Physics

"A large part of the relativity community is in denial - refusing even to contemplate the idea that black holes may not exist in nature, or seriously consider the idea that any kind of new matter such as the new putative dark energy can play a fundamental role in gravity theory."

"The most far-reaching implication of general relativity... is that the universe is not static, as in the orthodox view, but is dynamic, either contracting or expanding. Einstein, as visionary as he was, balked at the idea... One reason... was that, if the universe is currently expanding, then... it must have started from a single point. All space and time would have to be bound up in that "point," an infinitely dense, infinitely small "singularity." ...this struck Einstein as absurd. He therefore tried to sidestep the logic of his equations, and modified them by adding... a "cosmological constant." The term represented a force, of unknown nature, that would counteract the gravitational attraction of the mass of the universe. That is, the two forces would cancel... it is the kind of rabbit-out-of-the-hat idea that most scientists would label ad-hoc. ...Ironically, Einstein's approach contained a foolishly simple mistake: His universe would not be stable... like a pencil balanced on its point."

"Our particular laws are not at all unique. ...they could change from place to place and from time to time. The Laws of Physics are much like the weather... controlled by invisible influences in space almost the same way as that temperature, humidity, air pressure, and wind velocity control how rain and snow and hail form. ...The Landscape... is the space of possibilities... all the possible environments permitted by the theory. ...[T]heoretical physicists ...have always believed that the laws of nature are the unique, inevitable consequence of some elegant mathematical principle. ...the empirical evidence points much more convincingly to the opposite conclusion. The universe has more in common with a Rube Goldberg machine than with a unique consequence of mathematical symmetry. ...Two key discoveries are driving the paradigm shift—the success of inflationary cosmology and the existence of a small cosmological constant."

"At about the time of Malcadena's discovery, physicists started to become convinced (by cosmologists) that we live in a world with a nonvanishing cosmological constant [footnote: 10-23 in Planck units...[t]he incredible smallness... had fooled almost all physicists into believing that it didn't exist.], smaller by far than any other physical constant... the main determinant of the future history of the universe... also known as ... a thorn in the side of physicists for almost a century. ...If \Lambda is positive, the cosomological term creates a repulsive force that increases with distance; if it is negative, the new force is attractive; if \Lambda is zero, there is no new force and we can ignore it."

"String theory seems to be incompatible with a world in which a cosmological constant has a positive sign, which is what the observations indicate."

"[Einstein's cosmological constant] is a name without any meaning. ...We have, in fact, not the slightest inkling of what it's real significance is. It is put in the equations in order to give the greatest possible degree of mathematical generality."

"There is no direct observational evidence for the curvature [of space], the only directly observed data being the mean density and the expansion, which latter proves that the actual universe corresponds to the non-statical case. It is therefore clear that from the direct data of observation we can derive neither the sign nor that value of the curvature, and the question arises whether it is possible to represent the observed facts without introducing the curvature at all. Historically the term containing the 'cosmological constant λ' was introduced into the field equations in order to enable us to account theoretically for the existence of a finite mean density in a static universe. It now appears that in the dynamical case this end can be reached without the introduction of λ."

"The cosmological constant['s]... most important consequence: the repulsive force, acting at cosmological distances, causes space to expand exponentially. There is nothing new about the universe expanding, but without a cosmological constant, the rate of expansion would gradually slow down. Indeed, it could even reverse itself and begin to contract, eventually imploding in a giant cosmic crunch. Instead, as a consequence of the cosmological constant, the universe appears to be doubling in size about every fifteen billion years, and all indications are that it will do so indefinitely."

"It was early 1932, when Einstein and I both were at the California Institute of Technology in Pasedena, and we just decided to look for a simple relativistic model that agreed reasonably well with the known observational data, namely, the Hubble recession rate and the mean density of matter in the universe. So we took the space curvature to be zero and also the cosmological constant and the pressure term to be zero, and then it follows straightforwardly that the density is proportional to the square of the Hubble constant. It gives a value for the density that is high, but not impossibly high. That's about all there was to it. It was not an important paper, although Einstein apparently thought that it was. He was pleased to have a simple model with no cosmological constant. That's it."

"Even today, our picture of a world woven together by a gravitational force, and electromagnetic force, a strong force, and a weak force may be incomplete. Astronomers are gathering evidence that an additional fundamental interaction, a repulsive effect opposite to gravity, may be at work over vast distances and possibly changing with time."

"In Einstein's scheme there was no end, no outside. Shoot an arrow or a light beam infinitely far in any direction and it would come back and hit you in the butt. ...But there was a problem with the curved-back universe. Such a configuration was unstable, it would fly apart or collapse. Einstein didn't know about galaxies. He thought, and was reassured as much by the best astronomers of the time, that the universe was a static cloud of stars. To explain why his curved universe didn't collapse like a struck tent, therefore, he fudged his equations with a term he called the cosmological constant, which produced a long-range repulsive force to counteract cosmic gravity. It made the equations ugly and he never really liked it. That was in 1917, twelve years before Hubble showed that the universe was full of galaxies rushing away from each other."

"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 s that produced the transient dense dance of s. 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."

"In 1917 de Sitter showed that Einstein's field equations could be solved by a model that was completely empty apart from the cosmological constant—i.e. a model with no matter whatsoever, just dark energy. This was the first model of an expanding universe. although this was unclear at the time. The whole principle of general relativity was to write equations for physics that were valid for all observers, independently of the coordinates used. But this means that the same solution can be written in various different ways... Thus de Sitter viewed his solution as static, but with a tendency for the rate of ticking clocks to depend on position. This phenomenon was already familiar in the form of gravitational time dilation... so it is understandable that the de Sitter effect was viewed in the same way. It took a while before it was proved (by Weyl, in 1923) that the prediction was of a redshifting of spectral lines that increased linearly with distance (i.e. Hubble's law). ..."

"The models of Einstein and de Sitter are static solutions of Einstein's modified gravitational equations for a world-wide homogeneous system. They both involve a positive cosmological constant λ, determining the curvature of space. If this constant is zero, we obtain a third model in classical infinite Euclidean space. This model is empty, the space-time being that of Special Relativity. It has been shown that these are the only possible static world models based on Einstein's theory. In 1922, Friedmann... broke new ground by investigating non-static solutions to Einstein's field equations, in which the radius of curvature of space varies with time. This Possibility had already been envisaged, in a general sense, by Clifford in the eighties."

"After putting the finishing touches on general relativity in 1915, Einstein applied his new equations for gravity to a variety of problems. ... Despite the mounting successes of general relativity, for years after he first applied his theory to the most immense of all challenges—understanding the entire universe—Einstein absolutely refused to accept the answer that emerged from the mathematics. Before the work of Friedmann and Lemaître... Einstein, too, had realized that the equations of general relativity showed that the universe could not be static; the fabric of space could stretch or it could shrink, but it could not maintain a fixed size. This suggested that the universe might have had a definite beginning, when the fabric was maximally compressed, and might even have a definite end. Einstein stubbornly balked at this... because he and everyone else "knew" that the universe was eternal and, on the largest scales, fixed and unchanging. Thus, notwithstanding the beauty and successes of general relativity, Einstein reopened his notebook and sought a modification of the equations... It didn't take him long. In 1917 he achieved the goal by introducing a new term... the cosmological constant."

"The miracle of physics that I'm talking about here is something that was actually known since the time of Einstein's general relativity; that gravity is not always attractive. Gravity can act repulsively. Einstein introduced this in 1916... in the form of the cosmological constant, and the original motivation of modifying the equations of general relativity to allow this was because Einstein thought that the universe was static, and he realized that ordinary gravity would cause the universe to collapse if it was static. ...The fact that general relativity can support this gravitational repulsion, still being consistent with all the principles that general relativity incorporates, is the important thing which Einstein himself did discover.."

"It's a term that Einstein recognized as allowed by his theory — he threw it in and then, in disgust, threw it out again ... It's back!"

"... The way in which string theory addresses the cosmological constant problem can be summarized as follows: • Fundamentally, space is nine-dimensional. There are many distinct ways (perhaps 10500) of turning nine-dimensional space into three-dimensional space by compactifying six dimensions. ... • Distinct compactifications correspond to different three-dimensional metastable vacua with different amounts of vacuum energy. In a small fraction of vacua, the cosmological constant will be accidentally small. • All vacua are dynamically produced as large, widely separated regions in space-time. • Regions with Λ 1 contain at most a few bits of information and thus no complex structures of any kind. Therefore, observers find themselves in regions with Λ ≪ 1."

"The theoretical view of the actual universe, if it is in correspondence to our reasoning, is the following. The curvature of space is variable in time and place, according to the distribution of matter, but we may roughly approximate it by means of a spherical space. ...this view is logically consistent, and from the standpoint of the general theory of relativity lies nearest at hand [i.e. is most obvious]; whether, from the standpoint of present astronomical knowledge, it is tenable, will not be discussed here. In order to arrive at this consistent view, we admittedly had to introduce an extension of the field equations of gravitation, which is not justified by our actual knowledge of gravitation. It is to be emphasized, however, that a positive curvature of space is given by our results, even if the supplementary term [] is not introduced. The term is necessary only for the purpose of making possible a quasi-static distribution of matter, as required by the fact of the small velocity of the stars."

"Most constants are adjusted with a deviation of one percent, which means that if the value differs by one percent everything collapses. Physicists can certainly claim that this is a fluke, but it must be acknowledged that this cosmological constant is adjusted to an accuracy of 1/10120. No one thinks that this is solely a fluke. It is the most extreme example of hyperfine regulation... (Leonard Susskind)"

"Much later, when I was discussing cosmological problems with Einstein, he remarked that the introduction of the cosmological term was the biggest blunder he ever made in his life."

"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."

"De Sitter proposed three types of nonstatic universes: the oscillating universes and the expanding universes of the first or second kiind. The main characteristic of the expanding "family" of the first kiind is that the radius is continually increasing from a definite initial time when it had the value zero. The universe becomes infinitely large after an infinite time. In the second kind... the radius possesses at the initial time a definite minimum value... in the Einstein model... the cosmological constant is supposed to be equal to the reciprocal of R2, whereas de Sitter computed for his interpretation the constant to be equal to 3/R2. Whitrow correctly points out the significant fact that in special relativity the cosmological constant is omitted..."

"A star does not evolve over its lifetime through each spectral type, as Russell once thought; rather, each star experiences its own distinct history, based on its mass at birth. Smaller stars, such as tiny s, will never reach the red-giant stage but just dully burn away like red-hot ovens. Stars that are born with appreciably more mass than our Sun, such as the white-hot O and B stars, will burn swiftly and eventually blow up, leaving behind a city-sized or even a black hole, a gravitational pit from which no light or matter can escape. ...the term black hole wasn't even coined until 1968. Yet the first tentative steps toward understanding this great metamorphosis, the distinct and striking stages in a star's life, were taken at the turn of the century. The elements in the stars themselves were telling the tale in the spectral messages they were telegraphing throughout the cosmos."

"If grand unified theories are correct, we ought to be able to derive the relative power of the strong, weak, and electromagnetic interactions at accessible energies from their presumed equality at much higher energies. When this is attempted, a wonderful result emerges. ...in the form first calculated by Howard Georgi, Helen Quinn, and Steven Weinberg ...The couplings of strong-interaction gluons decrease, those of the [weak interaction] W bosons stay roughly constant, and those of the [electromagnetic interaction] photons increase at short distances [or high energies]—so they all tend to converge, as desired."

"Once helium burning has occurred... the next possible reaction—carbon burning—is not necessarily slow... This reaction involves ...a strong as opposed to a weak interaction. ...Carbon burning results in magnesium. ...Taking a cross section of a highly evolved star would reveal a system of many layers. The inner layers have been subjected to the largest pressures, thereby forced to the highest temperatures, and burned the furthest; the outermost layers, by contrast, have not burned at all. Thus, as we proceed from outside in, there will be an outermost layer with the initial mix of hydrogen and helium, a layer of mostly helium, a layer of carbon, a layer of magnesium, and so on. ...So we arrive at the picture of a star, in the latest stages of its evolution... now composed of mostly carbon nuclei and other explosive material."

"The weak force does not seem to hold anything together, only to break it apart. ...we do not observe s of the weak force. ...So the weak force seems a force apart... Interwoven with the surprising story of the weak force has been the story of s, arguably the most intriguing of the fundamental particles. ...the neutrinos provide a unique and valuable mirror on the weak force. ...In the 1920s, and for a while disputed the energy spectrum of electrons emitted in β decay. ...Chadwick demonstrated... that the spectrum was continuous, i.e. the electron could take on a whole range of energies. ...contrary to the single line expected from energy conservation if only... the electron and the nucleus, were involved... Neils Bohr advocated abandoning energy conservation... but in 1930 Wolfgang Pauli daringly proposed an unseen... neutrino... Pauli's intuition... inspired Enrico Fermi in his 'tentative theory of β decay'... to become the basis for ideas of a universal weak force."

"The first intimations that β decay is but one manifestation of some deeper fundamental interaction came during the 1940s from experiments which led to the discovery of the . ...A third charged , the tau, and three neutral neutrinos bring the number of family members to six. In addition there are six corresponding antiparticles. It appears that in any interaction a lepton can be created (or can disappear) only together with an antilepton. This empirical rule of 'lepton conservation'... implies... that it is an antineutrino that accompanies the electron in β decay. ...When the decay or capture of a muon was treated in the same way as β decay in Fermi's theory, the s... appeared remarkably similar. ...The agreement between the coupling constants for β decay, muon decay and muon capture led to the idea of a 'universal Fermi interaction' and... experiments began to reveal more and more new particles with similar weak interactions."

"Why can stars do better than the big bang? ...During the big bang, there were only a few minutes when nuclei could form. Very rare processes, or slow ones, played little role. A case in point is the key process from which the sun derives its energy. In this reaction, two protons collide to produce a deuterium nucleus, a neutrino, and a positron. ...This reaction belongs to the family of weak interactions. ...It remains... a remarkable—and for humanity, remarkably fortunate—circumstance that the central reaction that drives the sun is so rare. It is only this extraordinary rarity that allows the average proton in the sun to last so long, billions of years, even though it is colliding with other protons millions of times a second. ...an entertaining example of Treiman's theorem."

"[T]he work of a number of theoretical physicists in the 1960s culminated in the electroweak theory that is designed to unify electromagnetism and the weak force... This theory is sometimes called the 'GWS Theory', from... Sheldon Glashow, Steven Weinberg and Abdus Salam... The main feature of the theory is that at extremely high temperatures the electromagnetic and weak forces are two components of a single force, the electroweak force. The symmetry between the two forces would only be apparent at temperatures of trillions of degrees... in the Big Bang. At lower temperatures... electromagnetism remains a long range force, but the weak force takes on the characteristics of... a very weak force that acts over extremely short distances. ...But the theory is dependent on the existence of the Higgs particle..."

"[W]hat shall we say, then, to a nuclear event such as... beta decay... in which a neutron turns into a proton and also shoots out an electron together with an antineutrino? ...Coming from within... is the weak interaction. Not in all nuclei, but certainly in many... the weak interaction sometimes subverts the neutrons and protons bound otherwise so strongly. It takes only a change in flavor. The weak force, with the weak interaction charges as the source, transforms a into an and hence a into a . At the same time, an electron and antineutrino spring loose... The strong force plays no part here, since neither the electron nor the antineutrino carries a strong interaction charge. Electrically neutral, the antineutrino escapes the electromagnetic force as well. ...the weak force ...allows a neutron to decay into a proton, electron, and antineutrino. The four particles all carry weak interaction charges, and their common endowment makes them all actors in a single play."

"s were among the most paradoxical members of the zoo of elementary particles that were discovered after the war. Produced during radioactive decay, they supposedly had neither charge nor mass and they traveled, consequently, at the speed of light. Their only interaction with the world (besides gravity) was by something called the "weak" force, which causes some kinds of radioactive decay. It was so weak that, according to calculations, a typical neutrino could pass through a million miles of water unhindered—stars and planets were transparent to them."

"The mass of the W and Z prevents the weak force from extending beyond their Compton length (about a hundredth the size of a proton)..."

"In addition to transforming a neutron into a proton and vice versa, the weak force was evidently responsible for the decay of a muon into an electron. ...[W]hen the strange particles were found to decay without s it was realized that the force was more complex than had been posited in Fermi's theory of beta decay. Nevertheless, the fact that aspects of the force could be explained by an electromagnetic formalism implied that these forces shared an underlying symmetry."

"Antoine-Henri Becquerel discovered radioactivity. Becquerel's discovery preceded J. J. Thomson's... electron by one year. Radioactivity comes in three kinds, called alpha, beta, and gamma. ...only one ...(beta) has to do with the weak interactions. Today we know that the beta rays were actually electrons emitted by neutrons in the nucleus. ...Nothing in QED or QCD explains how a neutron can emit an electron and become a proton. ...Becquerel didn't know ...that another particle flew off... the antiparticle of the ghostly neutrino. ...The neutrino ...doesn't emit photons. It doesn't emit s. This means it [does not experience the respective electromagnetic or s] that electrically charged particles or s experience. The W-boson is key to the neutrino's activities. Not only can the electrons and quarks emit W-bosons—so too can the neutrino. ...[O]ne of the two d-quarks in a neutron can emit a W-boson and become a u-quark, thus turning a neutron into a proton. ...the W-boson is exchanged, where in a QED diagram, the photon would be exchanged. ...weak interactions are very closely related to the electric forces due to photons. ...The W-boson... splits into two particles: an electron and a neutrino "moving backward in time,"... an antineutrino. That's what Becquerel would have seen... had he had a powerful enough microscope."

"For the weak force... universality of coupling strength is not readily apparent. ic weak forces are very different in nature from ic weak processes."

"How can s be produced in the center of the sun and how can they be detected in laboratories here on earth if they are subject neither to the strong force nor to the electromagnetic one? Another force, the so-called weak force, is responsible. The electron neutrino does participate in that interaction, along with the electron."

"The weak force gives rise to reactions... These reactions involve a change of flavor... one version involving the exchange of a positively charged quantum and the other the exchange of a negatively charged quantum. The existence of such quanta was first discussed by some of us in the late 1950s, and they were discovered at CERN twenty-five years later, in experiments that procured a Nobel prize for Carlo Rubbia and Simon van der Meer. The quanta are usually called W + and W -, as they were designated in a celebrated paper by T. D. Lee and C. N. Yang..."

"The... weak force... couples to both s and s, and is very short-ranged due to the large rest mass of the messenger quanta involved. Its effective strength is usually many orders of magnitude weaker than electromagnetism, and its action can cause particles to change identity, as when a neutron decays. Unlike the electromagnetic and strong forces, the weak force violates parity conservation."

"It appears that the strong interactions and electromagnetic interactions are invariant with respect to C, P, and T separately, while the weak interactions do not conserve P or C. All experimental results are consistent with the assumption the T invariance holds true for all interactions; consequently, from the CPT theorem, weak interactions must be invariant under CP. One could not, then, determine if the photographed scene were a scene of particles viewed normally, or a scene of antiparticles projected in a mirror."

"The weak force... least fits into our typical picture of what a force should do. ...the categories of 'attractive' and 'repulsive' do not really fit the weak force ... because it has the ability to change particles from one type to another. ...The weak force can change one into another provided they are in the same generation. The electron can be changed into an electron and vice versa, but the electron cannot be turned into the ..."

"In 1952... I tried to explain the behavior of the new "strange particles," so called because they were copiously produced as though strongly interacting and yet decayed slowly as though weakly interacting. (Here "slowly" means a half-life of something like a ten billionth of a second... a strongly interacting particle means... a ten trillionth of a second, roughly the time it takes for light to cross such a particle.) ...I thought of assigning these strange particles isotopic spin I = 5/2... But the notion failed to work... I was invited to talk at the Institute for Advanced Study... By a slip of the tongue I said "I = 1" instead... Immediately I stopped dead, realizing I = 1 would do the job. ...But what about the alleged rule that ic strongly interacting particle states had to have values of I like 1/2 or 3/2 or 5/2? ...the rule was merely a superstition... unnecessary baggage that had come along with the useful concept of isotopic spin... [which now] could have wider applications than before. ...[T]he strange particle states differ from more familiar ones such as neutron or proton or s by having at least one s or "strange" quark in place of a u or d quark. Only the weak interaction can convert one flavor of quark into another, and that process happens slowly."

"In his theory of beta reactivity Fermi introduced a new type of interactions among elementary particles, which today we call "weak interactions". Many new manifestations of weak interactions, which could be interpreted using Fermi's 1933 theory, were found in the following decades. The study of weak interactions has led to surprising discoveries, among which the violation of specular symmetry (known as parity symmetry or P symmetry), and the violation of time reversal symmetry (T symmetry) and of the symmetry between matter and antimatter (CP symmetry)."

"The strong and weak forces are less familiar because their strength rapidly diminishes over all but subatomic distance scales; they are the s. This is why these two forces were discovered only much more recently. The strong force is responsible for keeping quarks "glued" together inside of protons and neutrons and keeping protons and neutrons tightly crammed together inside atomic nuclei. The weak force is best known for the radioactive decay of substances such as uranium and cobalt."

"In 1933 Enrico Fermi suggested that beta radioactivity, and the manner in which the neutron spontaneously decayed, could be described using a formalism similar to that developed by Dirac for the electromagnetic force, but 10-10 times weaker. With its range of only about 1/1,000th the diameter of the nucleus, it could not play a role in binding the nucleus, but it could affect individual s. The fact that the metastable particles exhibited the same characteristic time of 10-10 second indicated that this weak force acted on many types of particles. ...a 'characteristic time' ...being the time for an interaction across a nucleus 3 fm in diameter; an event taking place in a shorter time [than 10-23 seconds for the strong force] has 'no meaning'. ...For electromagnetic interactions, the strength is 10-3 of the strong force, and so the characteristic time is longer (10-20 [seconds]); this is roughly the time for a photon to cross an atom."

"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."

"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 s, light bulbs and s. Now the 'empty' space itself started to be probed. ...There was always something left: a that permeated every fibre of the Universe."

"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."

"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."