Vacuum is space devoid of matter. The word stems from the Latin adjective vacuus for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often discuss ideal test results that would occur in a perfect vacuum, which they sometimes simply call "vacuum" or free space, and use the term partial vacuum to refer to an actual imperfect vacuum as one might have in a laboratory or in space. In engineering and applied physics on the other hand, vacuum refers to any space in which the pressure is lower than atmospheric pressure. The Latin term in vacuo is used to describe an object that is surrounded by a vacuum.
- If Dirac’s idea restores the stability of the spectrum by introducing a stable vacuum where all negative energy states are occupied, the so-called Dirac sea, it also leads directly to the conclusion that a single-particle interpretation of the Dirac equation is not possible.
- Luis Álvarez-Gaumé, Miguel Á. Vázquez-Mozo, An Invitation to Quantum Field Theory (2012) Ch. 1 : Why Do We Need Quantum Field Theory After All?
- Aristotle believed that the world did not come into being at some time in the past; it had always existed and it would always exist, unchanged in essence for ever. He placed a high premium on symmetry and believed that the sphere was the most perfect of all shapes. Hence the universe must be spherical. ...An important feature of the spherical shape... was the fact that when a sphere rotates it does not cut into empty space where there is no matter and it leaves no empty space behind. ...A vacuum was impossible. It could no more exist than an infinite physical quantity. ...Circular motion was the most perfect and natural movement of all.
- John D. Barrow, The Book of Universes: Exploring the Limits of the Cosmos (2011)
- These rays, as generated in the vacuum tube, are not homogeneous, but consist of bundles of different wave-lengths, analogous to what would be differences of colour could we see them as light. Some pass easily through flesh, but are partially arrested by bone, while others pass with almost equal facility through bone and flesh.
- Now his principal doctrines were these. That atoms and the vacuum were the beginning of the universe; and that everything else existed only in opinion.
- Where a calculator like the ENIAC today is equipped with 18,000 vacuum tubes and weighs 30 tons, computers in the future may have only 1,000 vacuum tubes and perhaps weigh only 1½ tons.
- Andrew Hamilton, "Brains that Click", Popular Mechanics 91 (3), March 1949, (pp. 162 et seq.) p. 258.
- When you look at a vacuum in a quantum theory of fields, it isn't exactly nothing.
- With respect to the ultimate constitution of... masses, the same two antagonistic opinions which had existed since the time of Democritus and of Aristotle were still face to face. According to the one, matter was discontinuous and consisted of minute indivisible particles or atoms, separated by a universal vacuum; according to the other, it was continuous, and the finest distinguishable, or imaginable, particles were scattered through the attenuated general substance of the plenum. A rough analogy to the latter case would be afforded by granules of ice diffused through water; to the former, such granules diffused through absolutely empty space.
- The real value of the new atomic hypothesis... did not lie in the two points which Democritus and his followers would have considered essential—namely, the indivisibility of the 'atoms' and the presence of an interatomic vacuum—but in the assumption that, to the extent to which our means of analysis take us, material bodies consist of definite minute masses, each of which, so far as physical and chemical processes of division go, may be regarded as a unit—having a practically permanent individuality. ...that smallest material particle which under any given circumstances acts as a whole.
- Thomas Henry Huxley, The Advance of Science in the Last Half-Century (1889)
- The primitive atomic theory, which has served as the scaffolding for the edifice of modern physics and chemistry, has been quietly dismissed. I cannot discover that any contemporary physicist or chemist believes in the real indivisibility of atoms, or in an interatomic matterless vacuum. Atoms appear to be used as mere names for physico-chemical units which have not yet been subdivided, and 'molecules' for physico-chemical units which are aggregates of the former. And these individualised particles are supposed to move in an endless ocean of a vastly more subtle matter—the ether.
- In general, the rate of evaporation (m) of a substance in a high vacuum is related to the pressure (p) of the saturated vapor by the equation Red phosphorus and some other substances probably form exceptions to this rule.
- Irving Langmuir, "The Constitution and Fundamental Properties of Solids and Liquids. Part I. Solids" (September 5, 1916) Journal of the American Chemical Society
- All those who maintain a vacuum are more influenced by imagination than by reason. When I was a young man, I also gave in to the notion of a vacuum and atoms; but reason brought me into the right way. ...The least corpuscle is actually subdivided in infinitum, and contains a world of other creatures, which would be wanting in the universe, if that corpuscle was an atom, that is, a body of one entire piece without subdivision. In like manner, to admit a vacuum in nature, is ascribing to God a very imperfect work... space is only an order of things as time also is, and not at all an absolute being. ...Now, let us fancy a space wholly empty. God could have placed some matter in it, without derogating in any respect from all other things: therefore he hath actually placed some matter in that space: therefore, there is no space wholly empty: therefore all is full. The same argument proves that there is no corpuscle, but what is subdivided. ...there must be no vacuum at all; for the perfection of matter is to that of a vacuum, as something to nothing. And the case is the same with atoms: What reason can any one assign for confining nature in the progression of subdivision? These are fictions merely arbitrary, and unworthy of true philosophy. The reasons alleged for a vacuum, are mere sophisms.
- To those who maintained the existence of a plenum as... principle, nature's abhorrence of a vacuum was a sufficient reason for imagining an all-surrounding aether, even though every other argument should be against it. ...Descartes ...made ...matter a necessary condition of extension... It is only when we remember the extensive and mischievous influence on science... that we can appreciate the horror of aethers which sober-minded men had during the 18th century, and which... descended even to... John Stuart Mill. ...Newton himself... endeavoured to account for gravitation by differences of pressure in an aether... The only aether which has survived is that which was invented by Huygens to explain the propagation of light. The evidence for... the luminiferous aither has accumulated as additional phenomena of light and other radiations have been discovered; and the properties of this medium... have been found to be... those required to explain electromagnetic phenomena. ...the interplanetary and interstellar spaces are not empty...
- To make way for the regular and lasting Motions of the Planets and Comets, it's necessary to empty the Heavens of all Matter, except perhaps some very thin Vapours, Steams or Effluvia, arising from the Atmospheres of the Earth, Planets and Comets, and from such an exceedingly rare Æthereal Medium … A dense Fluid can be of no use for explaining the Phænomena of Nature, the Motions of the Planets and Comets being better explain'd without it. It serves only to disturb and retard the Motions of those great Bodies, and make the frame of Nature languish: And in the Pores of Bodies, it serves only to stop the vibrating Motions of their Parts, wherein their Heat and Activity consists. And as it is of no use, and hinders the Operations of Nature, and makes her languish, so there is no evidence for its Existence, and therefore it ought to be rejected. And if it be rejected, the Hypotheses that Light consists in Pression or Motion propagated through such a Medium, are rejected with it.
And for rejecting such a Medium, we have the authority of those the oldest and most celebrated philosophers of ancient Greece and Phoenicia, who made a vacuum and atoms and the gravity of atoms the first principles of their philosophy, tacitly attributing Gravity to some other Cause than dense Matter. Later Philosophers banish the Consideration of such a Cause out of natural Philosophy, feigning Hypotheses for explaining all things mechanically, and referring other Causes to Metaphysicks: Whereas the main Business of natural Philosophy is to argue from Phenomena without feigning Hypotheses, and to deduce Causes from Effects, till we come to the very first Cause, which certainly is not mechanical.
- Isaac Newton, Opticks (1704) Query 28
- If all the properties of the universe, such as charge and momentum, balanced out, as Guth, who was a fan as well as a scholar of theories of nothing, pointed out to me, no laws of physics forbade the spontaneous appearance of the universe—or a quantum piece of one. ...Nothing, some physicist implied, might be the ultimate symmetry, everywhere, everywhen the same... Mostly we knew what nothing was not. It was not anything. But it was the possibility of everything. And perhaps such beauty, nothing, was unstable. And the result was every once in an eternity it twitched. ...The first soul brave enough to suggest the universe was indeed nothing was Ed Tryon... [who] blurted it out during a seminar with Sciama, "Suppose the universe is just a quantum fluctuation." Everybody laughed. ... Tryon eventually published these notions in Nature in 1975 and was mostly ignored. Peebles and Dicke had mentioned his work in their famous 1979 paper about enigmas and conundrums.
- When the Higgs field froze and symmetry broke, Tye and Guth knew, energy had to be released... Under normal circumstance this energy went into beefing up the masses of particles like the weak force bosons that had been massless before. If the universe supercooled, however, all this energy would remain unreleased... according to Einstein, it was the density of matter and energy in the universe that determined the dynamics of space-time. ...The issue of vacuum energy had been a tricky problem for physics ever since Einstein. According to quantum theory, even the ordinary "true" vacuum should be boiling with energy—infinite energy... due to the the so-called vacuum fluctuations that produced the transient dense dance of virtual particles. This energy... could exert a repulsive force on the cosmos just like the infamous cosmological constant... quantum theories had reinvented it in the form of vacuum fluctuations. The orderly measured pace of the expansion of the universe suggested strongly that the cosmological constant was zero, yet quantum theory suggested it was infinite. Not even Hawking claimed to understand the cosmological constant problem... a trapdoor deep at the heart of physics.
- Dennis Overbye, Lonely Hearts of the Cosmos (1991)
- I have endeavoured to attain this end (viz. the production of a vacuum in the cylinder) in another way. As water has the property of elasticity, when converted into steam by heat, and afterwards of being so completely recondensed by cold, that there does not remain the least appearance of this elasticity, I have thought that it would not be difficult to work machines in which, by means of a moderate heat and at a small cost, water might produce that perfect vacuum which has vainly been sought by means of gunpowder.
- Denis Papin, Recueil de diverses Pièces touchant quelques nouvelles Machines (1695) p. 53 as quoted by Dionysius Lardner, The Steam Engine Explained and Illustrated (1840) pp. 45-46.
- It's illegal to make superpositions with different vacua. That's one of the rules of quantum field theory.
- His reluctance to pay for elaborate or expensive equipment, perhaps the result of an impoverished childhood, had established the legendary "sealing wax-and-string" tradition of the Cavendish, where everyday materials were ingeniously used to make and patch up experimental equipment, with sealing wax proving particularly useful for vacuum seals.
- Dianna Preston, Before the Fallout from Marie Curie to Hiroshima (2005).
- Natura abhorret vacuum. (Nature abhors a vacuum.)
- The first machine of Papin was very similar to the gunpowder-engine... of Huyghens. In place of gunpowder, a small quantity of water is placed at the bottom of the cylinder, A; a fire is built beneath it, "the bottom being made of very thin metal," and the steam formed soon raises the piston, B, to the top where a latch, E, engaging a notch in latch engaging the piston rod, H, holds it up until it is desired that it shall drop. The fire being removed, the steam condenses, and a vacuum is formed below the piston, and the latch, E, being disengaged, the piston is driven down by the superincumbent atmosphere and raises the weight which has been, meantime, attached to a rope... passing from the piston rod over pulleys... The machine had a cylinder two and a half inches in diameter, and raised 60 pounds once a minute; and Papin calculated that a machine of a little more than two feet diameter of cylinder and of four feet stroke would raise 8,000 pounds four feet per minute—i.e., that it would yield about one horse-power.
- In June, 1699, Captain Savery exhibited a model of his engine before the Royal Society, and the experiments he made with it succeeded to their satisfaction. ...One of the steam vessels being filled with steam, condensation was produced by projecting cold water, from a small cistern E, against the vessel; and into the partial vacuum made by that means, the water, by the pressure of the atmosphere, was forced up the descending main D, from a depth of about twenty feet...
- [E]xperiments with a simple little machine, designed to mimic certain elementary features of animal behavior... Consisting only of two vacuum tubes, two motors, a photoelectric cell and a touch contact, all enclosed in a tortoise-shaped 'shell, the model was a species of artiﬁcial creature which could explore its surroundings and seek out favorable conditions. It was named Machine speculatrix.
- William Grey Walter, A machine that learns, Scientific American (1951)
- There is one topic I was not sorry to skip: the relativistic wave equation of Dirac. It seems to me that the way this is usually presented in books on quantum mechanics is profoundly misleading. Dirac thought that his equation was a relativistic generalization of the non-relativistic time-dependent Schrödinger equation that governs the probability amplitude for a point particle in an external electromagnetic field. For some time after, it was considered to be a good thing that Dirac’s approach works only for particles of spin one half, in agreement with the known spin of the electron, and that it entails negative energy states, states that when empty can be identified with the electron’s antiparticle. Today we know that there are particles like the [W bosons] that are every bit as elementary as the electron, and that have distinct antiparticles, and yet have spin one, not spin one half. The right way to combine relativity and quantum mechanics is through the quantum theory of fields, in which the Dirac wave function appears as the matrix element of a quantum field between a one-particle state and the vacuum, and not as a probability amplitude.
- Steven Weinberg, Preface, Lectures on Quantum Mechanics (2012)
- It is quite easy to include a weight for empty space in the equations of gravity. Einstein did so in 1917, introducing what came to be known as the cosmological constant into his equations. His motivation was to construct a static model of the universe. To achieve this, he had to introduce a negative mass density for empty space, which just canceled the average positive density due to matter. With zero total density, gravitational forces can be in static equilibrium. Hubble's subsequent discovery of the expansion of the universe, of course, made Einstein's static model universe obsolete. ...The fact is that to this day we do not understand in a deep way why the vacuum doesn't weigh, or (to say the same thing in another way) why the cosmological constant vanishes, or (to say it in yet another way) why Einstein's greatest blunder was a mistake.
- The phase transition paradigm: The standard model of fundamental physics incorporates, as one of its foundational principles, the idea that “empty space” or “vacuum” can exist in different phases, typically associated with different amounts of symmetry. Moreover, the laws of the standard model itself suggest that phase transitions will occur, as functions of temperature. Extensions of the standard model to build in higher symmetry (gauge unification or especially supersymmetry) can support effective vacua with radically different properties, separated by great distance or by domain walls. That would be a form of failure of universality, in our sense, whose existence is suggested by the standard model.
Pneumatica (c. 50)
- Hero of Alexandria, as quoted in The Pneumatics of Hero von Alexandria (1851) Tr. Bennet Woodcroft, unless otherwise noted.
- Some assert that there is absolutely no vacuum; others that, while no continuous vacuum is exhibited in nature, it is to be found distributed in minute portions through air, water, fire and all other substances: and this latter opinion, which we will presently demonstrate to be true from sensible phenomena, we adopt.
- Vessels which seem to most men empty are not empty, as they suppose, but full of air. Now the air, as those who have treated of physics are agreed, is composed of particles minute and light, and for the most part invisible. If, then, we pour water into an apparently empty vessel, air will leave the vessel proportioned in quantity to the water which enters it. This may be seen from the following experiment. Let the vessel which seems to be empty be inverted, and, being carefully kept upright, pressed down into water; the water will not enter it even though it be entirely immersed: so that it is manifest that the air, being matter, and having itself filled all the space in the vessel, does not allow the water to enter. Now, if we bore the bottom of the vessel, the water will enter through the mouth, but the air will escape through the hole. Again, if, before perforating the bottom, we raise the vessel vertically, and turn it up, we shall find the inner surface of the vessel entirely free from moisture, exactly as it was before immersion.
- The particles of the air are in contact with each other, yet they do not fit closely in every part, but void spaces are left between them, as in the sand on the sea shore: the grains of sand must be imagined to correspond to the particles of air, and the air between the grains of sand to the void spaces between the particles of air. Hence, when any force is applied to it, the air is compressed, and, contrary to its nature, falls into the vacant spaces from the pressure exerted on its particles: but when the force is withdrawn, the air returns again to its former position from the elasticity of its particles, as is the case with horn shavings and sponge, which, when compressed and set free again, return to the same position and exhibit the same bulk.
- Thus, if a light vessel with a narrow mouth be taken and applied to the lips, and the air be sucked out and discharged, the vessel will be suspended from the lips, the vacuum drawing the flesh towards it that the exhausted space may be filled. It is manifest from this that there was a continuous vacuum in the vessel. The same may be shown by means of the egg-shaped cups used by physicians, which are of glass, and have narrow mouths. When they wish to fill these with liquid, after sucking out the contained air, they place the finger on the vessel's mouth and invert them into the liquid; then, the finger being withdrawn, the water is drawn up into the exhausted space, though the upward motion is against its nature. Very similar is the operation of cupping-glasses, which, when applied to the body, not only do not fall though of considerable weight, but even draw the contiguous matter toward them through the apertures of the body.
- They... who assert that there is absolutely no vacuum may invent many arguments on this subject, and perhaps seem to discourse most plausibly though they offer no tangible proof. If, however, it be shewn by an appeal to sensible phenomena that there is such a thing as a continuous vacuum, but artificially produced; that a vacuum exists also naturally, but scattered in minute portions ; and that by compression bodies fill up these scattered vacua, those who bring forward such plausible arguments in this matter will no longer be able to make good their ground.
Commentarius in VIII Libros Physicorum Aristoteles (c. 1230-1235)
- Vacuum stands and remains a mathematical space. A cube placed in a vacuum would not displace anything, as it would displace air or water in a space already containing those fluids.
- In a vacuum which is imagined as infinite there cannot be local differences, both on account of its infinity, and also because of the fact that the vacuum, if it exists, would have no nature but a privation, and therefore it can have no natural differences.
- The space of the real physical world must be considered full, that is a plenum, because a vacuum could have no physical existence.
Pascal's Life, Writings, and Discoveries (1844)
- The North British Review Vol. 1 (August, 1844) p. 285, Art. I.—Lettres écrites à un Provincial par Blaise Pascal, précédées d'un Eloge de Pascal, par M. Bordas Demoulin, Discours qui a remporté le Prix décerné par l'Académie Française, le 30 Juin 1842, et suivies d'un Essai sur les Provinciales et le style de Pascal. Par Francois de Neufchateau. Paris, 1843. See also "Life, Genius, and Scientific Discoveries of Pascal", The Provincial Letters of Blaise Pascal (1866) ed. O. W. Wight, pp. 15-63.
- When the engineers of Cosmo de Medicis wished to raise water higher than thirty-two feet by means of a sucking-pump, they found it impossible to take it higher than thirty-one feet. Galileo, the Italian sage, was applied to in vain for a solution of the difficulty. It had been the belief of all ages that the water followed the piston, from the horror which nature had of a vacuum, and Galileo improved the dogma by telling the engineers that this horror was not felt, or at least not shown, beyond heights of thirty one feet! At his desire, however, his disciple Toricelli investigated the subject. He found, that when the fluid raised was mercury, the horror of a vacuum did not extend beyond 30 inches, because the mercury would not rise to a greater height; and hence he concluded that a column of water 31 feet high, and one of mercury 30 inches, exerted the same pressure upon the same base, and that the antagonist force which counterbalanced them must in both cases be the same; and having learned from Galileo that the air was a heavy fluid, he concluded, and he published the conclusion in 1645, that the weight of the air was the cause of the rise of water to 31 feet and of mercury to 30 inches. Pascal repeated these experiments in 1646, at Rouen before more than 500 persons, among whom were five or six Jesuits of the College, and he obtained precisely the same results as Toricelli. The explanation of them, however, given by the Italian philosopher, and with which he was unacquainted, did not occur to him; and though he made many new experiments on a large scale with tubes of glass 50 feet long, they did not conduct him to any very satisfactory results. He concluded that the vacuum above the water and the mercury contained no portion of either of these fluids, or any other matter appreciable by the senses; that all bodies have a repugnance to separate from a state of continuity, and admit a vacuum between them; that this repugnance is not greater for a large vacuum than a small one; that its measure is a column of water 31 feet high, and that beyond this limit, a great or a small vacuum is formed above the water with the same facility, provided no foreign obstacle prevents it. These experiments and results were published by our author in 1647, under the title of Nouvelles Experiences touchant le Vuide; but no sooner had they appeared, than they experienced, from the Jesuits, and the followers of Aristotle, the most violent opposition.
- To these objections Pascal replied in two letters, addressed to [Stephen] Noel; but though he had no difficulty in overturning the contemptible reasoning of his antagonist, he found it necessary to appeal to new and more direct experiments. The explanation of Toricelli had been communicated to him a short time after the publication of his work; and assuming that the mercury in the Toricellian tube was suspended by the weight or pressure of the air, he drew the conclusion that the mercury would stand at different heights in the tube, if the column of air was more or less high. These differences, however, were too small to be observed under ordinary circumstances; and he therefore conceived the idea of observing the mercury at Clermont, a town in Auvergne... and on the top of the Puy de Dome, a mountain 500 toises above Clermont The state of his own health did not permit him to undertake a journey... but in a letter dated the 15th November 1647, he requested his brother-in-law, M. Perier, to go... M. Perier began the experiment by pouring into a vessel sixteen pounds of quicksilver which he had rectified... He then took two [straight] glass tubes, four feet long, of the same bore, and hermetically sealed at one end, and open at the other; and making the ordinary experiment of a vacuum with both, he found that the mercury stood in each of them at the same level... This experiment was repeated twice with the same result. One of these... was left under the care of M. Chastin... who undertook to observe and mark any changes... and the party... set out, with the other tube, for the summit of the Puy de Dome... Upon arriving there, they found that the mercury stood at the height of 23 inches, and 2 lines—no less than 3 inches and 1½ lines lower... The party was "struck with admiration and astonishment at this result;" and "so great was their surprise, that they resolved to repeat the experiment under various forms." During their descent of the mountain, they repeated the experiment at Lafond de l'Arbre, an intermediate station... and they found the mercury to stand at the height of 25 inches, a result with which the party was greatly pleased, as indicating the relation between the height of the mercury and the height of the station. Upon reaching the Minimes, they found that the mercury had not changed its height...
- Pascal's Treatise [De la Pesanteur de la Masse de l'Air] on the weight of the whole mass of air forms the basis of the modern science of Pneumatics. In order to prove that the mass of air presses by its weight on all the bodies which it surrounds, and also that it is elastic and compressible, he carried a balloon half filled with air to the top of the Puy de Dome. It gradually inflated itself as it ascended, and when it reached the summit it was quite full, and swollen, as if fresh air had been blown into it; or what is the same thing, it swelled in proportion as the weight of the column of air which pressed upon it was diminished. When again brought down, it became more and more flaccid, and when it reached the bottom, it resumed its original condition. ...[H]e shews that all the phenomena and effects hitherto ascribed to the horror of a vacuum arise from the weight of the mass of air; and after explaining the variable pressure of the atmosphere in different localities, and in its different states, and the rise of water in pumps, he calculates that the whole mass of air round our globe weighs 8,983,889,440,000,000,000 French pounds.
A Short Story of Thomas Newcomen (1904)
- by Dwight Goddard, source
- Newcomen's invention was radically different from that of Savery or any other single person. Papin invented the cylinder and piston as a means for transforming energy into motion. At first he used the explosive force of gunpowder, and later the use of the expansive force of steam, to raise the piston, and then by removing the fire to cause it to fall again. He made no further use of this principle. Savery discovered that the sudden condensation of steam made a vacuum that he utilized to draw up water. His pumps were actually used to drain mines, but were never satisfactory. They had to be placed within the mine to be drained, not over forty feet from the bottom, and then could be used to force up water an additional height of perhaps 100 feet. Beyond this the process must be repeated. ...
Newcomen used Papin's cylinder and piston, and Savery's principle of the condensation of steam to produce a vacuum. But unlike Papin he used the expansive force of steam to do his work, and unlike Savery he used a cylinder and piston actuated by alternate expansion and condensation of steam to transform heat into mechanical motion.
- At first [Newcomen] made a double cylinder, using the space between for condensing water. This was not very satisfactory. The vacuum was secured very slowly and imperfectly. ...One day the engine made two or three motions quickly and powerfully. Newcomen immediately examined the cylinder and found a small hole, through which a small jet from the water that was on top of the piston to make it steam tight, was spurting into the cylinder. He... dispensed with the outer water jacket and injected the water for condensation, through a small pipe in the bottom of the cylinder. It... increased the speed of the engine from eight to fifteen strokes a minute, besides getting the advantage of a good vacuum.
The Book of Nothing (2009)
- The spooky ether was persistent. It took an Einstein to remove it from the Universe. ...Gradually, over the last twenty years, the vacuum has turned out to be more unusual, more fluid, less empty, and less intangible than even Einstein could have imagined. Its presence is felt on the very smallest and largest dimensions over which the forces of Nature act.
- The physicist's concept of nothing—the vacuum... began as empty space—the void... turned into a stagnant ether through which all the motions of the Universe swam, vanished in Einstein's hands, then re-emerged in the twentieth-century quantum picture of how Nature works.
- Chapter nought "Nothingology—Flying to Nowhere"
- The quantum revolution showed us why the old picture of a vacuum as an empty box was untenable. ...Gradually, this exotic new picture of quantum nothingness succumbed to experimental exploration... in the form of vacuum tubes, light bulbs and X-rays. Now the 'empty' space itself started to be probed. ...There was always something left: a vacuum energy that permeated every fibre of the Universe.
- Chapter nought "Nothingology—Flying to Nowhere"
- Einstein showed us that the Universe might contain a mysterious form of vacuum energy. ...Last year, two teams of astronomers used Earth's most powerful telescopes... to gather persuasive evidence for the reality of the cosmic vacuum energy. Its effects are dramatic. It is accelerating the expansion of the Universe.
- Chapter nought "Nothingology—Flying to Nowhere"