On the quantitative effects

Transcription

1 International Journal of Modern Physis and Appliation 4; (): 8-4 Published online September, 4 ( On the quantitatie effets Chang-Wei Hu Beijing Relatiity Theory Researh Federation Shanghai Branh China mail address huhangwei@sina.n Citation Chang-Wei Hu. On the Quantitatie ffets. International Journal of Modern Physis and Appliation. Vol., No., 4, pp Keywords The Theory of Relatiity, Absolute Spae-Time Theory, Quantitatie ffets, Analyti Method of ffet nergy, Quantum ffets Reeied: August 5, 4 Reised: September, 4 Aepted: September, 4 Abstrat The physial phenomena what modern physis desribes seem all ery peuliar, whih results from the quantitatie effets deiating from the absolute spae-time theory. The absolute spae-time theory, whih desribes the world with inariable spae-time standards, is a fundamental spae-time theory; while atual spae-time standards an ary with enironment, and thus, the atual measuring data are always to deiate from the absolute spae-time theory and the quantitatie effets our. A light is the most exat tool measuring spae-time in the modern physis, whose spae-time standards hae a ariability and leads up to the quantitatie effets suh as relatiisti and quantum effets. The relatiisti equations of the quantitatie effets and the analyti method of effet energy are proposed, they an be used to desribe relatiisti phenomena simply.. Introdution In physial world, it is onsidered generally that a mathematial model in aord with experimental data reflets the truth of thing. Atually it must neessarily be so. The meaning of many things are beoming more and more lear along with the deelopment of siene, but the meaning of some things een are beoming more and more fuzzy, the time and spae are just suh. The spae, time and mass are the most foundational physial quantity in lassial physis, where the three dimensional spae is the stage, the one dimensional time is the proess and the objets (the matter with mass) are the performers, they are interrelated as well as independent eah other. Suh a desription aords with human sensation. The theory of relatiity hanged the spae-time theory of lassial physis, it beliees that the spae and time an ary with eloity or graitational potential, and the spae-time may be bent, whih gie us a feel that look at oneself in the distorting mirror. The onepts of spae and time een are blurred by the statistial interpretation of the wae funtion, the unertainty relation and so on in the quantum theory, where the physial quantities inluding spae and time all are replaed by the unpreditable operators. The spae een is desribed into a high dimensional world in the theories of supersymmetry and extra dimension et[][]., in whih there are inisible many dimensional spaes exept the isible three dimensional spaes. Consequently, een some onsider that the onept of spae and time are the phantasms, say, they apply only to the marosopi as haing statistial essene as temperature[]. But spae and time exist eerywhere, an we leae the spae-time in reality? Why are the spae and time with uniersality beoming more and more elusie along with the deelopment of physis? Some would say: the world is ompliated originally, human understanding is always from the simple to the ompliated. It is right only half of this word, in fat, humanity an turn a theory from the ompliated into the simple on a new theoretial highness. I hae pointed out[4] that the absolute and relatiisti spae-time theories are two different spae-time theories in nature, and

2 9 Chang-Wei Hu: On the Quantitatie ffets proposed the idea of the quantitatie effets, whih an simplify the understanding to the modern physis to some extent. The absolute spae-time theory, whih desribes the world with an inariable spae-time standards, an be thought as the most foundational spae-time theory. Howeer, the atual standard tools of length and time, suh as rulers, loks and light, an ary with the enironment due to temperature, eloity and graitational potential. The physis is a experimental siene, its theoretial data should aord with the experimental data. Thus, there are always ertain differenes between the physial quantitatie relation and the absolute spae-time theory. The effets aused by this differenes are alled quantitatie effets, whih are the insignifiant in the ondition of low eloity or the marosopi, otherwise they would beome obious. Both of the relatiisti and quantum effets are the quantitatie effets, that is to say, they are the results that the atual quantitatie relations deiate from the absolute spae-time theory. Then, what the modern physis desribes are the quantitatie effets on the basis of lassial physis. It is the quantitatie effets that twist the physial desription.. Two Different Spae-Time Theories in Nature The quantitatie effets relate to spae-time, let us state begin with the Newtonian spae-time theory. Newtonian spae-time theory is alled the absolute spae-time theory. Newton said[5]: I do not define time, spae, plae and motion, as being well known to all. Only I must obsere, that the ulgar oneie those quantities under no other notions but from the relation they bear to sensible objets. And thene arise ertain prejudies, for the remoing of whih, it will be onenient to distinguish them into absolute and relatie, true and apparent, mathematial and ommon. Absolute, true, and mathematial time, of itself, and from its own nature flows equably without regard to anything external, and by another name is alled duration; relatie, apparent, and ommon time, is some sensible and external (whether aurate or unequable) measure of duration by the means of motion, whih is ommonly used instead of true time ; suh as an hour, a day, a month, a year. Absolute spae, in its own nature, without regard to anything external, remains always similar and immoable. Relatie spae is some moable dimension or measure of the absolute spaes. For the aboe saying, there are absolute spae-time as well as the relatie spae-time in the absolute spae-time theory. Measuring is a ourse of omparison between measuring tool and measured body, and the absolute spae and time an not be measured diretly beause they hae nothing to do with matter and its motion. Therefore physial spae-time are all the measurable relatie spae-time, and we know the absolute spae-time through the relatie spae-time. Then, what is the most foundational harateristi of the absolute spae-time theory? It is the inariability of spae-time standards, whih leads to the eah independene of spae and time, and both of them hae nothing to do with material enironment. An intuition of indiidual person or organization is unreliable generally, and it is probable that the human total intuition is just the truth. The as being well known to all is like an axiom. The absolute spae-time theory, whih is an axiom in lassial physis, an be regarded as the most foundational spae-time theory. Owing to the inariability of spae-time standards, eerywhere we an establish a rigid three dimensional oordinate system and one dimension time axis, whih are just a mathematial expression of a relatie spae-time in the absolute spae-time theory. The mathematial expression of absolute spae-time theory is the Galilean transformation where the interals of spae and time are the onstant quantity, namely the inariability of spae and time standards. The general measuring-rods and loks an ary with the temperature, whih an not be belieed that the spae and time are hanging beause people may proe that these hanges are only the hanges of the measuring-rods and loks themseles with more aurate spae-time measuring tools. The sientists would take the hanges of spae-time standards as the hanges of spae-time itself if the most exat spae-time measuring tool an hange. The light eloity is the known most quik eloity spreading information. Now the most aurate standards of length and time are defined by light. For example, a metre, the SI unit of length, being the length of the path traelled by light in auum during a time interal of /(99,79,458 8 ) seond[6], where the length of the path traeled by light in auum during a time interal of one seond is always meters whether it is fast or slow, the light speed beome an inariable definitional speed. The modern physis is just established on the basis of suh a spae-time standard, whih means what the modern physis desribes are the quantitatie effets with light as the measure of spae-time. We an imagine there is a standing wae fixed on a moing body, its wae length would ontrat obsered in the stationary system along with an inrease of the eloity, and it is ontrated into a point when the eloity of this body reah the light eloity. An obserer in the stationary system, he would onsider that the distane traeled by light in a unit time is dereased, or the time beomes slower in moing system than it in the stationary system if the light eloity is inariable. Taking a hange of the spae-time standard as a hange of spae-time itself is a pratiable mathematial model in the modern physis. The desription on the basis of absolute spae-time theory is alled absolute desription; and the desription on the basis of experimental data is alled quantitatie desription.

3 International Journal of Modern Physis and Appliation 4; (): The quantitatie effets are aused by the differene between these two desriptions. dt dt dt = = + φ / / GM r (4). The Quantitatie ffets of Relatiity The theory of relatiity is a theory of the quantitatie desription and the relatiisti effets are the quantitatie effets. The theory of relatiity, in fat, does not depart from the absolute spae-time theory beause it explains how the spae-time standard hanges with the help of the proper quantities, and aording to the explanation that a rigid three dimensional oordinate system and one dimensional time axis are just a mathematial expression of a relatie spae-time in the absolute spae-time theory, the proper quantities in the relatiity are the quantities of absolute desription. The oordinate system and time axis in the relatiity are nonrigid, and an ary with eloity or graitational potential. The speial theory of relatiity shows that in a inertia frame of referene, the relationships between unit length dr or unit time dt and eloity are as in qs. () and (): dt = dt / dr / dr, () =, () Where dr and dt are the proper unit length and time, respetiely. They do not ary with eloity and are used to measure the hange of spae-time standards on an objets in relatie motion with any eloity. Thus, they are the unit length and time in the absolute desription on this inertia frame of referene, and qs.() and () are the equations of quantitatie effets in the speial theory of relatiity. Similarly, the general theory of relatiity states that the unit length dr or unit time dt an ary with graitational potential. A simple expression an be obtained with the equialent priniple and onseration of energy: Let an objet whose initial eloity is zero falls freely in an isolated graitational field of a star. When it is a distane r away from the star, its eloity is, and the graitational potential is φ, whih is zero when it is infinitely far away from the star. Then, i.e., m mφ + = φ = () Substituting () into () and () gies dr = + φ / dr = GM / rdr (5) qs. (4) and (5) are idential with the results of the Shwarzshild solution in the general theory of relatiity[7]. The dt and dr in (4) and (5) are the unit length and unit time on the referene frame that is far away from the graitational field. They do not ary with the graitational potential; that is, they are the unit length and unit time in the absolute desription. qs. (4) and (5)are the equations of quantitatie effets in the general theory of relatiity. The equations of quantitatie effets an be used to explain relatiisti phenomena simply. Two examples are gien below. The experiment on the delay of radar eho showed that the eloity of light beomes slower in a graitational field, whih an be soled simply using qs. (4) and (5): the relation between the eloities of the quantitatie desription ( dr / dt ) and the absolute desription ( dr / dt ) is + φ / dr dr dt = = + φ dr dt / ( / ) / dt / + φ / Let the eloity of light without the graitational field be. Then, the eloity of light with unit of dr / dt in the graitational field is GM ( φ / ) ( ) r = + = ( / ) (6) dr dt (7) q. (7) is idential to the result of the general theory of relatiity[8]. Obiously, the onlusion that the eloity of light beomes slower in a graitational field is an absolute desription, whih is the result of measuring the eloity of light oer the whole graitational field with an inariable spae-time standard, say, the spae-time standard on the earth. Quantitatiely, the priniple of the inariability of the eloity of light is still established in the graitational field beause where the standards of spae-time an ary with graitational potential. Using the quantitatie spae-time standard of one point to measure the eloity of light of this point, aording to (6), if the quantitatie unit dr / dt is substituted for the absolute unit dr / dt in (7), then the eloity of light is always onstant. Therefore the inariability of light eloity is a quantitatie effet, and there are ertain omplementarities between absolute and quantitatie desriptions. As for the graitational red shift, it is beause the spae-time standards an ary with graitational potential. A. instein pointed out that the frequeny of light orresponds to the time frequeny of a lok[9]. Aording to (4), it is

4 4 Chang-Wei Hu: On the Quantitatie ffets = GM / r quation (8) shows that the frequeny of light an ary with the graitational potential. If the etor radii of a light beam are r and r suessiely in a graitational field, it an be shown that GM / r = GM / r quation (9) is the formula of the graitational red shift of spetral-line in the Shwarzshild geometry[8]. 4. The Analyti Method of ffet nergy Aording to the mass-energy relation = m, the relatiisti mass-eloity equation m = m an be / turn into energy-eloity equation: = + / Substituting () into () gies ( ) = ( ) = + + φ / φ MG r (8) (9) () () qs. () and () show that the energy of a relatiisti body may be resoled into proper energy of proper motion and effet energy or GM of effet r motion, where the proper energy is the energy in the absolute desription; while the effet energy is a energy aused by quantitatie effets. The effet motion is only a quantitatie effet, whih an not hange the system of proper motion, and yet it an only hange the system s diretion of proper motion. Suh a analyti method is alled analyti method of effet energy, whih is a reognized fashion to quantitatie effet. Is this analyti method effetie? Let us try to alulate the preession of a planet perihelion with it. The system of proper motion of a planet is the ellipse, its effet energy does not hange the form of this ellipse, and only makes whole ellipse rotated slowly, namely the preession. Calulating along the orbit of a planet, the angular displaement between two adjaent perihelia is π + α, where the α is the preession angle. Here the energy of ellipti motion system is the proper energy, and the preession is aused by effet energy, whih rolls ellipse as a whole. The preession energy is a extra kineti energy of angular diretion, and its diretion is idential with the kineti energy of angular diretion of proper motion. Then the preession angle an be deried simple: to derie the ratio of angular diretion kineti energy between preession and proper motion, and thus, applying the analyti method of effet energy, the preession angle an be obtained in proportion when the planet aomplishes a period s ellipti motion. For irular orbit, all of kineti energy are the angular diretion kineti energy, whose alue is half of potential GM energy beause the graitational aeleration a = r =, r whih leads to GM m = m. Therefore angular diretion r kineti energy of a planet is ( is the sum of energy of proper motion). For ellipti orbit, part of kineti energy is the radial diretion kineti energy, whih has nothing to do with angular diretion motion. When the planet lies to an aphelion, its kineti energy is the least ; when the ( a + ) planet lies to a perihelion, its kineti energy is the largest, then the aerage kineti energy of ellipti motion ( a ) is: + = 4 a a + a e ( ), ( e is the eentriity); while the kineti energy of irular motion with radius a is a, whih is e times as muh as the aerage kineti energy of ellipti motion with long axis a. Therefore the angular diretion kineti energy of e proper motion is approximately. Aording to the the analyti method of effet energy, the angular diretion kineti energy of the planet preession is φ them is, while that of proper motion is φ ( e ) e, the ratio of. Therefore when the planet aomplishes a period s ellipti motion ( π ), the angle of preession is π ( φ) 6π GM α = = a ( e ) ( e ) () whih is idential with the formula that is deried by the general theory of relatiity[8], whih shows that the analyti method of effet energy is effetie. 5. Quantum ffet, a Quantitatie ffet in Mirosopi System The quantum mehanis was established on the basis of a series of experiments. Therefore the quantum effet would is a quantitatie effetit. Let us make some analyses from

5 International Journal of Modern Physis and Appliation 4; (): different angles below. Applying the analyti method of effet energy to uniform motion in a straight line, its effet motion an only be a transerse ibration or the spin whose diretion is parallel to the moing diretion beause its proper motion system is a straight line. Is there suh an effet motion? Marosopially it seems not probable, but it is only too true mirosopially beause the mirosopi partiles all possess the wae-partile duality and intrinsi spin, whih may be regarded as the manifestations of quantitatie effets in mirosopi system. Moreoer the Shrodinger equation is a semi-qualitatie, semi-quantitatie and non-relatiisti theory, it an derie the quantization of some physial quantities, but the spin is plaed into the theoretial framework as an additional degree of freedom; while Dira equation, a relatiisti equation of quantum mehanis, inludes automatially the spin quantum number of partiles[], whih indiates further that the quantization of intrinsi spin of a partile is a refletion of the quantitatie effet of the speial theory of relatiity in the mirosopi system The inariability of light eloity is a most basi relatiisti quantitatie effet, whih means that any photon model would hae ertain ommon nature, we assume that one period of a high-frequeny light wae is a photon, and the eletromagneti amplitude of any photon is idential quantitatiely. Attention please, low-frequeny eletromagneti wae s one period is not one photon, whih relates to the mirosopi struture of a physialauum, and it does not be made disussion in this paper. I had pointed out that the light is a seond sound in the superfluid of marosopi physial auum, whose density is homogeneous and isotropi in quantitatie desription[4]. As is known to all, the aerage alue ε of energy density of a wae is ρ A ω ε =, where the ρ is the density of a medium, the A is amplitude and the ω is irular frequeny. In a auum, the ρ and A are the onstant quantitatiely, then the ε is only related to ω, ω. ε On the other hand, A single photon is the plane polarized wae, and the area of a photon is inersely proportional to its frequeny, therefore the energy of a photon is ω, thus, = h ( h is the Plank onstant). 6. Conlusion Physial spae-time is measurable relatie spae-time. The theory of absolute spae-time, whih inludes the relatie spae-time, desribes the world with a inariable spae-time standard,it an be regarded as a foundational spae-time theory; while modern physis desribe physial phenomona with light as the measure of spae-time, whose standards are ariable, and thus, what the modern physis desribes deiate from the absolute spae-time theory in quantity and the quantitatie effets inluding the relatiisti and quantum effets our. The proper quantities in the relatiity are the partiular quantities of absolute desription. There are ertain omplementarities between the absolute and quantitatie desriptions. In the final analysis, the quantitatie effets rusult from the funtion of physial auum: the spae-time standards an ary with the density of physial auum[4]. A. instein belieed that God does not play die. He is right in essene, but he does not know the existene of quantitatie effets. What the quantitatie experiments sustain are the iewpoints of N. Bohr beause quantitatie experiments inlude the results of quantitatie effets. If we found a method of measuring spae-time whih is uninfluened by physial auum, we should hae a new spae-time theory. Objetiely, the spae is three dimensional, and the time is one dimensional. The relatiisti and quantum effets result from the quantitatie effets. As for so alled high dimensional spaes are to take some independent physial parameters as the spaes, whih are only mathematial models and not real spaes, just as the isospin spae is not a real spae and is a mathematial model desribing the harge independene of nulear fore. For aording with the fats, these higher dimensional theories stress that the spaes higher than three dimensions are the inisible due to the ompatifiation or strong bend[]. Moreoer the duality relationships between the theories of ten dimensional superstring and eleen dimensional supergraity onfuse the onept of dimension and show that these higher dimensions are not real dimensions of the spae. The physis does not depart from the mathematis, but a quantitatie relationship is only a presentation. the mathematis an not replae the physis. Referenes [] S. T. Yan, S. Nadis, The Shape of Inner Spae, Brokman In (). [] L. Randail, Warped Passages, Penguin Press (6). [] B. Greene, The Fabri of the Cosmos: Spae, Time and the Texture of Reality, Penguin Press (4). [4] C. W. Hu, Vauum, Spae-Time, Matter and Models of Smarandahe Geometry, duational Publishers, USA (). [5] I. Newton, The Mathematial Priniples of Natural Philosophy, Daniel Adee, New-york (846). [6] A Ditionary of Physis, Oxford, New York, 9 [7] J. D. Waleka, Introdution to Modern Physis Theoretial Foundation, Word Sientifi PublisingCo, Lodon(8) [8] H. C. Ohanian, R. Ruffini, Graitation and Spaetime, W. W. Norton & Company, In. (994). [9] A. instein, Relatiity The Speial and The General Theory, Methuen & Co. Ltd, London, (955). [] R. K. Su, Quantum Mehanis, Higher duation Press, Beijing ()