A Brief History of Time

A Brief History of Time

by

Stephen Hawking

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A Brief History of Time: Chapter 11 Summary & Analysis

Summary
Analysis
It is too hard to create a theory that covers everything in the universe in one go. So far there are partial theories that focus on different aspects of science. But in the end, it would be good to have a unified theory that covers everything, without having to make up certain numbers for certain aspects to make them fit. This mission is called the unification of physics.
Hawking’s central focus throughout the book is how the partial theories that humans have devised so far point toward an overarching, unified theory of physics. He makes a case for having such a unified theory as the best possible option to understanding the universe, rather than making the theories fit certain observations.
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Einstein tried and failed to find a theory of everything, mainly because not enough was known about nuclear science at the time, but also because of his own refusal to accept quantum theory despite his own input into its creation. The uncertainty principle, on which quantum theory is based, is fundamental, and must be incorporated into any unified theory.
Even Einstein fell on the wrong side of science history, opposing quantum theory and therefore obstructing scientific progress in this field. Yet quantum theory has become central to modern understandings of the universe, and has since earnt its place next to general relativity.
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Over-confidence should be dampened, as there have been false starts before. For example, Max Born asserted, “Physics, as we know it, will be over in six months,” after Paul Dirac discovered the workings of the electron. Of course, the discovery of the neutron and nuclear forces just opened up more questions. Even so, science is still progressing toward an answer.
Hawking argues human arrogance is as natural and as obstructive as human obstinacy. Misplaced confidence can distract scientists from the mission just as much as their refusal to accept new ideas. Only objectivity is a suitable approach, amid the seemingly endless questions that arise in the curious human mind.
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Previous chapters covered general relativity, incomplete gravity theories,  and the three forces that can be combined in grand unified theories, although these do not include the gravitational force. The problem with incorporating the gravity into GUTs is that it does not take into account the uncertainty principle that defines quantum mechanics.
There are many aspects of science that remain in complete or incompatible with other areas. Even supposedly unifying theories of the major forces do not include all the forces. Therefore, there is work still to be done.
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Thus, the first step is to combine the uncertainty principle and general relativity. This has already resulted in significant rethinks, such as black holes not being black and the universe having no edges. The problem is that under the uncertainty principle there are technically infinite numbers of particles, which add infinite mass to the universe, and so curve space-time into an infinitely small size.
Hawking again emphasizes the crucial first step of finding a way to intgrate the two great discoveries of the 20th century: the general theory of relativity and quantum mechanics.Other partial theories that account for both of these grand theories have demystified even the unseeable phenomena in the universe, such as black holes.
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Mathematically, infinities in partial theories can be canceled out by introducing infinites elsewhere. But this means certain values have to be chosen from observation. The theories themselves cannot predict these values, which is a serious drawback. When incorporating the uncertainty principle and general relativity one can either adjust the strength of gravity or the cosmological constant. But this still will not remove all the infinities from the predictions, which do not match with measurable observations.
Infinities are indications of unknowns, indicating gaps in human knowledge, and work left to be done. The presence of such infinities makes the math less accurate, as certain numbers are chosen from observation rather than explained with a theory, which does not necessarily contribute to definitively understanding of the problem at hand, nor the solution devised.
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In the 1970s, a possible solution was offered, called supergravity. It combined the graviton, the gravity wave-carrying particle, with other particles with different spin. These were all considered different forms of one superparticle, which unified certain matter and force particles with different spin whose positive/negative energy canceled each other out. But the calculations to see if any infinities remained were too long and difficult to do.
Supergravity was an attempt to unify certain particles with different spin, but it proved beyond humanity’s current power to prove mathematically. Ultimately, such theories need to be provable. If the theory can stand the test of time until computers can manage the math, it could gain the confidence of the scientific community.
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1984 saw a total change in approach with the creation of string theory. This suggested that particles were not a dot, but very thin lengths with one dimension. They could be open strings with ends or closed strings, like loops. Particles are in one place at one time, and their histories are drawn as a line in space-time. Strings occupy lines in space-time at any one point. This gives it a two-dimensional history called a world-sheet, where one axis is time and the other the position on a point of the string.
Since then, however, string theory was proposed. This involved a complete perspective change on the form and features of particles, which were now viewed as one-dimensional string-like lengths or loops. Scientists devised new graphs to represent the histories of these strings.
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Two strings can join, either at the ends for open strings or to create a larger circle for closed strings. They can also divide. String theory replaces the idea of particles with waves down the string. Absorption or emission of energy and particles is represented by the merging or division of strings. Gravity passing from the sun to the earth would previously be seen as a graviton passing from one to the other. String theory creates an H-shaped pipe, where the vertical sun and earth pipes are linked by the gravitational force in the middle.
With this totally new perspective on particle movement and interaction, scientists are almost reworking the basics, such as how energy passes between particles. Hawking describes this process to emphasize the earlier point he made that scientific theories are only used until a new and improved version comes along. The scientists must be ready to reassess any and everything they thought they knew.
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String theory first arose in the 1960s, to describe the strong nuclear force. Small particles in the atom were waves on a string, and the nuclear forces between them were strings that formed a web. These strings would have their own tension of about 10 tons.
This reassessment started with the some of the smallest particles, as physicists started to rebuild their knowledge from the ground up.
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In the 1970s Joel Scherk and John Schwarz said string theory could describe gravity, but only if the tension were significantly higher. This would leave most of general relativity’s predictions unchanged, except on the miniscule level. Their work didn’t gain much attention at first. Sadly, Scherk died from diabetes, leaving Schwarz to continue the work alone.
Scherk and Schwarz’s suggestion is a type of unification theory, with relevance for both. general relativity and quantum mechanics. Hawking notes that their ideas didn’t gain much traction, as the scientific community was busy trying other leads. This is not due to stubbornness, but the sheer amount of open questions outstanding.
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String theory came back into fashion in 1984 after supergravity failed to make much more progress and a joint paper from Schwarz and Mike Green on left-handed particles garnered attention. Soon, a new version of the theory, called the heterotic string, arose. These strings could eliminate all infinities, although this is not yet proven. But the biggest problem with string theories is they require either 10 or 26 dimensions.
String theory came back into fashion after other theories fell through or hit dead ends, as the tide of scientific progress must advance. String theory requires significantly more dimensions than physicists have been used to dealing with, but the wide acceptance of the idea shows that modern scientists are willing to consider entirely new approaches.
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It is possible we cannot see all these other dimensions because they are curved up into very small spaces. We only see the three spatial dimensions that we are used to because they are fairly flat. If you look at a straw from far away it looks one-dimensional—just a line. Closer up you can identify many more points on the straw. In string theory, looking on a very small scale reveals ten dimensions. No room for space ships, then.
The next question, then, is how to see all these new dimensions that string theory relies on. Hawking provides an everyday example of how more dimension become apparent on closer inspection. Therefore, the next step for scientists is to learn how to look ever-more closely, something they have been doing for centuries.
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The question then arises as to why the four dimensions of space and time that we can see happened to flatten out, while the others didn’t. Again, the anthropic principle gives a partial explanation. Two dimensional animals could not exist, as they could not form the complex inner systems required to feed themselves.
As with most theories, the question of why the universe has turned out this way, rather than any other, arises. The anthropic principle is always on standby as a go-to response, but as ever, this answer is not satisfactory for those who wish to know why the universe turned out the way it did.
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There are also problems with more dimensions. Gravitational forces are increasingly weaker at the same distance with more dimensions at play. This would create instability, causing the earth to spiral away from the sun under the influence of any disturbances. The sun itself would be unstable because its own gravity might not hold it together, and atoms would face the same instability.
There are not only problems with visualizing or locating these extra dimensions. The effect these dimensions have on the laws of physics also raise new issues. The effect these additional dimensions have on the earth’s orbit, for example, do not accord with observation. Therefore, many questions remain, but this has not killed the idea. It simply requires more thought.
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The anthropic principle suggests life is only possible in space-times with the four flat dimensions we are used to. String theory allows some regions of the universe to have the same properties as ours, while in other regions maybe the other dimensions have flattened out. Though, there may be no intelligent beings in those dimensions.
Intelligent life forms will always wonder why their region of the universe is a certain way, but string theory suggests there could be regions that have more dimensions, and which would not be able to support life. One resulting question would be whether humans would be able to travel to such regions.
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Another problem is there are many string theories, and millions of configurations for the different dimensions. In 1994, scientists discovered dualities, which produce the same effects in four-dimensional space-time from various configurations. They also found p-branes, which take up two or more dimensions in space, while particles are 0-brane and strings are 1-brane. Supergravity, string, and p-brane theories could all be estimations of one overarching theory, and useful in their own ways. 
Hawking briefly outlines more modern theories that consider the universe from new perspectives, which do feature some agreement and consistency with string theory. It seems each of these theories is merely a reflection of the unifying theory that would comprehensively explain all of the gaps between all of the partial theories.
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Hawking suggests there might not be one single formula to the unifying theory, just as Gödel showed there was no one formula to arithmetic. Instead, it might be better to see science as a patchwork of maps that overlap and together provide a whole view. All the maps would agree on points they overlap on.
Yet, perhaps there is no one, single theory of everything after all. Perhaps humans will have to rely on overlapping theories that will continue to provide more accurate predictions. The process of scientific discovery could therefore continue indefinitely.
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There are three possibilities: there is a unifying theory of physics; there are only partial theories, but they add up to explain everything; or the laws of the universe are random. Some argue the third in order to leave room for God. With our understanding of the uncertainty principle, we have removed the third option. Activity is random to a certain degree, but laws do hold sway in the universe.
Hawking discounts the third option on the basis it does not agree with observation—scientific laws have done a good job so far in predicting outcomes and explaining the universe. He suggests that any argument against that fact is based on prejudice, and the primary example he gives is the stubbornness people turn to in protecting their religious beliefs.
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The second possibility agrees with what we have seen so far. Scientists have always found new phenomena to explore, and they may well find a new layer of particles beyond quarks. But gravity might limit this otherwise infinite series of discoveries as we achieve higher energy production rates. There are upper limits of energy after which black holes form just from one particle. Though scientists cannot achieve these levels of energy anytime soon, these high energies were around at the beginning of the universe, so studying that era could uncover a unifying theory within this lifetime.
The history of science so far has been the gradual accumulation of knowledge, and the replacement of older theories with ever-increasingly accurate explanations. Every new discovery has led to further questions, driving forward this race toward total knowledge. Hawking is optimistic that everything will one day be understood, even in the not too distant future.
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Even if the unifying theory was found, it would still only be a theory, and could later be disproven. But if its predictions were consistent with observations, scientists could be confident in it. This would be the end of an era, one in which humanity strived for ultimate knowledge of the universe. It would also revolutionize the ordinary person’s view of the universe. Today, scientists specialize in certain fields, and no one can stay up to date on all subjects. Eddington suggested only two people understood the theory of general relativity in his day. Today many thousands do. If we were to find the unifying theory of physics, in time everyone could understand it.
Throughout the ages, humans have always looked up at the sky and wondered about the universe, and how it all works. Today, even scientists cannot keep up with the rapid flow of new discoveries in every subject. But after finding one unifying theory of the universe, after all the currently unsolved mysteries are answered, there would be time for everyone to gain a general understanding of it. After all, these are questions that all humans share.
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But even with such a theory, scientists cannot predict exactly the events of the universe, due to the uncertainty principle and the fact the math is simply too hard. While scientists know in essence how most of the universe works, that does not help to mathematically predict human behavior, for example. It will take longer to create useful approximation methods, even after the theory is found. So, the first step is finding the theory. The next step is understanding everything, including the reason for humanity’s existence.
Humans looked at the sky not only to wonder at the mysteries of the universe, but also with uncertainty of their own role within that wider realm of existence. Finding a unifying theory would only be the first step in answering this more complex question, as the theory can provide the tools to predict the universe. The next step will be applying that knowledge to truly understand it, helping humans to see where they fit in.
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