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121 " Anselm conceives of God as something than which nothing greater or more perfect can be conceived. Since this idea arises in our minds it certainly has an intellectual existence. But does it have an existence outside of our minds? Anselm argued that it must, for otherwise we fall into a contradiction. For we could imagine something greater than that which nothing greater can be conceived; that is the mental conception we have together, plus the added attribute of real existence. "
― John D. Barrow , The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe
122 " Since so much of the physical universe, from brain waves to quantum waves, relies upon travelling waves we appreciate the key role played by the dimensionality of our space in rendering its contents intelligible to us. "
― John D. Barrow , Theories of Everything: The Quest for Ultimate Explanation
123 " As we look way back into the first instants of the Big Bang, we find the quantum world that we described in Chapter 3. From that state, where like effects do not follow from like causes, there must somehow emerge a world resembling our own, where the results of most observations are definite. This is by no means inevitable and may require the Universe to have emerged from a rather special primeval state. "
124 " This 'Planck length' is the only quantity with the dimensions of a length that can be built from the three mist fundamental constants of Nature: the velocity of light c, Planck's constant h, and Newton's gravitational conatant G. It is given by Lp = (Gh/c^3)^1/2 = 4 X 10 ^ -33 cm. This tiny dimension encapsulates the attributes of a world that is at once relativistic (c), quantum mechanical (h), and gravitational (G). It is a standard of length that makes no reference to any artefact of man or even of the chemical and nuclear forces of Nature. Relative to this unit of length, the size of the entire visible universe today extends roughly 10^60 Planck lengths, but the cosmological constant must be less than 10^-118 when referred to these Planck units of length rather than centimetres. To have to consider such a degree of smallness is unprecedented in the entire history of science. Any quantity that is required to be so close to zero by observation must surely in reality be precisely zero. This is what many cosmologists believe. But why? "
125 " Fitzgerald had noticed that if this sqrt(I-v^2/c^2) correction factor was applied to the analysis of Michelson's apparatus fixed on the earth's surface as it moved around the Sun, it could explain why Michelson measured no effect from the ether. The arm of the interferometer contracts by a factor sqrt(I-v^2/c^2) in the direction of its motion through the ether at a speed v. At an orbital speed of 29 kilometers per second this results in a contraction of only one part in 200,000,000 in the direction of the Earth's orbital motion. The length of the arm perpendicular to the ether's motion is unaffected. This small contraction effect exactly counterbalances the time delay expected from the presence of a stationary ether. If the Fitzgerald-Lorentz contraction occurred then it allowed the existence of a stationary ether to be reconciled with the null result of the Michelson-Morley experiment. Space need not be empty after all. "
126 " For many years, cosmologists have sought, with little success, some fundamental principle which would reveal why the cosmological constant mist be zero. The elementary-particle physicists have searched as well, but far from finding an answer to the problem they have merely compounded it by showing that, even if such a principle were to exist which started the universe on its way at the Big Bang with a zero value of the cosmological constant, there arise complicated elementary-particle processes which produce stresses that mimic the presence of a cosmological constant with an unacceptably large value, billions and billions of times larger than observation allows. "
127 " All the best physical theories are associated with equations which allow the continuation of data defined at present into the future, and hence allow prediction. But this situation requires space and time to possess a rather particular type of mathematical property which we shall call 'natural structure'. Other theories, like those describing statistical or probabilistic outcomes, which attempt to use mathematics for prediction, often fail to possess a mathematical substratum with a 'natural structure' of this sort, and so there is no guarantee that its future states are smooth continuations of its present ones. "
128 " It was the same with the revolutionary quantum theories that were found in the first quarter of this century. They provided a more complete description than Newton of the way the world works when we probe the realm of the very small. Their predictions about the non-Newtonian microworld are stupendously accurate. But again, when they deal with large objects they become more and more like Newton's description of motion. This is how the core of truth within a past theory can remain as a limiting part of a new and better theory. Scientific revolutions don't seem to happen any more. "
― John D. Barrow , The Constants of Nature: The Numbers That Encode the Deepest Secrets of the Universe
129 " Whatever the ultimate Theory of Everything is found to be, it will have a limiting form which describes motion at speeds far less than that of light in weak gravity fields where quantum wavelike features of mass are negligible. This form will be the one that Newton found. "
130 " Aristotle's later view of the relationship between mathematics and Nature could not have been more different. He wanted to rescue physical science from the mathematical stranglehold that Plato had placed upon it. He believed there to exist three completely autonomous realms of purely theoretical knowledge-metaphysics, mathematics, and physics-each possessing its own methods of explanation and accordant subject matter. But over-arching these divisions there existed a more general principle of 'homogeneity'-that like follows like-which mush always be obeyed: "
131 " At first we might be tempted to think that a world in which the speed of light was slower would be a different world. But this would be a mistake. If c, h and e were all changed so that the values they have in metric (or any other) units were different when we looked them up in our tables of physical constants, but the value of α remained the same, this new world would be observationally indistinguishable from our world. The only thing that counts in the definition of the world are the values of the dimensionless constants of Nature. If all masses are doubled in value you cannot tell because all the pure numbers defined by the ratios of any pair of masses are unchanged. "
132 " Everything that is made of atoms has a density quite close to the density of a single atom given by the mass of an atom divided by its volume. "
133 " Aristotle draws a sharp dividing-line between the activities of the physicist and those of the mathematician. The mathematician limits his enquiry to the quantifiable aspects of the world and so dramatically restricts what is describable in mathematical terms. Physics, for Aristotle, was far wider in scope and encompassed the earthly reality of sensible things. Whereas Plato had maintained that mathematics was the true and deep reality of which the physical world was but a pale reflection, Aristotle claimed mathematics to be but a superficial representation of a piece of physical reality. Such is the contrast between idealism and realism in the ancient world. "
134 " Suppose we take the whole mass inside the visible Universe19 and determine its quantum wavelength. We can ask when this quantum wavelength of the visible Universe exceeds its size. The answer is when the Universe is smaller than the Planck length in size (10–33 cm), less than the Planck time in age (10–43 secs), and hotter than the Planck temperature (1032 degrees). Planck's units mark the boundary of applicability of our current theories. To understand what the world is like on a scale smaller than the Planck length we have to understand fully how quantum uncertainty becomes entangled with gravity. "
135 " The quantum wavelength of a particle gets smaller the more massive the particle. Situations are dominated by quantum waviness when the quantum wavelength of their participants exceeds their physical size. Everyday objects, like cars and speeding cricket balls, have such high masses that their quantum wavelengths are vastly smaller than their sizes and we can forget about quantum influences when driving cars or watching cricket matches. "
136 " One of the curious problems of physics is that it has two beautifully effective theories – quantum mechanics and general relativity – but they govern different realms of Nature. "
137 " Quantum mechanics holds sway in the microworld of atoms and elementary particles. It teaches us that every mass in Nature, however solid or pointlike it may appear, has a wavelike aspect. This wave is not like a water wave. It is more analogous to a crime wave or a wave of hysteria: it is a wave of information. "
138 " Others might point to the warning that the most dangerous thing in science is the idea that arrives before its time. "
139 " Moreover it is assumed that wormholes only join universes to baby universes, or universes to themselves; there are no wormholes joining different baby universes in this approximation, nor are there allowed to be wormholes which split up into two or more other wormholes. "