Warped Passages Quotes

“But speculation is the only way to make progress in our understanding.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“How can a four-dimensional and a five-(or ten-)dimensional theory have the same physical implications? What is the analog of an object traveling through the fifth dimension, for example? The answer is that an object moving through the fifth dimension would appear in the dual four-dimensional theory as an object that grows or shrinks.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“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.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“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.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“In the warped scenario, the field lines are equally distributed in all the directions on the brane. However, off the brane the field lines bend back around so that they become essentially parallel to the brane, almost as if the fifth dimension were finite. Even with an infinite dimension, the gravitational field is localized near the brane, and field lines spread essentially as if there were only four (spacetime) dimensions.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“Spacetime can be so warped that the gravitational field becomes highly concentrated in a small region near a brane—so concentrated that the huge expanse of an infinite dimension is inconsequential.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“The warp factor is a function that changes the overall scale for position, time, mass, and energy at each point in the fifth dimension.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“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

“Gravity in our world would be weak because extra dimensions are large, not because there is fundamentally a big mass responsible for the tiny gravitational force.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“If an extra dimension is rolled up into a circle, the mass of the lightest such particle would differ from the electron’s mass by an amount inversely proportional to the extra dimension’s size. That means that, the larger the extra dimension, the smaller the particle’s mass.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“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.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“In a supersymmetric universe, the partners of quarks and leptons would be new bosons. Physicists, who enjoy whimsical (but systematic) nomenclature, call them squarks and sleptons.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“The uncertainty principle tells us that it would take infinitely long to measure energy (or mass) with infinite precision, and that the longer a particle lasts, the more accurate our measurement of its energy can be. But if the particle is short-lived and its energy cannot possibly be determined with infinite precision, the energy can temporarily deviate from that of a true long-lived particle. In fact, because of the uncertainty principle, particles will do whatever they can get away with for as long as they can.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“When a field takes a nonzero value, the best way to think about it is to imagine space manifesting the charge that the field carries, but not containing any actual particles.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“The uncertainty principle tells us that you need high-momentum particles to probe or influence physical processes at short distances, and special relativity relates that momentum to a mass.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“However, you will need to know about flavors and generations because of the strong constraints on the particles’ properties, which give us vital clues and constraints on the physics that lies beyond the Standard Model. Chief among these constraints is that different flavors of quarks and leptons with the same charges rarely, if ever, turn into one another.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“All of the lightest stable quarks and leptons have heavier replicas. No one knows why they are there, or what they are good for. When physicists first realized that the muon, a particle first seen in cosmic rays, was nothing other than a heavier version of the electron (200 times heavier), the physicist I.I. Rabi asked, “Who ordered that?”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“Trillions of solar neutrinos pass through you each second, but interact so weakly that you never notice.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“The weak force violates parity symmetry by acting differently on left-handed and right-handed particles. It turns out that only left-handed particles experience the weak force. For example, a left-handed electron would experience the weak force, whereas one spinning to the right would not. Experiments show this clearly—it’s the way the world works—but there is no intuitive, mechanical explanation for why this should be so.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“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.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“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.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“Maxwell was a brilliant scientist who counted among his many interests optics and color, the mathematics of ovals, thermodynamics, the rings of Saturn, measuring latitude with a bowl of treacle, and the question of how cats land upright while conserving angular momentum when dropped upside down.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“The uncertainty principle of quantum mechanics, coupled with the relations of special relativity, tell us that, using physical constants, we can relate a particle’s mass, energy, and momentum to the minimum size of the region in which a particle of that energy can experience forces or interactions.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“The fermionic nature of most fundamental particles determines many properties of the matter around us. The Pauli exclusion principle, in particular, states that two fermions of the same type will never be found in the same place. The exclusion principle is what gives the atom the structure upon which chemistry is based.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“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.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“Nonetheless, in all cases matter tells spacetime how to curve, and spacetime tells matter how to move.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“For two events separated in time, a geodesic is the natural path things would take in spacetime to connect one event to the other.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“That’s what’s “special” in special relativity: the “special” inertial frames are only a small subset of all possible reference frames.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“The goal of particle physics is to discover matter’s most basic constituents and the most fundamental physical laws obeyed by those constituents.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

“The problem is that string theory is defined at an energy scale that is about ten million billion times larger than those we can experimentally explore with our current instruments.”
― Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions