A Brief History of Time

A Brief History of Time

A Brief History of Time Chapter 8 Summary & Analysis

Summary
Analysis
Einstein’s general relativity predicted that space-time began as a singularity in the big bang, and ends in the potential big crunch singularity when everything collapses back in on itself, or in localized singularities in black holes. But when applying quantum mechanics, it is clear that black holes re-emit mass and energy into the universe, eventually disappearing. Applying quantum mechanics to the big bang, then, might change our understanding altogether.
By applying both general relativity and quantum mechanics to the study of black holes, scientists were able to re-evaluate their understanding of the phenomena. This is the draw of finding a unified theory that can incorporate both, as the theory could well change human understanding of the universe altogether.
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Hawking’s interest in the origin and fate of the universe reawakened while at a conference in the Vatican. The Catholic Church was seeking input from scientists, centuries after making a bad call on challenging Galileo’s assertion the earth orbited the sun. At the end of the meetings, the Pope met with scientists, telling them not to enquire too deeply in the big bang, because it was the work of God. Hawking had just spoken on the topic of a no boundary finite universe, which would have no beginning, of which thankfully, the Pope was unaware.
The church’s attempt to squash Galileo’s ideas came to nothing, as the latter’s logic and agreement with observation meant that Galileo’s work survived the test of time. Centuries later, it was the church that had fallen behind with the pace of progress, and thus sought input and assistance from the scientific community to catch up. Hawking emphasizes this point to warn of the errors of obstructing scientific progress. Yet, from the Pope’s advice not to study the big bang, it seems the lessons has not been learnt.
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But first, one should understand the “hot big bang model.” This model is a Friedmann model, in which matter cools as the universe expands, meaning the matter has less energy. With a lower temperature, and therefore lower energy, matter begins to clump together as the particles attract each other, because their ability to escape is lower. When particles collide at high temperatures, more particles are produced, while at lower temperatures they are more likely to annihilate with their corresponding anti-particles. Thus, as the universe cools, fewer particles are created.
In this model, after the big bang, particles begin to lose energy (as represented in their temperature) and thus cannot escape attractive forces. Fewer particles are also produced in this cooling phase. It is worth noting this is just one model—scientists have suggested many, and Hawking refers to numerous. Each should be weighed and assessed independently, and each could be thrown out immediately with the introduction of better ideas. This is all part of the process of discovery.
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At the moment of the big bang, the universe would have been infinitely dense with zero size, and, as such, infinitely hot. Right after the big bang the universe would have been made up of photons, electrons, and neutrinos, along with their anti-particles, and some protons and neutrons. As the universe cooled, electron and anti-electron pairs would annihilate each other at a rate higher than the pairs were being produced, which creates more photons as a result of the annihilation.
This model has infinities, which as we have seen scientists tend to struggle with. Newton himself couldn’t get his head around how an infinite universe would work. Nevertheless, scientists seem to allow these infinities to remain in their models as a place marker, while they expand on the rest of the theory.
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One hundred seconds after the big bang, the universe’s temperature would be 1 billion degrees, meaning protons and neutrons could not escape the strong nuclear force and began to form into the nuclei of heavy hydrogen atoms, followed by atoms of heavier elements. George Gamow first proposed this model with Ralph Alpher in a 1948 paper.
Scientists can propose fairly specific approximations of the state of the early universe based on the observations made today. Because physicsts understand the strong nuclear force and how it works, they can make an educated guess of the temperatures under which it would begin to command particles, even though it is impossible now to observe the early universe directly.
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Gamow and Alpher said radiation from that first hot stage of the universe should still be present in the universe today, which Penzias and Wilson found to be true. Gamow and Alpher’s assumption aligns with the large amount of helium in the universe, meaning scientists can be fairly sure their picture of the universe after the first few seconds following the big bang is accurate. After the first few hours, the production of new elements would have stopped, though the universe itself would have continued expanding.
While the early universe cannot be detected directly, Penzias and Wilson’s findings demonstrate that knowledge can still be gleaned about the long-distant past thanks to traces still around in the universe today. This gives scientists confidence that their model is accurate, as it accounts for the realities still seen today. Still, the danger of making the evidence fit the theory always remains.
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Once the temperature of the universe dropped to a certain point, the electromagnetic force would be stronger than particles’ energy to escape it, drawing more particles together to form more atoms. In denser than average regions of the universe, the gravitational force of this clumping matter would have slowed expansion. Some regions would stop expanding altogether and start to collapse. Gravitational forces outside of these regions would, in turn, cause the regions to start spinning, and they would spin faster as they contracted. Soon the spin would balance out with the gravity to stop the collapsing phase, creating disk-like rotating galaxies. There are also oval non-rotating galaxies.
Weaker than the strong nuclear force, the electromagnetic force would come into play at lower temperatures, where the particles lose the ability to escape the electromagnetic pull. With all this clumping, gravity comes into play too, causing isolated regions of contraction, slowing the overall expansion of the universe. These galaxies, as they are called today, often spin due to outside forces, counteracting the gravity. Again, this model works because it agrees with the view of the night’s sky, a view that has intrigued humans for millennia.
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After more time passed, hydrogen and helium would form into smaller clouds and collapse, due to their own gravity. Contraction would force collisions between atoms, raising the particles’ temperature, starting nuclear fusion reactions. This would transform hydrogen into helium, creating heat and pressure, balancing the gravity to halt the contraction of the gas clouds.
Here, the discussion returns to stars, forming with the contraction of gas clouds. The process creates more helium, in turn creating stronger reactions and more pressure to balance out the gravitational force. This understanding of stars’ balancing act was crucial to uncovering the mysteries of black holes.
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Stars can stay stable in this form for long periods of time, emitting heat and light. Bigger stars will use up their fuel much quicker to balance their gravitational force, creating carbon and oxygen as they contract again. The central portions of the star contract into dense regions, becoming neutron stars or black holes, though this is not yet fully understood. Sometimes outer parts of a star can be blown off, flinging heavier matter out for the next generation of stars or for the forming of planets.
The lifecycle of stars feeds into the lifecycle of planets, with the heavier elements created in the stars’ inner nuclear fusion reactors bursting out into the universe to give birth to surrounding planets. Now, understanding stars’ balancing act directly links to humans’ desire to understand where life came from. Each discovery links to the next, fueled by humanity’s insatiable inquisitiveness.
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The earth was at first very hot with no atmosphere. Slowly, it cooled and gaseous emissions from the rocks created an atmosphere. Primitive life formed in these poisonous conditions, mostly likely in the oceans, and converted these gases into oxygen. Small errors in reproduction would create new genes, some of which would aid those new organisms in surviving, giving them an advantage over others. This process of evolution led to more complex organisms, including humans, and the atmosphere we have today.
Gradually, the world humans occupy today was formed. This picture is humbling, placing humans in a vulnerable and dependent role amid the long and complex history of the universe. The earth was born of a star born of gaseous clouds somewhere in a rotating galaxy, one of innumerable others. And humans are not the only life form to have inhabited the earth, but one of many in a long line of evolution. Knowing this has not deterred humankind from seeking further answers.
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This picture corresponds with the observable universe today, but still doesn’t answer why the early universe was so hot, why it is so uniform today, why it expands at so precisely the rate that stops it from recollapsing, and why there are regions of higher density (e.g. galaxies).
Despite this detailed, complex, and humbling model of the universe, humans are still full of questions. Why is it this way, and not another, is the next problem in this ongoing line of interrogation.
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General relativity alone cannot answer these questions. Its laws and all laws we have so far break down at the singularity. We cannot know what happened before the big bang. This gives the universe a boundary—the start of time at the big bang.
The theories scientists have today are not sufficient to answer these questions, and Hawking implies a unified theory is required. If the laws of science breakdown at the big bang, it must be considered the beginning and boundary.
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God seems to have left a set of rules to determine the universe, within the limits of the uncertainty principle, but how did he decide these laws? We could say we cannot possibly hope to understand his intention. But if the start of the universe was incomprehensible, why can we understand more and more of the universe today? We find the universe is ordered, so that order should also apply to the space-time boundary.
Not only are humans curious, but they are also ingenious. Scientists have uncovered many of the universe’s rules, and are confident in their findings because they agree with observation and other theories. Thus, one can assume that the universe is knowable. If scientists can make accurate predictions in certain areas, it follows they should be able to in all areas. Hawking notes that just because humans understand the world, that does not preclude the idea that God made it in the first place.
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One answer is the theory of chaotic boundary conditions, which assumes there are infinite universes or that the universe is infinite. The theory assumes the initial state of the universe was completely random, creating an irregular and disordered early universe. It is hard to see how such an early universe would become more uniform like our own, and how there are not more black holes dating from that early period.
While Hawking discusses the idea of chaotic boundary conditions, he notes that this model does not accord with the observable universe, meaning the theory can be assessed for useful components, but should not be directly applied onto this current reality. While scientists are free to use their imagination in their investigations, their theories must ultimately accord with reality.
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Even with a chaotic early state, some regions of the universe could have smoothed out, and we could just be living in one of these regions. This is called the anthropic principle. Although it seems improbable that we happen to live in a region or universe that is smooth and uniform, it would only be such regions that support complex life able to ask such questions in the first place. Some people go further to propose the “strong version” of the anthropic principle, which states that in those regions that support life it will seem like those laws were chosen on purpose for the intelligent beings to exist.
The strong version of the anthropic principle borders on religious philosophy, stating that because the nature of the universe is so specifically positioned so as to support life, it follows that it could have been. This approach is born of humanity’s desire to place itself in the universe. Thus, while looking at the universe, humanity’s role within it is the underlying motivation in such an approach.
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Scientific laws contain many numbers that must be measured by observation, such as the mass of certain particles, as scientists cannot predict them yet. One day, there might be a unified theory for predicting these numbers, which seem perfectly calibrated for supporting life. Alternatively, perhaps life formed around the rules in our universe, or our region of the universe. But it still seems there could only be a narrow range of possible configurations of the universe that allow life to form. This could be seen as the divine purpose in the universe, or the strong anthropic principle.
Hawking holds out hope that a unified theory of everything would explain why these numbers are at the exact level to support life. In the meantime, people turn to religious theories, or rely on the strong anthropic principle. But Hawking suggests that only by knowing why the universe is the way it is, which is so fine-tuned to support life, will humanity’s curiosity be satisfied.
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There are many challenges posed to the strong anthropic principle. First, if there are other universes, we cannot detect them and they do not seem to affect us, so we don’t need to factor them into our theories. Further, there cannot be different laws in different regions of the universe, or we could not move between them. Second, the wider universe has no direct bearing on our existence, so there is no basis on which to claim it exists for us.
Hawking shows the strong anthropic principle divides opinion. He only describes the notion rather than directly backing it. Here, Hawking shows that simply accepting a theory that seems to make sense is still not a scientific approach. Challenging new ideas os not the same as unthinking stubbornness. Thinking people ought to thoroughly assess all theories’ worth and accuracy.
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To answer these questions, we need to know the make up of the early universe. In the hot big bang model, it seems there was not a uniform temperature in the early stages, as there was not time for heat to move throughout the universe. The make up of the universe we see today seems to have been precisely chosen if it has to fit the hot big bang model. This could be hard to explain other than to say simply the universe, and we, are the creation of God.
To make the observable universe fit with the hot big bang model, the universe would have needed to develop in very specific ways for it to reach the point that it could support life. This could support religious belief, or question the veracity of the model itself. Science must continue searching, it seems.
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To explain how the universe might have started from many different initial situations but still emerged in a uniform manner like we see today, Alan Guth said the early universe might had expanded very rapidly. In fact, he said it could have been inflationary, rather than the deflationary expansion seen today. This inflationary idea states that while expanding rapidly, particles had enough energy for the strong and weak nuclear forces and electromagnetic force to be unified in a single force. As the universe cooled, these forces broke their symmetry from each other, meaning they no longer act in the same way, and appear to be different forces altogether.
Referring back to the earlier idea of symmetry breaking, at the high energies during the rapid expansion, the three unifiable forces (minus gravity) would act as a single force.  Later, as the universe cooled, meaning overall energy levels were decreasing, these three forces would begin to operate in the different manners seen today. This idea of unification, referring only to these forces, rather than all of physics, still reflects Hawking’s wider dreams of understanding all of the universe with just one set of rules.
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But, Guth suggested that just as water can super cool—pass freezing point without actually freezing—perhaps these forces could avoid symmetry breaking too as the universe cooled. This would give the universe more energy than if the symmetry had broken. This extra energy has anti-gravitational effects due to strong repulsion, acting like Einstein’s cosmological constant. These areas would increasingly expand, with the space between particles expanding and smoothing out the region, much like the expansion of a balloon smooths its wrinkles.
Hawking offers the simple visual aid of a balloon as an example of the universe expanding, again, having previously repeated Friedmann’s use of the analogy. It fits well, and every reader has seen a balloon expand, though no one has directly observed the universe expand. The human imagination is strong and draws direct parallels between two completely separate events.
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Guth’s model, where expansion sped up for a period, allows time for light to travel across the early universe, meaning different parts of the universe could have the same properties. It could also account for the universe still being at the critical rate of expansion, without assuming divine input.
Nothing can travel faster than the speed of light. Therefore, finding a model where light can travel across the universe opens up the possibility for other forces or effects to spread across the universe too, meaning it could be more uniform. This explanation could replace the need for a deity to control this process.
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This would also account for why there is so much matter in the universe. According to quantum theory, particles can be created by energy, which raises the question of where the energy comes from. In the universe, there is exactly zero energy, because positive charges balance negative charges. All matter has positive energy, and thus repels other matter;  at the same time the gravitational force attracts all matter, and so could be said to be a negatively charged force as the particles expend their energy to escape its pull.
Positive cancels out negative, meaning the universe is balanced at a sum total of zero energy. Matter, however, always has positive energy (unless falling toward a black hole, as seen earlier). As gravity acts in the opposite way to particles, drawing other objects in rather than repelling them, it can be said to be a negative form of energy.
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If the size of the universe doubled, its energy still amounts to zero. In the inflationary model, the energy density remains constant despite the universe expanding, so the overall energy constant is not violated. But in the current universe expansion phase, the energy density lowers. In the inflationary expansion, the universe expands very quickly, and the overall energy available to particles is very large.  
No matter how much matter there is in the universe, positive energy will always cancel out negative. But particles have access to greater overall energy in the inflationary expansion phase suggested by Guth. 
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Just as water always does eventually freeze, so would the symmetry eventually break between the strong nuclear force, the weak nuclear force, and the electromagnetic force. This would bring the universe back to the slower rate of expansion and cooling seen today, and explains how the universe came to be uniform despite a range of possible, chaotic beginnings.
Guth’s model actually encompasses many potential initial models of the universe. His intention was not to set out exactly how the universe looked immediately after the big bang, but to offer an explanation of how the current make up of the universe could be made far more probable by showing this current outcome was possible from many different original configurations.
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Guth’s original theory imagined bubbles, or different regions, of matter slowing at different rates. He said these bubbles would eventually all join up. But many people, including Hawking, pointed out they’d be moving too fast to join up. At a lecture in Moscow in 1981 where Hawking discussed this, with the aid of a graduate student, he met Andrei Linde, who said our entire universe could be one of these bubbles. Hawking later showed the bubbles idea wouldn’t work at all, mathematically, but encouraged Linde’s work nevertheless. Hawking published a paper with Ian Moss at the same time to resolve the issues with the theory.
In a reversal of the usual situation of a new, good but challenging idea coming out and facing severe criticism from obstinate opponents, here Hawking shows the value in supporting clever but flawed ideas to drive forward the overall progress of scientific development. Taking a mature and objective approach, Hawking backed Linde’s work so the valuable portions could be shared, as well as to encourage a budding new scientist.
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Paul Steinhardt and Andreas Albrecht proposed similar ideas to Linde’s at a similar time, and are given credit with him for the new inflationary model, based on slow-breaking symmetry. The ideas are still discussed, but have been largely discredited, as we ought to see more differences in background radiation than we do.
Some continue to use Linde’s and his counterparts’ concepts, but Hawking shows the tide of scientific discovery has already begun to leave these suggestions behind amid the unstoppable pursuit for greater knowledge.
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Linde put forward the chaotic inflationary model in 1983, which said there would be spin-0 in certain regions that, “because of quantum fluctuations, would have large values in some regions of the early universe.” The energy in those fields would have anti-gravity effects, like a cosmological constant, increasing the rate of expansion. The energy would slowly decrease to the rate we see in the big bang model. One such region could be the observable universe.
Linde’s work was not wasted. As seen with many other theories, his inflationary model provided the impetus for more accurate deductions. He was not put off by earlier failures, and his curiosity did not diminish, as proven by his return with a more complex model only a few years later.
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This new model left open a range of early universe configurations that would still result in the uniform universe seen today. There would still be starting points from which our universe could not have arisen, however, meaning we might still have to turn to the anthropic principle.
Like Guth’s work, Linde’s opened up more possibilities for the early universe’s initial configuration. Instead of simply accepting the anthropic principle, which does not provide direct knowledge of, or measurable laws governing the early universe, these scientists rethought the models themselves to find a better fit.
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To know how the universe started, we need laws that hold at the beginning. General relativity relies on singularities, which involve the break down of scientific law. Really, what singularity theories show is that gravity becomes so strong that we need to return to the quantum level, and use a quantum theory of gravity.
Humans are driven by a desire to know the universe, not just get the general gist of it. Otherwise scientists would have lost interest long ago, and the funding would have long dried up. Instead the quest continues, and as Hawkign states here, the best path is to find the unified theory of everything, which will settle the matter once and for all.
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There is no consistent theory that combines quantum theory and gravity. If there were, it should involve Feynmann’s sum over histories proposal, which states particles move from A to B by every possible path. Scientists know how to measure this, but actually doing the math requires using imaginary numbers. This is a normal mathematical tool, by which numbers can be multiplied against themselves to produce negative numbers, something “real” numbers cannot do: -2 times -2 is 4, but i2 time i2 is -4. If real numbers go left to right on an axis, imaginary numbers go up and down.
This unified theory has not yet been found, but scientsts can tell which key theories it must feature. The sum over histories proposal changes science’s approach from attempting to exactly map out the history of the universe, to understanding the most probably course of events. Here, Hawking introduces the tool of imaginary numbers, aptly named in that it powers the human mind to calculate largely unobservable situations.
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To calculate sum over histories, one must use imaginary time, that is, imaginary numbers to represent time, which clears away any difference between space and time. Euclidean space-time (so-called after Euclid, the Ancient Greek who founded two-dimensional geometric studies) is four-dimensional, but really the device is just used to do the math.
Using imaginary numbers to represent imaginary time to calculate events in curved, four-dimensional space-time that does not appear the exact same as the universe does to human eyes, demonstrates the human brain’s lateral reasoning abilities, applied in the pursuit of ultimate knowledge.
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Another feature of the unified theory of quantum mechanics and general relativity is that gravity is represented in a curved space-time. Applying the sum over histories to Einstein’s ideas on gravity, the history of a particle is a complete curved space-time that represents the whole universe. To find a space-time that is really possible, one adds up all the wavelengths of all the associated possible particle histories of that universe.
The second key theory that must be incorporated into any unified theory of physics is gravity, and when comined with the first key component, sum over histories, the math starts to become a real challenge, accounting for all the wavelengths of all the possible histories of particles in the universe. Hopefully any unified theory would help to simply this approach.
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In both quantum and general relativity theory, if we know the make up of the universe at the beginning, we can know the history and state of the universe now. Under general relativity, the universe can only be finite or infinite in time. But quantum theory adds a third option: that the universe could be finite, but with no boundary, like the earth’s two-dimensional surface. In this model, there would be no need for singularities, or for God. The laws of science would not break down. The universe would just be.
Hawking introduces a third option—that the universe could be finite in space but with no boundary. Just as one can walk around the earth and come back to the starting point, so a ship could travel around the universe in one direction forever, coming back round on itself. There would thus be no beginning or end, and no need for a creator. 
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Hawking first put forward this idea at the Vatican conference, but its implications for a beginning and therefore God were not understood. He spent the next summer working with Jim Hartle in the U.S. on this idea, and back in the U.K. with Julian Luttrel and Jonathan Halliwell. The idea remains a proposal, and making predictions with it remains complex because the math is beyond current abilities.
Hawking was brave, then, to report on this potentially atheist idea at the Vatican, the center of the Catholic Church. He emphasizes that it is an idea, because it lacks the basic feature of any good theory—being able to make observably correct predictions. That has not stopped Hawking from investigating the idea further.
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Each sum over histories history offers a comprehensive account of space-time and its contents. Again, the anthropic principle can explain why one history is right rather than others—we know we exist, so life must be involved in the model. But it would be preferable to know which history is the most probable.
Although there is reasoning to allow a “good enough” approach, Hawking stresses that knowing that science has found the right answer is the only way to settle the inquisitive human mind. Double checking seems a natural urge and fair demand.
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One group of histories turns out to be more probable than others. The histories of the universe would expand and contract, just as the lines of latitude circling the earth get bigger as one moves away from the North Pole (equivalent to the universe’s starting point) and toward the equator (the universe’s maximum size). These lines of latitude then contract again as one moves on toward the South Pole. The poles are not singularities in this model, which uses imaginary time as the axis from pole to pole, though they may seem like them in real time.
Hawking uses the image of the three-dimensional globe to represent the expansion of the universe. The distance traveled from the North Pole represents the progress of imaginary time, so even after the universe hits its widest point at the equator and begins to contract again, imaginary time is still progressing in the same direction. The key argument of this model is that the poles are not singularities, just points.
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It seems, there might be no singularities in imaginary time, undoing Hawking’s earlier work. But, singularity theories showed gravity to be so powerful at these points that it had to be considered on the quantum theory scale. Singularities will only appear as such in real time, but one could equally say maybe our real time is the imaginary time, if imaginary time doesn’t have singularities. Perhaps imaginary time is more simple, and our real time is just a helpful way to explain what we see. But all theories exist only in our heads. So this question is pointless, and one can use whichever is most helpful in each situation.
Hawking discusses theories that undermine his own work, accepting that outdated ideas must be left by the road side on the journey toward total understanding of the universe. He also points out that if real time blocks our understanding of the universe, the sense that it is “real” at all begins to crumble. If imaginary time provides the perspective with which to properly understand phenomena such as black holes, it begins to seem less imaginary.
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By applying the sum over histories and no boundary theory, one can find which characteristics of the universe are likely to happen together. The no boundary theory predicts it is very probable the current rate of expansion is uniform across the universe, for example. This is backed up by Penzias and Wilson’s discovery of uniform microwave radiation.
The no boundary theory does have some predictions scientists are able to confirm, and already have. Penzias and Wilson’s Nobel Prize seems ever-more well-earned here, with another proven theory tucked under their belt. Such are the rewards of following up on loose ends.
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Work is ongoing on the small differences in the early universe that later created the galaxies, and so on. The uncertainty principle tells us there was a minimum level of fluctuations, and the no boundary theory tells us the early universe must have been not uniform at exactly this minimum level. The universe then rapidly expanded, which would have amplified any non-uniformities. This agrees with observation that density varies from place to place, creating galaxies and people.
Hawking shows in this chapter, as highlighted in this small summary, that science has come a long way toward understanding how humans came to exist. By mapping out the potential histories of the early universe, and finding the most probable development patterns, humans have come closer to understanding their own place in the complex history of the universe.
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The idea that space-time has a closed surface with no boundary seems to eliminate the role of God. People thought the fact that we can discover and know the laws of science does not preclude a creator, who now chooses not to intervene. But if there was no beginning, how was there a Creator?
In the no boundary model there are no singularities at which the laws of science break down, meaning everything can be measured. Also, Hawking adds, a no boundary universe would have no beginning or end, so no big bang. With a decreasing amount fo unknowables in the universe, the space left for God is growing ever smaller, emphasizing how religious thought is increasingly left only in the areas science cannot yet account for. That is, science is slowly replacing belief.
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