Entropy, Complexity and the Strong Anthropic Principle

ScreenHunter_1637 Oct. 17 09.26

Observers are necessary to bring the Universe into being. The Universe must have those properties which allow life to develop within it at some stage in its history. The Universe (and hence the fundamental parameters on which it depends) must be such as to admit the creation of observers within it at some stage. These statements are known as the Strong Anthropic Principle according to Carter and Barrow and Tipler.

In all its forms, the Anthropic Principle is, in our view, unnecessary even though, from an intellectual and philosophical standpoint, it is undeniably beautiful and elegant. The so-called fine-tuning of all the fundamental parameters (Plank’s constant, cosmological constant, proton to electron mass ratio, etc., etc., appears so fantastically unique and precise that ultimately one is forced to believe that the Universe has a purpose: to create conscious observers. We believe that this makes things unnecessarily intricate and complicated.

With a sufficiently broad suite of elementary particles (e.g. the twelve fermionic fundamental particles and twelve bosons, as well as the corresponding anti-particles and the Higgs boson, etc.), able to interact in a sufficiently rich manner, life becomes an inevitable consequence. Intelligent life comes just a billion or two years later. This is not the big deal. Clearly, whatever form of intelligent life that evolves in some Universe it will always fit in the big picture with remarkable precision and harmony – precisely because it has evolved within that particular universe. So, there is no fantastic top-down coincidence – just bottom-up co-evolution in which everything that takes part in the game fits in perfectly precisely because it takes part in the process from day one.

It is claimed that if all the mentioned constants had minute deviations from their current observed values our Universe (i.e. the one that we observe) would not exist. This is a very strong statement to make – we still haven’t been able to unify the four interactions into one (must they all come from one Theory?) yet we are ready to sustain such a far-fetched claim. If the mass of the electron differed by 0.1% from the current value, God knows what the values of masses and charges one would observe in the plethora of elementary particles that we know today. How can we be sure that other stable life-sustaining universes wouldn’t be possible? Science is not mature enough to answer similar questions. We still have to make up our minds on such issues as the amount of dark matter in the Universe or if it is flat! With different physical constants our universe would not exist but another one probably would.

If the initial set of elementary particles and laws (let’s indicate this set as S:{P, L}) is sufficiently complex, then, upon appropriate initiation (e.g. via a Big Bang – which, by the way, is a great way to hide the initial conditions from any potential future observers) one will always obtain a puzzle (Universe) in which all pieces fit simply because they all co-evolve. If S:{P, L} is sufficiently complex, the puzzle will eventually contain intelligent beings. These will find themselves fitting beautifully into the big picture and an observer will recognize with awe that all physical constants have just the right values so as to guarantee his existence.

The big deal is not having a set of physical constants that seem fine-tuned. The big deal is to have such S:{P, L} that C(S) is sufficient to lead to intelligent beings (C(S) indicates complexity of S). Mathematically, one could state this as follows:

Given a set S of elementary particles, P, a set of elementary interaction laws, L, it is possible to imagine how this set may lead to a Universe U as follows:

S:{P, L}⇒U

Where the symbol ” ⇒ ” indicates some form of mapping or transformation. One can, at this point, imagine that the complexity of the resulting universe is function of the initial complexity of S:

C(U) = f(C(S))

Suppose that in order to sustain life, the initial set S must have a minimum value of complexity. Let us indicate this as C*. In other words, intelligent life emerges iff:

C(S) > C*

This means that a Universe develops intelligent beings iff C(U) > U*, i.e. if it has more than a certain minimum complexity. What this means is that we can abandon the idea of super fine-tuning of physical constants and state the problem differently, in a weaker form as follows:

We certainly live in a Universe in which C(S) > C*

It is unnecessary to fine tune anything at this point. In fact, it is not necessary to insist on C(S) = C*, C(S) > C* is more than enough. We don’t know how far C(S) is from C* but this is quite irrelevant. We can, in effect, assume that life emerges earlier if C(S) is much greater than C* and that it takes more time to develop if C(S) is just slightly greater than C*. With this minimum threshold complexity of the elementary set S a certain minimum time T* is necessary for life to develop. We also know, with certain approximation, how much time T it took for life to develop since the Big Bang in our Universe but we don’t know the value of T*. All we know is that for sure is T > T*.

We know that Complexity is a function of Entropy. The Entropy of the Universe increases inexorably. Complexity also increases until it reaches a maximum value, then it drops, never again to increase. This means that life has the first chance to spring during the period C(U) crosses U* for the first time and before it drops below U*. In theory, this can mean billions of years. This means that there may be much life out there, in the face of the Fermi Paradox. It all becomes a matter of time, not of fine-tuning.

What does all this mean? In theory, infinitely many universes (i.e. combinations of physical constants) can exist in which intelligent life emerges spontaneously without the need of fine-tuning. It is sufficient to ensure before the Big Bang that C(S) > C*. This leaves the Creator with a much simpler task. And puts an end to the Panglossian Paradigm. One just cannot help but see a parallel between the fantastically matching physical constants in our Universe and the Spandrels of San Marco.







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