The early 1900s saw the abandonment of the idea that everyone would be able to agree on the time an event took place, provided they had a good clock. After the speed of light was found to appear the same to every observer, time was determined to be relative, just like space.
The fact people were willing to accept the challenging idea that ime is not the same for everyone, meaning it is not “absolute,” shows the general climate of thought in that day. Science has earned people’s trust, and new ideas were more likely to gain wide acceptance.
To unify gravity with quantum mechanics, one must apply imaginary time. Imaginary time is no different from the dimensions of space. You can go back and forth in imaginary time, just as you can head south or turn back north. But in real time, there are real constraints on how we move through time.
Unifying two of the most central concepts of modern science requires stretching the imagination into previously unchartered realities—imaginary time. Navigating in imaginary time is actually easier, suggesting that once a unifed theory of physics is found, other unimaginable realities will become navigable.
Scientific laws obey the combined symmetries of C, P, and T. C refers to particles acting as anti-particles do. P refers to their mirror image. T refers to reversing time. Scientific laws will be the same in the symmetry of C and of P, meaning mirror-image anti-matter people would live in a mirror-image anti-matter universe that resembled ours.
Returning to an idea previously discussed, Hawking recaps the different types of symmetries that the laws of physics are thought to follow. Again, this is something like entering imaingary territory, analyzing how the universe, or just one situation, wold unfold in different but symmetrical circumstances.
But the laws of science do not run the same if you run time backward instead of forward. Just think of a glass falling off the table and smashing. You would not see it jump back up and re-form. This is because of the law of entropy, which states that disorder in any system will usually increase as time goes on. A smashed cup is disordered, and does not reassemble itself back into order.
Time, however, always seems to run one way in normal situations, and its direction matters when considering the laws of physics. The concept of entropy links to time, because disorder tends to increase in any system. This is not a certainty, but the overwhelming likelihood.
Entropy, a concept defined in the second law of thermodynamics, directs the first, thermodynamic, arrow of time. Second is the psychological arrow of time, which is the direction we feel time passing, as we make memories. The third and final arrow of time is the cosmological arrow, which is the direction of the universe’s expansion. These determine the direction of time.
Because disorder always increases, entropy can be considered an arrow of time, directing and indicating its movement. Another is humanity’s observation of time, and the third is the universe’s development trajectory. For humans, time is not an assumed property of the universe, but a measurable and complex question.
Hawking suggests the no boundary universe model and the weak anthropic principle explain why these three arrows all point the same way, and why they exist at all. The thermodynamic arrow determines the psychological arrow, so they always point the same way. The cosmological arrow, however, will not always point the same way, though it does right now. When the three do point in the same direction, however, the universe is suitable for life forms able to ask why the three arrows all point in the same direction (the anthropic principle).
Luckily for the reader, Hawking has an explanation to offer for why these three arrows of time are currently pointing in the same direction. The anthropic principle is a key aspect of this approach, as all three arrows must necessarily be pointing in the same direction to allow life to form, as Hawking will explain. But, as before, this alone is not a satisfactory explanation for inquisitive humans.
The thermodynamic arrow relies on the law of entropy, which states disorder becomes more likely as time goes on. Imagine a jigsaw box in which all the pieces start off in the ordered places to form the picture on the front of the box. The more someone shakes the box, the more likely it is the pieces will separate and become more disordered. It is possible the pieces would fall back into the original, ordered state, but this is far less likely. If the reverse was true, and disorder decreased with time, broken glasses would jump back onto tables and repair themselves.
Increasing disorder, or entropy, is an inherent feature of the universe, as evidenced by the day-to-day examples Hawking provides. Despite being such a normal occurrence, just as familiar as apples falling to the floor, the fact that disorder nearly always increases has caused humans to ask why events occur in that order, rather than the reverse.
For the psychological arrow of time, the process of making memories creates more order internally, but the energy used to create memories is emitted outward, creating more overall disorder. This means humans, and computers, only remember things in the direction of entropy, making the psychological arrow of time almost trivial, as it is determined by the thermodynamic arrow. Humans remember and measure time in the direction that disorder increases.
This inherent concept of entropy holds true even in the process of recording time, as based on the thermodynamic arrow, fusing the two together. These two arrows will always point in the same direction as one depends on the other. This idea seems ironic, as humans’ strongest sense of time, memory, is the weakest of the three arrows of time, Hawking argues.
General relativity cannot tell us what happened at the very beginning or what happens in singularities, because there the laws of science break down. The universe might have been smooth at first, but it might also have been lumpy and disordered. If the universe was completely disordered, the thermodynamic arrow might well point the opposite way from the cosmological arrow, but that is not what we observe. One requires a quantum theory of gravity to know how it all began, rather than guess.
Hawking returns to the fact that humans still do not know for certain how the universe started or what it looked like in its earliest stages. This is a great, open question that he believes will only be solved when a unifying theory of physics unlocks the answers on the final mysteries of the universe. Until then, humans will continue to wonder, but also work toward potential theories.
The no boundary principle does away with singularities and edges, meaning the world is finite, smooth and uniform, to the extent the uncertainty principle allows. After a period of inflationary expansion, regions would slow their expansion and begin to clump, forming galaxies, stars, and people. In this way disorder increased, creating the thermodynamic arrow of time, pointing the same way as the cosmological arrow of time, or the universe’s expansion.
The universe cannot be perfectly uniform because the uncertainty principle states there in an inherent randomness in everything. Thus, disorder is always increasing in the expansionary phase of the universe. That means the universe’s expansion can be considered an arrow of time, and one that coincides with the thermodynamic arrow.
The question then arises as to whether disorder decreases as the universe begins to collapse—would the thermodynamic arrow reverse as the cosmological arrow does? At first Hawking believed so. He thought the universe would return to a smooth and ordered state when it shrunk. This would also make it the time reverse, he thought.
Having determined the three arrows of time, more questions, inevitably, arose. Hawking wondered, would the universe’s contraction phase be the mirror image of its expansion? If so, this would suggest a total reversal of time as the universe retraced its steps.
But a colleague Don Page pointed out to Hawking the contraction phase did not have to be the time reverse in the no boundary model. Also, Hawking’s student, Raymond Laflamme, discovered the contracting phase should look very different to the expanding phase, and so Hawking changed his mind. Disorder ought to continue to increase when the cosmological arrow reverses and the universe begins to contract.
In the end, Hawking decided that disorder would continue to increase during the universe’s contraction. This means that the cosmological arrow of time will reverse, but the other two will continue to point in the direction that disorder increases.
Hawking had to admit his mistake. When Eddington opposed black holes, he did so because he could not admit a mistake. Others often pretend they had never made the mistake in the first place, and pretend it never happened. But Einstein gave a better example when he called the cosmological constant the greatest regret of his life.
When it becomes clear that a scientist has made a mistake, he or she has two options: deny or accept that fact. What Hawking shows here is these options reveal scientists’ priority: protecting their own ego, or advancing the progress of science.
Hawking wondered, if disorder always increases, and the psychological arrow follows the thermodynamic one, then why does the cosmological arrow happen to point toward expansion and not contraction? The anthropic principle offers one answer, as conditions within the contracting phase would not be conducive to life (as all stars would have burned out), so we end up asking why we exist in the expanding phase, when it is the only period capable of creating life.
The anthropic principle offers, again, an unsatisfactory answer. It follows that intelligent life living in a time when the three arrows of time all point in the same direction would wonder why it happens to be that this is the case. But Hawking wants to specifically know why the other options are off the table.
At the turn of the contracting phase there would be no strong thermodynamic arrow as the universe would be in almost total disorder. Yet life requires the thermodynamic arrow, as it breaks down food (ordered forms of energy) to live, creating heat (disordered energy). The expansion doesn’t drive disorder, but the no boundary condition means the thermodynamic and cosmological arrows must point the same way to support intelligent life.
The process of supporting life involves breaking down ordered forms of energy to power living organisms. That energy is emitted, for example as heat, back into the universe in a more disordered format. For the universe to approach its contracting phase, it must be in a state of near total disorder, meaning there is no first arrow of time at all, and no ordered energy for food or fuel, meaning life cannot be supported.
The laws of science do not distinguish between the forward and backward direction of time, but the three arrows of time do. Human understanding has created order in a small corner of an ever-more disordered reality. By reading this book, you will have created order in your own mind by creating new memories, but the disordered heat used to power your body and radiated into the world will outweigh that order many, many times.
Hawking argues that humans strive for order, as reflected in their pursuit of a theory to categorically explain everything. Yet this mission cannot ensure actual order in the universe. The very attempt creates more disorder, as an inevitable trend that characterizes the universe.