Vl.4, N., pp.4-8, Ma 016 THREE DIMENSIONAL SPACE-TIME Lu Shan N.1144, East f Jiuhu Avenue, Zhuhai 509015, Guangdng Prvince P. R. China ABSTRACT: The space-time descriptin in Phsics was cmpsed f 3D space and the 1D time which was independent f 3D space befre the prpsal f the 3D space-time. Therefre, space-time was regarded as 4-dimensinal. With the metrical methd, the authr finds ut that time and space can be quantified b the same quantit value which can be described b three numbers (crdinate values) if the metric fr the space distance is selected as the time wave length. Hence, space-time can be regarded as nt nl the bservable quantit but als 3 dimensinal. KEYWORDS: Space Time; Metric; Space; Distance; Time INTRODUCTION Phsical phenmenn is cmpsed f varius events amng which each event is described b space and time. Then, is the space-time cmpsed f bth space and time 3 dimensinal r 4 dimensinal? The descriptin f space-time in the past phsics was cmpsed f the 3D space cntinuum and the 1D time cntinuum which is independent f space. Hence, space-time is cnsidered as 4 dimensinal 1 3. Since the structures f time and space are cnsidered as independent f each ther, it is difficult t quantif them with the same quantit value, which makes it hard t derive the space-time quantit value relatinship. Hwever, it culd prvide a new thinking fr the phsical cncept f space and time if the metric fr space distance is selected as the time wave length based n the metric methd. Space time Structure In Phsics in the case f measuring the length f a distance, the reference pint f a lcatin is needed accrding t the phsical eplanatin f distance. Then, the distance quantit value frm the reference pint t the given pint can be determined with the metrical methd. The simplest wa is t use gemetrical principle t cnnect tw pints with a straight line. The unit measuring gauge is used t measure the distance between the reference pint and the given pint. The numbers f the unit measuring gauge thereb is the distance quantit value, while the unit measuring gauge is the metric fr this distance, which can be metre, centimetre, r millimetre, etc. This law can be epressed b the fllwing equatin: Set as the reference pint, p as the given pint, as the unit measuring gauge, the metric fr the distance quantit value frm p t. As shwn in Fig. 1, the relative distance frm p t is: n 1 In Eq. (1), n is the quantit value fr the relative distance frm p t measured b the unit measuring gauge. ISSN 053-4108(Print), ISSN 053-4116(Online) 4
Vl.4, N., pp.4-8, Ma 016 If the metric fr the relative distance frm p t is selected as the time wavelength ( ), such setting can be epressed in the fllwing equatin based n the fllwing cnsideratin. Set a clck n the reference pint (static), as shwn in Fig., the relative distance frm p t can be adapted frm Eq. (1) t: N Meanwhile, as the time velcit f clck v is a characteristic cnstant, let T /v Eq. () divided b v n bth sides is: t p N T 3, t r v, p p / In Eq. () and Eq. (3), N is nt nl the distance quantit value using the time wave length t measure the relative distance frm p t, but als the time quantit value using the time perid T t measure the relative time frm p t. Therefre, such space and time quantified b the same quantit value N is called the relative space-time frm p t. The lcatin f the space is described b three numbers (crdinate values). Set as the reference pint, p,, as the crdinate fr the lcatin f an given pint, and. If the metric fr the quantit value f the relative space distance frm p t is the unit measuring gauge, as shwn in Fig. 3, the relative space distance frm p t is: n 4 In Eq. (4), n is the quantit value f the relative space distance frm p t measured b the unit measuring gauge. If the metric fr the quantit value f the relative space distance is selected as the time wave length ( ), such setting can be epressed in the fllwing epressin: Set a clck n the reference pint (static), as shwn in Fig. 4, Eq. (4) can be adapted as: N 5 Meanwhile, as the time velcit f clck v is a characteristic cnstant, let v t / v, T /v, Eq. (5) divided b v n bth sides is: t /, t / v, t t t N( T) 6 In Eq. (5) and (6), N is the space-time which can be described b three numbers (crdinate values). The fllwing equatin can be btained b cmparing the relatinship between space and time frm Eq. (1) and Eq. () r frm (4) and (5): N n 1 ISSN 053-4108(Print), ISSN 053-4116(Online) 5
Vl.4, N., pp.4-8, Ma 016 Let /, then n N Where the rati between the time wavelength and the unit measuring gauge is called space-time cefficient. When 1, then N n, i.e. space-time is equal t space; when 1, then N n, i.e. space-time cntracts relative t space; when 1, then N n, i.e. space-time epands relative t space. DISCUSSION We can imagine an event f a man kncked dwn b a car when crssing the street. What is needed fr the happening f this event is that this man and that car must appear in the same place and at the same time. Otherwise, it wuld nt happen. Therefre, events in the real wrld are cmpsed f spatial pint and the time upn this pint. Phsicall, t describe the space-time structure f an event, we must eplain n which pint in space and at which time the bject f this event is. The space-time f this event, in essence, can be regarded as the bservable quantit. The space-time descriptin in phsics was cmpsed f 3D space and the 1D time which was independent f 3D space befre the prpsal f the 3D space-time. Therefre, space-time was regarded as 4-dimensinal 1 3. Hwever, an measurement is carried ut b cmparing the metrics and then the times f metrics respectivel in phsics. The metric is sme basic quantit chsen t derive the relatinships f thehsical quantities, which is the precnditin f phsics using mathematical methds b inference. It can be seen with metrical methds that time and space can be quantified b the same quantit value described b three numbers (crdinate values) if the time wave length is selected as the metric fr the space distance quantit value. Hence, space-time can be regarded nt nl as bservable quantit, but als 3 dimensinal. In the past studies, space is a 3D cntinuum, namel the lcatin f an pint in space can be described b 3D crdinate values (,, ), the unit measuring gauge f space being taken as the metric t measure these three values. In additin, there are infinite numbers f pints near this pint, which can be described b such spatial crdinate values as 1, 1, 1 and the values f which can be as clse t the spatial crdinate values,, f the first pint as pssible. Thus, the space f this area is 3D cntinuum because f the latter feature. Similarl, the event f an pint in space-time is als described b 3D crdinate values (,, ). What is different is that the time wavelength is taken as the metric t measure these three values. As t each space-time pint, the "adjacent" space-time pint can be selected infinitel, with an infinitesimal quantit frm the crdinate values 1, 1, 1 f the "adjacent" space-time pint t thse,, f the initiall cnsidered pint. Thus, 3D space-time is als a cntinuum like 3D space. Space-time equals t space when the time wavelength equals t the unit measuring gauge f space ; space-time cntracts relative t space when the time wavelength is less than the unit measuring gauge f space; space-time epands relative t space when the time wavelength is greater than the unit measuring gauge f space. The abve mentined space-time structure is nl a certain clear cncept limited t the relativel static state withut which 3D space-time in the relative mtin state culd nt be funded. ISSN 053-4108(Print), ISSN 053-4116(Online) 6
Vl.4, N., pp.4-8, Ma 016 It can be seen that with the metrical methds, the space-time which culd be quantified b the same quantit value can be regarded as bservable quantit if the time wave length is selected as the metric fr the space distance quantit value. It is difficult t regard the 4D space-time as bservable quantit, which is hard t accept fr the measurement f phsics. Rethinking the space-time structure culd help find ut that space and time are cvariant in 3D space-time. Such space-time culd nt nl determine the time that the event happens b the lcatin f the spatial pint f the real event, but als determine the lcatin f the spatial pint f that event b the time f the real event. What is mre imprtant is that the relatinship f the quantit values culd be derived since the 3D space-time is regarded as bservable quantit. Thus, it is eas t judge whether tw events happened at different time are n the same lcatin in space. Just like the table tennis springing in situ n the train, the bserver can judge whether the table tennis f different time is n the same lcatin in space. Therefre, it is the nature that space and time are mutuall independent in structure in 4D space-time that has made peple feel that this cnventin which regards time unrelated t space lacks supprt, which in turn makes it hard t help peple directl judge the lcatin and time that the natural event happens. It is a pit that phsics des nt realie that 4D space-time in essence is difficult t be regarded as bservable quantit. Cnsequentl, space-time is taken as the phsical entit, differing frm thehsical quantit. This is the reasn wh there are different descriptins f space-time fr the phsical event. Thus, rethinking the space-time structure culd help us rethink the phsical cncept fr space-time instead f thinking nl abut mathematical deductins. CONCLUSION Space-time culd nt nl be regarded as bservable quantit, but als 3 dimensinal if the time wave length is selected as the metric fr the space distance quantit value. REFERENCE [1] Henri Pincare (France). Translated int Chinese b Li Xingmin. La Science et l'hpthèse (Science and Hpthesis). (The Cmmercial Press, Beijing, Aug. 006, 7-3, 48-64) [] Henri Pincare (France). Translated int Chinese b Li Xingmin. Science et Méthde (Science and Methd), (The Cmmercial Press, Beijing, Dec. 006, 69-86) [3] Stephen Hawking(UK). Translated int Chinese b Xu Mingian and Wu Zhngcha. A Brief Histr f Time. (Hunan Science & Technlg Press, Jan. 00, 14-34 ) ISSN 053-4108(Print), ISSN 053-4116(Online) 7
Vl.4, N., pp.4-8, Ma 016 p Fig. 1 1D Space p Fig. 1D Space-time 5 5% % p,, Fig. 3 3D Space 5% 5% 5% % p,, Fig. 4 3D Space-time ISSN 053-4108(Print), ISSN 053-4116(Online) 8