Physics of Elemental Space-Time A Theoretical Basis For the New Planck Element Scale

Transcription

1 Phyi of Elemental Sae-Time A Theoretial Bai For the New Plank Element Sale Phyi of Elemental Sae-Time A Theoretial Bai For the New Plank Element Sale 1 Brian B.K. in Abtrat Our ae-time i otulated to have the following harateriti: (1) the ae i an oean filled with the amma element having energy and ma and of a ertain ize; () both time and ditane are diretized by the roe of light roagation from one amma element to the next in ome roe of relativiti boot of the internal energy. Thee otulate rovide u with a theoretial bai to exlain why the eed of light,, hould remain ontant in all inertial referene frame. The direte roe of light roagation lead u to a et of natural unit. A a reult, new hyially baed Plank element unit may be defined with the new ma ale being ~7.7 x 1-51 kg (~4.14 x 1-15 ev/ ). The length ale i etimated from the wavelength of the highet energy gamma ray, in the range of 1 x 1-19 m 1 x 1-5 m, and the new time ale then being in the range of.4 x x 1-4. The Plank element unit are hown to relate with the fundamental ontant, (eed of light), (gravitational ontant), and h (Plank ontant) with the ame dimenional relationhi a the onventional Plank unit, but the length and time unit are larger than thoe of the latter by order of magnitude while the ma i maller by whoing 1-4 order of magnitude. Keyword Sae Time Element Partile Wave Plank ale 1 Introdution The eial theory of relativity [1] i in art baed uon the ontany of the eed of light. On the one hand, our undertanding of light roagation i baed uon the ae being emty o that the hoton travel without hindrane with the eed of light. On the other, from the eretive of the field theory Feynman [] oberve that the eletromagneti field an arry wave; ome of thee wave are light, but that at higher freuenie they behave muh like artile, and that uantum mehani unifie the idea of the field and it wave, and the artile all into one. Wilzek [] deribe a viion of the rimary ingredient, the grid, that fill our ae and time, i alive with uantum ativity albeit ontaneou and unreditable, ontain material omonent, give ae-time rigidity, aue gravity, and weigh. With the lightbearing aether hyothei failing ome of the ritial tet, in artiular the eed of light, it i lear that our undertanding of the emty ae i far from omlete. In thi aer, a model of ae i reented along with one of the firt reult of the model, the Plank Element ale, in the hoe that it may eventually be develoed to inororate all the eential idea of the above. 1 Brian B.K. in 89 Lo Roble Avenue, Palo Alto, CA 946, U.S.A. bmin@nubron.om 1

2 Phyi of Elemental Sae-Time A Theoretial Bai For the New Plank Element Sale Elemental Sae-Time - The Definition of Time and Ditane That the eed of light i ontant in all inertial frame of referene wa hown by exeriment but thi ounter-intuitive truth ha never been onviningly exlained. Furthermore, even a we find all matter are uantized, the ontinuity of ae and time aear to be o obviou that to the author knowledge we eldom uetion the validity of that aumtion. We argue below that if both ae and time are diretized, we, the oberver of light, will ee the eed of light to be ontant regardle of the frame of referene. Newton law for gravity and oti were built on an abolute ae and time, rohibiting an oberver artiiation. The theory of relativity, on the other hand, wa derived by reuiring that a henomenon obey the ame law of hyi regardle of an oberver ytem of referene frame. Thi owerful tool of uing an oberver led to the diovery of the more general law of hyi that Newton law are only a eial ae for. We reognize now that the role of an oberver i now ritially imortant to our undertanding of the hyial world. When we hear ound, we diern the freueny of ound wave or the tone. When we ee light, we diern the freueny of light or olor. In both ae, we the oberver only have to ount the eak and valley of the ound wave and of light wave and omare the freueny with thoe with ome referene ound wave and referene light wave, reetively. The ame may be aumed to be true with time and ditane. We an meaure the ditane between any two oint by ounting the number of wavelength a referene light take to travel between them. We may otulate that our internal bio-lok ha the ability to ount the freuenie of the referene light and indeed we funtion and age baed uon uh bio-lok. Among all oberved eletromagneti wave etrum, we know the amma-ray reah the highet energy tate having the highet freueny and the hortet wavelength. We till don t know if we have oberved the limit yet but if the ae i diretized, we rake a view that there hould be a limit and that there are fundamental element aoiated with it. (We ignore the onventional Plank ale for the moment for the reaon to be aarent below.) We now otulate that the univere i full of thee element that we hall all amma element. Sae i an oean filled with the amma element. Light roagate through the amma element by energizing them, ay by mean of relativiti boot of the internal energy. The amma element then mut be the medium for the light energy to roagate through. The amma element are a form of matter having energy and ma. In thi reet, the amma element ae differ from the abandoned abolute aether ae. We live in the ae filled with the amma element but unaware of their exitene beaue their denity i extremely low. (We will diu their denity in another aer.) Even though they are aumed to exit in the above ene, muh of the roertie of the amma element may well be left for future reearh, inluding the detailed relationhi between the amma element and eletromagneti, uantum, and gravitational field. Here we only otulate that eah amma element ouie a ubile of ae with a linear dimenion l (hene a volume l.) Then the ditane between two neighboring amma element i alo l. Furthermore, the time reuired for light energy to roagate from one amma element to the next i the elemental time interval, whih we hall denote t. Thu t and l are the elemental unit of time

3 Phyi of Elemental Sae-Time A Theoretial Bai For the New Plank Element Sale and length, reetively, and l /t define the eed of light roagation, whih i ontant regardle of an oberver frame of referene by definition. The rinile of relativity and that i ontant in all inertial frame lead to the theory of the eial relativity. Thee two ondition of eial relativity are both atured by the aumtion that our ae-time i diretized and that l /t by definition in all inertial frame. We hall all the latter the rinile of elemental ae-time (EST), or imly the EST ondition. Thi aert that the elemental length and time are the mallet unit of length and time, reetively, and that we, the oberver, merely ount the number of l and t to ereive the ditane and time, reetively. The magnitude of l and t may hange by the relativiti effet but their ount don t, hene the ontany of the eed of light regardle of the oberver inertial frame of referene. To exlore thi further, let u build the bridge between the ontinuum hyi and the elemental ae-time. Now let n be the number of the amma element energized in euene er eond by light, i.e., 1 eond = n t. The ditane traveled by light (energy) in one eond then i n l. The eed of the light roagation i till alulated to be nl l = = (1) n t t whih i ontant in all inertial frame. The eial theory of relativity tell u that l and t an vary in different inertial frame but that n i ontant in all inertial frame. EST tell u that the abolute magnitude of l or t are immaterial to u, the oberver, ine the only thing we ereive i n for both time and ditane. But n i unknown ine we have yet to determine the dimenion of the amma element. In the next etion, we will infer the dimenion of the amma element to the firt aroximation from oberved wavelength of gamma-ray and neutrino ize. The following analyi whih we will all diretizing tranform an euation having the meaurement unit meter (m), kilogram (kg), and eond () to one having the elemental unit l,, and t aording to the rinile of the elemental aetime. ( i elemental ma a will be defined later.) Firt we exliitly write an euation to inlude the utomary unit, onvert the utomary unit to the elemental unit, and then aly the EST ondition. It i not a mere dimenional analyi but an exat analyi. For onveniene, let (m/) = o m/, i.e., i dimenionle number. We then have one light-eond length = m = n l. We will alo freuently ue 1 m = n m l where n m = n /. Let h = h kg m - and ν = ν -1 where h i the Plank ontant, ν the freueny, and h and ν are dimenionle number. The energy of a hoton (denoted by the ubrit h ) with the freueny ν i [4] E h = hν () = h o ν kg m - = h o ν kg (n m l ) (n t ) - = h o ν kg (n m /n ) (l /t ). But n m /n = 1/, l /t =, thu E h = (h o ν / ) kg. One reognize that h ν / kg i a ma, hene let h h ν / kg = hν/, then E = hν. () h = h

4 Phyi of Elemental Sae-Time A Theoretial Bai For the New Plank Element Sale Thi derivation at one how (1) the wave-matter euivalene and () the energyma onverion. How did we get thi euation o eaily? Thi how the ower of the EST rinile, l /t = whih imlifie the mehani of eial relativity. (In thi aer, we hall denote ma to be to ditinguih it from the length unit meter denoted by m. Thi i neeary ine we will inlude hyial unit in our diretized euation.) Thu from the Plank relation and the elemental ae-time model, we have derived the ma of the hoton to be h = hν/. Suh a redition wa already made reviouly by De Broglie [5]. Thi aarently ontradit with the revailing relativiti hyi whih generally believe and mathematially treat that hoton travel with veloity, are male, and their energy i all kineti. It i beaue in the EST model, light energy roagate a elemental wave, from one amma element to the next in euene with the hae veloity,, in a way that i inditinguihable from the aarent hoton artile traveling in vauum. Etimate of Elemental Proertie For brevity, here we hall dro the ubrit h from the deignation of hoton energy and hoton ma, reetively. The Plank-Eintein relation E = hν tate that the energy of light i diretized. We an rewrite E. () a E( ν ) = hν = ( ν). (4) Thi exree the fat that the energy of a hoton i a funtion of freueny and it ma then i alo a funtion of freueny. We then viualize a hoton a ν number of Plank element arriving in erie. ore orretly, we viualize a hoton a a amma element beating ν time er eond (ame a ν Plank element) with ν originating from an eletron that emit energy, E=hv at a time. Sine ν i a oitive integer, one reognize that the elemental energy, E, i obtained when thi i the mallet, i.e., when the freueny i one er eond, h h h E E(1) = =, (5) n t t where we define h h. (6) n h may be alled time-diretized Plank ontant. From E. () we alo define the orreonding ma, hν ( ν ) =. (7) Thi tate that the energy of light may be onverted to ma, a funtion of freueny ν with an elemental value when ν =1: h 1 h 1 E (1) = = =. (8) t i the ma of a amma element loaded with the light energy for a eriod of t. For ditintion, we hall all an energized amma element to be a Plank element. The lifetime of Plank element i t. The amma element are aoiated with the maximum energy amma-ray and ized from it wavelength. Thu i the ma of a Plank element. It value may be alulated from the above, 4

5 Phyi of Elemental Sae-Time A Theoretial Bai For the New Plank Element Sale h 1 = = kg, or 1 kg = 1.6 x 1 5. We hall define an integer, N kg = 1.6 x 1 5, o we may diretize any ma, = o kg = o N kg. We an alo write for the energy of a Plank element, 1kg E = = N. (9) Wherea the ma of the Plank element wa dedued in the above from the Plank ontant, an exerimentally meaured value, we don t find an exeriment from whih to dedue the value l and t. We note, however, l i the low limit for the wavelength of eletromagneti wave and take an aroah that the bet etimate of thee an ome from known meaurement. We look for the mallet wavelength that ha been exerimentally oberved and find the known low limit value for the eletromagneti wavelength ome from the ultrahigh energy gamma ray [6, 7, 8, 9] in the range, λ γ-ray 1 x 1-19 m 1 x 1-5 m. Interetingly the mallet diameter of neutrino [1] i alo etimated to be Λ D-nutrino 1 x 1-19 m. Even lower wavelength are oberved for omi ray [11] whih are known to be roton artile with the energy greater than even that of the highet gamma ray. (a) ZK limit: λ gzk =.48 x 1-6 m. (b) Ultra High Energy Comi Ray: λ uhe = 4.1 x 1-7 m. () EeV omi ray: λ EeV = 1.4 x 1-7 m. Sine roton are omoite artile, however, their matter wave wavelength may be relativitially ontrated. Thee wave are not the eletromagneti wave arried by the amma-plank element; hene their energy level may not tranlate into thoe of amma-plank element. For thi reaon we adot the wavelength of the highet gamma ray and etimate l i in the range, l = 1 x 1-19 m 1 x 1-5 m, hene t i in the range, t = l / =.4 x x The EST v. Conventional Plank Unit A et of natural unit alled the Plank unit may be derived from the fundamental univeral ontant,,, and h. The natural unit for length, time, and ma denoted a l, t, and, reetively, may be derived by writing their dimenional relationhi, kg 5

6 Phyi of Elemental Sae-Time A Theoretial Bai For the New Plank Element Sale with the reult being: = l l = h = t h l = 4.5 x 1-5 m, / t, t l h = 5.46 x 1-8 kg, and,and h t = x 1-4. The above may be alled the onventional Plank unit to ditinguih from the natural unit to be derived aording to the reent elemental ae-time. The onventional Plank ale influene our undertanding of the univere in both rofound and onfounding way. The onventional Plank unit [1] rereent a ale far maller in ditane than what i urrently aeible at high energy artile aelerator at arox. 1 - time the roton radiu but far heavier than a roton at arox time the roton ma. A Plank artile [1] i a hyothetial artile defined a a tiny blak hole whoe ma i thu aroximately the Plank ma, and it Comton wavelength and Shwarzhild radiu are about the Plank length. They lay a role in ome model of the evolution of the univere during the Plank eoh. One of the diffiultie of uantum gravity i that uantum gravitational effet are only exeted to beome aarent near the Plank ale. It i intereting to note that the above inlude a feature, l = t, whih i imilar to l = t, a fundamental relationhi of the reent theory. One might dedue from thi that the onventional Plank unit imliitly reent the idea of the elemental ae and time. No uh ignifiane wa reviouly deribed, however, to the bet of the author knowledge. E. (1) merely rereent dimenional relationhi hene the olution alo merely rereent the dimenional relationhi. To obtain more meaningful natural unit for the reent elemental ae-time, let u diretize the gravitational ontant,, = N m kg n l kg = m kg K where and K are both dimenionle ontant with K defined by K. (1) N kg The three euation to olve, then, are the following; = n l (1) (11) 6

7 Phyi of Elemental Sae-Time A Theoretial Bai For the New Plank Element Sale = l = K h = / t, n l n t, and The lat of the above three euation ome from E. (8). The reult, inluding the relationhi with the onventional Plank unit, are 1 h l l = ( =,) Kn Kn = K h. ( = K,) and 1 h t t = ( =.) 5 Kn Kn Thee are the natural unit from the elemental ae-time model. They retain the ame dimenional relationhi with reet to the fundamental ontant,,, and h, a the onventional Plank unit, with the etimated numerial value to be, m l = 1 x 1 n -19 m 1 x 1-5 m, t 7.7 x 1-51 kg (or ~4.14 x 1-15 ev/,) and 1 = n.4 x x 1-4. We note that i the ma of a Plank element, l i the linear dimenion of a ingle amma or Plank element, and t i time taken for light energy to roagate from one amma element to the next. t i alo the lifetime of a Plank element. We may therefore all the above Plank element unit. The Plank element unit rereent a ditane ale at arox time the roton radiu and arox. 1-4 time the roton ma - muh more amenable for our artile hyi than the onventional Plank unit. We alo note that the length and time element range are till aroximate, o the value of n i not yet reiely known. From the above etimate, we an bakalulate n and K, the ontant aearing in E. (14) a follow: n =. x 1 7. x 1 K=1.5 x 1-4 Note that the roertie of the Plank element ome from an entirely different origin than that of the onventional Plank artile diued in the above, although their dimenional relationhi with the three fundamental ontant,,, and h, are the ame. Thi jutifie our alling the former by the name Plank element rather than by the name of the onventional Plank artile. 5 Summary and Conluding Remark The EST model may be viewed a an evolution of our undertanding of the aetime, from aether-filled to vauum to now a matter-filled ae. In a ene, we bring the aether bak anyway, only thi time the aether i not abolute, but omried of material element having energy and orreonding ma. We all them amma (1) (14) 7

8 Phyi of Elemental Sae-Time A Theoretial Bai For the New Plank Element Sale element. They tranmit light and define the very onet of our time and ditane. Time and ditane are diretized, with the ratio of direte length over direte time, l /t, to be the eed of light roagation by definition. The energized amma element are alled Plank element with the life time, t. The energy of a Plank element i given by the Plank ontant (er eond) and it ize i given by the wavelength of the γ-ray of the highet oible energy, etimated to be within the oberved range of 1 x 1-19 m 1 x 1-5 m. A hoton i now undertood to be a amma element beating with a freueny ν or euivalently a erie of Plank element arriving to a oint with a freueny ν. The ma of a tationary hoton i given by =hν/ although a hoton may be treated mathematially a artile of ma zero, energy hν and alway travelling with the eed,. The diretene of elemental ae-time naturally lead u to new fundamental unit at the Plank element ale. A et of Plank element unit are derived by diretizing the fundamental ontant,,, and h, and hown to have the ame dimenional relationhi with reet to them a the onventional Plank unit. The Plank element ma, however, i maller than the onventional Plank ma by whoing 1-4 order of magnitude while the Plank element length and time unit are etimated to be larger than thoe of the onventional Plank unit by order of magnitude. It i to be noted that the Plank element unit ome from the amma/plank element with a hyial bai deribed in thi aer wherea the onventional Plank unit ome only from a dimenional analyi with no uh hyial bai. Referene 1. Eintein, A.: On the Eletrodynami of oving Bodie, Englih tranlation of the original 195 erman-language aer (ublihed a Zur Elektrodynamik bewegter Körer, in Annalen der Phyik. 17:891, 195) in The Prinile of Relativity, ethuen and Comany, Ltd. of London, (19).. Feynman, R. P.: Feynman' Leture on Phyi, Volume 1, Chater. Calteh. (196).. Wilzek, F.: The Lightne of Being, Chater 8, Bai Book (8). 4. Eintein, A.: On a Heuriti Point of View about the Creation and Converion of Light, in The Old Quantum Theory, Pergamon Pre, (1967). 5. Wikiedia, the free enyloedia, htt://en.wikiedia.org/wiki/loui_de_broglie (1). 6. htt://imagine.gf.naa.gov/do/ak_atro/anwer/9741e.html, Ak an Atrohyiit: I there an uer limit to the Eletromagneti Setrum? 7. Wikiedia, the free enyloedia, htt://en.wikiedia.org/wiki/ultra-high-energy_gamma_ray (14). 8. Aharonian, F.: et al, The time averaged TeV energy etrum of kn 51 of the extraordinary 1997 outburt a meaured with the tereooi Cherenkov teleoe ytem of HERA, arxiv:atro-h/9986v (Jul 1999). 9. H.E.S.S. Collaboration, A. Abramowki, et al., HESS J an exetionally luminou TeV gamma-ray uernova remnant, arxiv: v [atro-h.he] (Feb 14). 1. Steker, F.W.: Exloring the ultrahigh energy neutrino univere, arxiv:atro-h/459v1 (ar ). 11. Steker, F.W.: The uriou adventure of the ultrahigh energy omi ray, arxiv:atroh/117v (11 Jan 1). 1. Wikiedia, the free enyloedia, htt://en.wikiedia.org/wiki/plank_unit, Jan Wikiedia, the free enyloedia, htt://en.wikiedia.org/wiki/plank_artile, De