bear in mind that the set of odd numbers goes to the infinite 1, 3, 5, 7, 9…) In this way, all the odd-numbered rooms become free. Thus, the infinite number of guests will occupy the infinite number of rooms with odd numbers. In the meantime the number of hotel rooms remains the same; the rate of the hotel’s occupation is still infinite, as it has always been! On the other hand, considering that every guest corresponds to a natural number, a new guest that appears cannot be accommodated. The reason is that one can add nothing to the infinite. Moreover, even though we erect a new hotel next to the existing one and accommodate guests therein, we can still not claim that there has been an increase in the number of guests (For infinite + any number = infinite).
The examination of the concept of infinite shows that a set consisting of successive additions does not lead to the “actual infinite.” Every moment in time follows the previous one and time advances in one direction solely. Given the fact that every moment is added to the preceding one, no “actual infinite” can exist in time. William Lane Craig summarizes this as follows:
1-The temporal series of events is a collection formed by successive addition.
2-A collection formed by successive addition cannot be an actual infinite.
3-Therefore the temporal series of events cannot be an actual infinite.
This reasoning leads us to the fact that time, and, consequently, the universe had a beginning.
MY SUGGESTION FOR A SOLUTION OF KANT’S ANTINOMIES
While developing the antinomies, mutual contradiction of two principles or inferences resting on premises of equal validity, Kant contends that both statements related to the existence or inexistence of the beginning of the universe are valid or not valid, in other words indeterminable. I believe a distinction must be made between something that is “absurd” (impossible) and a phenomenon that is “inconceivable.” According to this train of thought, on the basis of evidence we have produced so far we may term as absurd (reductio ad absurdum) the contention that the universe has existed since eternity. But the assertion that the universe was created from nothing cannot be reduced to absurdity. The only question that comes to mind would be: “How was it created?” This cannot constitute a reason for its refutation and falsification. Kant’s antinomies can be solved in this manner. It is certain that one of the two antinomies expressed is correct. What is postulated by antinomies is their mutual negation. However, if one can prove that one of the alternatives is absurd, the correctness of the other proposition becomes evident. To this end one must try to demonstrate that one of the alternatives is absurd. This will reveal the correctness of the other one.
To state that 2 is bigger than 3 is absurd (impossible). On the other hand, for a lay person, the working of an aircraft engine is “inconceivable.” “Absurd” is the expression of something impossible, unrealizable, while the second alternative denotes something that is unknown, but can well be possible.
Kant was in error in giving equal values to mutually contradicting propositions. G. J. Whitrow refuted the antithesis of Kant about the eternal existence of the universe, saying that the time concept prior to the beginning of the universe is wrong. As a matter of fact, the formulas of the theory of relativity linked time to space, demonstrating that where the universe did not exist, time would not. However Kant, who based his antinomies on Newton’s “absolute time”independent from the universe, committed the error that Whitrow detected.
My aim in the present chapter has been to briefly show in philosophical terms the necessity for a beginning of the universe. This is why I have focused on the fact that the past of the universe could not go backward to the infinite. Philosophical evidences are in harmony with the evidences of the Big Bang theory, thermodynamics and the theory of relativity.