## Consciousness, the Arrow of Time and Quantum Mechanics – part I

Flow turning turbulent, from Abhik Basu, Saha Institute of Nuclear Physics, Calcutta

Consciousness, especially subjective consciousness has always bugged the hell out of me. It appears to bug Sam Harris as well, whom has written two lengthy posts about it on his blog. I find myself disagreeing with Harris on only one point: that we have no hope at all of approaching subjective consciousness from a scientific perspective. The reason why I disagree needs some elaboration. If you read this quickly, you might be left with the impression that I am going Deepak Chopra on you. Still, I don’t even feel arrogant saying that I know physics better than him, and that the point I will be making makes sense in light of established science. Also, it doesn’t even claim to improve your personal life.

It all begins with the problem of the arrow of time, about which the Time Lord Sean Carroll is quite an expert. We have a partial solution to the problem of the arrow of time, but I should probably start by telling you what the problem is. In our most fundamental physical laws, time is reversible. The laws of physics have no intrinsic time flow. Time is treated as just another dimension, and you can predict the future just as well as you can predict the past. In practice, we can only do this for the simplest of systems.

The solar system is an excellent example. We can just as easily predict solar eclipses a thousand years from now as figure out the exact date of ancient mythical accounts of the sky suddenly darkening and the sun going black. However, you don’t have to go much more complicated than the solar system to enter into the realm of chaos where predictions can only be short and probabilistic.

Chaos is a real scientific concept that manifests itself as what looks like randomness. Very simple systems can be chaotic. We can describe them with our fundamental laws and obtain exact predictions. But modelling the system with the laws is not enough to make a prediction. You also need to know the state of the system at a given time. For example you could have a pendulum to which is attached a second pendulum. If you hold the two pendula to a position that you know infinitely precisely, you can predict their behavior arbitrarily far into the future once you release it. However, if you make only a tiny error in the position of either of the pendula, your prediction will go awry after a very short time. Small changes in the initial configuration of the system result in large changes in behavior after some time.

The chaotic double pendulum. Make one and watch it be awesomely unpredictable! Play with the length of the strings to achieve chaotic motion. You don't want your two masses to oscillate in phase!

In practice, it is impossible to know infinitely precisely the configuration of any system at any time. Therefore, chaotic systems look to us as though they are behaving randomly. Yes, the die that you throw on the table is in fact a chaotic, theoretically predictable system. In fact, everything we call random in the Universe would truly be chaos if it wasn’t for quantum mechanics. We’ll come back to quantum mechanics in the next post.

Chaos is one thing that renders our laws of physics useless to predict the future, but it also makes it hard to extrapolate into the past. Film a movie of a swinging double-pendulum and play it backwards. You won’t be able to tell time goes in the wrong direction. Of course, as time passes, the double-pendulum slowly stop swinging, so playing it backwards will still look weird. There is something else at play here that betray the arrow of time.

Your double-pendulum is in fact more complex than the two masses and two strings you would put into your classical mechanics equations. It is an unbelievably large collection of smaller objects which can also move about. Everything that can move in a system for which the parts are attached together in some way will end up moving at some point. The energy propagates throughout the degrees of freedom.

The energy that makes the masses swing in the beginning will eventually start transferring to the atoms making the strings and the masses. As the masses slowly stop swinging, the atoms making the double-pendulum will shake a little bit more. This is heat. What we are seeing here is an increase in entropy, the manifestation of the second law of thermodynamics. Let’s look at another example.

A hot cup of coffee is an incredibly complex system of innumerable atoms, but we can still predict exactly the rate at which it will cool down. We give up on predicting the trajectory of each and every atom in there, and look at average properties instead. By a very clever math trick, we can predict the large scale behavior of countless number of atoms. This very clever trick shows the first hint of an explanation for the arrow of time.

Using math, it is possible to look at all the possible configurations of a system. Some of these configurations will be very unique and easily identifiable. For example, you just poured the cream into your cup of coffee, and you can see a nice pattern of cream floating on top of the dark coffee. Some other configurations will simply be indistinguishable from each other, when the cream is uniformly diffused in the rest of coffee for example. You can change that configuration by exchanging the liquid on top of the cup with the liquid at the bottom of the cup, and you won’t be able to see the difference. You just discovered a new configuration, which looks identical to the previous one. Try to count how many of these there are…

The atoms in the cup of coffee are in motion, so the configuration of all the atoms is changing all the time. Since there are a gazillion more configurations where the cream is uniformly spread in the cup, the state of the coffee cup will slowly drift towards such a configuration.

It’s exactly like putting 120 dice on a table, all 6 on the upside. Kick the table repeatedly hard enough for some of  the dice to flip. You will eventually end up with something close to 20 dice on each side. Keep kicking the table and you will probably never get back to 120 dice with 6 side up. This is the second law of thermodynamics: inexorably going from less probable states to more probable states. You can see the arrow of time in there.

Our brains are subject to the second law as well. The processes in our brains that result in subjective consciousness must follow the same direction as the rest of the large and complex systems of the Universe. Even if time is just a dimension like the others which you can travel back and forth, complex systems will inherit an asymmetry in this dimension just by the virtue of being complex. For such systems, the past is automatically different from the future.

Here is another way of seeing it. Travelling through time is equivalent to following the order of cause and effect. However, for very simple systems, cause and effect are indistinguishable. Causality boils down to just a link between events. This link is the laws of physics. I’m sorry for making such an apparently obscure statement, but it would take me another entire post to explain it.

For large and complex systems however, we can make a distinction. The cause being the less probable, identifiable state, and the effect being the more probable state that follows after the cause. It is quite difficult to wrap one’s head around this, but it really doesn’t matter what is the direction of cause and effect. All you really need to get an arrow of time is large complex systems and causality.

Still, all of this leaves one question unanswered. A question hidden in plain sight. A question that has tremendous implications on the phenomenon of subjective consciousness. A question that I can argue is tied to the deepest mysteries of quantum mechanics, even if brain function has nothing to do with quantum mechanics (at least not in the sense that Roger Penrose means it).

In the picture of large complex systems and causality, there is no single moment in time that is singled out. There is nothing in this view that tells me that there should be such a thing as the present, the past or the future. Now that we know that time has a direction, we need to find out why there is a moving point on the time axis that is not like the others.

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