Of Time, Entropy and Consciousness

My fascination with entropy began during my Freshman year, when a colleague suggested me to read a book written by the Nobel laureate Ilya Prigogine . For some reason unknown to me, the Belgian-Russian physicist was awarded the honorary citizenship of my hometown – an honour later awarder to another Nobel laureate, Gerard ‘t Hooft – so maybe it was really worth listening to his ideas. As a matter of fact, the basic laws of physics do not distinguish the past from the future: it is said they are time-symmetric. For example, if a planet can orbit its star clockwise, it can also do the same thing counter-clockwise. Both scenarios are equally possible, at least in principle, and there is no way to tell “which one is true”.

However, it is well-known that once you have poured a spoonful of sugar in your coffee, it is virtually impossible to take the sugar away, unless you do some work. In my opinion, this is one of the deepest understanding of how Nature works: systems have a tendency to evolve from a simple states to more complex arrangements. The probability to find a state in a particular configuration is measured by a quantity called entropy.  This “tendency” is encoded in the Second Law of Thermodynamics (the total entropy of a closed system can only increase or remain the same), and is explained in terms of probability: the higher the number of microscopic states that correspond to the same macroscopic appearance, the higher the entropy. Ilya Prigogine’s insight is that the evolution of the entropy of the Universe determines the arrow of time.

So it seems that time is an intrinsic property of our Universe. Or is it just an illusion? Or even something that depends only on our perspective? Let me give an example: 2 + 2 = 4 . If you were asked “How can you get a 4 by adding only two numbers?”, you could give multiple correct answers: 0+4, 1+3, 2+2, 3+1, 4+0. In some way, the operation of addition is not time-symmetric: once you have done the addition, you have lost the information about the operands. Similarly, the act of observing the Universe seems to have exactly the same effect.

According to Quantum Mechanics, or at least its mainstream interpretation, microscopic objects such as elementary particles have properties (usually called observables) that can take up different values. The key point is that it is the act of observation that forces the object to select one particular value among many, with a probability that is determined by the application of the Schrödinger equation to a mathematical entity called the wave function (this process is called collapse). You have probably heard about the unfortunate cat in the box, which is both alive and dead until someone opens the lid and “measures” its state. It is a matter of debate if the wave function has some physical meaning, or is just a mathematical device that is useful for the purpose of calculating these probabilities. Going even deeper (or weirder), the state of two particles can be completely correlated in a phenomenon known as entanglement,  first proposed by Albert Einstein in 1935, in a famous paper written with Boris Podolsky and Nathan Rosen. That is to say, the two objects A and B are not individual particles, but are an inseparable whole: measuring a given property of A gives the value of the entangled property of B with no need to perform the other measurement. What is disturbing is that there seems to be a flow of information that happens at infinite speed, or in no time. I like to say this process is in fact timeless.

In the early 1960s, two theoretical physicist attempted to apply quantum mechanics to the evolution of the wave function of the whole Universe. The resulting equation borrows their names and is known as the  Wheeler – DeWitt equation . In order to come up with such an equation, the duo approached the problem by describing the space-time not with the usual Einstein field equations, which depend explicitly on a variable than be recognized as time, but with the Hamiltonian formalism of General Relativity. In fact, this is the same language the Schrödinger equation is written in. Under simple assumptions of homogeneity and isotropy, the evolution of the Universe can be described in terms of its matter content, the pressure it exert and the curvature of the spacetime. These equations (known as Friedmann equations) can be interpreted as the evolution of the total energy, which determines the interaction between matter and the curvature of the spacetime. This function can be easily translated to the quantum real thanks to a mathematical trick usually referred to as correspondence rule. At this point, something unexpected happens: by requiring the conservation of energy ( \hat{H}\Psi = 0 ), these equations become independent of time!

There’s no obvious interpretation for this fact. Obviously, the equation may just be plain wrong. If correct, a possible explanation is that it is the act of observing the Universe that triggers its time evolution. If nobody is looking, the Universe can be in any of the possible arrangements: it is only when observed that one, and only one of them is picked up. At this point, the Second Law kicks in, generating the arrow of time. It may not be just a coincidence that one of the basic property of consciousness is to tell the past from the future of an observer. Moreover, according to the theory of Special Relativity, two events that appear to happen one after the other,  can be seen in reverse order by another observer in relative motion, but in a way that preserve the relationship between cause and effect. In some way, the laws of physics seem to be very careful about the consistency of causality.

To summarize, the dynamics of the Universe might have been set in motion by the appearance of observers, i.e. conscious being like ours. A provocative question remains: can a Universe which laws of physics are incompatible with the presence of conscious observers exist at all?

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