Time According to Sir Stephen Hawking

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Stephen Hawking, one of the world's most renowned contemporary theoretical physicists, proposes a unique view of time, building on the theories established by Newton, Einstein, and even Kant (though Kant took a philosophical approach, Hawking incorporates this factor as well).  Hawking visualizes time as a series of 3 "arrows."  There is the thermodynamic arrow, the cosmological arrow, and the psychological arrow.  The concept of these arrows help explain why we see time as moving "forward," and what this "flow" of time actually is in terms of the expansion and contraction of the universe.  Essentially, these arrows help distinguish the past from the future, and give a direction to time.

In our current state of the universe, all these arrows are pointing in the same direction, however, this will not always be the case, according to Hawking.  The thermodynamic arrow is derived from the second law of thermodynamics, which states that in any closed system, disorder (entropy) always increases with time.  Take an example of a glass falling from a table.  The glass begins in a state of heightened order; it is all in one piece.  As time passes, the glass hits the floor, and shatters into many pieces, increasing the disorder, or entropy, tremendously.

 
Entropy increasing in a system

When viewing the universe as a closed system, it also stands to reason the universe began in a state of high order, and when it ends, will be in a state of extreme disorder.  Based on the quantum theory of gravity and "no boundary condition" of spacetime (which Hawking explains in his book, A Brief History of Time, but which we will not discuss in detail), the universe did indeed begin in a very smooth and ordered state, which a few fluctuations in the density and velocities of particles as required by the quantum uncertainty principle.  These fluctuations eventually caused matter to cluster due to their own gravity (in regions of higher density) after the Big Bang, and eventually form galaxies, stars, and planets.  Having regions of high density, regions of low density, and then more regions of high density translate to an increase in entropy since the initial, smooth ball of matter before the Big Bang.  Thus, the thermodynamic arrow's direction is confirmed; as time progresses, entropy increases. 

Hawking initially believed that since the universe began as an ordered, smooth point in spacetime, it would eventually return to this state after the "Big Crunch," when the universe starts to collapse upon itself (now, it is still in a stage of expansion and will expand for at least another ten thousand million years).  Thus, if the entropy of the universe began to decrease as the universe collapses (which happens to determine the direction of the cosmological arrow), Hawking reasoned that the psychological arrow of time would also reverse itself.  This is because the psychological arrow and thermodynamic arrow always point in the same direction.  The psychological arrow, as described earlier, is the direction of time that dictates what we remember as the "past."  To understand how this related to entropy, it is valuable to imagine our brains as computers.  They begin in a state of heightened disorder; a random series of 1's and 0's, for example.  When data is input, these 1's and 0's rearrange themselves into an ordered state, which becomes a part of the computer's "memory."  However, the energy required to order those 1's and 0's was converted from electrical energy to heat energy during the process, and then expelled into the atmosphere, resulting in an overall increase in entropy (greater heat means faster velocities and random motion of particles - see diagram to the right).  Our brains work in similar ways, converting the chemical energy in the food we eat into heat energy when we live, breathe, and create memories in the form of neural connections in our brains.  Thus, we remember events in the same direction of time that entropy takes; we perceive the "past" as a time of heightened order, or less entropy.  Therefore, the psychological and thermodynamic arrows of time point in the same direction.

By this virtue, Hawking theorized that when he universe began to collapse, and the cosmological and thermodynamic arrows switched direction, so would the psychological arrow.  Whoever would be living on Earth when the universe began to contract would "remember" things that happen in the future; their lives would run in reverse order, beginning when they were very old, right before their death, and ending when they were born.  They would not see the wine glass break and shatter, but rather re-coalesce from thousands of tiny pieces into a new, whole wine glass.  However, as Don Page and Raymond Laflamme, Hawking's colleague and student, respectively, pointed out, no law of physics, quantum mechanics, or relativity said that the universe would have to contract in reverse-time and that entropy would have to decrease.  Hawking backtracked and realized they were right; the psychological and thermodynamic arrows would not reverse direction.

One last relationship had to be determined, why did the thermodynamic and cosmological arrows run in the same direction (or, why does entropy increase as the universe expands)?  As it turned out, the reason was fairly simply explained.  The universe as we see it today is expanding and increasing in entropy; that is not in dispute.  However, by the time the rate of expansion of the universe falls below critical speed and the universe's own matter begins to pull in on itself, all the stars will have burnt out, galaxies will have collapsed, and protons and neutrons will have decayed into radiation and photons; basically, the ultimate state of disorder (or very close to ultimate).  When the universe begins to contract and the cosmological arrow reverses direction, there will be no solid direction for the thermodynamic arrow to point in, since entropy could not increase much more.  Furthermore, the psychological arrow would be entirely insignificant in this state of the universe; at ultimate entropy, life could not possibly exist.