The Planck Mass Particle Finally Discovered! The True God Particle! Good bye to the Point Particle Hypothesis!

Transcription

1 The Plank Mass Patile Finally Disoveed! The Tue God Patile! Good bye to the Point Patile Hypothesis! Espen Gaade Haug Nowegian Univesity of Life Sienes Septembe, 06 Abstat In this pape we suggest that one single fundamental patile exists behind all matte and enegy. We laim that this patile has a spatial dimension and diamete eual to the Plank length and a mass eual to half of the Plank mass. Futhe, we will laim this patile is indivisible, that is it was neve eated and an neve be destoyed. All othe subatomi patiles, in spite of having muh lowe masses than the Plank mass, ae easily explained by the existene of suh an indivisible patile. Isaa Newton stated that thee had to be a fundamental patile, ompletely had, that ould not be boken down. He also laimed that light onsisted of a steam of suh patiles. Newton s patile theoy was vey simila to that of the anient atomists Demoitus and Leuippus; see, fo example, [,, 3, 4]. Howeve, the atomist view of an indivisible patile with spatial dimensions has geneally been pushed aside by moden physis and eplaed with hypothetial point patiles and the mysteious wave-patile duality. Although the Plank mass is enomous ompaed to any known subatomi patiles, inluding the Higgs patile, we will explain how all known subatomi patiles ontain and ae eated fom the Plank mass. In this pape we will show that the Plank mass is found eveywhee at the subatomi level and that the Plank mass pobably onsists of two indivisible patiles. Thee ae good easons to believe that the Plank mass an only exist fo an instant eual to a Plank seond. We show that what moden physis onsides a est-mass is, in eality, objets apidly flutuating between thei mass state and an enegy state. Ou new view of matte and enegy seems to addess a seies of unsolved poblems in moden physis, inluding the uestion of why we have not obseved a patile with a mass lose to the Plank mass, despite the fat that the Plank mass plays an impotant ole in etain aspets of theoetial physis. We also show how ou view of matte and enegy is onsistent with Heisenbeg s Unetainty piniple, but gives a di eent and moe logial intepetation than the intepetation given by moden uantum mehanis. Futhe, ou theoy o es a ompletely new intepetation of the so-alled Shwazshild adius at the subatomi sale. In the last setion we povide a new solution to Einstein s infinite mass poblem. As we show, all elementay patiles will tun into enegy just befoe they eah the speed of light. In othe wods, thee is no need fo infinite enegy to aeleate a mass to the speed of light. This does not eplaes Einstein s elativisti mass fomula, whih we laim is oet; it only gives additional insight on how it should be used based on new pespetive on what mass tuly is. Key wods: Plank mass, Plank patile, Motz patile, indivisible patile, enegy, mass, spatial dimension, Heisenbeg s Unetainty piniple, mini blak-holes, elativisti mass limit. Intodution Isaa Newton assumed that eveything, inluding light, onsists of solid, had, impenetable moving patiles o, in Newton s own wods, [5]: All these things being onside d it seems pobable to me, that God in the Beginning fom d Matte in solid, massy, had, impenetable, movable Patiles, of suh Sizes and Figues, and in espenhaug@ma.om. Thanks to Vitoia Tees fo helping me edit this manusipt and thanks to Taden4Alpha fo useful omments and to Jeemy Dunning-Davies fo pointing me towads some vey inteesting olde efeenes that I not was awae of. Also thanks to Alan Lewis, Daniel Du y, Ppaupe and AvT and fo useful tips on how to do high peision alulations.

2 suh Popotion to Spae, as most ondue to the End fo whih he fom d them; and that these pimitive Patiles being Solids, ae inompaably hade than any poous Bodies ompounded of them; even so vey had, as neve to wea o beak in piees; no odinay Powe being able to divide what God himself made one in the fist Ceation. While the Patiles ontinue entie, they may ompose bodies of one and the same Natue and Textue in all Ages; But should they wea away, o beak in piees, the Natue of Things depending on them, would be hanged. Those minute ondues, swimming in spae, fom the stu of the wold: the solid, oloued table I wite on, no, less than the thin invisible ai I beathe, is onstuted out of small olouless opusles; the wold at lose uates looks like the night sky a few dots of stu, satteed spoadially though and empty vastness. Suh is moden opusulaianism. The opusula patiles of Newton wee vey simila to the anient atomist view of matte: that eveything onsisted of indivisible patiles moving in the void. The void an be imagined as empty spae, but it is moe than that, as all obsevable subatomi patiles onsist of indivisible patiles and void; see [6] fo an in-depth disussion on this. In this pape we will suggest that by eintoduing an indivisible patile we will be able to takle some of the unsolved poblems in moden physis. We suggest that the moden hypothesis of point patiles, athe than a fundamental indivisible patile with spatial dimensions, is one of the main auses of muh of the non-intuitive intepetations in some aeas of moden physis. Befoe we eunite the Newton opusula God patile, whih is ooted in anient atomism, with moden physis we will biefly disuss the Plank mass and the Plank patile. The Plank mass and a seies of Plank units play an impotant ole in moden physis. And yet even physiists involved with the Lage Hadon Collide have not obseved a subatomi patile with a mass even lose to the Plank mass. In 906, Max Plank intodued the following mass m p kg, see [7]. This G is an extemely lage mass ompaed to the mass of all known subatomi patiles. The Plank mass is about the same as that of a flea egg; to put it in ontext the mass is so lage that we an elate it to something maosopi. The Plank mass is eual to the poton masses and about.4 0 the eleton masses. Its mass is enomous ompaed to any subatomi patile and even to the mass of the heaviest atoms. Table list the mass as well as the edued Compton wavelength of some elementay patiles. As we an see fom the table, even the lage Higgs patile mass is inedibly small ompaed to the Plank mass. While the Plank mass is vey lage, its edued Compton wavelength: m p is eual to the Plank length l p mete, and this is inedibly small ompaed to the edued Compton wavelength of all known patiles in pesent day patile physis. Patile Mass Patiles Redued Compton pe Plank mass Wavelength Plank mass.77e-08.66e-35 Higgs patile.30e E+6.577E-8 Neuton.675E-7.99E+9.00E-6 Poton.673E-7.30E+9.03E-6 Eleton 9.09E-3.389E+ 3.86E-3 Table : The mass and edued Compton wavelength of some patiles. Lloyd Motz, while woking at the Ruthefod Laboatoy, [8, 9, 0] suggested that thee was pobably a vey fundamental patile with a mass eual to the Plank mass. Motz named this patile the uniton. Motz suggested that the uniton ould be the most fundamental of all patiles and that all othe patiles wee initially made of unitons. Motz aknowledged that his unitons (Plank mass patile) had fa too muh mass ompaed to known subatomi masses. He tied to get aound this issue by laiming the unitons had adiated most most of thei enegy away: Aoding to this point of view eletons and nuleons ae the lowest bound states of two o moe unitons that have ollapsed down to the appopiate dimensions gavitationally and adiated away most of thei enegy in the poess. Lloyd Motz Othes have suggested that thee wee plenty of Plank mass type patiles aound just afte the Big Bang, see [], but that most of the mass of these supe heavy patiles has adiated away. Moden physis has also suggested a hypothetial Plank patile that has p moe mass than the uniton suggested See also [] thatintoduesasimilapatilethatheallsmaximons.

3 3 by Motz. Some physiists inluding Motz and Hawking has suggested suh patiles ould be mioblak-holes [3, 4, 5]. Plank mass patiles has even been suggested as a andidate fo osmologial dak matte, [6, 7]. Othes again, like Cothes and Dunning-Davies [8], have stongly itiized the blak-hole intepetation of the Plank patile and have even uestioned the existene of the Plank patile. Even the existene of Plank mass size patiles eminds a unsolved mystey. We think uent intepetations of the Plank mass and Plank type patiles do not make muh sense and instead we o e a fesh altenative based on an anient way of looking at matte and enegy. In the final setion of the pape we will even give a new intepetation of so alled mini-blak holes. Hee we will assume thee ultimately is only one fundamental patile and this patile makes up all othe patiles, as well as enegy. We will assume that this patile has the following popeties:. Indivisible patile with a diamete of l p and a est mass eual to half that of the Plank mass.. This indivisible patile is always taveling at the speed of light, as measued with Einstein-Poinaé synhonized loks. 3. This patile tavels in the void ( empty spae ). This is neessay, so the patiles have something to tavel in. In othe wods, ou indivisible patile has half the mass of the uniton patile suggested by Motz in 96 (Plank mass size patile). In 979, Motz and Epstein [4] suggested thee likely existed a fundamental patile with half the Plank mass, that is exatly the same mass as in the patile suggested hee. Still they did not have a good explanations fo why this patile was so muh lage than all existing subatomi patiles, what this patile tuly was, and if it was indivisible o not. Instead of assuming that most of this supe heavy patile mass has adiated away, we will suggest that all mass (and enegy) of the indivisible patile hides inside eah known subatomi patile and even inside enegy. To get this to wok we will have to undestand enegy and mass fom a new pespetive, that is fom a muh simple and moe logial pespetive than given by moden patile physis. If the indivisible patiles make up both enegy and matte, then how an enegy and matte appea to be so di eent? As fist explained by Haug [6] based on atomism, the only di eene between enegy and matte is how the indivisible patiles move elative to eah othe. Enegy is simply indivisible patiles moving in the same dietion (at the speed of light) afte eah othe, while matte is indivisible patiles moving bak and foth at the ound-tip speed of light and ounte-stiking with eah othe. Haug [6] has shown how this view of matte and enegy leads to all of the well known fomulas of speial elativity theoy, inluding E m and E m, as well as elativisti Dopple shift and v moe. Fo example, length ontation has to do with a edution in the void-distane between a goup of indivisible patiles. Still, Haug [6] has not shown befoe how his theoy dietly an be linked to the Plank mass, as well as known subatomi patiles suh as the eleton. That is what I will show hee. We will define mass as existing only at the instant when two indivisible patiles ollide, what we will all a ounte-stike. At a typial ollision, thee is nomally some damage, but as the indivisible patiles ae indivisible and have no pats, they ae unhanged afte ollision, so ounte-stike is a bette wod to desibe suh an event. All they do at ounte-stike is to hange the dietion of movement. What two fully had bodies do when they ollide was one of the most di ult and signifiant uestions duing the 6th entuy; giants like Newton and Desates attempted to answe this uestion, but it was not esolved at that time, see [5]. As shown by [9, 0] the Plank mass an also be ewitten (without hanging its value) as m p G l p kg () We will assume that the indivisible patile (the sole fundamental patile) has a mass of half the Plank mass, that is: m i mp l p () G We use the notation m i as mathematial symbol fo the indivisible patile mass. Still, at all instants when an indivisible patile does not ollide it is enegy and this is then its potential mass. Moe peisely, indivisible patiles that ae, at any instant, not ounte-stiking (olliding) ae what an be onsideed as pue enegy. When they ae ounte-stiking, we an onside them as half the Plank mass. Even if this ounte-stike ollision only lasts fo an instant, we will laim fo hypothetial obsevable puposes that it lasts fo one Plank seond, that is t p lp. This is beause if we have a zeo time Idisoveedthis979papeofMotzandEpstienfistafteputtingoutvesionofthispapeonVixa. Theyae,fom what I have found out so fa, the fist ones that have suggested a fundamental patile with this mass.

4 4 inteval, then how ould we talk about mass o even obseve any mass? Obsevations euie time and due to the diamete of the indivisible patile, the minimum time inteval we an measue hypothetially is the Plank time. With the aveat hypothetially, I am simply thinking that even if we had the most advaned euipment available, this is something that possibly only an be done in a thought expeiment at this time. Even so, expeimental physis and logi stongly point towads the atomist view of matte and enegy. Late we will look at mass in a slightly di eent view that involves ontinuous time. Based on Einstein s fomula E m we know that a mass at est ontains a lage enegy potential [,, 3]. We will hee laim that enegy (photons, eletomagnetism) also has built-in mass potential. This lies in ontadition with moden physis intepetations that laim photons have absolutely zeo mass, that they ae massless. In ou view, photons have zeo est-mass as long as they ae not ountestiking; in this ase, the photons have only potential mass. The photons ae nothing othe than indivisible patiles moving afte eah othe in the same dietion (simila to the Newton model of light). Some will possibly immediately laim this is invalid based on the moden wave patile view. We will howeve laim that the expeiments used to suppot the wave-patile duality stand on thin gound. We ae not the fist ones uestioning the wave-patile hypothesis, see fo example [4, 5, 6, 7, 8]. Inteestingly, othes have also eently bought atomism bak into the disussion of moden physis and uantization, see [9]. Only the ounte-stiking between indivisible patiles podues what we an all mass, o athe lies at the oigin of what we all mass. Just at the instant two indivisible patiles ounte-stike, they ae ombined a Plank mass, as illustated in this figue Figue : Illustation of Plank mass. A Plank mass exists in the moment two indivisible patiles ountestike. Eah indivisible patile has a mass of half the Plank mass. The small aows illustate that the indivisible patiles will immediately move in opposite dietions afte a ounte-stike. So even if the Plank mass is inedibly lage ompaed to known subatomi patiles, it only lasts fo an instant befoe being dissolved into enegy (non-olliding indivisible patiles) again. The shotest time (the instant) we hypothetially an measue the existene of a Plank mass is likely to be a Plank seond t p lp, whih is simply the diamete of the indivisible patile divided by the speed of light. We an say that the Plank mass lasts only a Plank seond. Just afte the instant of the ounte-stike (the eation of mass), the two indivisible patiles sepaate and ae no longe a mass; they ae now enegy again. Eah indivisible patile, when not ounte-stiking, only has potential mass, but no est-mass. Eah indivisible patile then has potential mass eual to half the Plank mass. Only at ounte-stike the indivisible patiles ae at est fo an instant, so they have est-mass, but only fo a Plank seond fom an obsevable point of view. Inteesting to note in this ontext is that the Lamo adiation fomula [30], when woking with the hage of Plank masses, will adiate into enegy within a Plank seond, see [3]. Howeve, the intepetation of adiation fom Plank masses will be vey di eent hee than in moden physis. Despite thei many vey auate fomulas fo enegy, it is impotant to note that moden physis atually has no deep explanation of what enegy is exatly; as Rihad Feynman one said: It is impotant to ealize that in physis today, we have no knowledge what enegy is. Radiation into enegy fom a moden atomist point of view simply means the two indivisible patiles have left thei ounte-stiking state; this likely happens in an instant, but fom an obseve s point of view it will take a Plank seond to see this hange, even in the best possible thought expeiment set-up. The Lamo fomula futhe indietly pedits that the Plank aeleation is fom zeo to the speed of light in a Plank seond. The intepetation of this fom the atomist point of view is simply that the indivisible patile, upon a ounte-stike with anothe indivisible patile, hanges its ouse of dietion

5 5 instantaneously and ontinues at the speed of light, but now it is moving in the opposite dietion fom its oiginal path. Even if at the deepest level this happens instantaneously, it would theoetially take a minimum of one Plank seond to measue this aeleation. In atomism the only things that exist at the depth of eality ae indivisible patiles and void, and the only thing we an obseve is ounte-stikes between indivisible patiles. The diamete of an indivisible patile is, in ou theoy, eual to the Plank length l p and sine the indivisible patiles always moves with speed of light, itwouldtakeaplank seond to see an indivisible patile leave o aive. Even the most peise measuing devie would have to be onstuted of indivisible patiles with diamete l p. So fa we have disussed what we assume the Plank mass patile is, but nobody has eve obseved a Plank patile and it is fai to ask how is all this elated to ou moden obseved patiles that ae so muh smalle than the Plank mass. One an think of an eleton as two indivisible patiles moving bak and foth ove a distane eual to the twie the edued Compton wavelength of the eleton (eah moving the edued Compton wavelength fo eah ounte-stike). That is to say, eah indivisible patile will ounte-stike evey time it has moved a distane eual to the edued Compton wavelength. 3 The indivisible patile is moving along edued Compton wavelength at the speed of light. Beause the edued Compton wavelength of the eleton is muh longe than the diamete of the indivisible patile, this means thee ae only e ounte-stikes pe seond. If we assume the hypothetial time to obseve the ounte-stike between two indivisible patiles is lp, then the amount of ounte-stikes in a eleton an be seen as a fation of lp elative to a Plank mass, even if the eleton onsists of a Plank e mass (ounte-stikes). It is vey impotant that the ound-tip speed of the indivisible patile is. Ifthespeedwasslowe o faste than this, then the indivisible patile model explaining mass as ounte-stikes would not have woked to desibe suh things as the mass of the eleton. One should also see this pape in onnetion with the many deivations done by Haug 04 showing that speial elativity an be deived dietly fom indivisible patiles and void. Eah time eah the indivisible patiles that make up the eleton have taveled the edued Compton wavelength of the eleton, they ounte-stike. In othe wods, the eleton is in eality in a mass state only a fation of the time. This is why the Plank mass an be so enomous ompaed to the eleton est-mass and still make up the eleton as well as any othe subatomi patile. The numbe of tansitions between mass and enegy fo example fo an eleton is times pe seond. We an say the eleton is lp e as a funtion of the Plank mass eual to the well known fation of a Plank mass. This means the eleton must have a mass m e lp m p e kg (3) 3 One ould even say that all deteted patiles with so alled est-mass neve, even when at so alled est, ae onstantly in a mass state, but apidly ae going between being in a mass state when thei indivisible patiles ae ounte-stiking and in an enegy state when they ae not ounte-stiking. This natually means matte and enegy ae almost the same and it explains why we an tun mass into enegy and enegy into mass. We an say the enegy in a est-mass is used to maintain the mass and the potential mass is used to maintain the enegy. The shote the edued Compton wavelength, the moe feuent will the indivisibles making up the mass ounte-stike and the moe mass the patile will ontain. With a vey shot Compton wavelength, the mass will appoah the Plank mass, beause it then will ounte-stike vey feuently. Futhe, we an say that an indivisible patile is matte-like when it tavels bak and foth in a stable patten, ounte stiking with othe indivisible patiles, and it is enegy-like when it is feed fom this patten. Figue illustates an eleton Evey obsevable patile mass an mathematially be desibed as m mp lp lp l p whee is the edued Compton wavelength of the patile of inteest. The fato lp is the fato deiding how often the patiula patile tiks (ounte-stikes) ompaed to the maximum mass of a subatomi patile, whih is the Plank mass. Eah so-alled elementay patile is nothing moe than (minimum) two indivisible patiles moving bak and foth ove a distane and ounte-stiking. What we onside patiles ae in eality not onstantly in a mass state, that is they do not have ontinuously intenal ounte-stikes between the indivisible patiles making them up. Patiles ae like disete 3 Bea in mind that the mutual veloity (also known as the losing speed) as obseved fom a efeene fame di eent than the two indivisible patiles even unde Einstein s speial elativity theoy, see [3] foahistoialoveview (4)

6 6 Figue : Illustation of Eleton mass. An Eleton is muh smalle than the Plank mass as the mass event only takes up lp of the size (length) of the eleton. e tiking loks and at eah tik they ae a Plank mass. The shote the edued Compton wavelength is, the moe feuent the ounte-stikes (tiks) will be and theefoe the lage the mass of the patile is. In patie things ae moe ompliated; one would also need to take into aount suounding indivisible patiles enteing and leaving the mass (spae) of inteest. Fo indivisible patiles taveling afte one anothe in the same dietion (enegy) (and not bak and foth), thee will not be ounte stiking (as long as they ae not olliding with othe patiles going in thei way). This means that thei euivalent matte distane (edued Compton wavelength) is infinite and we an theefoe say that a non-ounte-stiking indivisible patile must have the following est-mass m i 0 (5) That the Compton wavelength is infinite fo a photon is nothing new and has been pointed out by Hawking in 97 [3], fo example. Zeo est-mass simply means that even though it is not ountestiking, the indivisible patile still has a potential mass of half the Plank mass. The potential mass is tuning into est-mass when it is ounte-stiking anothe indivisible patile; this is the only moment duing whih it is at est. Moe peisely, that is the only moment it hanges its dietion, and in the instant between hanging dietion we an say it is at est. Rest-mass is elated to the numbe of times indivisible patiles ae at est (ounte-stiking), and this again is dependent on the so-alled edued Compton wavelength of the subatomi patile. Unde atomism the edued Compton wavelength has nothing to do with a wave, but has to do with the void distane between the indivisible patiles making up the mass. The void-distane between indivisible patiles in a beam of enegy, that is indivisible patiles moving afte eah othe will have vey di eent impliations than an idential edued Compton wavelength. Fo example, two indivisible patiles taveling afte eah othe ould have a void-distane (what moden physis think is a wavelength) eual to the edued Compton wavelength of the eleton. Still this would not be the matte length of the indivisibles, as a matte length (edued Compton wavelength) is the length an indivisible patile tavels bak and foth in a stable patten in between eah ounte-stike. Table illustates how all masses theoetially an be onstuted fom two indivisible patiles that togethe have a mass eual to the Plank mass. Table 3 lists a seies of popeties of the assumed indivisible patile. What is of geat impotane is that the indivisible patile must always tavel with the speed 4 of light, itsdiametemustbel p and its mass must be half the Plank mass, and the Plank mass last fo a Plank seond as seen fom a obseve. Like the atomist Giodano Buno 5, we ae assuming that all indivisible patile ae unifom and sphee shaped; this leads to a seies of popeties suh as the iumfeene, sufae aea, and volume that also ae listed in the table. To what degee these patiula popeties (below the line) potentially will have 4 As measued with Einstein-Poinaé synhonized loks. 5 Who was bunt by the stake fo his view.

7 7 Patile Mass ( kg ) Time-speed ( s/m ) Indivisible patile m i.088e-08 None Plank mass patile (Motz) m p.77e E-09 Higgs patile m h lp m p.30e-5 3.4E-6 Neuton m N lp m n p.675e-7.57e-8 Poton m P lp m p p.673e-7.56e-8 Eleton m e lp e m p 9.09E-3.40E-3 Table : The table shows the mass in kg and the mass in time-speed fo some subatomi patiles. any impotane in deiving useful physis fomulas o to give us deepe insight in existing physis is unlea. Popety SI Units Dimensionless l p, Diamete D i l p.66e-35 m (L) Radius i l p 8.08E-36 m 0.5 ( L ) Shwazshild adius s l p.66e-35 m (L) Round-tip speed 99, 79, 458 m/s ( L/T ) Potential mass at hit m i m p l p.088e-08 kg ( M ) Potential mass at hit m i m p.668e-09 time-speed 0.5 ( T/L ) Enegy E i m p l p 978, 074, 758 J p Potential hage i E-9 C 4, Othe popeties with potential futue inteest: Ciumfeene C i l p 5.077E-35 m ( L ) Sphee sufae aea A i lp 8.06E-70 m ( L ) Sphee volume V i 6 l3 p.0e-05 m 3 6 ( L3 ) Euivalent suae aea lp.6e-70 m (L ) Euivalent ube volume lp 3 4.E-05 m 3 (L) Table 3: The table shows the popeties of the indivisible patile. Based on the analysis above, the mass of this most fundamental patile is half the Plank mass and this also means its mass is elated to half the edued Plank onstant,, athe than. Theonstant has eently been desibed by [34] as the fogotten onstant. We think indeed an be seen as an even moe fundamental onstant than, sine the indivisible patile seems to be the only tuly fundamental patile making up all enegy and matte. D Angelo also intodues the Plank iumfeene idential to the one listed in the table hee and links it to atomism. 6 Mass as kg and Mass as Time-Speed In moden physis, mass is typially given in the notation of kg. Fo example, a Plank mass in kg is given by m p G l p kg (6) Futhe, an eleton mass is given by m e lp e kg (7) G e Both G and ae elated to kg. In 04, Haug has shown that mass also an be deived and analyzed fom atomism without kg and without elation to G. Haug also intodued what he alls time-speed. As 6 IthinkD Angelohasimpotantpointselatedtoeintoduing and also the iumfeene of the indivisible patile. Howeve, I doubt that the onstant he alls the Demoitean unit Y has anything dietly to do with the indivisible patiles othe than being anothe onstant useful fo some alulation puposes. Still, only time will tell if thee is moe to it.

8 8 we have explained above, mass is atually elated to ounte-stikes between indivisible patiles. Suh ounte-stikes ae not only the foundation of mass, but they ae also the foundation of time. Only ounte-stikes an ause obsevable hanges and time is hange. Eah ounte-stike (mass event) an be seen as a tik of time. Evey subatomi patile an be seen as a disete lok with its own lok feueny, that is numbe of tiks pe seond. With time-speed we simply think about the numbe times the indivisibles ounte-stike ompaed to an ideal mass whee thee ae ontinuous ounte-stikes. We an think of an ideal fully solid mass whee a seies of Plank patiles ae laid out next to eah (o appoximately next to eah othe). The indivisible patiles always move at the speed of light and if they ae lying appoximately side-by-side, then they will ontinuously ounte-stike. This means the time-speed of a Plank mass an be desibed as simply ˆm p lp l p ontinuous seonds pe mete (8) That is to say, the dimension of a mass in the fom of time-speed is T. Suh an ideal mass is vey L useful fo standadizing mass and ompaing othe masses to it. Continuously ounte-stiking an be seen as a ontinuous lok. Fo evey mete an indivisible patile moves, it an maximum ounte-stike an infinite numbe of times, o in othe wods it is an tik 3 ontinuous nano seonds fo evey mete it moves. Just as the Plank mass in kg an be seen as the most fundamental kg mass, then nano seonds pe mete, an be seen as the euivalent ontinuous time-speed of a Plank mass. An eleton does not have ontinuous ounte-stikes; it is not a ontinuously tiking lok. An eleton is euivalent to ˆm e lp e ontinuous seonds pe mete, (9) ontinuous seonds pe mete the indivisible patiles moves. Thus if we know the Plank length and the edued Compton wavelength of the mass of inteest, we an do without the Plank onstant o the Newton gavitational onstant when we wok with any mass, as well as with gavity. Fo an indivisible patile, we have the potential mass in fom of time-speed eual to is ˆm i l p l p, (0) this is also the est-mass when ounte-stiking. Futhe, its est-mass when it is not ounte-stiking ˆm i l p 0. () That an indivisible patile has no est-mass when not ounte-stiking does not mean that it does not have a potential mass. It is enegy and has potential mass (time-speed) when not ounte-stiking, and it has est-mass (time-speed) and potential enegy when ounte-stiking. Again, this is a new way of looking at matte and enegy. It is a logial way whee enegy and mass not ae something undefined only desibed by mathematial fomulas ombined with a seies of buzz wods. By dessing up atomism in mathematis and ombining it with insight fom moden physis, then physis is again tuly Physis. Math is extemely useful and neessay to add peision to the language and to alulate what a theoy pedits; this an then be ompaed to expeiments and the wold aound us. Still, mathematial physis alone, no matte how well it fit expeiments, is no guaantee fo auiing an in-depth undestanding of eality. Atomism seems to ome handy in hee. 3 Heisenbeg s Unetainty Piniple in a New Pespetive Ou new atomist view of matte and enegy also seems to povide a new intepetation of Heisenbeg s Unetainty piniple. Heisenbeg s Unetainty piniple [35] is given by x p () whee x is onsideed to be the unetainty in the position, p is the unetainty in the momentum, and is the edued Plank onstant. Fo an indivisible patile we must have

9 9 x p x x x x p m i mp l p x l p (3) And this is no supise; as the indivisible patile has a diamete of l p, we annot eally say its loation is inside o in a point inside its spatial dimension. The indivisible patile natually oves its entie spatial dimension. So ou minimum unetainty onening the exat position of the patile (in a one-dimensional analysis) must natually be l p. The wod unetainty is not a well-desibed tem hee, as this is simply the one-dimensional minimum length the patile always must oupy, see figue 3. 7 Figue 3: Illustation of Atomism intepetation of Heisenbeg s Unetainty piniple fo a indivisible patile with mass eual to half the Plank mass. This emoves some of the mystey of Heisenbeg Unetainty piniple. Fom an atomist point of view, the Heisenbeg Unetainty piniple simply onfims that at the vey depth of eality we have indivisible patiles with spatial-dimension and a diamete of l p, athe than the non-logial hypothetial point patiles. Still, all obsevable subatomi patiles, like eletons, fo example, ae neithe point patiles no patiles with a spatial dimension eual to thei edued Compton wavelength. All obsevable subatomi paties onsist of indivisible patiles and void, and the indivisible patiles with spatial dimension ae moving at the speed of light along the edued Compton wavelength. Futhe, the momentum of an indivisible patile is given by x p p l p p l p (4) 7 Based on speial elativity theoy we have length ontation and we should think this was fame dependent. As shown by Haug 04, the length ontation is simply elated to edued void-distane between indivisible patiles and the indivisible patiles themselves annot ontat. But all masses onsist of indivisible patiles moving bak and foth in the void.

10 0 whih we aleady know, sine the momentum of an indivisible patile must be p i m i l p (5) l p We onlude that Heisenbeg s Unetainty piniple fomula makes logial sense fo indivisible patiles and opens up fo a moe logial intepetation based on an indivisible patile with spatial dimension and diamete l p. Next let us look at a subatomi patiles with mass less than half the Plank mass, fo example the eleton, m e. We laim the ight intepetation hee is given by using m e as the momentum of the eleton, this gives the unetainty in the position of x x m e e x This is fully onsistent with atomism. The indivisible patile moves bak and foth with the speed of light along the edued Compton wavelength of the eleton. And sine the patile moves so fast, the best guess to minimize ou eo of whee the indivisible patile elies on hoosing the midpoint of the edued Compton wavelength. Then we know it must be within half the edued Compton wavelength of the eleton. Simila an be done fo any subatomi patiles. Moden physis is a top-down theoy whee one has tied to dig deepe and deepe with some wondeful suess in fomula deivations and peditions. Howeve, moden physis is lost at undestanding the depth of eality. Atomism on the othe hand is mostly a bottom-up theoy. This alone is not any guaantee fo suess, but the geat pogess in mathematial atomism in eent yeas is vey pomising. Based on atomism we know that an indivisible patile must take up a diamete of l p.itismeaningless to ty to pin point the loation of the patile futhe, at least without talking about also the ente of the patile and so on. Atomism does not need Heisenbeg s Unetainty piniple to figue out the unetainty (that is not eally an unetainty) in the patile extension. Still, atomism is fully onsistent with the Heisenbeg Unetainty piniple fomula. Moden physis, with the hypothetial idea of point patiles, often has the oet fomulas but the intepetations seem to be fa-fethed. In addition, thei fomulas an often be boken down into simple fomulas based on Plank uantization as eently shown by [9, 33] e (6) 4 Patile Radius o Point Patile? Not so long ago it was assumed that known subatomi patiles suh as the eleton had a adius. The moden view is that subatomi patiles ae point patiles with no spatial-dimension. Fom the moden atomist pespetive, neithe of these views is oet. An obsevable subatomi patile, like an eleton, does not have a adius. The eleton is not a sphee. Based on atomism, the eleton is also not a point patile. The eleton likely onsists of two indivisible patiles (at a minimum) moving bak and foth at the speed of light ove a distane eual to twie the edued Compton wavelength of the eleton. Unde atomism the only patile that has a spheial shape and does not onsist of moving pats is the indivisible patile. It has a diamete eual to the Plank length and a adius eual to half the Plank length. Futhe, the indivisible patile is not a patile based on the iteia fom moden physis, beause it has no est-mass, exept when it is ounte-stiking; alone, when it is not ounte-stiking anothe indivisible patile, it only has potential mass (eual to half the Plank mass). All known subatomi patiles ae not point patiles, no do they have a adius. Instead they onsist of extemely small indivisible patiles moving bak and foth in a patten at the speed of light ountestiking with eah othe. Fo moden physis this is a entiely new way of thinking about matte and enegy. Based on atomism matte is haateized by an indivisible-void duality athe than a patilewave duality. But unde atomism this duality is nothing moe mystial than indivisible patiles always moving at the speed in empty spae (void). 5 Shwazshild Radius of the Indivisible Patile The so-alled Shwazshild adius is given by (see [36, 37, 38, 39, 40] )

11 s Gm (7) The patile with half the Plank mass is the only patile whee the Shwazshild adius is eual to the Plank length: s Gmi G mp l p (8) One an input the standad values of G, the Plank mass m p, and to hek that it gives a Shwazshild adius of l p. Altenatively, based on eent findings by [9, 33, 4], it ould also be witten as s G mp s l p 3 l p l p (9) Most physiists assume that the Plank length plays an impotant ole at the depth of eality. The indivisible patile is vey uniue; it must have a mass of half the Plank mass, its Shwazshild adius is l p, and futhemoe, it is the only patile that has an esape veloity of when we ae opeating all the way down to the Plank length l p v e Gmi s s G mp l p (0) In ou view, the half a Plank mass patile is an indivisible patile, always moving with the speed of light that makes up all othe patiles. The fat that it is dietly elated to the esape veloity with l p simply onfims this onept. As we soon will see, this onept also leads to a new intepetation of so-alled mini-blak holes. The idea of an esape veloity and blak holes atually goes all the way bak to 784 when Mihell, based on Newtonian mehanis, speulated on what he alled dak stas, see [4, 43, 44]. Thee exists a somewhat ompeting patile that is often alled the Plank patile; among many physiist it has been intepeted as a mini-blak hole. This is a patile with mass p times the Plank mass. Its esape veloity is, when using its Compton wavelength as the adius in the esape veloity fomula. Howeve, we do not think that this patile an exist and it is not as uniue as some physiists might think, even fom a mathematial point of view. See [8]. Altenatively, we an look at a mass with p times the Plank mass and when setting the edued Compton wavelength (instead of the Compton wavelength) eual to the adius in the esape veloity fomula, we again get an esape veloity of. So is this yet anothe mini-blak hole? We doubt it. On the othe hand, the indivisible patile does have many similaities with the oiginally oneption of the popeties of a blak hole. The indivisible patile is indivisible, that is unbeakable; it is fully ontained inside a length eual to the Shwazshild adius and theefoe nothing an esape fom it, beause it is singula and indivisible. Nothing adiates out fom it o into it. Thee is no Hawking adiation fom an indivisible patile. The indivisible patile is in one instant, that is fo one Plank seond, pat of a mass (ounte-stiking) and in the next instant it is enegy again, so it is adiating into itself. Howeve, the mass and adiation ae nothing moe than enteing and leaving the ounte-stiking state. Hawking [3] has expessed the opinion that a blak hole annot have a mass smalle than about 0 5 gam, whih inteestingly is the same as the mass of half the Plank mass. Howeve, the intepetation given hee is vey di eent. The tem blak hole is misleading if the fomulas ae atually hinting at the existene of an indivisible patile. The blak hole intepetation fo a patile with esape veloity is just a hypothesis. The indivisible patile theoy seems moe logial and it also solves the mystey of why do we not obseve anything with a Plank mass o lose to a Plank mass, even when the Plank mass and the Plank length appea to be so impotant fo etain pats of mathematial physis. Hawking intepeted suh mini-blak holes as ollapsed objets shown in the fom of vey densely paked masses due to vey stong gavitation and a type of gavitational ollapse. Unde atomism, in ontast, this epesents indivisible patiles that annot ollapse o get any smalle; it is simply a mathematial expession of thei indivisibility. Futhe, it is impotant to note that the indivisible patile has a spatial dimension; it is not a point patile. Compaed to othe masses, suh as an eleton that mostly onsist of void, an indivisible patile is indeed vey dense. When they ae lose of eah othe, these patiles have an extemely stong foe, namely the Plank foe. Howeve, this stong foe only

12 lasts fo a Plank seond fom an obseves pespetive, at the time when an indivisible patile ountestikes with anothe indivisible patile. It is oet that any mass that we an obseve in patile fom, even in a thought expeiment set-up, annot have a mass of less than the Plank mass. This ould happen if we stip a patile suh as an eleton of its void, that is if we pushed indivisible patiles togethe. Altenatively, if we had euipment to obseve the patiles at lose to a Plank seond time inteval, we would likely have obseved Plank mass objets aleady and almost eveywhee. Unfotunately, ou uent tehnology is vey fa fom being able to measue suh shot time windows. Again the atomism theoy seems fully onsistent with the idea that thee is something vey speial fo patiles with esape veloity ; namely that these ae vey likely to be indivisible patiles always taveling at speed. Anothe impotant point is that the view of enegy and matte pesented by atomism eliminates singulaities, and, as we will soon see, it also gets id of infinities. The appeaane of singulaities should typially be seen as an indiation of model beak down, but instead the pupoted detetion of singulaities has lead to a seies of mystial intepetations suh as blak holes. Figue 4 gives an illustation of the atomism intepetation of Shwazshild adius and esape veloity at the Plank sale. Figue 4: Illustation of Atomism intepetation of Shwazshild adius and esape veloity at the Plank sale. Fou mathematially inteesting Plank type patiles, whih ae losely elated to the Plank mass ae listed in table 4. Thee ae good easons to think that only two of these patiles atually epesent something eal: the Plank mass patile that onsists of two indivisible patiles and the most impotant of all patiles, namely the indivisible patile, that has half the Plank mass. Patile Mass Redued Compton Shwazshild Esape name in kg Compton wavelength adius veloity a wavelength m lp G h h m m s Gm Gm v e Plank mass patile m p p l p l p l p and p Plank type patile m b p m p l p p l p p l p p and Plank type patile m p m p p lp p 8 lp p lp and Indivisible patile m i mp lp b n/a l p Table 4: Plank patiles. a The esape veloity is alulated twie, fist by using the edued Compton wavelength as the adius and seond by using the Compton wavelength as the adius. b This patile has pe definition no Compton o edued Compton wavelength of its own. This is the diamete of the patile. See omments below the table. The indivisible patile has, by definition, no Compton o edued Compton wavelength on its own. The indivisible patile does have an assumed diamete of l p. In eality, to have a edued Compton wavelength unde ou theoy we need at a minimum two indivisible patiles, as the edued Compton wavelength in this theoy is the aveage distane between two indivisible patiles making up a mass. In a Plank mass, fo example, the edued Compton wavelength is l p. Bea in mind that the indivisible p

13 3 patile has no est-mass exept when ounte-stiking with anothe indivisible patile. When ountestiking with anothe indivisible patile, the two indivisible ae ombined the Plank mass and then this mass has a edued Compton wavelength of l p as also shown in the table. That is the distane ente to ente between two indivisible patiles (that eah have a diamete of l p)lyingnexttoeahothe (ounte-stiking) fo signifiantly longe than the Plank length. 6 A New Solution to Einstein s Infinite Mass Challenge Let s look at elativisti masses next. Einstein [3, 45] gave the following elativisti mass fomula: m. () v Futhe, Einstein ommented on his own fomula This expession appoahes infinity as the veloity v appoahes the veloity of light. The veloity must theefoe always emain less than, howevegeatmaybetheenegiesusedto podue the aeleation 8 We etainly agee with Einstein s fomula; it is fully onsistent and an also be deived fom atomism, as shown by Haug in 04. Einstein s agument is that the mass will beome infinite as v appoahes and this means that we would need an infinite amount of enegy to aeleate even an eleton to the speed of light. Howeve, fom a deepe fundamental point of view the undestanding of mass and enegy in moden physis is still vey limited. Based on a bette undestanding of uantization of mass and the Plank mass in patiula, when ooted in atomism, we will show this leads to a exat speed limit fo any given fundamental patile as long as we known the patile s est-mass. At this maximum speed limit we will soon disuss, the subatomi patiles will have eahed a mass limit, whih is the Plank mass. Next the Plank mass will dissolve moe o less instantaneously into enegy, whih is moving at the speed of light. Hee, we will not need infinite enegy to move a mass to the speed of light. Bea in mind that a Plank mass omes into existene exatly in the instant when two indivisible patiles ollide. Even if the indivisible patiles eating the Plank mass ae moving at the speed of light just befoe and afte they ollide (ounte-stike), they ae standing still in the vey instant they eate the mass. The Plank mass is simply a ollision. One ollision between two indivisible patiles is one ollision no matte what fame it is obseved fom. That is to say, the Plank mass is atually vey uniue in that it always has the same mass no matte what fame it is obseved fom. This is a speial ase, as it only holds fo the Plank mass (the Plank mass patile that exist in the instant of the ollision between two indivisible patiles) and fo no othe subatomi patiles. Not only is the Plank mass invaiant to what fame it is obseved fom; it must also be lagest possible mass that a subatomi patile an take. Futhe, the Plank mass has the shotest possible edued Compton wavelength. Its edued Compton wavelength is eual to the Plank length. It is atually impossible fo two indivisible patiles to ome lose towads eah othe when they ounte-stike. They ae indivisible and fully had, just as the patiles that Newton desibed. The indivisible patile has a diamete of l p and the losest it an be between the two patiles ente to ente is the Plank length, whih again is the edued Compton wavelength of the Plank mass, when the two indivisibles ae lying side-by-side ounte-stiking. All known subatomi patiles, suh as an eleton, have a muh longe edued Compton wavelength than the Plank mass. The indivisible patiles making up an eleton move bak and foth along the edued Compton wavelength of the eleton. The shote the edued Compton wavelength of a patile, the lage the mass will be. The edued Compton wavelength of any mass othe than the Plank mass has mostly empty spae (void) in the edued Compton wavelength. Assume two indivisible patiles making up a est-mass have a edued Compton wavelength of. Due to length ontation, when a mass is moving the edued Compton wavelength of that mass will be obseved as ontated fom any othe fame. This is the ase at least as long as it is dietly o indietly measued with Einstein synhonized loks; an extensive disussion and a seies of deivations on this is given in [6]. When the speed of the subatomi patile is so lage that the edued Compton wavelength has length ontated to l p, then the mass will simultaneously have eahed its Plank mass. The Plank mass will howeve not be stable, but will, within a Plank seond, bust into enegy 9. Well, the poof is in the pudding, that is to say hee, in the mathematial pudding 0 : 8 This uote is taken fom page 53 in the 93 edition of Einstein s book Relativity: The Speial and Geneal Theoy. English tanslation vesion of Einstein s book by Robet W. Lawson. 9 Atually it will bust instantaneously into enegy, but fom an obseve s pespetive using Einstein-Poinaé synhonized loks this would take plae, unde vey idealized onditions, in one Plank seond. This is atually due to a minimum synhonization eo; see [6] foadisussiononloksynhonizationeos. 0 See an altenative deivation that gives the same end esult in the Appendix A.

14 4 m p m v m m p v m v v v m p s s v v u t v u v t v v m m p m m p m m p l p l p l p () The maximum speed any patile an take is a funtion of the Plank length and the edued Compton wavelength of the patile in uestion. Again, when a patile eahes this maximum speed that always is v max <, then it will beome a Plank mass, and the Plank mass is extemely unstable and will bust into enegy within a Plank seond fom an obseve s point of view. Also, the edued Compton wavelength of the mass will have ontated to l p, as obseved dietly o indietly using Einstein- Poina e synhonized loks to measue the length ontation of the edued Compton wavelength. Using the known edued Compton wavelength of some subatomi patiles we an find thei maximum speed. An eleton has a edued Compton wavelength e m and an neve be aeleated to a veloity faste than s lp v e In the above alulation we have assumed a Plank length of Howeve the Plank G length: l p is dependent on big G in addition to and. Theefoe ou assumed theoetial speed 3 limit fo the eleton is also dependent on big G. As thee is onsideable unetainty about the exat value fo big G, thee is also some unetainty about the theoetial value fo the maximum speed limit of the eleton. In 007, a eseah team measued big G to ,whileanotheteamin04 measued big G to ,see[46, 47], fo example. Assuming and to as the ange fo big G, we get a theoetial ange fo the speed limit of the eleton eual to: G oesponds to l p and v and G oesponds to l p and v These alulations euie vey high peision and wee alulated in Mathematia. hypotetially tun into pue enegy at the speed of A poton will We used seveal di eent set-ups in Mathematia; hee is one of them: N[St[ (6699 0^( 4))^/( ^( 9))^], 50], whee ^( 4) is the Plank length and ^( 9) is the edued Compton wavelength of the eleton. An altenative way to wite it is: N[St[ (SetPeision[ ^( 35))^, 50]/(SetPeision[ ^( 3))^, 50]], 50]. Hee assuming l p and P

15 5 v s l p P Fo ompaison at the Lage Hadon Collide in 008, the team talked about the possibility of aeleating potons to the speed of % of the speed of light [48]. When the Lage Hadon Collide went full foe in 05, they ineased the maximum speed slightly above this (likely to aound % of the speed of light). In any ase, the maximum speeds (and enegy levels) mentioned in elation to poton aeleations at the LHC ae fa below what is needed to eah the maximum speed of a poton o an eleton as given by atomism. Supisingly the minimum enegy needed to aeleate any subatomi patile (fundamental) to its maximum speed is the same. This is only possible beause the maximum speeds based on ou theoy is invesely elated to the patile s est-mass, and natually beause the maximum mass any subatomi fundamental patile an eah is the Plank mass. The enegy needed to aeleate any mass to its maximum mass is the Plank mass enegy, whih is E m p. 0 6 TeV. The LHC is uently opeating at 3 TeV and it is theefoe extemely unlikely we will see this theoy veified expeimentally, as it would euie a muh moe poweful patile aeleato. Still, the main point is that we in no way need infinite enegy fo a mass to eah the speed of light. It will bust into enegy when eahing its maximum speed, whih is just below that of the speed of light, and we an alulate that speed auately based on the atomist view of matte. In eality, if a poton onsists of a seies of othe subatomi patiles, then the speed limit given above fo a poton will not be vey auate. Altenatively, we ould have looked at the edued Compton wavelength of the uaks that the standad model laims is making up the poton. As the uaks in the poton have di eent edued Compton wavelengths, then the poton ould have seveal maximum speeds whee pats of the poton mass tuns into a Plank mass and then bust into enegy. We an also alulate the maximum speed fom the mass onept of time-speed athe than kg, this is shown in Appendix B. 3 l The speed limit fomula we have deived is v max p. When is set to l p,wehaveaspeed limit of. This means only something dietly elated to the Plank mass an move with speed, and that is the two indivisible patiles making up the Plank mass. The patiles making up the Plank mass always moves at speed. All othe masses onsist of void and of indivisible patiles moving bak and foth; suh stutues an and must move slowe than the speed of light. 7 Maximum Kineti Enegy Kineti enegy fo low veloities, v<<an be appoximated by the well known 4 fomula E k mv, although at high speeds we need to use Einstein s elativisti kineti enegy fomula E k m v This means that the kineti enegy appoahes infinity as v appoahes. The elativisti kineti enegy fomula an also be deived dietly fom atomism as shown by Haug 04. In the setion above, we have seen thee must be a maximum speed limit of any mass eual to v max Fom this standpoint, the maximum kineti enegy fo any fundamental mass patile must be 3 Aleady in 04 Haug [6] deivedaspeedlimit(oatleastanattemptfoaspeedlimit)foanyunifommassdeivedbak then without any link to the Plank mass, that given by ou notation hee would by v ( l p) ( +l 4 l p p). This fomula was deived fom a one-sided (one-dietional) Dopple shift. Afte eently having e-investigating this fomula futhe it is now lea that this is the speed whee a subatomi fundamental patile gets a elativisti mass eual to half the Plank mass. This is not the same as a potential half Plank mass, so it does not mean it is one indivisible patile. To get a elativisti mass of half a Plank mass one needs a minimum of two indivisible patiles to eate this mass. If we had deived the speed limit based on a two-sided Dopple shift instead, we would have gotten the fomula pesented in this pape, and only this is likely a speed limit fo masses. The speed whee a mass eahes a half Plank mass is likely not a speed limit, but it is a speed that we will investigate futhe. 4 This fomula was likely fist deived by Gottfied Wilhelm Leibniz and also deived expeimentally by Gavesande and published by Gavesande in 70; see [49]. m l p (3)