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.Newton s laws ofmotion predict that a spinning body will have a bulging equator andflattened poles, as does the Earth.The rotation of the Earth relative tothe distant stars, or, more accurately, remote galaxies, produces thiseffect, but how does the Earth know about the average distribution ofJohn Gribbin ElecBook White Holes: Cosmic Gushers in the Universe 161all the rest of the material in the Universe?In Newton s time, the point was put by Bishop Berkeley, inconnection with what is now a well-known experiment involving abucket of water.The idea of the experiment is that if a bucket of water isrotated by hanging it by the handle from a cord and giving it a goodspin, friction between the bucket and the water will cause the water tospin.The water will rise up the sides of the bucket to form a concavesurface.Stop the bucket suddenly and the water will continue to rotateand it will still form a concave surface until friction stops its motion.Bishop Berkeley s view was that if the stars are rotating relative to thewater surface, then the surface is curved, and he concluded that thestars or, as we would now say, the average matter distribution in theUniverse cause the physical effects associated with rotation.Thisconcept is crucial to much of modern cosmological thought, and it isunfortunate that Bishop Berkeley was so far ahead of his time that hisname was almost forgotten.His ideas were generally credited to ErnstMach, who tidied them up one-and-a-half centuries later and wasimmortalized by Einstein, who called the concept Mach s principle.Thename has stuck, but today Bishop Berkeley, having gained his rightfulplace in cosmological history, is acknowledged as the originator ofMach s principle.The Theory of General Relativity is, in large measure, Einstein sattempt to incorporate Mach s principle into a gravitational view of theUniverse, with gravity as the underlying force by which the total mass ofthe Universe influences local events.The behavior of falling bodies,orbiting satellites, swinging pendulums, and buckets of water are but afew examples of the influence of the Universe on our daily lives.According to some theorists, there may be more detailed influences atwork, influences which have not been explained as satisfactorily as Gen-John Gribbin ElecBook White Holes: Cosmic Gushers in the Universe 162eral Relativity explains the gravitational influences.The idea that there may be a fundamental link between atomic andelementary particle processes and the overall structure of the Universecomes from a comparison of some of the constants of physics andcosmology.The idea goes back to the thirties, when speculations werepublished by the great physicist, Paul Dirac, whose name at least will befamiliar since it has been taken up by several science-fiction writersdescribing pseudoscientific space drives.3Dirac s theory of large numbers rests on the construction of two large,dimensionless numbers one from atomic physics and one fromcosmology.The idea behind this construction is that, in physics, it isoften possible to produce dimensionless equations independent of theunits of measurement chosen, and these usually have important physicalsignificance.For example, we may say that one person is twice as old asanother, and that would be true whether we measure age in years, days,months, or whatever.When describing the two people, that single factwould be a more valuable piece of information than knowing what unitsare used to measure their ages in.In atomic physics, what seems to bea fundamental constant emerges when we compare the electric forceacting between a proton and an electron and the gravitational forcebetween the same pair of particles.The first is proportional to theproduct of the charges and to the inverse of the square of the distancebetween them; the second is proportional to the product of their massesand to the inverse of the square of the distance between them.The ratioof the two forces, the force constant, is a dimensionless number whichhas the large, even by astronomical standards, value of 2.3 X 1039.Ourexperience of dimensionless numbers suggests that this figure meanssomething important but what?John Gribbin ElecBook White Holes: Cosmic Gushers in the Universe 163Dirac s second number is equally large, almost exactly so, and that iswhat makes the pair remarkable.Taking the age of the Universe interms of a fundamental unit of time, the time needed for light to crossthe tiny distance occupied by an atom, Dirac arrives at a number closeto 1039, and by dividing the mass of the Universe by the mass of ahydrogen atom, cosmologists have argued that the total number ofparticles in the observable Universe is approximately 1078, which is thesquare of 1039.It doesn t matter what multiple of 1039 is used; they arenot accurate enough for that to be meaningful.But all agree to withinless than one multiple of ten, in a coincidence that stretches acrossthirty-nine multiples of ten.If you find it difficult to grasp the meaningof such numbers, you are not alone; Jagjit Singh4 mentions the legendof a king who was inveigled into promising an advisor a reward madeup of wheat which would be counted by placing one grain on the firstsquare of a chessboard, two on the second, four on the third, and soon.The total from the sixty-four squares would be about two-thousandtimes the amount of wheat produced in the world each year today; andthat number only involves twenty multiples of ten, a tiny fraction of oneof Dirac s large numbers.A remarkable aspect of this work is that after Dirac s first thoughtson the subject were published in the thirties, forty years elapsed beforehe rounded the ideas off and completed his theory of large numbers inpapers published in the seventies.This theory certainly produces astriking view of the Universe, since its continued expansion and itsincreasing age imply that if the agreement between these large numberstoday is not just a coincidence then they must all be increasing togetheras the Universe expands so that even the fundamental force constant ofatomic physics is actually a variable.There is one aspect to thecomplete theory which will be familiar to those who have come acrossJohn Gribbin ElecBook White Holes: Cosmic Gushers in the Universe 164other alternatives to Einstein s theory.Once again, it adds a two-component structure to the metric of space-time.This time onecomponent enters through Einstein s equations, which remain valid inthe Dirac universe, and the other affects what we can actually measurein the laboratory when investigating atomic behavior.According to Dirac,the variation in the force constant is due to a change in the constant ofgravity, which enters into the gravitational part of the calculation of theforce constant, so that the gravity constant G decreases as the age of theuniverse t increases.The other figure to be juggled is that magic number for the number ofparticles in the observable Universe.According to Dirac, it must increasein proportion to t2 and we are back in the Steady State scenario.Diracoffers two versions of the theory, one with the creation of matteroccurring uniformly through space, and the other bringing new matterinto the model universe in concentrated lumps close by existing masses,a picture superficially reminiscent of cosmic gushers [ Pobierz całość w formacie PDF ]
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.Newton s laws ofmotion predict that a spinning body will have a bulging equator andflattened poles, as does the Earth.The rotation of the Earth relative tothe distant stars, or, more accurately, remote galaxies, produces thiseffect, but how does the Earth know about the average distribution ofJohn Gribbin ElecBook White Holes: Cosmic Gushers in the Universe 161all the rest of the material in the Universe?In Newton s time, the point was put by Bishop Berkeley, inconnection with what is now a well-known experiment involving abucket of water.The idea of the experiment is that if a bucket of water isrotated by hanging it by the handle from a cord and giving it a goodspin, friction between the bucket and the water will cause the water tospin.The water will rise up the sides of the bucket to form a concavesurface.Stop the bucket suddenly and the water will continue to rotateand it will still form a concave surface until friction stops its motion.Bishop Berkeley s view was that if the stars are rotating relative to thewater surface, then the surface is curved, and he concluded that thestars or, as we would now say, the average matter distribution in theUniverse cause the physical effects associated with rotation.Thisconcept is crucial to much of modern cosmological thought, and it isunfortunate that Bishop Berkeley was so far ahead of his time that hisname was almost forgotten.His ideas were generally credited to ErnstMach, who tidied them up one-and-a-half centuries later and wasimmortalized by Einstein, who called the concept Mach s principle.Thename has stuck, but today Bishop Berkeley, having gained his rightfulplace in cosmological history, is acknowledged as the originator ofMach s principle.The Theory of General Relativity is, in large measure, Einstein sattempt to incorporate Mach s principle into a gravitational view of theUniverse, with gravity as the underlying force by which the total mass ofthe Universe influences local events.The behavior of falling bodies,orbiting satellites, swinging pendulums, and buckets of water are but afew examples of the influence of the Universe on our daily lives.According to some theorists, there may be more detailed influences atwork, influences which have not been explained as satisfactorily as Gen-John Gribbin ElecBook White Holes: Cosmic Gushers in the Universe 162eral Relativity explains the gravitational influences.The idea that there may be a fundamental link between atomic andelementary particle processes and the overall structure of the Universecomes from a comparison of some of the constants of physics andcosmology.The idea goes back to the thirties, when speculations werepublished by the great physicist, Paul Dirac, whose name at least will befamiliar since it has been taken up by several science-fiction writersdescribing pseudoscientific space drives.3Dirac s theory of large numbers rests on the construction of two large,dimensionless numbers one from atomic physics and one fromcosmology.The idea behind this construction is that, in physics, it isoften possible to produce dimensionless equations independent of theunits of measurement chosen, and these usually have important physicalsignificance.For example, we may say that one person is twice as old asanother, and that would be true whether we measure age in years, days,months, or whatever.When describing the two people, that single factwould be a more valuable piece of information than knowing what unitsare used to measure their ages in.In atomic physics, what seems to bea fundamental constant emerges when we compare the electric forceacting between a proton and an electron and the gravitational forcebetween the same pair of particles.The first is proportional to theproduct of the charges and to the inverse of the square of the distancebetween them; the second is proportional to the product of their massesand to the inverse of the square of the distance between them.The ratioof the two forces, the force constant, is a dimensionless number whichhas the large, even by astronomical standards, value of 2.3 X 1039.Ourexperience of dimensionless numbers suggests that this figure meanssomething important but what?John Gribbin ElecBook White Holes: Cosmic Gushers in the Universe 163Dirac s second number is equally large, almost exactly so, and that iswhat makes the pair remarkable.Taking the age of the Universe interms of a fundamental unit of time, the time needed for light to crossthe tiny distance occupied by an atom, Dirac arrives at a number closeto 1039, and by dividing the mass of the Universe by the mass of ahydrogen atom, cosmologists have argued that the total number ofparticles in the observable Universe is approximately 1078, which is thesquare of 1039.It doesn t matter what multiple of 1039 is used; they arenot accurate enough for that to be meaningful.But all agree to withinless than one multiple of ten, in a coincidence that stretches acrossthirty-nine multiples of ten.If you find it difficult to grasp the meaningof such numbers, you are not alone; Jagjit Singh4 mentions the legendof a king who was inveigled into promising an advisor a reward madeup of wheat which would be counted by placing one grain on the firstsquare of a chessboard, two on the second, four on the third, and soon.The total from the sixty-four squares would be about two-thousandtimes the amount of wheat produced in the world each year today; andthat number only involves twenty multiples of ten, a tiny fraction of oneof Dirac s large numbers.A remarkable aspect of this work is that after Dirac s first thoughtson the subject were published in the thirties, forty years elapsed beforehe rounded the ideas off and completed his theory of large numbers inpapers published in the seventies.This theory certainly produces astriking view of the Universe, since its continued expansion and itsincreasing age imply that if the agreement between these large numberstoday is not just a coincidence then they must all be increasing togetheras the Universe expands so that even the fundamental force constant ofatomic physics is actually a variable.There is one aspect to thecomplete theory which will be familiar to those who have come acrossJohn Gribbin ElecBook White Holes: Cosmic Gushers in the Universe 164other alternatives to Einstein s theory.Once again, it adds a two-component structure to the metric of space-time.This time onecomponent enters through Einstein s equations, which remain valid inthe Dirac universe, and the other affects what we can actually measurein the laboratory when investigating atomic behavior.According to Dirac,the variation in the force constant is due to a change in the constant ofgravity, which enters into the gravitational part of the calculation of theforce constant, so that the gravity constant G decreases as the age of theuniverse t increases.The other figure to be juggled is that magic number for the number ofparticles in the observable Universe.According to Dirac, it must increasein proportion to t2 and we are back in the Steady State scenario.Diracoffers two versions of the theory, one with the creation of matteroccurring uniformly through space, and the other bringing new matterinto the model universe in concentrated lumps close by existing masses,a picture superficially reminiscent of cosmic gushers [ Pobierz całość w formacie PDF ]