The Time Illusion (Kindle Single)

by John Gribbin

Classical physics rests upon three laws of motion, summarised and explained in the Principia. The first (which Hooke pointed out to Newton) is that every object stays at rest or moves in a straight line at a constant speed unless a force acts upon it. As Hooke also pointed out, this explains the orbits of the planets around the Sun. They “want” to move in a straight line, but are tugged into curved orbits by the force of gravity, pulling them inwards (centripetally) towards the Sun. Several people realised, early in the second half of the seventeenth century, that the force needed to do the job must obey an inverse square law – that is, it is one-quarter as strong at twice the distance, one-ninth as strong at three times the distance, and so on. But it was Newton who proved that only such an inverse square law would do the job, so it became known as Newton’s law of gravity.

The third law says that if one object exerts a force on another object, the second object exerts an equal and opposite force on the first (action and reaction are equal and opposite). So the force of gravity from the Sun pulling on the Earth, for example, is exactly balanced by the force of gravity from the Earth pulling on the Sun, and if I am foolish enough to kick a brick, the force of the kick on the brick makes it move, but the force of the stone on my foot gives me a bruise.

It’s worth quoting Newton’s own words, from the Principia: I. Absolute, true, and mathematical time, for itself, and from its own nature flows equably without regard to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure for duration by means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year. II. Absolute space, in its own nature, without regard to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces; which our senses determine by its position to bodies. I say, a part of space; not a situation nor the external surface of a body. So, according to Newton, time and space are independent aspects of reality, separate from each other and unaffected by the events going on within time and space. This image of the Universe dominated science until the work of Albert Einstein in the twentieth century.

The Pointing Arrow The standard understanding of why we perceive a preferred direction of time – the arrow of time – stems from the industrial revolution of the nineteenth century, and in particular the development of steam engines. The development of a science of heat and motion (thermodynamics) grew out of the need to understand what was going on in steam engines, and to use that knowledge to improve the efficiency of the engines. But the advancing understanding of thermodynamics soon outstripped its practical applications, and gave insight into the workings of the Universe as a whole.

Even before the development of the full statistical mechanical treatment, physicists had discovered, from a combination of theory and experiment, the most profound feature of thermodynamics. In spite of its importance, this became known as the second law of thermodynamics, because the first law is merely a kind of throat-clearing statement which says that in a closed system (one which has no connections with the outside world) the total energy stays the same. The second law can be expressed in different ways, but the most simple is the statement that heat cannot move from a cooler object to a hotter object without some outside influence. This is so obvious from our everyday experience that it hardly seems worth dignifying with the status of a law, but closer study shows that it really is one of the pre-eminent laws of nature.

You never see an ice cube forming spontaneously in a glass of water left alone on the table, while the water around the ice warms up. Now imagine knocking that glass of water off the table on to a stone floor. It will shatter. You never see a mess of shattered glass in a puddle of water on the floor rearrange itself into a glass of water and jump back on to the table. The second law of thermodynamics defines an (or the) arrow of time. If you made a video recording of either of the events I have just described and ran it backwards, you would know something was wrong. We all know the “right” way for the video to run.

Places where entropy seems to decrease locally always involve a greater increase in entropy elsewhere. An ordinary domestic refrigerator, for example, gets cold inside because energy is being used to, in effect, pump heat out of the fridge and release it into the air through the pipes at the back. This does indeed move heat from a colder to a hotter place; but the fridge is not an isolated system. The input of energy required involves an increase in entropy where the energy is being released and distributed. Similarly, life on Earth seems to violate the second law by growing and becoming more ordered; but it is feeding off an input of energy from the Sun, where entropy is increasing. The loss of entropy by the Earth as a whole is vastly offset by the gain in entropy of the Sun. But even the Sun will not last forever. What happens when the Sun and stars die?

In round terms, the Poincaré cycle time is 10N seconds, where N is the number of particles (atoms or whatever) involved. A box containing just two atoms will repeat its starting position every 100 seconds; with 10 atoms the cycle time is 1010 seconds, which is rather more than 300 years. A small box of gas might actually hold about 1023 atoms; so you don’t need to be a whizz at maths to see that Poincaré cycle times for realistic systems are ridiculously long. But, and this is the point, they are not infinite.

In Boltzmann’s scenario, in an infinite Metaverse, anything – that is, anything allowed by the laws of physics – is possible. And as physicists have been known to quip, anything which is not forbidden is compulsory. In a Metaverse that is infinite in both time and space, and which is on average in thermodynamic equilibrium, there must be bubbles (Universes) that temporarily deviate from thermodynamic equilibrium, even if the bubbles are billions of light years across (and “temporarily” here means for billions of years).

There is no need even for a whole human body, since all a brain “knows” is the sense impressions it receives; everything “out there” could all be, if you like, a kind of virtual reality. Maybe it is your brain that has just popped into existence, with the impression of a lifetime of being you and the sense that you are reading this book. I am reminded of Alice’s reflection in Lewis Carroll’s Through the Looking Glass: “He was part of my dream of course – but then I was part of his dream too!” Nobody takes the Boltzmann’s Brain paradox seriously. It is a reductio ad absurdum to demonstrate that there must be a flaw in the argument. The most likely flaw is that on the smallest scale, down among the atoms themselves, the laws of physics are not entirely time reversible, and that an arrow of time is built in to those laws.