the national science foundation available languages : english, spanish this classroom - tested learning module gives a condensed, easily - understood view of the development of atomic theory from the late 19th through early 20th century. the key idea was the discovery that the atom is not an " indivisible " particle, but consists of smaller constituents : the proton, neutron, and electron. it discusses the contributions of john dalton, j. j. thomson, ernest rutherford, and james chadwick, whose experiments revolutionized the world view of atomic structure. see related materials for a link to part 2 of this series. atomic structure, cathode ray experiment, electron, helium atom, history of atom, history of the atom, hydrogen atom, neutron, proton metadata instance created july 12, 2011 by caroline hall october 10, 2012 by caroline hall last update when cataloged : january 1, 2006 aaas benchmark alignments ( 2008 version ) 4. the physical setting 4d. the structure of matter 6 - 8 : 4d / m1a. all matter is made up of atoms, which are far too small to see directly through a microscope. 9 - 12 : 4d / h1. atoms are made of a positively charged nucleus surrounded by negatively charged electrons. the nucleus is a tiny fraction of the volume of an atom but makes up almost all of its mass. the nucleus is composed of protons and neutrons which have roughly the same mass but differ in that protons are positively charged while neutrons have no electric charge. 9 - 12 : 4d / h2. the number of protons in the nucleus determines what an atom ' s electron configuration can be and so defines the element. an atom ' s electron configuration, particularly the outermost electrons, determines how the atom can interact with other atoms. atoms form bonds to other atoms by transferring or sharing electrons. 10. historical perspectives 10f. understanding fire 9 - 12 : 10f / h1. in the late 1700s and early 1800s, the idea of atoms reemerged in response to questions about the structure of matter, the nature of fire, and the basis of chemical phenomena. 9 - 12 : 10f / h3. in the early 1800s, british chemist and physicist john dalton united the concepts of atoms and elements. he proposed two ideas that laid the groundwork for modern chemistry : first, that elements are formed from small, indivisible particles called atoms, which are identical for a given element but different from any other element ; and second, that chemical compounds are


proposed two ideas that laid the groundwork for modern chemistry : first, that elements are formed from small, indivisible particles called atoms, which are identical for a given element but different from any other element ; and second, that chemical compounds are formed from atoms by combining a definite number of each type of atom to form one molecule of the compound. 9 - 12 : 10f / h4. dalton figured out how the relative weights of the atoms could be determined experimentally. his idea that every substance had a unique atomic composition provided an explanation for why substances were made up of elements in specific proportions. this resource is part of a physics front topical unit. topic : particles and interactions and the standard model unit title : history and discovery this classroom - tested learning module gives a condensed, easily - understood view of the development of atomic theory from the late 19th through early 20th century. the key idea was the discovery that the atom is not an " indivisible " particle, but consists of smaller constituents : the proton, neutron, and electron. it discusses the contributions of john dalton, j. j. thomson, ernest rutherford, and james chadwick, whose experiments revolutionized the world view of atomic structure. % 0 electronic source % a carpi, anthony % d january 1, 2006 % t visionlearning : atomic theory i % i visionlearning % v 2013 % n 21 may 2013 % 8 january 1, 2006 % 9 text / html % u http : / / www. visionlearning. com / library / module _ viewer. php? mid = 50 & l = disclaimer : compadre offers citation styles as a guide only. we cannot offer interpretations about citations as this is an automated procedure. please refer to the style manuals in the citation source information area for clarifications.


an electron is a subatomic particles of spin 1 / 2. it couples with photons and, thus, is electrically charged. it is a lepton with a rest mass of 9. 109 * 10 − 31kg and an electric charge of − 1. 602 * 10 − 19 c, which is the smallest known charge possible for an isolated particle ( confined quarks have fractional charge ). the electric charge of the electron e is used as a unit of charge in much of physics. electron pairs within an orbital system have opposite spins due to the pauli exclusion principle ; this characteristic spin pairing allows electrons to exist in the same quantum orbital, as the opposing magnetic dipole moments induced by each of the electrons ensures that they are attracted together. current theories consider the electron as a point particle, as no evidence for internal structure has been observed. as a theoretical construct, electrons have been able to explain other observed phenomena, such as the shell - like structure of an atom, energy distribution around an atom, and energy beams ( electron and positron beams ). - ↑ massimi, m. ( 2005 ). pauli ' s exclusion principle, the origin and validation of a scientific principle. cambridge university press. pp. 7 – 8 - ↑ mauritsson, j.. " electron filmed for the first time ever ". lunds universitet. retrieved 2008 - 09 - 17. http : / / www. atomic. physics. lu. se / research / attosecond _ physics - ↑ chao, a. w. ; tigner, m. ( 1999 ). handbook of accelerator physics and engineering. world scientific. pp. 155, 188. isbn 981 - 02 - 3500 - 3.


heat is a sad fact of life for current generation electronics. any android, iphone, or blackberry user can tell you that smartphones tend to get pretty hot at times. and by today ' s standards a balmy 85 degrees celsius, while hot enough to cook an egg, is a pretty " good " operating temperature for a high - powered pc graphics processing unit. but that could all soon change, according to the results of a new study by researchers at the university of illinois. examining graphene transistors, a team led by mechanical science and engineering professor william king [ profile ] and electrical and computer engineering professor eric pop [ profile ] made a remarkable discovery - - graphene appears to self - cool. i. what is graphene? graphene is somewhat like a miniature " fence " of carbon. the material consists of a single - atom thick layer composed of hexagonal units. at each point of the hexagon sits a carbon atom that is bonded to its three close neighbors. the material behaves like a semiconductor, despite being made of organic atoms. it offers remarkable performance at an incredibly small scale, thus the electronics industry views it as a potential material to power electronic devices of the future. a variety of methods exist for producing graphene. the earliest method was an exfoliation technique that involved stripping individual graphene layers off a layer of graphite ( the material found in pencil lead ) - - this technique ( as of 2008 ) cost as much as $ 100m usd to produce a single cubic centimeter of material. however, rapid advances in production have allowed manufacturers to begin scaling up production to the point where tons of exfoliated graphene can now be produced. techniques promise to drop the price even further. one method, epitaxial growth on silicon cost $ 100 per cubic centimeter in 2009. its limitation is that, obviously, it requires silicon ( eliminating some desirable properties like flexibility ). south korean researchers have tested another promising method, nickel metal transfer. graphene is fascinating from a physics perspective. in 2005 physicists at the university of manchester and the philip kim group from columbia university demonstrated that quasiparticles inside graphene were massless dirac fermions. these unusual particles help give rise to the material ' s unique characteristics. ii. graphene as a self - cooling device despite the extreme interest in the material, deal of mystery still surrounds graphene. because it is so extremely thin, it is difficult to test and measure accurately certain properties of the material. overcoming technical challenges,


. graphene as a self - cooling device despite the extreme interest in the material, deal of mystery still surrounds graphene. because it is so extremely thin, it is difficult to test and measure accurately certain properties of the material. overcoming technical challenges, the university of illinois team used an atomic force microscope tip as a temperature probe to make the first nanometer - scale temperature measurements of a working graphene what they found was that the resistive heating ( " waste heat " ) effect in graphene was weaker than its thermo - electric cooling effect at times. this is certainly not the case in silicon or other semiconductors where resistive heating far surpasses cooling effects. what this means is that graphene circuits may not get hot like traditional silicon - based ones. this could open the door to dense 3d chips and more. further, as the heat is converted back into electricity by the device, graphene transistors may have a two - fold power efficiency gain, both in ditching energetically expensive fans and by recycling heat losses into usable electricity. professor king describes, " in silicon and most materials, the electronic heating is much larger than the self - cooling. however, we found that in these graphene transistors, there are regions where the thermoelectric cooling can be larger than the resistive heating, which allows these devices to cool themselves. this self - cooling has not previously been seen for graphene devices. " professor pop adds, " graphene electronics are still in their infancy ; however, our measurements and simulations project that thermoelectric effects will become enhanced as graphene transistor technology and contacts improve. " a paper has been published [ full text ] in nanotechnology ' s most prestigious peer - reviewed journal, nature nanoscience. university of illinois graduate student kyle undergraduate feifei lian and postdoctoral researcher myung - ho bae [ profile ] are listed as co - authors on the paper. iii. what ' s next? the study should provide even more motivation for semiconductor manufacturing companies like intel, globalfoundries, and tmsc to lay down the process work necessary to mass - produce circuits based on graphene transistors, capacitors, etc. as for the university of illinois team, they plan to next use their new measurement technique to analyze carbon nanotubes and other novel structures that are of interest to future electronics applications. their work is funded via a grant from the air force office of scientific research and the office of naval research.


researchers at new jersey institute of technology ( njit ) have developed an inexpensive solar cell that can be painted or printed on flexible plastic sheets. “ someday, homeowners will even be able to print sheets of these solar cells with inexpensive home - based inkjet printers. consumers can then slap the finished product on a wall, roof or billboard to create their own power stations, ” said somenath mitra, ph. d., lead researcher, professor and acting chair of njit ’ s department of chemistry and environmental sciences. harvesting energy directly from abundant solar radiation using solar cells is increasingly emerging as a major component of future global energy strategy, mitra said. yet, when it comes to harnessing renewable energy, challenges remain. expensive, large - scale infrastructures, such as windmills or dams, are necessary to drive renewable energy sources, such as wind or hydroelectric power plants. purified silicon, also used for making computer chips, which continue to rise in demand, is a core material for fabricating conventional solar cells. however, the processing of a material such as purified silicon is beyond the reach of most consumers. “ developing organic solar cells from polymers, however, is a cheap and potentially simpler alternative, ” mitra said. “ we foresee a great deal of interest in our work because solar cells can be inexpensively printed or simply painted on exterior building walls and / or rooftops. imagine some day driving in your hybrid car with a solar panel painted on the roof, which is producing electricity to drive the engine. the opportunities are endless. ” the solar cell developed at njit uses a carbon nanotubes complex, which is a molecular configuration of carbon in a cylindrical shape. although estimated to be 50, 000 times smaller than a human hair, just one nanotube can conduct current better than any conventional electrical wire. mitra and his research team took the carbon nanotubes and combined them with tiny carbon fullerenes ( sometimes known as buckyballs ) to form snake - like structures. buckyballs trap electrons, although they can ’ t make electrons flow. add sunlight to excite the polymers, and the buckyballs will grab the electrons. nanotubes, behaving like copper wires, then will be able to make the electrons or current flow. “ someday, i hope to see this process become an inexpensive energy alternative for households around the world, ” mitra said. ec


breakthroughs bring the next two major leaps in computing power into sight breakthroughs might make quantum computing, replacement for silicon practical within a decade one of the best things about covering technology is that you ' re always on the edge of a completely new generation of stuff that will make everything completely different than it ever was before, even before the last generation made everything different. " completely different " always seems pretty much the same, with a few more complications, higher costs and a couple of cool new capabilities, of course. unless you look back a decade or two and see that everything is completely different from the way it was then … must be some conceptual myopia that keeps us in happy suspense over the future, nostalgic wonder at the past and bored annoyance with the present. the next future to get excited about is going to be really cool, though. you know how long scientists have been working on quantum computers that will be incomparably more powerful than the ones we have now because don ' t have to be built on a " bit " that ' s either a 1 or a zero? they would use a piece of quantum data called a qubit ( or qbit, consistent with everything in the quantum world, the spelling wants to be two things at once ), that can exist in several states at the same time. that would turn the most basic function in computing from a toggle switch to a dial with many settings. multiply the number of pieces of data in the lowest - level function of the computer and you increase its power logarithmically. making it happen has been a trick ; they ' ve been under development for 20 years and probably won ' t show up for another 10. teams of austrian scientists may cut that time down a bit with a system they developed they say can create digital models of quantum - computing systems to make testing and development of both theory and manufacturing issues quicker and easier. they did it the same way lord of the rings brought gollum to life : putting a living example in front of cameras and taking detailed pictures they could use to recreate the image in any other digital environment. rather than an actor, the photo subject was a calcium atom, drastically cooled to slow its motion, then manipulated it using lasers, putting it through a set of paces predicted by quantum - mechanical theory, and recorded the results. abstracting those results lets the computer model predict the behavior of almost any other quantum particle or environment, making it possible to use the quantum version of a cad / cam system to develop and test new


by quantum - mechanical theory, and recorded the results. abstracting those results lets the computer model predict the behavior of almost any other quantum particle or environment, making it possible to use the quantum version of a cad / cam system to develop and test new approaches to the systems that will actually become quantum computers, according to a paper published in the journal science by researchers from the university of innsbruck and the institute for quantum optics and quantum information ( iqoqi ). far sooner than quantum computers will blow our digitized minds, transistors made from grapheme rather than chunkier materials will allow designers to create processors far more dense – and therefore more potentially powerful – than anything theoretically possible using silicon and metallic alloys we rely on now. graphene is a one - atom - thick layer of carbon that offers almost no resistance to electricity flowing through it, but doesn ' t naturally contain electrons at two energy levels, as silicon does. silicon transistors flip on or off by shifting electrons from one energy level to another. even silicon doesn ' t work that way naturally. it has to be " doped " with impurities to change its properties as a semiconductor. for graphene to work the same way, researchers have to add inverters that that mimic the dual energy levels of silicon. so far they only work at 320 degrees below zero fahrenheit ( 77 degrees kelvin ). researchers at purdue ' s birck nanotechnology center built a version that operates at room temperature, removing the main barrier to graphene as a practical option for computer systems design the researchers, led by doctoral candidate hong - yan chen presented their paper at the device research conference in santa barbara. calif. in june to publicize their results with the inverter. real application will have to wait for chen or others to integrate the design into a working circuit based on graphene rather than silicon. systems built on graphene have the potential to boost the computing power of current processors by orders of magnitude while reducing their size and energy use, but only if they operate in offices not cooled to 77 degrees kelvin. it will still be a few years before graphene starts showing up in airline magazines, let alone in it budgets. we ' ll probably be tired of them, too, by the time quantum computers show up, but there ' s just no satisfying some people. read more of kevin fogarty ' s coreit blog and follow the latest it news at itworld. follow kevin on twitter at @ kevinfogarty. for the latest it news, analysis


in this study, ni and cu nanowire arrays and ni / cu superlattice nanowire arrays are fabricated using standard techniques such as electrochemical deposition of metals into porous anodic alumina oxide templates having pore diameters of about 50 nm. we perform optical measurements on these nanowire array structures. optical reflectance ( or ) of the as - prepared samples is recorded using an imaging spectrometer in the wavelength range from 400 to 2, 000 nm ( i. e., from visible to near - infrared bandwidth ). the measurements are carried out at temperatures set to be 4. 2, 70, 150, and 200 k and at room temperature. we find that the intensity of the or spectrum for nanowire arrays depends strongly on the temperature. the strongest or can be observed at about t = 200 k for all samples in visible regime. the or spectra for these samples show different features in the visible and near - infrared bandwidths. we discuss the physical mechanisms responsible for these interesting experimental findings. this study is relevant to the application of metal nanowire arrays as optical and optoelectronic devices. keywords : nanowire array ; optical properties ; visible and near - infrared ; temperature dependence in recent years, quasi one - dimensional ( 1d ) nanostructured materials have received much attention attributed to their interesting physical properties in sharp contrast to the bulk ones and to the potential applications as electronic, magnetic, photonic, and optoelectronic devices [ 1 - 4 ]. from a viewpoint of physics, the basic physical properties of nanostructured materials differ significantly from those of bulk materials with the same chemical components. in particular, quantum confinement effects can be observed in the dimensionally reduced nanomaterial systems. therefore, nanowires have been a major focus of research on nanoscaled materials which can be taken as a fundamental building block of nanotechnology and practical nanodevices. it should be noticed that metal nanowires have displayed unique optical and optoelectronic properties due to surface plasmon resonance ( spr ) which is a resonant oscillation of the conducting electrons within the metallic nanostructures. the spr effect in nanowire structures can cause a tremendous enhancement of the electromagnetic near - field in the immediate vicinity of the particles and can give rise to enhanced scattering and absorption of light radiation. the spr in metal nanowires and related phenomena ( such as the surface - enhanced raman spectroscopy, nonlinear optic response, plas


- field in the immediate vicinity of the particles and can give rise to enhanced scattering and absorption of light radiation. the spr in metal nanowires and related phenomena ( such as the surface - enhanced raman spectroscopy, nonlinear optic response, plasmonic excitation, to mention but a few ) contributes greatly to their promising applications in biosensors, optical devices, and photonic and plasmonic devices [ 5 - 8 ]. moreover, metal nanowire wave guides can excite and emit terahertz ( 1012 hz or thz ) surface plasmon polaritons, which can fill the gap of terahertz electronics and optoelectronics. on the other hand, superlattice nanowires have even richer physical properties owing to further quantum confinement of electron motion along the wire direction. they have been proposed as advanced electronic device systems to observe novel effects such as giant magnetoresistance and even high thermoelectric figure of merit [ 10, 11 ]. furthermore, with the rapid development of nanotechnology, it is now possible to fabricate nanowire arrays and superlattice nanowire arrays [ 12, 13 ]. one of the major advantages to apply nanowire arrays and superlattice nanowire arrays as optic and optoelectronic devices is that the optical response of the array structures can be tuned and modulated via varying sample parameters such as the diameter of the wire and the pattern of the array structure. due to potential applications of the nanowire arrays and superlattice nanowire arrays as optical devices, it is of importance and significance to examine their basic optical properties. in this article, we present a detailed experimental study on the optical properties of three kinds of nanowire array structures such as ni and cu nanowire arrays and ni / cu superlattice nanowire arrays. we would like to examine how these advanced nanostructured material systems can respond to light radiation, how their optical properties depend on temperature and radiation wavelength, and why the optical properties of the nanowire arrays differ from those observed in bulk materials. samples and measurements in this study, three kinds of nanowire array structures are fabricated, including ni arrays, cu arrays, and ni / cu superlattice arrays. samples are prepared by direct current electrodeposition [ 14 - 16 ] of metal into the holes of porous anodic alumina membrane ( paam ) with the pore size of about 50 nm. noteworthy is the diameter


is used for the detection of 400 - to 800 - nm wavelength regime, and the ingaas photodetector is employed for the measurement of 1 - to 2 - μm wavelength regime. for measurements in the visible regime, the temperatures are set at 4. 2, 70, 150, and 200 k and at room temperature. the change of temperature is achieved in an oxford cooling system. the measurements in the near - infrared regime are undertaken at room temperature. results and discussion the or spectra for ni and cu nanowire arrays and ni / cu superlattice nanowire arrays are shown in figure 2 in visible bandwidth for different temperatures at 4. 2, 70, 150, 200, and 297 k, respectively. as can be seen, the intensity of or in nanowire array structures depends strongly on temperature. when temperature ( t ) < 200 k, the intensity of or for a ni nanowire array sample increases with temperature. when t > 200 k, the or intensity decreases with increasing temperature. the strongest or can be observed at about 200 k. a similar phenomenon can be found for a ni / cu superlattice nanowire array sample. in contrast, the or spectra for cu nanowire arrays ( see figure 2c ) show different temperature dependence. with increasing temperature, the intensity of or for a cu nanowire array first decreases in the 4. 2 - to 70 - k regime, then increases in the 70 - to 200 - k regime, and decreases again when t > 200 k. again, the strongest or for cu nanowire arrays can be observed at about t = 200 k. these experimental findings suggest that 200 k is an appropriate temperature for the enhancement of optical reflection from cu, ni, and ni / cu superlattice nanowire array structures. this can provide a basis for further investigation into other optical properties such as optical absorption and emission from metal nanowire arrays in visible regime. we find that when t > 200 k, the or spectrum for ni / cu superlattice nanowire array lies between those for cu and ni nanowire arrays. however, at lower temperatures ( e. g., at 150 k ), the intensity of the or spectrum for ni / cu superlattice nanowire array is lower than those for cu and ni nanowire arrays. figure 2. the spectra of optical reflection for nanowire arrays measured at different temperatures of 4. 2, 70, 150, 200, and 297 k as indicated. the results for a ni nanowire array ( a ), a


nanowire arrays. figure 2. the spectra of optical reflection for nanowire arrays measured at different temperatures of 4. 2, 70, 150, 200, and 297 k as indicated. the results for a ni nanowire array ( a ), a ni / cu superlattice nanowire array ( b ), and a cu nanowire array ( c ) are shown. in figure 3, the or spectra are shown at room temperature for three metal nanowire array samples in visible and near - infrared bandwidths. in the visible regime ( see figure 3a ), two relatively wide reflection peaks can be observed for all samples at about 500 to 650 nm and 650 to 700 nm, respectively. the 650 - to 700 - nm peaks for the three samples appear at almost the same position ( at about 667 nm ), while the 500 - to 650 - nm ones redshift slightly with respect to that of the incident light source. the peak position of the light source is at about 554 nm, whereas the peaks for cu and ni / cu superlattice nanowire arrays are at about 585 nm and that for ni nanowire arrays is at about 600 nm. it should be noted that the visible light source provided by the tungsten halogen lamp has two main peaks in the 400 - to 800 - nm wavelength regime. the intensity of infrared light source given by the si carbide rod decreases when the radiation wavelength approaches 2 μm. the variation of the intensity of the light sources is enhanced via measurement systems. we notice that ni nanowire arrays reflect more strongly the visible light ; cu nanowire arrays reflect relatively weakly, and the or spectrum for ni / cu superlattice nanowire arrays is just in between them. in the near - infrared range of 1, 000 to 2, 000 nm ( see figure 3b ), the peaks of or spectra for cu nanowire arrays and ni / cu superlattice nanowire arrays are at about 1, 808 nm, and ni nanowire arrays and light source are at about 1, 727 nm. the or spectra for nanowire arrays redshift slightly with respect to the spectrum of the light source. in contrast to the visible regime, the cu nanowire array reflects more strongly the infrared radiation than ni nanowire array. interestingly, the or spectrum for ni / cu superlattice nanowire array is below that for ni nanowire array when radiation wavelength is less than 1, 730 nm, and it is located in between the or spectra for ni


arrays do. because the quantum confinement effect affects mainly the electronic states in different bands in the array structure, the main features of or due to interband electronic transition does not change very significantly. this is why ni nanowire arrays can reflect more strongly the visible radiation than cu arrays can, as shown in figure 3a and similar to the case for bulk materials. moreover, our results show that in the visible regime and when t > 200 k, the or spectrum for ni / cu superlattice nanowire arrays lies between those for cu and ni nanowire arrays. however, at relatively lower temperatures ( e. g., at 150 k ), the intensity of the or spectrum for ni / cu superlattice nanowire array is lower than those for cu and ni nanowire arrays. we believe that this may have resulted from different features of the phonon modes and electron - phonon scattering in nanowire and superlattice nanowire structures. in superlattice nanowire systems formed by different host materials, the phonon modes can be quantized and the conducting electrons are confined along the wire direction. the quantized phonon modes can weaken the electron - phonon scattering because a scattering event requires momentum and energy conservation. on the other hand, the localized electrons can interact more strongly with phonons. our results suggest that when t > 200 k, the former case is dominant, and when t 150 k, the latter effect is stronger. in this study, cu, ni, and ni / cu nanowire arrays have been fabricated using state - of - the - art nanotechnology. the optical measurements on these nanowire arrays have been carried out in visible and near - infrared bandwidths for different temperatures. we have found that the optical reflection spectra of these samples depend strongly on temperature and on radiation wavelength. in particular, ( 1 ) the strongest or in the visible regime can be observed at about 200 k for all samples, and ( 2 ) the or for cu nanowire arrays show a different dependence on temperature and radiation wavelength from that for ni nanowire arrays. these results indicate that the surface plasmon resonances induced by inter - and intraband electronic transitions, the electron - phonon interaction, and the quantum confinement effect can play important roles in affecting optical properties of the metal nanowire array structure. we hope that the interesting experimental findings from this study can provide an in - depth understanding of optical properties of cu and ni nanowire arrays and cu / ni superlattice nano


important roles in affecting optical properties of the metal nanowire array structure. we hope that the interesting experimental findings from this study can provide an in - depth understanding of optical properties of cu and ni nanowire arrays and cu / ni superlattice nanowire arrays and can provide a physical base for the application of metal nanowire arrays as advanced optical and optoelectronic devices. the authors declare that they have no competing interests. wx proposed the research work, coordinated the collaboration, and carried out the analyses of experimental results. yyz designed the experiment and experimental setup, carried out the measurements, and drafted the manuscript. shx and gtf fabricated the nanowire and superlattice nanowire array samples. ymx and jgh participated in experimental measurements, results and discussion, and analyses. all authors read and approved the final manuscript. this work was supported by the national natural science foundation of china ( grant no. 10974206 ), department of science and technology of yunnan province, and by the chinese academy of sciences. j crystal growth 2003, 254 : 14. publisher full text j appl phys 2002, 91 : 4590 - 4594. publisher full text appl surf sci 2008, 255 : 1901. publisher full text surf coat technol 2010, 205 : 2432 - 2437. publisher full text c r physique 2008, 9 : 215 - 231. publisher full text appl phys lett 1994, 65 : 2484. publisher full text appl phys lett 1994, 65 : 3019. publisher full text nano lett 2002, 2 : 83. publisher full text


is light made of waves, or particles? this fundamental question has dogged scientists for decades, because light seems to be both. however, until now, experiments have revealed light to act either like a particle, or a wave, but never the two at once. now, for the first time, a new type of experiment has shown light behaving like both a particle and a wave simultaneously, providing a new dimension to the quandary that could help reveal the true nature of light, and of the whole quantum world. the debate goes back at least as far as isaac newton, who advocated that light was made of particles, and james clerk maxwell, whose successful theory of electromagnetism, unifying the forces of electricity and magnetism into one, relied on a model of light as a wave. then in 1905, albert einstein explained a phenomenon called the photoelectric effect using the idea that light was made of particles called photons ( this discovery won him the nobel prize in physics ). [ what ' s that? your physics questions answered ] ultimately, there ' s good reason to think that light is both a particle and a wave. in fact, the same seems to be true of all subatomic particles, including electrons and quarks and even the recently discovered higgs boson - like particle. the idea is called wave - particle duality, and is a fundamental tenet of the theory of quantum mechanics. depending on which type of experiment is used, light, or any other type of particle, will behave like a particle or like a wave. so far, both aspects of light ' s nature haven ' t been observed at the same time. but still, scientists have wondered, does light switch from being a particle to being a wave depending on the circumstance? or is light always both a particle and a wave simultaneously? now, for the first time, researchers have devised a new type of measurement apparatus that can detect both particle and wave - like behavior at the same time. the device relies on a strange quantum effect called quantum nonlocality, a counter - intuitive notion that boils down to the idea that the same particle can exist in two locations at once. " the measurement apparatus detected strong nonlocality, which certified that the photon behaved simultaneously as a wave and a particle in our experiment, " physicist alberto peruzzo of england ' s university of bristol said in a statement. " this represents a strong refutation of models in which the photon is either a wave or a particle. " peruzzo


a wave and a particle in our experiment, " physicist alberto peruzzo of england ' s university of bristol said in a statement. " this represents a strong refutation of models in which the photon is either a wave or a particle. " peruzzo is lead author of a paper describing the experiment published in the nov. 2 issue of the journal science. the experiment further relies on another weird aspect of quantum mechanics — the idea of quantum entanglement. two particles can become entangled so that actions performed on one particle affect the other. in this way, the researchers were able to allow the photons in the experiment to delay the choice of whether to be particles or waves. mit physicist seth lloyd, who was not involved in the project, called the experiment " audacious " in a related essay in science, and said that while it allowed the photons to delay the choice of being particles or waves for only a few nanoseconds, " if one has access to quantum memory in which to store the entanglement, the decision could be put off until tomorrow ( or for as long as the memory works reliably ). so why decide now? just let those quanta slide! " - twisted physics : 7 mind - blowing findings - quantum weirdness goes big – molecules act like waves | video - wacky physics : the coolest little particles in nature © 2012 livescience. com. all rights reserved.


pppl scientists propose a solution to a critical barrier to producing fusion posted april 23, 2012 ; 05 : 00 p. m. physicists from the u. s. department of energy ' s princeton plasma physics laboratory ( pppl ) have discovered a possible solution to a mystery that has long baffled researchers working to harness fusion. if confirmed by experiment, the finding could help scientists eliminate a major impediment to the development of fusion as a clean and abundant source of energy for producing electric power. an in - depth analysis by pppl scientists zeroed in on tiny, bubble - like islands that appear in the hot, charged gases — or plasmas — during experiments. these minute islands collect impurities that cool the plasma. and these islands, the scientists report in the april 20 issue of the journal physical review letters, are at the root of a longstanding problem known as the " density limit " that can prevent fusion reactors from operating at maximum efficiency. fusion occurs when plasmas become hot and dense enough for the atomic nuclei contained within the hot gas to combine and release energy. but when the plasmas in experimental reactors called tokamaks reach the mysterious density limit, they can spiral apart into a flash of light. " the big mystery is why adding more heating power to the plasma doesn ' t get you to higher density, " said david gates, a principal research physicist at pppl and co - author of the proposed solution with luis delgado - aparicio, a postdoctoral fellow at pppl and a visiting scientist at the massachusetts institute of technology ' s plasma science fusion center. " this is critical because density is the key parameter in reaching fusion and people have been puzzling about this for more than 30 years. " a discovery by princeton plasma physics laboratory physicists luis delgado - aparicio ( left ) and david gates could help scientists eliminate a major impediment to the development of fusion as a clean and abundant source of energy for producing electric power. listen to a podcast with the scientists discussing their discovery. ( photo by elle starkman ) the scientists hit upon their theory in what gates called " a 10 - minute ' aha! ' moment. " working out equations on a whiteboard in gates ' office, the physicists focused on the islands and the impurities that drive away energy. the impurities stem from particles that the plasma kicks up from the tokamak wall. " when you hit this magical density limit, the islands grow and coalesce and the plasma ends up in a disruption, " said delgado - ap


energy. the impurities stem from particles that the plasma kicks up from the tokamak wall. " when you hit this magical density limit, the islands grow and coalesce and the plasma ends up in a disruption, " said delgado - aparicio. these islands actually inflict double damage, the scientists said. besides cooling the plasma, the islands act as shields that block out added power. the balance tips when more power escapes from the islands than researchers can pump into the plasma through a process called ohmic heating — the same process that heats a toaster when electricity passes through it. when the islands grow large enough, the electric current that helps to heat and confine the plasma collapses, allowing the plasma to fly apart. gates and delgado - aparicio now hope to test their theory with experiments on a tokamak called alcator c - mod at mit, and on the diii - d tokamak at general atomics in san diego. among other things, they intend to see if injecting power directly into the islands will lead to higher density. if so, that could help future tokamaks reach the extreme density and 100 - million - degree temperatures that fusion requires. the scientists ' theory represents a fresh approach to the density limit, which also is known as the " greenwald limit " after mit physicist martin greenwald, who has derived an equation that describes it. greenwald has another potential explanation for the source of the limit. he thinks it may occur when turbulence creates fluctuations that cool the edge of the plasma and squeeze too much current into too little space in the core of the plasma, causing the current to become unstable and crash. " there is a fair amount of evidence for this, " greenwald said. however, he added, " we don ' t have a nice story with a beginning and end and we should always be open to new ideas. " gates and delgado - aparicio pieced together their model from a variety of clues that have developed in recent decades. gates first heard of the density limit while working as a postdoctoral fellow at the culham centre for fusion energy in abingdon, england, in 1993. the limit had previously been named for culham scientist jan hugill, who described it to gates in detail. separately, papers on plasma islands were beginning to surface in scientific circles. french physicist paul - henri rebut described radiation - driven islands in a mid - 1980s conference paper, but not in a periodical. german physicist wolfgang suttrop speculated a decade later that


science, students are learning to isolate important characteristics, enumerate characteristics, use appropriate terminology, and use synonyms which are important reading skills ( carter & simpson, 1978 ). when students have used the process skills of observing, identifying, and classifying, they are better able to discriminate between vowels and consonants and to learn the sounds represented by letters, letter blends, and syllables ( murray & pikul ski, 1978 ). science instruction provides an alternative teaching strategy that motivates students who may have reading difficulties ( wellman, 1978 ). children ' s involvement with process skills enables them to recognize more easily the contextual and structural clues in attacking new words and better equips them to interpret data in a paragraph. science process skills are essential to logical thinking, as well as to forming the basic skills for learning to read ( barufaldi & swift, 1977 ). guszak defines reading readiness as a skill - complex. of the three areas within the skill - complex, two can be directly enhanced by science process skills : ( 1 ) physical factors ( health, auditory, visual, speech, and motor ) ; and ( 2 ) understanding factors ( concepts, processes ). when students see, hear, and talk about science experiences, their understanding, perception, and comprehension of concepts and processes may improve ( barufaldi & swift, 1977 and bethel, 1974 ). the hands - on manipulative experiences science provides are the key to the relationship between process skills in both science and reading ( lucas & burlando, 1975 ). science activities provide opportunities for manipulating large quantities of multi - sensory materials which promote perceptual skills, i. e., tactile, kinesthetic, auditory, and visual ( neuman, 1969 ). these skills then contribute to the development of the concepts, vocabulary, and oral language skills ( listening and speaking ) necessary for learning to read ( wellman, 1978 ). studies viewed cumulatively suggest that science instruction at the intermediate and upper elementary grades does improve the attainment of reading skills. the findings reveal that students have derived benefits in the areas of vocabulary enrichment, increased verbal fluency, enhanced ability to think logically, and improved concept formation and communication skills ( campbell, 1972 ; kraft, 1961 ; olson, 1971 ; quinn & kessler, 1976 ).


please read how you can help keep the encyclopedia free absolute and relational theories of space and motion since antiquity, natural philosophers have struggled to comprehend the nature of three tightly interconnected concepts : space, time, and motion. a proper understanding of motion, in particular, has been seen to be crucial for deciding questions about the natures of space and time, and their interconnections. since the time of newton and leibniz, philosophers ’ struggles to comprehend these concepts have often appeared to take the form of a dispute between absolute conceptions of space, time and motion, and relational conceptions. this article guides the reader through some of the history of these philosophical struggles. rather than taking sides in the ( alleged ) ongoing debates, or reproducing the standard dialectic recounted in most introductory texts, we have chosen to scrutinize carefully the history of the thinking of the canonical participants in these debates — principally descartes, newton, leibniz, mach and einstein. readers interested in following up either the historical questions or current debates about the natures of space, time and motion will find ample links and references scattered through the discussion and in the other internet resources section below. - 1. introduction - 2. aristotle - 3. descartes - 4. newton - 5. absolute space in the twentieth century - 6. leibniz - 7. ‘ not - newton ’ versus ‘ be - leibniz ’ - 8. mach and later machians - 9. relativity and motion - 10. conclusion - other internet resources - related entries things change. a platitude perhaps, but still a crucial feature of the world, and one which causes many philosophical perplexities — see for instance the entry on zeno ' s paradoxes. for aristotle, motion ( he would have called it ‘ locomotion ’ ) was just one kind of change, like generation, growth, decay, fabrication and so on. the atomists held on the contrary that all change was in reality the motion of atoms into new configurations, an idea that was not to begin to realize its full potential until the seventeenth century, particularly in the work of descartes. ( of course, modern physics seems to show that the physical state of a system goes well beyond the geometrical configuration of bodies. fields, while determined by the states of bodies, are not themselves configurations of bodies if interpreted literally, and in quantum mechanics bodies have ‘ internal states ' such as particle spin. ) while not all changes seem to be merely the ( loco )


bodies. fields, while determined by the states of bodies, are not themselves configurations of bodies if interpreted literally, and in quantum mechanics bodies have ‘ internal states ' such as particle spin. ) while not all changes seem to be merely the ( loco ) motions of bodies in physical space. yet since antiquity, in the western tradition, this kind of motion has been absolutely central to the understanding of change. and since motion is a crucial concept in physical theories, one is forced to address the question of what exactly it is. the question might seem trivial, for surely what is usually meant by saying that something is moving is to say that it is moving relative to something, often tacitly understood between speakers. for instance : the car is moving at 60mph ( relative to the road and things along it ), the plane is flying ( relative ) to london, the rocket is lifting off ( the ground ), or the passenger is moving ( to the front of the speeding train ). typically the relative reference body is either the surroundings of the speakers, or the earth, but this is not always the case. for instance, it seems to make sense to ask whether the earth rotates about its axis west - east diurnally or whether it is instead the heavens that rotate east - west ; but if all motions are to be reckoned relative to the earth, then its rotation seems impossible. but if the earth does not offer a unique frame of reference for the description of motion, then we may wonder whether any arbitrary object can be used for the definition of motions : are all such motions on a par, none privileged over any other? it is unclear whether anyone has really, consistently espoused this view : aristotle, perhaps, in the metaphysics ; descartes and leibniz are often thought to have but, as we ' ll see, those claims are suspect ; possibly huygens, though his remarks remain cryptic ; mach at some moments perhaps. if this view were correct, then the question of whether the earth or heavens rotate would be meaningless, merely different but equivalent expressions of the facts. but suppose, like aristotle, you take ordinary language accurately to reflect the structure of the world, then you could recognize systematic everyday uses of ‘ up ’ and ‘ down ’ that require some privileged standards — uses that treat things closer to a point at the center of the earth as more ‘ down ’ and motions towards that point as ‘ downwards '. of course we would likely explain this usage in terms of the fact that we and our language evolved


standards — uses that treat things closer to a point at the center of the earth as more ‘ down ’ and motions towards that point as ‘ downwards '. of course we would likely explain this usage in terms of the fact that we and our language evolved in a very noticeable gravitational field directed towards the center of the earth, but for aristotle, as we shall see, this usage helped identify an important structural feature of the universe, which itself was required for the explanation of weight. now a further question arises : how should a structure, such as a preferred point in the universe, which privileges certain motions, be understood? what makes that point privileged? one might expect that aristotle simply identified it with the center of the earth, and so relative to that particular body ; but in fact he did not adopt that tacit convention as fundamental, for he thought it possible for the earth to move from the ‘ down ’ point. thus the question arises ( although aristotle does not address it explicitly ) of whether the preferred point is somewhere picked out in some other way by the bodies in the universe — the center of the heavens perhaps? or is it picked out quite independently of the arrangements of matter? the issues that arise in this simple theory help frame the debates between later physicists and philosophers concerning the nature of motion ; in particular, we will focus on the theories of descartes, newton, leibniz, mach and einstein, and their interpretations. but similar issues circulate through the different contexts : is there any kind of privileged sense of motion, a sense in which things can be said to move or not, not just relative to this or that reference body, but ‘ truly ’? if so, can this true motion be analyzed in terms of motions relative to other bodies — to some special body, or to the entire universe perhaps? ( and in relativity, in which distances, times and measures of relative motion are frame - dependent, what relations are relevant? ) if not, then how is the privileged kind of motion to be understood, as relative to space itself — something physical but non - material — perhaps? or can some kinds of motion be best understood as not being spatial changes — changes of relative location or of place — at all? to see that the problem of the interpretation of spatiotemporal quantities as absolute or relative is endemic to almost any kind of mechanics one can imagine, we can look to one of the simplest theories — aristotle ' s account of natural motion ( e. g., on the heavens i. 2 ). according


the space that it occupies. thus it doesn ' t change place, which is should be to say that it doesn ' t move after all! descartes resolved this difficulty by taking all motion to be the motion of bodies relative to one another, not a literal change of space. now, a body has as many relative motions as there are bodies but it does not follow that all are equally significant. indeed, descartes uses several different concepts of relational motion. first there is ‘ change of place ’, which is nothing but motion relative to this or that arbitrary reference body ( ii. 13 ). in this sense no motion of a body is privileged, since the speed, direction, and even curve of a trajectory depends on the reference body, and none is singled out. next, he discusses motion in ‘ the ordinary sense ’ ( ii. 24 ). this is often conflated with mere change of arbitrary place, but it in fact differs because according to the rules of ordinary speech one properly attributes motion only to bodies whose motion is caused by some action, not to any relative motion. ( for instance, a person sitting on a speeding boat is ordinarily said to be at rest, since ‘ he feels no action in himself ’. ) finally, he defined motion ‘ properly speaking ’ ( ii. 25 ) to be a body ' s motion relative to the matter contiguously surrounding it, which the impossibility of a vacuum guarantees to exist. ( descartes ’ definition is complicated by the fact that he modifies this technical concept to make it conform more closely to the pre - theoretical sense of ‘ motion ’ ; however, in our discussion transference is all that matters, so we will ignore those complications. ) since a body can only be touching one set of surroundings, descartes ( dubiously ) argued that this standard of motion was unique. what we see here is that descartes, despite holding motion to be the motion of bodies relative to one another, also held there to be a privileged sense of motion ; in a terminology sometimes employed by writers of the period, he held there to be a sense of ‘ true motion ’, over and above the merely relative motions. equivalently, we can say that descartes took motion ( ‘ properly speaking ’ ) to be a complete predicate : that is, moves - properly - speaking is a one - place predicate. ( in contrast, moves - relative - to is a two - place predicate. ) and note that the predicate is complete


) to be a complete predicate : that is, moves - properly - speaking is a one - place predicate. ( in contrast, moves - relative - to is a two - place predicate. ) and note that the predicate is complete despite the fact that it is analyzed in terms of relative motion. ( formally, let contiguous - surroundings be a function from bodies to their contiguous surroundings, then x moves - properly - speaking is analyzed as x moves - relative - to contiguous - surroundings ( x ). ) this example illustrates why it is crucial to keep two questions distinct : on the one hand, is motion to be understood in terms of relations between bodies or by invoking something additional, something absolute ; on the other hand, are all relative motions equally significant, or is there some ‘ true ’, privileged notion of motion? descartes ' views show that eschewing absolute motion is logically compatible with accepting true motion ; which is of course not to say that his definitions of motion are themselves tenable. there is an interpretational tradition which holds that descartes only took the first, ‘ ordinary ’ sense of motion seriously, and introduced the second notion to avoid conflict with the catholic church. such conflict was a real concern, since the censure of galileo ' s copernicanism took place only 11 years before publication of the principles, and had in fact dissuaded descartes from publishing an earlier work, the world. indeed, in the principles ( iii. 28 ) he is at pains to explain how ‘ properly speaking ’ the earth does not move, because it is swept around the sun in a giant vortex of matter — the earth does not move relative to its surroundings in the vortex. the difficulty with the reading, aside from the imputation of cowardice to the old soldier, is that it makes nonsense of descartes ' mechanics, a theory of collisions. for instance, according to his laws of collision if two equal bodies strike each other at equal and opposite velocities then they will bounce off at equal and opposite velocities ( rule i ). on the other hand, if the very same bodies approach each other with the very same relative speed, but at different speeds then they will move off together in the direction of the faster one ( rule iii ). but if the operative meaning of motion in the rules is the ordinary sense, then these two situations are just the same situation, differing only in the choice of reference frame, and so could not have different outcomes — bouncing


faster one ( rule iii ). but if the operative meaning of motion in the rules is the ordinary sense, then these two situations are just the same situation, differing only in the choice of reference frame, and so could not have different outcomes — bouncing apart versus moving off together. it seems inconceivable that descartes could have been confused in such a trivial way. ( additionally, as pooley 2002 points out, just after he claims that the earth is at rest ‘ properly speaking ’, descartes argues that the earth is stationary in the ordinary sense, because common practice is to determine the positions of the stars relative to the earth. descartes simply didn ' t need motion properly speaking to avoid religious conflict, which again suggests that it has some other significance in his system of thought. ) thus garber ( 1992, chapter 6 - 8 ) proposes that descartes actually took the unequivocal notion of motion properly speaking to be the correct sense of motion in mechanics. then rule i covers the case in which the two bodies have equal and opposite motions relative to their contiguous surroundings, while rule vi covers the case in which the bodies have different motions relative to those surroundings — one is perhaps at rest in its surroundings. that is, exactly what is needed to make the rules consistent is the kind of privileged, true, sense of motion provided by descartes ' second definition. insurmountable problems with the rules remain, but rejecting the traditional interpretation and taking motion properly speaking seriously in descartes ' philosophy clearly gives a more charitable reading. in an unpublished essay — de gravitatione ( newton, 2004 ) — and in a scholium to the definitions given in his 1687 mathematical principles of natural philosophy ( see newton, 1999 for an up - to - date translation ), newton attacked both of descartes ' notions of motion as candidates for the operative notion in mechanics. ( see stein 1967and rynasiewicz 1995 for important, and differing, views on the issue. ) ( this critique is studied in more detail in the entry newton ' s views on space, time, and motion. ) the most famous argument invokes the so - called ‘ newton ' s bucket ’ experiment. stripped to its basic elements one compares : - a bucket of water hanging from a cord as the bucket is set spinning about the cord ' s axis, with - the same bucket and water when they are rotating at the same rate about the cord ' s axis. as is familiar from any rotating system,


the sense of motion relative to an arbitrary reference body, is not the mechanical sense, since that kind of rotation is not unique at all, but depends on the motion of the reference body. and so descartes ’ change of place ( and for similar reasons, motion in the ordinary sense ) is not the mechanically significant sense of motion. in our discussion of descartes we called the sense of motion operative in the science of mechanics ‘ true motion ’, and the phrase is used in this way by newton in the scholium. thus newton ' s bucket shows that true ( rotational ) motion is anti - correlated with, and so not identical with, proper motion ( as descartes proposed according to the garber reading ) ; and newton further argues that the rate of true ( rotational ) motion is unique, and so not identical with change of place, which is multiple. newton proposed instead that true motion is motion relative to a temporally enduring, rigid, 3 - dimensional euclidean space, which he dubbed ‘ absolute space ’. of course, descartes also defined motion as relative to an enduring 3 - dimensional euclidean space ; the difference is that descartes space was divided into parts ( his space was identical with a plenum of corpuscles ) in motion, not a rigid structure in which ( mobile ) material bodies are embedded. so according to newton, the rate of true rotation of the bucket ( and water ) is the rate at which it rotates relative to absolute space. or put another way, newton effectively defines the complete predicate x moves - absolutely as x moves - relative - to absolute space ; both newton and descartes offer the competing complete predicates as analyses of x moves - truly. newton ' s proposal for understanding motion solves the problems that he posed for descartes, and provides an interpretation of the concepts of constant motion and acceleration that appear in his laws of motion. however, it suffers from two notable interpretational problems, both of which were pressed forcefully by leibniz ( in the leibniz - clarke correspondence, 1715 – 1716 ) — which is not to say that leibniz himself offered a superior account of motion ( see below ). ( of course, there are other features of newton ' s proposal that turned out to be empirically inadequate, and are rejected by relativity : newton ' s account violates the relativity of simultaneity and postulates a non - dynamical spacetime structure. ) first, according to this account, absolute velocity is a well - defined


hand, presumably it is supposed to be part of the physical, not mental, realm. in de gravitatione, newton rejected both the standard philosophical categories of substance and attribute as suitable characterizations. absolute space is not a substance for it lacks causal powers and does not have a fully independent existence, and yet not an attribute since it would exist even in a vacuum, which by definition is a place where there are no bodies in which it might inhere. newton proposes that space is what we might call a ‘ pseudo - substance ’, more like a substance than property, yet not quite a substance. ( note that samuel clarke, in his correspondence with leibniz, which newton had some role in composing, advocates the property view, and note further that when leibniz objects because of the vacuum problem, clarke suggests that there might be non - material beings in the vacuum in which space might inhere. ) in fact, newton accepted the principle that everything that exists, exists somewhere — i. e., in absolute space. thus he viewed absolute space as a necessary consequence of the existence of anything, and of god ' s existence in particular — hence space ' s ontological dependence. leibniz was presumably unaware of the unpublished de gravitatione in which these particular ideas were developed, but as we shall see, his later works are characterized by a robust rejection of any notion of space as a real thing rather than an ideal, purely mental entity. this is a view that attracts even fewer contemporary adherents, but there is something deeply peculiar about a non - material but physical entity, a worry that has influenced many philosophical opponents of absolute space. after the development of relativity ( which we will take up below ), and its interpretation as a spacetime theory, it was realized that the notion of spacetime had applicability to a range of theories of mechanics, classical as well as relativistic. in particular, there is a spacetime geometry — ‘ galilean ’ or ‘ neo - newtonian ’ spacetime — for newtonian mechanics that solves the problem of absolute velocity ; an idea exploited by a number of philosophers from the late 1960s ( e. g., earman 1970, friedman 1983, sklar 1974 and stein 1968 ). for details the reader is referred to the entry on spacetime : inertial frames, but the general idea is that although a spatial distance is well - defined between any two simultaneous points of this spacetime, only the temporal interval is well - defined between non


the reader is referred to the entry on spacetime : inertial frames, but the general idea is that although a spatial distance is well - defined between any two simultaneous points of this spacetime, only the temporal interval is well - defined between non - simultaneous points. thus things are rather unlike newton ' s absolute space, whose points persist through time and maintain their distances ; in absolute space the distance between p - now and q - then ( where p and q are points ) is just the distance between p - now and q - now. however, galilean spacetime has an ‘ affine connection ’ which effectively specifies for every point of every continuous curve, the rate at which the curve is changing from straightness at that point ; for instance, the straight lines are picked out as those curves whose rate of change from straightness is zero at every point. ( another way of thinking about this space is as possessing — in addition to a distance between any two simultaneous points and a temporal interval between any points — a three - place relation of colinearity, satisfied by three points just in case they lie on a straight line. ) since the trajectories of bodies are curves in spacetime the affine connection determines the rate of change from straightness at every point of every possible trajectory. the straight trajectories thus defined can be interpreted as the trajectories of bodies moving inertially, and the rate of change from straightness of any trajectory can be interpreted as the acceleration of a body following that trajectory. that is, newton ' s second law can be given a geometric formulation as ‘ the rate of change from straightness of a body ' s trajectory is equal to the forces acting on the body divided by its mass ’. the significance of this geometry is that while acceleration is well - defined, velocity is not — in accord with empirically determinability of acceleration but not velocity according to newtonian mechanics. ( a simple analogy helps see how such a thing is possible : betweenness but not ‘ up ’ is a well - defined concept in euclidean space. ) thus galilean spacetime gives a very nice interpretation of the choice that nature makes when it decides that the laws of mechanics should be formulated in terms of accelerations not velocities ( as aristotle and descartes proposed ). put another way, we can define the complete predicate x accelerates as trajectory ( x ) has - non - zero - rate - of - change - from - straightness, where trajectory maps bodies onto


as aristotle and descartes proposed ). put another way, we can define the complete predicate x accelerates as trajectory ( x ) has - non - zero - rate - of - change - from - straightness, where trajectory maps bodies onto their trajectories in galilean spacetime. and this predicate, defined this way, applies to the water in the bucket if and only if it is rotating, according to newtonian mechanics formulated in terms of the geometry of galilean spacetime ; it is the mechanically relevant sense of the word in this theory. but all of this formulation and definition has been given in terms of the geometry of spacetime, not relations between bodies ; acceleration is ‘ absolute ’ in the sense that there is a preferred ( true ) sense of acceleration in mechanics and which is not defined in terms of the motions of bodies relative to one another. ( note that this sense of ‘ absolute ’ is broader than that of motion relative to absolute space, which we defined earlier. in the remainder of this article we will use it in the broader sense. the reader should be aware that the term is used in many ways in the literature, and such equivocation often leads to massive misunderstandings. ) thus if any of this analysis of motion is taken literally then one arrives at a position regarding the ontology of spacetime rather like that of newton ' s regarding space : it is some kind of ‘ substantial ’ ( or maybe pseudo - substantial ) thing with the geometry of galilean spacetime, just as absolute space possessed euclidean geometry. this view regarding the ontology of spacetime is usually called ‘ substantivalism ’ ( sklar, 1974 ). the galilean substantivalist usually sees himself as adopting a more sophisticated geometry than newton but sharing his substantivalism ( though there is room for debate on newton ' s exact ontological views, see disalle, 2002 ). the advantage of the more sophisticated geometry is that although it allows the absolute sense of acceleration apparently required by newtonian mechanics to be defined, it does not allow one to define a similar absolute speed or velocity — x accelerates can be defined as a complete predicate in terms of the geometry of galilean spacetime but not x moves in general — and so the first of leibniz ' s problem is resolved. of course we see that the solution depends on a crucial shift from speed and velocity to acceleration as the relevant senses of ‘ motion ’ : from the rate of change of


in general — and so the first of leibniz ' s problem is resolved. of course we see that the solution depends on a crucial shift from speed and velocity to acceleration as the relevant senses of ‘ motion ’ : from the rate of change of position to the rate of rate of change. while this proposal solves the first kind of problem posed by leibniz, it seems just as vulnerable to the second. while it is true that it involves the rejection of absolute space as newton conceived it, and with it the need to explicate the nature of an enduring space, the postulation of galilean spacetime poses the parallel question of the nature of spacetime. again, it is a physical but non - material something, the points of which may be coincident with material bodies. what kind of thing is it? could we do without it? as we shall see below, some contemporary philosophers believe so. there is a ‘ folk - reading ’ of leibniz that one finds either explicitly or implicitly in the philosophy of physics literature which takes account of only some of his remarks on space and motion. the reading underlies vast swathes of the literature : for instance, the quantities captured by earman ' s ( 1999 ) ‘ leibnizian spacetime ’, do not do justice to leibniz ' s view of motion ( as earman acknowledges ). but it is perhaps most obvious in introductory texts ( e. g., ray 1991, huggett 2000 to mention a couple ). according to this view, the only quantities of motion are relative quantities, relative velocity, acceleration and so on, and all relative motions are equal, so there is no true sense of motion. however, leibniz is explicit that other quantities are also ‘ real ’, and his mechanics implicitly — but obviously — depends on yet others. the length of this section is a measure, not so much the importance of leibniz ' s actual views, but the importance of showing what the prevalent folk view leaves out regarding leibniz ' s views on the metaphysics of motion and interpretation of mechanics. that said, we shall also see that no one has yet discovered a fully satisfactory way of reconciling the numerous conflicting things that leibniz says about motion. some of these tensions can be put down simply to his changing his mind ( see cover and hartz 1988 for an explication of how leibniz ' s views on space developed ). however, we will concentrate on the fairly short period in


. some of these tensions can be put down simply to his changing his mind ( see cover and hartz 1988 for an explication of how leibniz ' s views on space developed ). however, we will concentrate on the fairly short period in the mid 1680 - 90s during which leibniz developed his theory of mechanics, and was most concerned with their interpretation. we will supplement this discussion with the important remarks that he made in his correspondence with samuel clarke around 30 years later ( 1715 – 1716 ) ; this discussion is broadly in line with the earlier period, and the intervening period is one in which he turned to other matters, rather than one in which his views on space were dramatically evolving. arguably, leibniz ' s views concerning space and motion do not have a completely linear logic, starting from some logically sufficient basic premises, but instead form a collection of mutually supporting doctrines if one starts questioning why leibniz held certain views — concerning the ideality of space, for instance — one is apt to be led in a circle. still, exposition requires starting somewhere, and leibniz ' s argument for the ideality of space in the correspondence with clarke is a good place to begin. but bear in mind the caveats made here — this argument was made later than a number of other relevant writings, and its logical relation to leibniz ' s views on motion is complex. leibniz ( lv. 47 — this notation means leibniz ' s fifth letter, section 47, and so on ) says that ( i ) a body comes to have the ‘ same place ’ as another once did, when it comes to stand in the same relations to bodies we ‘ suppose ’ to be unchanged ( more on this later ). ( ii ) that we can define ‘ a place ’ to be that which any such two bodies have in common ( here he claims an analogy with the euclidean / eudoxan definition of a rational number in terms of an identity relation between ratios ). and finally that ( iii ) space is all such places taken together. however, he also holds that properties are particular, incapable of being instantiated by more than one individual, even at different times ; hence it is impossible for the two bodies to be in literally the same relations to the unchanged bodies. thus the thing that we take to be the same for the two bodies — the place — is something added by our minds to the situation, and only ideal. as a result, space, which is after all constructed from these ideal places,


bodies. thus the thing that we take to be the same for the two bodies — the place — is something added by our minds to the situation, and only ideal. as a result, space, which is after all constructed from these ideal places, is itself ideal : ‘ a certain order, wherein the mind conceives the application of relations ’. it ' s worth pausing briefly to contrast this view of space with those of descartes and of newton. both descartes and newton claim that space is a real, mind - independent entity ; for descartes it is matter, and for newton a ‘ pseudo - substance ’, distinct from matter. and of course for both, these views are intimately tied up with their accounts of motion. leibniz simply denies the mind - independent reality of space, and this too is bound up with his views concerning motion. ( note that fundamentally, in the metaphysics of monads that leibniz was developing contemporaneously with his mechanics, everything is in the mind of the monads ; but the point that leibniz is making here is that even within the world that is logically constructed from the contents of the minds of monads, space is ideal. ) so far ( apart from that remark about ‘ unchanged ’ bodies ) we have not seen leibniz introduce anything more than relations of distance between bodies, which is certainly consistent with the folk view of his philosophy. however, leibniz sought to provide a foundation for the cartesian / mechanical philosophy in terms of the aristotelian / scholastic metaphysics of substantial forms ( here we discuss the views laid out in sections 17 - 22 of the 1686 discourse on metaphysics and the 1695 specimen of dynamics, both in garber and ariew 1989 ). in particular, he identifies primary matter with what he calls its ‘ primitive passive force ’ of resistance to changes in motion and to penetration, and the substantial form of a body with its ‘ primitive active force ’. it is important to realize that these forces are not mere properties of matter, but actually constitute it in some sense, and further that they are not themselves quantifiable. however because of the collisions of bodies with one another, these forces ‘ suffer limitation ’, and ‘ derivative ’ passive and active forces result. ( there ' s a real puzzle here. collision presupposes space, but primitive forces constitute matter prior to any spatial concepts — the primitive active and passive forces ground motion and extension respectively. see garber and rauzy


active forces result. ( there ' s a real puzzle here. collision presupposes space, but primitive forces constitute matter prior to any spatial concepts — the primitive active and passive forces ground motion and extension respectively. see garber and rauzy, 2004. ) derivative passive force shows up in the different degrees of resistance to change of different kinds of matter ( of ‘ secondary matter ’ in scholastic terms ), and apparently is measurable. derivative active force however, is considerably more problematic for leibniz. on the one hand, it is fundamental to his account of motion and theory of mechanics — motion fundamentally is possession of force. but on the other hand, leibniz endorses the mechanical philosophy, which precisely sought to abolish aristotelian substantial form, which is what force represents. leibniz ' s goal was to reconcile the two philosophies, by providing an aristotelian metaphysical foundation for modern mechanical science ; as we shall see, it is ultimately an open question exactly how leibniz intended to deal with the inherent tensions in such a view. the texts are sufficiently ambiguous to permit dissent, but arguably leibniz intends that one manifestation of derivative active force is what he calls vis viva — ‘ living force ’. leibniz had a famous argument with the cartesians over the correct definition of this quantity. descartes defined it as size times speed — effectively as the magnitude of the momentum of a body. leibniz gave a brilliant argument ( repeated in a number of places, for instance section 17 of the discourse on metaphysics ) that it was size times speed2 — so ( proportional to ) kinetic energy. if the proposed identification is correct then kinetic energy quantifies derivative active force according to leibniz ; or looked at the other way, the quantity of virtus ( another term used by leibniz for active force ) associated with a body determines its kinetic energy and hence its speed. as far as the authors know, leibniz never explicitly says anything conclusive about the relativity of virtus, but it is certainly consistent to read him ( as roberts 2003 does ) to claim that there is a unique quantity of virtus and hence ‘ true ’ ( as we have been using the term ) speed associated with each body. at the very least, leibniz does say that there is a real difference between possession and non - possession of vis viva ( e. g., in section 18 of the discourse ) and it is a small step


speed associated with each body. at the very least, leibniz does say that there is a real difference between possession and non - possession of vis viva ( e. g., in section 18 of the discourse ) and it is a small step from there to true, privileged speed. indeed, for leibniz, mere change of relative position is not ‘ entirely real ’ ( as we saw for instance in the correspondence ) and only when it has vis viva as its immediate cause is there some reality to it. ( however, just to muddy the waters, leibniz also claims that as a matter of fact, no body ever has zero force, which on the reading proposed means no body is ever at rest, which would be surprising given all the collisions bodies undergo. ) an alternative interpretation to the one suggested here might say that leibniz intends that while there is a difference between motion / virtus and no motion / virtus, there is somehow no difference between any strictly positive values of those quantities. it is important to emphasize two points about the preceding account of motion in leibniz ' s philosophy. first, motion in the everyday sense — motion relative to something else — is not really real. fundamentally motion is possession of virtus, something that is ultimately non - spatial ( modulo its interpretation as primitive force limited by collision ). if this reading is right — and something along these lines seems necessary if we aren ' t simply to ignore important statements by leibniz on motion — then leibniz is offering an interpretation of motion that is radically different from the obvious understanding. one might even say that for leibniz motion is not movement at all! ( we will leave to one side the question of whether his account is ultimately coherent. ) the second point is that however we should understand leibniz, the folk reading simply does not and cannot take account of his clearly and repeatedly stated view that what is real in motion is force not relative motion, for the folk reading allows leibniz only relative motion ( and of course additionally, motion in the sense of force is a variety of true motion, again contrary to the folk reading ). however, from what has been said so far it is still possible that the folk reading is accurate when it comes to leibniz ' s views on the phenomena of motion, the subject of his theory of mechanics. the case for the folk reading is in fact supported by leibniz ' s resolution of the tension that we mentioned earlier, between the fundamental role of force


an order of successions ” ( liii. 4 ), which is naturally taken to mean that space is at base nothing but the distance and temporal relations between bodies. ( though even this passage has its subtleties, because of the ideality of space discussed above, and because in leibniz ' s conception space determines what sets of relations are possible. ) and if relative distances and times exhaust the spatiotemporal in this way, then shouldn ' t all quantities of motion be defined in terms of those relations? we have seen two ways in which this would be the wrong conclusion to draw : force seems to involve a notion of speed that is not identified with any relative speed, and ( unless the equivalence of hypotheses is after all a principle of general relativity ) the laws pick out a standard of constant motion that need not be any constant relative motion. of course, it is hard to reconcile these quantities with the view of space and time that leibniz proposes — what is speed in size times speed2 or constant speed if not speed relative to some body or to absolute space? given leibniz ' s view that space is literally ideal ( and indeed that even relative motion is not ‘ entirely real ’ ) perhaps the best answer is that he took force and hence motion in its real sense not to be determined by motion in a relative sense at all, but to be primitive monadic quantities. that is, he took x moves to be a complete predicate, but he believed that it could be fully analyzed in terms of strictly monadic predicates : x moves iff x possesses - non - zero - derivative - active - force. and this reading explains just what leibniz took us to be supposing when we ‘ supposed certain bodies to be unchanged ’ in the construction of the idea of space : that they had no force, nothing causing, or making real any motion. it ' s again helpful to compare leibniz with descartes and newton, this time regarding motion. commentators often express frustration at leibniz ' s response to newton ' s arguments for absolute space : “ i find nothing … in the scholium that proves or can prove the reality of space in itself. however, i grant that there is a difference between an absolute true motion of a body and a mere relative change … ” ( lv. 53 ). not only does leibniz apparently fail to take the argument seriously, he then goes on to concede the step in the argument that seems to require absolute space


the kind of folk - reading of newton that underlies much of the contemporary literature replaces mach ' s interpretation with a more charitable one. according to this reading, newton ' s point is that his mechanics — unlike descartes ' — could explain why the surface of the rotating water is curved, that his explanation involves a privileged sense of rotation, and that absent an alternative hypothesis about its relative nature, we should accept absolute space. but our discussion of newton ' s argument showed that it simply does not have an ‘ abductive ’, ‘ best explanation ’ form, but shows deductively, from cartesian premises, that rotation is neither proper nor ordinary motion. that is not to say that newton had no understanding of how such effects would be explained in his mechanics. for instance, in corollaries 5 and 6 to the definitions of the principles he states in general terms the conditions under which different states of motion are not — and so by implication are — discernible according to his laws of mechanics. nor is it to say that newton ' s contemporaries weren ' t seriously concerned with explaining inertial effects. leibniz, for instance, analyzed a rotating body ( in the specimen ). in short, parts of a rotating system collide with the surrounding matter and are continuously deflected, into a series of linear motions that form a curved path. but the system as leibniz envisions it — comprised of a plenum of elastic particles of matter — is far too complex for him to offer any quantitative model based on this qualitative picture. ( in the context of the proposed ‘ abductive ’ reading of newton, note that this point is telling against a rejection of intrinsic rigidity or forces acting at a distance, not narrow relationism ; it is the complexity of collisions in a plenum that stymies analysis. and since leibniz ' s collision theory requires a standard of inertial motion, even if he had explained inertial effects, he would not have thereby shown that all motions are relative, much less that all are equal. ) although the argument is then not newton ' s, it is still an important response to the kind of relationism proposed by the folk - leibniz, especially when it is extended by bringing in a further example from newton ' s scholium. newton considered a pair of identical spheres, connected by a cord, too far from any bodies to observe any relative motions ; he pointed out that their rate and direction of rotation could still be experimental


in a further example from newton ' s scholium. newton considered a pair of identical spheres, connected by a cord, too far from any bodies to observe any relative motions ; he pointed out that their rate and direction of rotation could still be experimentally determined by measuring the tension in the rod, and by pushing on opposite faces of the two globes to see whether the tension increased or decreased. he intended this simple example to demonstrate that the project he intended in the principia, of determining the absolute accelerations and hence gravitational forces on the planets from their relative motions, was possible. however, if we further specify that the spheres and cord are rigid and that they are the only things in their universe, then the example can be used to point out that there are infinitely many different rates of rotation all of which agree on the relations between bodies. since there are no differences in the relations between bodies in the different situations, it follows that the observable differences between the states of rotation cannot be explained in terms of the relations between bodies. therefore, a theory of the kind attributed to the folk ' s leibniz cannot explain all the phenomena of newtonian mechanics, and again we can argue abductively for absolute space. ( of course, the argument works by showing that, granted the different states of rotation, there are states of rotation that cannot merely be relative rotations of any kind ; for the differences cannot be traced to any relational differences. that is, granted the assumptions of the argument, rotation is not true relative motion of any kind. ) this argument ( neither the premises nor conclusion ) is not newton ' s, and must not be taken as a historically accurate reading, however, that is not to say that the argument is fallacious, and indeed many have found it attractive, particularly as a defense not of newton ' s absolute space, but of galilean spacetime. that is, newtonian mechanics with galilean spacetime can explain the phenomena associated with rotation, while theories of the kind proposed by mach cannot explain the differences between situations allowed by newtonian mechanics, but these explanations rely on the geometric structure of galilean spacetime — particularly its connection, to interpret acceleration. and thus — the argument goes — those explanations commit us to the reality of spacetime — a manifold of points — whose properties include the appropriate geometric ones. this final doctrine, of the reality of spacetime with its component points or regions, distinct from matter, with geometric properties, is what we earlier identified as ‘ substantiv


deny any relations between bodies and spacetime itself. like the actual leibniz, they allow absolute quantities of motion, but claim that space and time themselves are nothing but the relations between bodies. of course, such views raise the question of how a motion can be not relative to anything at all, and how we are to understand the privileging of frames ; huggett ( 2006 ) contains a proposal for addressing these problems. ( note that sklar and van fraassen are committed to the idea that in some sense newton ' s laws are capable of explaining all the phenomena without recourse to spacetime geometry ; that the connection and the metrical properties are explanatorily redundant. a similar view is defended in the context of relativity in brown 2005. ) between the time of newton and leibniz and the 20th century, newton ' s mechanics and gravitation theory reigned essentially unchallenged, and with that long period of dominance, absolute space came to be widely accepted. at least, no natural philosopher or physicist offered a serious challenge to newton ' s absolute space, in the sense of offering a rival theory that dispenses with it. but like the action at a distance in newtonian gravity, absolute space continued to provoke metaphysical unease. seeking a replacement for the unobservable newtonian space, neumann ( 1870 ) and lange ( 1885 ) developed more concrete definitions of the reference frames in which newton ' s laws hold. in these and a few other works, the concept of the set of inertial frames was first clearly expressed, though it was implicit in both remarks and procedures to be found in the principia. ( see the entries on space and time : inertial frames and newton ' s views on space, time, and motion ) the most sustained, comprehensive, and influential attack on absolute space was made by ernst mach in his science of mechanics ( 1883 ). in a lengthy discussion of newton ' s scholium on absolute space, mach accuses newton of violating his own methodological precepts by going well beyond what the observational facts teach us concerning motion and acceleration. mach at least partly misinterpreted newton ' s aims in the scholium, and inaugurated a reading of the bucket argument ( and by extension the globes argument ) that has largely persisted in the literature since. mach viewed the argument as directed against a ‘ strict ’ or ‘ general - relativity ’ form of relationism, and as an attempt to establish the existence of absolute


( and by extension the globes argument ) that has largely persisted in the literature since. mach viewed the argument as directed against a ‘ strict ’ or ‘ general - relativity ’ form of relationism, and as an attempt to establish the existence of absolute space. mach points out the obvious gap in the argument when so construed : the experiment only establishes that acceleration ( rotation ) of the water with respect to the earth, or the frame of the fixed stars, produces the tendency to recede from the center ; it does not prove that a strict relationist theory cannot account for the bucket phenomena, much less the existence of absolute space. ( the reader will recall that newton ' s actual aim was simply to show that descartes ' two kinds of motion are not adequate to accounting for rotational phenomena. ) although mach does not mention the globes thought experiment specifically, it is easy to read an implicit response to it in the things he does say : nobody is competent to say what would happen, or what would be possible, in a universe devoid of matter other than two globes. so neither the bucket nor the globes can establish the existence of absolute space. both in mach ' s interpretations of newton ' s arguments and in his replies, one can already see two anti - absolute space viewpoints emerge, though mach himself never fully kept them apart. the first strain, which we may call ‘ mach - lite ’, criticizes newton ' s postulation of absolute space as a metaphysical leap that is neither justified by actual experiments, nor methodologically sound. the remedy offered by mach - lite is simple : we should retain newton ' s mechanics and use it just as we already do, but eliminate the unnecessary posit of absolute space. in its place we need only substitute the frame of the fixed stars, as is the practice in astronomy in any case. if we find the incorporation of a reference to contingent circumstances ( the existence of a single reference frame in which the stars are more or less stationary ) in the fundamental laws of nature problematic ( which mach need not, given his official positivist account of scientific laws ), then mach suggests that we replace the 1st law with an empirically equivalent mathematical rival : mach ' s equation ( 1960, 287 ) the sums in this equation are to be taken over all massive bodies in the universe. since the top sum is weighted by distance, distant masses count much more than near ones. in a world with a ( reasonably ) static distribution of heavy distant bodies, such as we appear to live


to be taken over all massive bodies in the universe. since the top sum is weighted by distance, distant masses count much more than near ones. in a world with a ( reasonably ) static distribution of heavy distant bodies, such as we appear to live in, the equation entails local conservation of linear momentum in ‘ inertial ’ frames. the upshot of this equation is that the frame of the fixed stars plays exactly the role of absolute space in the statement of the 1st law. ( notice that this equation, unlike newton ' s first law, is not vectorial. ) this proposal does not, by itself, offer an alternative to newtonian mechanics, and as mach himself pointed out, the law is not well - behaved in an infinite universe filled with stars ; but the same can perhaps be said of newton ' s law of gravitation ( see malament 1995, and norton 1993 ). but mach did not offer this equation as a proposed law valid in any circumstances ; he avers, “ it is impossible to say whether the new expression would still represent the true condition of things if the stars were to perform rapid movements among one another. ” ( p. 289 ) it is not clear whether mach offered this revised first law as a first step toward a theory that would replace newton ' s mechanics, deriving inertial effects from only relative motions, as leibniz desired. but many other remarks made by mach in his chapter criticizing absolute space point in this direction, and they have given birth to the mach - heavy view, later to be christened “ mach ' s principle ” by albert einstein. the mach - heavy viewpoint calls for a new mechanics that invokes only relative distances and ( perhaps ) their 1st and 2nd time derivatives, and thus ‘ generally relativistic ’ in the sense sometimes read into leibniz ' s remarks about motion. mach wished to eliminate absolute time from physics too, so he would have wanted a proper relationist reduction of these derivatives also. the barbour - bertotti theories, discussed below, provide this. mach - heavy apparently involves the prediction of novel effects due to ‘ merely ’ relative accelerations. mach hints at such effects in his criticism of newton ' s bucket : newton ' s experiment with the rotating vessel of water simply informs us that the relative rotation of the water with respect to the sides of the vessel produces no noticeable centrifugal forces, but that such forces are produced by its relative rotation with respect to the mass of the earth and the other celestial bodies. no


us that the relative rotation of the water with respect to the sides of the vessel produces no noticeable centrifugal forces, but that such forces are produced by its relative rotation with respect to the mass of the earth and the other celestial bodies. no one is competent to say how the experiment would turn out if the sides of the vessel [ were ] increased until they were ultimately several leagues thick. ( 1883, 284. ) the suggestion here seems to be that the relative rotation in stage ( i ) of the experiment might immediately generate an outward force ( before any rotation is communicated to the water ), if the sides of the bucket were massive enough. more generally, mach - heavy involves the view that all inertial effects should be derived from the motions of the body in question relative to all other massive bodies in the universe. the water in newton ' s bucket feels an outward pull due ( mainly ) to the relative rotation of all the fixed stars around it. mach - heavy is a speculation that an effect something like electromagnetic induction should be built into gravity theory. ( such an effect does exist according to the general theory of relativity, and is called ‘ gravitomagnetic induction ’. the recently finished gravity probe b mission was designed to measure the gravitomagnetic induction effect due to the earth ' s rotation. ) its specific form must fall off with distance much more slowly than 1 / r2, if it is to be empirically similar to newtonian physics ; but it will certainly predict experimentally testable novel behaviors. a theory that satisfies all the goals of mach - heavy would appear to be ideal for the vindication of strict relationism and the elimination of absolute quantities of motion from mechanics. direct assault on the problem of satisfying mach - heavy in a classical framework proved unsuccessful, despite the efforts of others besides mach ( e. g., friedlander 1896, fopl 1904, reissner 1914, 1915 ), until the work of barbour and bertotti in the 1970s and 80s. ( between the late 19th century and the 1970s, there was of course one extremely important attempt to satisfy mach - heavy : the work of einstein that led to the general theory of relativity. since einstein ' s efforts took place in a non - classical ( lorentz / einstein / minkowski ) spacetime setting, we discuss them in the next section. ) rather than formulating a revised law of gravity / inertia using relative quantities, barbour and bertotti attacked the problem using the framework of lagrangian