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21 " If large extra dimensions solve the hierarchy problem, higher-dimensional gravity would become strong at about a TeV. "
― Lisa Randall , Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions
22 " But speculation is the only way to make progress in our understanding. "
23 " When a species can’t adapt or relocate to a suitable habitat, it doesn’t stand a chance. In our rapidly changing environment, people would do well to take this into consideration. Technological advances notwithstanding, the lesson is probably relevant when evaluating the likely geopolitical implications of today’s changing environment. "
― Lisa Randall , Dark Matter and the Dinosaurs: The Astounding Interconnectedness of the Universe
24 " If particles had mass from the get-go, the theory would have been inconsistent and made nonsensical predictions such as probabilities of energetic particles interacting that were greater than one. Some new ingredient was required to allow for those masses. That "
― Lisa Randall , Higgs Discovery: The Power of Empty Space
25 " Recall that the Milky Way is a disk galaxy, meaning most of the stars and gas lie in a thin disk, about 130,000 light-years across but only roughly 2,000 light-years in thickness. The Sun is located at a distance of about 27,000 light-years from the galactic center, and happens at this moment to be close to the galactic midplane—less than 100 light-years away. It is also at the edge of a spiral arm. "
26 " The warp factor is a function that changes the overall scale for position, time, mass, and energy at each point in the fifth dimension. "
27 " see it. Dinosaurs, on the other hand . . . I doubt I need to explain dinosaurs. They were the dominant terrestrial vertebrates from 231 to 66 million years ago. Though both dark matter and dinosaurs are independently fascinating, you might reasonably assume that this unseen physical substance and this popular biological icon are entirely unrelated. And this might well be the case. But the Universe is by definition a single entity and in principle its components interact. "
28 " The photon is the first example we will encounter of a gauge boson, a fundamental, elementary particle that is responsible for communicating a particular force. "
29 " Whatever has been found—the Higgs boson, the particular implementation of the Higgs mechanism that seems simplest or something more elaborate—it is almost certainly something very new. The interest from the public and press has been very gratifying, indicating a thirst for knowledge and scientific advances that humanity to a large extent shares. After all, this discovery is part of the story of the universe’s evolution as its initial symmetry was broken, particles acquired masses, atoms were formed, structure, and then us. "
30 " A space of a particular dimension is a space requiring a particular number of quantities to specify a point. "
31 " By analogy, we know that if a hypersphere (a sphere with four spatial dimensions) were to pass through our universe, it would appear to us as a time sequence of three-dimensional spheres that increase, then decrease, in size. "
32 " The answer is that in RS2, the influence of four-dimensional gravity is inescapable, no matter where you are in the fifth dimension. Although the graviton’s probability function is largest on the Gravitybrane, objects everywhere can interact with one another by exchanging a graviton, and therefore all objects would experience four-dimensional gravity, independently of location. Gravity everywhere looks four-dimensional because the graviton’s probability function is never actually zero—it continues on for ever. In the localized scenario, objects far from a brane would have extremely weak gravitational interactions, but weak gravity would nonetheless behave in a four-dimensional manner. "
33 " After all, the speed of light is finite, and our universe has existed for only a finite amount of time. That means that we can only possibly know about the surrounding region of space within the distance that light could have traveled since the universe’s inception. That is not infinitely far away. It defines a region known as the horizon, the dividing line between information that is and is not accessible to us. "
34 " For two events separated in time, a geodesic is the natural path things would take in spacetime to connect one event to the other. "
35 " Naively, special relativity would therefore tell us that those particles should be able to travel forwards and backwards in time as well. But so far as we know, neither particles nor anything else we are aware of can actually travel backwards in time. What happens instead is that oppositely charged antiparticles replace the reverse-time-traveling particles. Antiparticles reproduce the effects the reverse-time-traveling particles would have so that even without them, quantum field theory’s predictions are compatible with special relativity. "
36 " According to quantum mechanics, at the Planck scale length, instead of a gradually undulating geometry, there should be wild fluctuations and loops and handles of spacetime branching off, the sort of topography that the futuristic Ike encountered. General relativity cannot be used in such untamed territory. "
37 " Nonetheless, in all cases matter tells spacetime how to curve, and spacetime tells matter how to move. "
38 " With general relativity, we know that before gravity can act, spacetime has to deform. This process does not happen instantaneously. It takes time. Gravity waves travel at the speed of light. Gravitational effects can kick in at a given position only after the time it takes for a signal to travel there and distort spacetime. "
39 " A brane is a distinct region of spacetime that extends through only a (possibly multidimensional) slice of space. The word “membrane” motivated the choice of the word “brane” because membranes, like branes, are layers that either surround or run through a substance. "
40 " Some branes are “slices” inside the space, but others are “slices” that bound space, like slices of bread in a sandwich. Either way, a brane is a domain that has fewer dimensions than the full higher-dimensional space that surrounds or borders it. "