BRIEF ANALYSIS OF THE KALAM COSMOLOGICAL ARGUMENT PART 3
In my last post I said my next post (this one, that is) will take at least two weeks. It has been three weeks now, partly due to the fact I had an exam in ecology. This is the third post in the small series on the Kalam Cosmological argument. If you have not read the previous two posts yet, it is highly recommended you do before reading this third post.
The Kalam Cosmological argument is, in short:
1) Whatever begins to exist has a cause.
2) The universe began to exist.
3) Therefore, the universe has a cause.
This cause is a timeless, space-less, immaterial, transcendent personal mind with unimaginable power. This is what is traditionally called “GOD”.
This post will deal with the second premise: The universe began to exist. One point can be made right away: There is no cosmological theory of an eternally existing universe that has been accepted by the majority of contemporary cosmologists.
This post will first explore the reasons to think the universe began to exist. Then, this post will discuss popular cosmological models that aim to get rid of the necessity for a beginning of the universe.
PHILOSOPHICAL REASONS FOR PREMISE 2
The first objection is a question: Why should one believe the universe began to exist; what reasons are there? Recall that when I say "universe", I mean all of space-time, so if one believes in a multiverse, that would be included in the word "universe". What follows now are a few philosophical reasons to think that the space-time-entity is not eternal, but had an absolute beginning a finite past ago. I start with a philosophical reasons because logic is the basis of all rational thinking, and is thus even more powerful than empirical science itself (which pre-supposes logic). Please remember that the A-theory of time is assumed throughout the entire Kalam Cosmological Argument.
1) The existence of a completed set of an actually infinite number of things is a mathematical contradiction. A universe that is eternal and had no beginning thus has existed for an infinite number of years, hours, seconds, etc. Since we are talking about the number of past events (i.e. number of seconds past), we are talking about a completed set of an actual infinity. However, a completed set of an actually infinite number of things (like an infinite number of events in the past) in the real physical world is mathematically contradictory. The best illustration of this is the so-called Hilbert's Hotel, named after David Hilbert (one of the most influential mathematicians of recent decades). However, this example is way too long for such a brief analysis (just Google it), and so here is a shorter, but similar illustration (one given quite often by Prof Craig). So, suppose you would have an infinite number of coins. And you give me one coin. How many coins do you have left? Well, you would still have an infinite number of coins. Infinity – 1 = infinity. Now suppose you again have an infinite number of coins, and you give me all the odd numbered coins. How many coins would you have left? Well, you would have: Infinity – infinity = infinity. Now suppose you give me all your coins. Now, how coins do you have left? Answer: Infinity-infinity=0. When one takes an infinite number of coins from an infinity number of coins, and thus subtract a number from an identical number, you get different, self-contradictory answers. In fact, the substraction “infinity – infinity = x”, the answer “x” can range from zero all the way to infinity. As David Hilbert himself said: “The infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought” (On the infinite, by David Hilbert, 1964. Part of: Philosophy of Mathematics: Selected Readings). Please note: this argument does not deny the mathematical use of the infinite. It merely states an actual infinity does not exist in physical reality. Now, an eternal universe has an infinite number of events in its past (i.e. infinite number of years). but since this mathematical argument shows an infinite number of things cannot exist in physical reality, the universe cannot be eternal.
2) Adding numbers after numbers cannot be actually infinite logically speaking. One might try to avoid the above metaphysical obviousness by saying that one can count numbers all the way to infinity. However, this is incorrect, at least not when applied to physical reality. Let's apply this to the infinite universe. If the universe has no beginning, and has existed for an infinite number of seconds, one could never reach ''now". This is so because, to reach "now", one must reach an infinite number of seconds. But when do you reach infinity? If the universe has existed an infinite number of seconds to reach "now", you can still add another second. And after that, you can still add another second. In fact, you can NEVER reach the "now", because another second can and must always be added. To illustrate, here's an analogy of my own: Suppose you have two buckets, one has a bottom and the other has no bottom. Suppose you poor water in both buckets. How much water is required to fill both buckets? You will probably immediately recognise that the water poured into bottomless bucket will never fill the bucket. This is the same with time: If you have no beginning (no bottom), time (the water) cannot accumulate to reach any point in time (the bottomless bucket cannot be filled). You can accumulate as much time as you want, but without a beginning, no point in time can be reached, and no time will effectively pass. Yet, time is accumulating and passing as you are reading this blog post. Thus, it is a logical necessity the universe had a beginning.
!) Important note: Now, please note that the above two reasons do not object to a potential infinity, but an actual infinity. What is the difference? Well, an actual infinity is a completed set of numbers - for example: the number of seconds the universe has existed on the first of January, 2015, at 0:600 o'clock. A potential infinity, however, is the ability to keep counting (i.e. the number of seconds the future will remain the exist). A potential infinity is not an actual infinity because it is not completed, since one can ALWAYS add another number. This is not a logical contradiction. But an actual infinity is a completed set of numbers, upon which no more numbers can be added, and yet it is still supposed to be an infinity. But since one can always add another number to an infinity, a fully completed set of an actual infinity in the physical world is therefore self-contradictory.
The above reasons show it is logically impossible for the universe to have existed forever.
EMPIRICAL REASON FOR PREMISE 2: LAWS OF THERMODYNAMICS
According to the second law of thermodynamics, any exchange of energy in a closed system will lead to an increase of entropy/ chaos/disorder. The universe is a closed system (the same goes for a multi-verse). Applying the second law to the space-time entity shows that one day the universe/multi-verse will reach maximum entropy. One could say that the universe will, in some sense, “die”. This unpleasant prediction raises a question: why is the universe not in maximum entropy today? If it has existed for an eternity, enough time should have passed for everything to be in a state of maximum entropy. Yet, it is not in maximum entropy state today. Therefore, it follows logically that the space-time-entity has not existed for an eternity, but had a beginning a finite past ago.
The above reasons show that it is far more reasonable to think the universe had a beginning a finite past ago, than to say the universe is eternal without a beginning or causation.
THE LETTERS BETWEEN VICTOR STENGER AND ALEXANDER VILENKIN
Professor Alexander Vilenkin, who by the way is an agnostic, is probably one of the most annoying cosmologists for atheists, along with Arvind Borde and Alan Guth, as their research showed quite strongly that the universe began to exist. In an attempt to find a way out of the Borde-Guth-Vilenkin singularity theorem, Professor Victor J. Stenger (PhD in physics), a famous atheist, wrote a letter to Alexander Vilenkin, asking the following question: “Does your theorem prove that the universe must have had a beginning?” Alexander Vilenkin replied: “No. But it proves that the expansion of the universe must have had a beginning. You can evade the theorem by postulating that the universe was contracting prior to some time. ; This sounds as if there is nothing wrong with having contraction prior to expansion. But the problem is that a contracting universe is highly unstable. Small perturbations would cause it to develop all sorts of messy singularities, so it would never make it to the expanding phase. That is why Aguirre & Gratton and Carroll & Chen had to assume that the arrow of time changes at t = 0. This makes the moment t = 0 rather special. I would say no less special than a true beginning of the universe.” (http://arizonaatheist.blogspot.nl/2010/05/william-lane-craigs-arguments-for-god.html). Vilenkin concludes in another e-mail: “[I]f someone asks me whether or not the theorem I proved with Borde and Guth implies that the universe had a beginning, I would say that the short answer is “yes”. If you are willing to get into subtleties, then the answer is “No, but…””. That is to say, such a universe would never make it to the expanding phase. Of course, we ARE in an expanding universe.
The reason I bring this is up is because in some debates I have seen of William Lane Craig (notably with Prof Peter Millican and also with Austin Dacey), the atheists misquote the letters between A. Vilenkin and V. Stenger. (Oh, and remember that personal letter Lawrence Krauss presented in his debate with Craig, where Krauss removed/censored the "technical details" so as to avoid admitting the Guth-Borde-Vilenkin theorem implies the beginning of the Universe? Yeah, I remember that one also...).
OSCILLATORY UNIVERSE
As promised, the most popular cosmological models to evade the beginning of the universe will be discussed. The first one, is the model of the oscillatory universe, sometimes called the oscillating universe. This model states that the universe expands, and then re-contracts (“Big Crunch”), expands again (“Big Bounce”), and re-contracts and does so eternally. With every re-contraction, the universe starts expanding all over again. Practically, this means that the universe is being reborn eternally. This theory aims to avoid the beginning of the universe. It fails to do so. Recall the reasons to think that the universe began to exist. The philosophical and mathematical reasons do not vanish. Time still needs a beginning to accumulate, and re-contraction will not remove the accumulation of time. Thus, to reach any point in time, the universe must have had a beginning, and the oscillating model does not remove this necessity.
The oscillating model also does not evade the second law of Thermodynamics. With each re-contraction, the amount of entropy is not refreshed. Entropy/chaos will keep increasing. As Novikov and Zel’dovich state in their article: “every cycle involves irreversible generation of entropy. If the baryon number remains constant, the total mass and the pressure must both increase from cycle to cycle, hence, the maximum radius must increase from cycle to cycle.” Thus, as one traces the oscillations back in time, they become progressively smaller until one reaches a first and smallest oscillation. Novikov and Zel’dovich come with the same conclusion, for they write: “The multicycle model has an infinite future, but only a finite past.” (reference for both quotes: “Physical processes near Cosmological singularities”, by D. Novikov and Ya. B. Zel’dovich, ANNUAL REVIEW OF ASTRONOMY AND ASTROPHYSICS, Volume 11 Pages 387-412, 1973).
Because of the previously mentioned problems with the second law of thermodynamics, astronomers have found out that even if the universe was oscillating, it could not have gone through more than 100 previous oscillation cycles. Therefore, the universe has a finite past as shown by astronomers. (The Big Bang, 2nd edition, by Joseph Silk, pages 311 and 312, 1998).
Furthermore, there is also no known mechanism in physics that could cause a re-contracting universe expand again. Nevertheless, there are more problems, far more problems. In fact, there are so many problems, one could fill an entire new blog post just on the oscillatory universe. Instead, I will just focus on two further problems:
First, the singularity theorem of Penrose and Hawking shows that even in a generalized universe, an intial cosmological singularity (beginning of space and time) is inevitable. As Stephen Hawking himself stated: “This [=their singularity theorem] led to the abandonment of attempts (mainly by the Russians) to argue that there was a previous contracting phase and a non singular bounce into expansion. Instead almost everyone now believes that the universe, and time itself, had a begining at the Big Bang” (The Nature of Space and Time, by Roger Penrose and Stephen Hawking, The Isaac Newton Institute Series of Lectures, Princeton, N. J.: Princeton University Press 1996, p. 20 -> Available online at: http://www.benpadiah.com/otherstuff/elib/HawkingNatureOfSpaceTime.pdf).
Second, because of the inefficiency of the universe with respect to entropy, the “bounce” cannot be strong enough to produce a “bang” as the Big Bang. In fact, it would re-collapse after the bounce (Nature, Volume 302, pages 505 – 506, 07 April 1983).
But none of these remarks are truly important to me. After all, none of theses models evade the mathematical nor the analytic philosophical reasons to think the universe began to exist. In fact, no cosmological model can avoid the philosophical reasons for the universe having a beginning since philosophy is the application of formal sciences, and all cosmological models (being part of empirical science) must obey the formal sciences.
PULSE OSCILLATORY MODEL
There is also a oscillatory model of the universe which only partially re-contracts in each cycle. Alas, also this model suffers from the same problems as the previous model.
QUANTUM GRAVITY MODELS
Stephen Hawking, James Hartle, Arvind Borde, and Alexander Vilenkin all recognize that the universe must have had a beginning. Yet, being atheists and agnostics, they still try to evade the beginning of the universe, by giving some alternative theory. William Lane Craig collectively calls this alternative the quantum gravity models (http://www.reasonablefaith.org/the-ultimate-question-of-origins-god-and-the-beginning-of-the-universe). This alternative states that the beginning of the universe may not have been a sharp point. However, his theory does not deny the beginning of the universe. Nevertheless, Hawking does state something else. He thinks to ask what happened before the beginning of the universe is useless. The analogy that Stephen Hawking gives is the following: “The universe would start as a point at the South Pole. As one moves north, the circles of constant latitude, representing the size of the universe, would expand. To ask what happened before the beginning of the universe would become a meaningless question, because there is nothing south of the South Pole.”(http://www.hawking.org.uk/the-origin-of-the-universe.html). Stephen Hawkings says the question of what started the universe is meaningless, because there is nothing south of the South Pole. That may be, but that is besides the point. I recognize there is also no time “before” time, no “events” before time. Yet, this does not at all remove the fact that the universe has NOT existed forever (the second premise), nor that whatever begins to exist has a cause (which actually was the first premise of the Kalam cosmological argument). In fact, Hawkins’ comments show exactly one of the points of the argument, namely that there was an initial first cause.
But back to the matter at hand: do quantum gravity models actually succeed in having a universe without a beginning? The answer is, No. One thing ALL quantum gravity models have in common is that they make use of imaginary numbers for time. But imaginary quantities for time have no value in interpreting actual time in the REAL world. As Hawkins himself admitted:”Only if we could picture the universe in terms of imaginary time would there be no singularities (…) When one goes back to the real time in which we live, however, there will still appear to be singularities.” (A Brief History of Time, page 136, by Stephen Hawking). Stephen Hawkins has no problem with the fact that quantum gravity models do not represent reality at all: “I don’t demand that a theory correspond to reality because I don’t know what it is”. Of course, one realizes that since quantum gravity models of the origin of the universe is only true in mathematical terms (that is to say: ignoring especially the metaphysical implications), but not true in reality, there is no point in using quantum gravity models to refute the Kalam Cosmological argument. Let us conclude with one clear statement from Hawking (instead of all the “imaginary” statements): “Instead almost everyone now believes that the universe, and time itself, had a begining at the Big Bang” (The Nature of Space and Time, by Roger Penrose and Stephen Hawking, The Isaac Newton Institute Series of Lectures, Princeton, N. J.: Princeton University Press 1996, p. 20 -> Available online at: http://www.benpadiah.com/otherstuff/elib/HawkingNatureOfSpaceTime.pdf).
Stephen Hawking, by the way, does not actually deny the existence of GOD, Prof Hawking simply finds it “unnecessary” to invoke a GOD. However, if the Kalam Cosmological argument is correct (and I think it is), and since Stephen Hawking made it clear the universe began to exist, I think there is good ground to think GOD exists.
THE MULTIVERSE HYPOTHESIS
The multiverse hypothesis is a popular theory for many reasons. However, it is relatively rare for it to be used for the sole purpose to evade an absolute beginning. After all, the Borde-Guth-Vilenkin – theorem is also true in a multiverse, and pretty much any form of universe regardless of the quantities and values of the space-time entity. Thus, an expanding multiverse does not avoid the Borde-Guth-Vilenkin – theorem.
Of course, here is where the popularizer jumps in and says, “well, maybe the multiverse is not expanding, but static”. This scenario, however, is equally hopeless in evading a beginning. For, as Dr Craig explained once, at any point in space of this static entity, there is probability higher than zero of any universe forming. Given an infinite amount of time, the space of the multi-verse would have filled with maximally large universes. Thus, if the multi-verse has existed for an infinite amount of time we would observe other universes running into our universe. But we don’t. So obviously, even a static multi-verse is not eternal.
MODELS, MODELS, MODELS
I have discussed a few models, but I'm not going to discuss all of them. The reasons are as follows:
1) Cosmological models are part of empirical science, and thus must obey the laws of logic. Since it can be logically deduced that, in the A theory of time, there was a first event (usually this first event is the beginning of the universe, but it does not have to be, as discussed at the very first post on the KCA), no amount of empirical science can change that.
2) Some cosmological models that do have an eternal past, sometimes do this using the B theory of time. But I use the KCA in the A theory of time. For a B theory of time, I wouldn't use the KCA in the first place (I don't have a personal preference for either the A or the B theory of time).
3) Some cosmological models evade the beginning of the universe by pasting an eternal quantum state of the universe before its "first event" (i.e. a big bang). However, as discussed before, going from an eternal quantum state to a"first event", is in the context of the KCA the beginning of the current universe.
THE SPECIAL THEORY OF RELATIVITY DENIES THE A THEORY OF TIME
One might say that the A theory of time is incorrect, because Einstein's Special Theory of Relativity pre-supposes the B Theory of Time. And since premise 2 pre-supposes the A theory of time, the premise is therefore incorrect. A quick look at the history of science will quickly reveal that this objection is incorrect: Einstein himself pre-supposed the A Theory of Time, because he knew not of the B Theory of Time when he formulated his relativity theory! Now, most physicists today prefer the B Theory of Time, this is correct. But Einstein's theory of relativity can be interpreted using either theory of time. Both Theories of Time can be seen in a relativistic manner. For example, the special relativity theory can be interpreted for the A Theory of Time using the Neo-Lorentzian interpretation. All interpretations of Einstein's theory so far are empirically equivalent, and give the same predictions.
CONCLUSION
There are more models, but I limited myself to those that are used often (mostly by lay-men). I would like to conclude with a quote from Prof Vilenkin, as I love how he puts it: “With the proof now in place, cosmologists can no longer hide behind the possibility of a past-eternal universe. There is no escape, they have to face the problem of a cosmic beginning.” (ref.: Many worlds in one – the search for many universes, by Prof Dr Alexander Vilenkin).
Even if one doesn't know the cosmological models, one can still be sure the universe had a beginning a finite time ago. This is because an eternal universe requires it to exist for infinite number of hours, years, millennia, etc. However, as stated in the discussion of premise two, an actual infinity of any countable number of things in the real world is philosophically impossible.