The Mystery of Mass as Understood from Atomism

Transcription

1 The Mystey of Mass as Undestood fom Atomism Esen Gaade Haug June, 08 Abstat Ove the ast few yeas I have esented a theoy of moden atomism suoted by mathematis [, ]. In eah aea of analysis undetaken in this wok, the theoy leads to the same mathematial end esults as Einstein s seial elativity theoy when using Einstein-Poinaé synhonized loks. In addition, atomism is gounded in a fom of uantization that leads to ue bounday limits on a long seies of esults in hysis, whee the ue bounday limits taditionally have led to infinity hallenges. In 04, I intodued a new onet that I oined time-seed and showed that this was a way to distinguish mass fom enegy. Mass an be seen as time-seed and enegy as seed. Mass an also be exessed in the nomal way in fom of kg (o ounds) and in this ae we will show how kg is linked to time-seed. Atually, thee ae a numbe of ways to desibe mass, and when they ae used onsistently, they eah give the same esult. Howeve, moden hysis still does not seem to undestand what mass tuly is. This ae is mainly aimed at eades who have aleady sent some time studying my mathematial atomism theoy. Atomism seems to o e a key to undestanding mass and enegy at a deee level than moden hysis has attained to date. Moden hysis is mostly a to-down theoy, while atomism is a bottom-u theoy. Atomism stats with the deth of eality and suisingly this leads to editions that fit what we an obseve. Key wods: Mass, enegy, time-seed, ollision-time, fom time-seed to kg, the Haug gavitational onstant. The Mystey of Mass In moden hysis, mass is athe mysteious. Thee is no doubt that moden hysis has good insights, both mathematially and exeimentally, egading the elationshi between enegy and mass. Howeve, fo all of the yeas of analysis and theoizing, hysiists still annot eally exlain what enegy and mass ae. As one stated by Rihad Feynman It is imotant to ealize that in hysis today, we have no knowledge what enegy is. Muh of moden hysis is to-down, in that is one has obseved a etain henomenon and then ties to exlain it by digging deee and deee. Atomism has an advantage hee, as it is bottom-u. In a bottom-u theoy, one stats with an idea onening what the wold is at the vey deeest level, then deives what that idea wiledit and omaes it with atual obsevations and with othe theoies. Natually a bottom-u theoy must be onsistent with exeiment; if not, then thee is lealy something wong with the fundamentals. Futhe, attemting to stat at the bottom does not guaantee suess. Howeve, atomism seems to have emakable suess: in ou exeiene, nothing that atomism has edited so fa goes against the findings of taditional exeiments. Howeve, it seems to lead to a moe logial and moe staightfowad theoy. Fo examle, we have shown that atomism leads to all of the same mathematial end esults as seial elativity when using Einstein-Poinaé synhonized loks; see []. In addition, atomism edits an exat maximum veloity of matte that is just below the seed of light; this seems to emove a seies of infinity hallenges in seial elativity theoy. The edition fom atomism on the maximum veloity of anything with est-mass is also the same limit we have found eently by ombining Heisenbeg s unetainty inile with some of Max Plank s key onets. The mass of subatomi atiles an be witten as esenhaug@ma.om. m kg ()

2 whee is the Plank onstant, is the edued Comton wavelength of the atile in uestion, and is the well-known seed of light. One neve sees moden hysis aes disuss what the seed of light eesents inside a mass fomula. It is well- known that the seed of light (suaed) is needed to go fom mass to enegy and fom enegy to mass, but that just shows thee is otentially an enomous amount of enegy in a small amount of mass. Howeve, why also onside the seed of light inside a mass? Moden hysis does not have an exlanation fo this. The field in geneaobably just look at this as something uely mathematial that one an deive fom othe onets. Howeve, we will soon see and undestand why the seed of light is so essential in a mass, and what it eesents. Time-Seed, Continuous Time, and Collision Time The uest fom of mass unde atomism omes into being at the vey ollision oint (ounte-stike) between indivisible atiles. A ollision between two indivisible atiles lasts fo one Plank seond. The numbe of intenal ollisions in an eleton e seond, fo examle, is simly the seed of light divided by the edued Comton wavelength of the eleton. That is to say, we have the following numbe of intenal ollisions in an eleton e seond ollisions e seond () This is what we an all the intenal feueny of an elementay atile. Eah elementay atile has an intenal ollision feueny. This is vey simila to Shödinge s [3] hyothesis in 930 of a Zittebewegung ( tembling motion in Geman) in the eleton that he indiated was aoximately m e tembling motions e seond (3) This is atually exatly twie ou numbe, but we think ou numbe is moe elevant in this eset. Shödinge also did not seem to have an exlanation of exatly what was behind this tembling motion. Hee we ae hyothesizing that it is the numbe of intenal ounte stikes inside an eleton that will also make the eleton stand and vibate. Futhe, eah ollision lasts fo one Plank seond; see [4, 5]. This means that, in total, the ollisions in an eleton last fo l ontinuous seonds e seond (4) This is atually a dimensionless numbe, but as we will exlain, it an be seen as the numbe of ontinuous seonds e seond. That is, we onside eah ollision as a eiod with ontinuous time and then add all the ollision times togethe and all this ontinuous time, even if it onsists of many disete ollisions. So one ould always ague about the use of wods hee. We ould also have looked at the amount of ontinuous seonds fo the time it takes fo light to tavel one mete in a vauum. This would be l (5) This is the amount of ontinuous time e mete of light tavel. Altenatively, we an say that it is the amount of ontinuous time e aoximately 3.3 nano-seonds, as light tavels one mete in this time. This is dietly elated to the time-seed onet intodued by Haug in 04. We onside the ollisions as ontinuous time, o seen anothe way, it ould be alled ollision time. How muh time ae the indivisible atiles in an elementay atile sending on ollisions e time unit? Bea in mind that unde atomism, an elementay atile like an eleton onsists of (minimum) two indivisible atiles moving bak and foth ounte-stiking. The indivisible atiles always move at the seed of light, with the exetion of that oint of ollision, when they stand still fo one Plank seond. Instead of alling this ontinuous time, we ould simly all this ollision time e time unit. The idea behind ontinuous time is that it eesents the time whee atiles ollide elative to the time the indivisible atiles making u the elementay atile ae not olliding. Time-seed is a atio of ollision time elative to non-ollision time. In othe wods, it is the time in est (ollision) elative to time in intenal motion of the indivisible atiles. Hyothetially, in a Plank mass atile thee is no distane between the indivisible atiles and they ae olliding as feuently as ossible. The time-seed of a Plank mass is ˆm l seond e mete (6) That is is 3.3 nano-seonds e mete, whih is the maximum ossible time-seed. In othe wods, it is olliding fo 3.3 nano-seonds, e 3.3 nano-seonds, o e mete the light tavels. A Plank mass an also be witten simly as

3 3 ˆm l ontinuousseondeseond () That is only a Plank mass is ue ontinuous time, and it only onsist of ollisions. All othe elementay atiles, >, must send the following amount of ontinuous time e mete that light tavels (that is e 3.03 nano-seonds) Fo examle, an eleton is ˆm l ontinuous seonds e mete (8) ˆm e l ontinuous seonds e mete (9) That is, fo evey 3.03 nano-seonds an eleton will have sent seonds on ollisions. It is woth noting that when we wok with mass as time-seed we do not need Plank s onstant. Futhe, when we wok with mass as time-seed, then the Plank mass is easily given and it only deends on the seed of light. Fo all othe masses, we also need the Plank length and the edued Comton wavelength. Fo a Plank mass, the edued Comton wavelength is eual to the Plank length and they anel out, so we ae only deendent on the seed of light. That is the seed of the indivisible atile in a vauum. 3 Mass as kg and How to Go fom kg to Time-seed It is inteesting to see fom the mass definitions in the evious setion that we have neve used the Plank onstant o the edued Plank onstant. As Haug has witten about eviously, the Plank onstant is a onvesion fato that is atually a omosite onstant, whih an be witten as m kg/s (0) whee is the numbe of intenal hits e seond in one kg. The mass of any elementay atile is defined unde standad hysis and an also be defined unde atomism Fo examle, fo an eleton we have m kg () Now let s elae with m and we get kg () (3) m Seen at a deee level, a mass in kg is simly the intenal hit feueny in the elementay atile divided by the hit feueny in one kg. One kg is a andom atial amount of matte that someone deided to all one kg. It was not too heavy (so it ould not be aied aound), but also not so light that it was had to measue. A kilogam is basially a dimensionless numbe in the sense that it is a hit feueny atio. To go fom kg to time-seed in ontinuous seonds e mete we need to divide the mass in kg with m kg s (4) The edued Plank onstant divided by the Plank onstant is a onvesion fato needed to go fom kg to time-seed, o fom time-seed to kg. One kg is 0.5 ontinuous seonds e mete, and ontinuous seonds e seond ( ). We must have that 6.5 kg is one ontinuous seond e mete and 99,9,458 ontinuous seonds e seond. Also 99,9,458 Plank masses is 6.5 kg. Any mass with a time-seed of moe than one ontinuous seond e seond annot be an elementay atile, but must onsist of a olletion of elementay atiles. And masses with time-seeds less than one ontinuous seond e seond an be olletions of elementay atiles, but they don t have to be. Fo examle, a Plank mass is one ontinuous seond e seond. Thee ae atually a numbe of ways to desibe a mass; they all ae oet, and they an be onveted fom one to the othe. Table show seveal ways to exess mass Table shows vaious ways to desibe the mass of elementay atiles. All of them ae oet and we an go fom one definition to anothe by using a onvesion fato

4 4 Geneal fomula: Time-seed Time-seed Feueny Feueny atio e mete e seond e seond known as kg Mass-ga Eleton Poton Plank mass One kg kg Table : The table shows mass as time-seed e mete, time-seed e seond, and mass as kg. Mass-ga Othe masses Plank mass Time-seed Time-seed Feueny Feueny atio e mete Pe seond kg l l One kg l l l 6.5 kg Table : The table shows ways of exessing mass; all of them ae oet. In some of the fomulas above, we have, on uose, mistakenly witten as (5) This is not tue fom a unit esetive; it is simly done beause we have a edued Comton wavelength that is eual to the length light tavels in one seond, so we have fo onveniene elaed it with in the ight-hand at (so it is easie to emembe and to see onnetions ). Both tables also mention the mass-ga. We will not go in muh disussion about that hee, but a deee disussion aound the mass-ga is given in [6]. The edued Comton wavelength of the mass-ga is mete e seond. The mass-ga in tems of feueny is always one, it is one ollision, one ollision will be obsevational time indeendent. Howeve, the mass-ga as a elative atio is the only mass that is always obsevational time deendent. 4 Relativisti Mass The masses in Tables and ae fo est-masses. Table 3 looks at elativisti masses. Einstein s elativisti mass fomula [, 8] fo an elementay atile an be witten as m m 0 v v v v kg (6) We see that elativisti mass has to do with ontation of the edued Comton wavelength, that is the aveage void distane between the indivisible atiles ae ontated as measued with Einstein-Poinaé synhonized loks. The indivisible atile itself annot ontat. Futhe, atomism (see [, 9, 0, ]) gives us an exat limit on the maximum veloity any elementay atile an take; this is given by v max This means that no elementay atile an attain a elativisti mass highe than the Plank mass atile. Futhe, the shotest edued Comton wavelength afte maximum length ontation is the Plank length. We also find that Loentz symmety is boken at the Plank sale, as oven by Haug in his eent Heisenbeg ae. Seial elativity theoy is atually not onsistent with a minimum length eual to the Plank length. The SR theoy needs to be modified in the way edited by atomism in ode to beome onsistent with Heisenbeg, when ombined with key onets fom Max Plank. l ()

5 5 Table 3 shows elativisti mass fomulas fo elementay atiles, the Plank mass atile is not a eted by veloity beause its maximum veloity is zeo. It is using all its time in ollision mode. Mass-ga e seond Othe masses Plank mass Time-seed Time-seed Feueny Feueny atio e mete Pe seond kg l v v v v Table 3: The table shows fomulas fo elativisti mass. 5 The Simliity of E m When Looking at Mass as Timeseed The Plank mass atile is the uest mass and has a time-seed of ˆm. It is inteesting to see that the famous Einstein fomula E m then simlifies to and natually we have Ê ˆm (8) ˆm E ˆm (9) In othe wods, in the E m fomula is at a deee level nothing othe than a onvesion fato to go fom time-seed (indivisibles moving bak and foth in a stable atten ounte-stiking, o olliding) to seed. Natually, fo ontinuous time masses that ae not in the uest fom, the euations ae slightly moe omliated Ê ˆm l (0) This exlains why the Plank mass atile is the only mass that is the same as obseved aoss all efeene fames. It is only the edued Comton wavelength that an ontat fo a moving mass. Howeve, it an neve be shote than the Plank length, beause this is the diamete of the Plank length. See also Figue, whih exlains uite well the intuition behind time-seed and the elationshi between enegy and mass. This method is moe intuitive than using kg as mass, but both kg and time-seed an be used to desibe mass.

6 6 Figue : This figue illustates the elationshi between enegy and mass, when mass is viewed as time-seed (ollision time). 6 Pobabilisti Atomist Theoy Fom atomism, we also get a simle obabilisti uantum theoy. Figue illustates an elementay atile. Assume we have an elementay atile suh as an eleton with a edued Comton wavelength of. What is the obability inside one Plank seond that the atile is in a mass state? Remembe, unde atomism thee is only one tue mass, the Plank mass that lasts fo one Plank seond, whih ous at the ollision oint of two indivisible atiles. The obability that the elementay atile is in a mass state in an obsevational time window of one Plank seond must be P l. () This is the uantum obability that the indivisible atile in the elementay atile is at est (olliding), that is to say, it is in a mass state, as we have defined ollision as what mass atually is. We see that the edued Comton wavelength,, is in the uantum obability. The Plank mass atile has the shotest ossible edued Comton wavelength,, whih means it is in a mass state if obseved. The Plank mass atile is the ollision oint between two indivisible atiles, as exlained ealie in this text. The obability of it being in a mass state duing the Plank seond duing whih we obseve the Plank mass atile is P l l l () That is onditional on the emise that if we obseve a Plank mass atile in a Plank seond obsevational time window, it must be in a mass state. All othe elementay atiles (when at est) always have a obability lowe than one of being in a mass state.

7 Figue : This figue illustates two indivisible atiles taveling bak and foth at the seed of light and standing still fo one Plank seond at eah ollision. 6. Relativisti Quantum Pobabilities When the atile is moving at seed v elative to the laboatoy fame, the edued Comton wavelength will ontat as obseved fom the laboatoy fame. Deivation of length ontation unde atomism is the same as that of seial elativity theoy when using Einstein Poinaé synhonized loks; this is shown by Haug []. This means ou elativisti uantum obabilities must be P (3) v At fist this may seem unealisti, as the obability an go above unity when v aoahes. Howeve, emembe that the indivisible atiles annot ontat; they ae indivisible. That is, the maximum length ontation in the edued Comton wavelength must be limited by the Plank length. The onet that the maximum length ontation is limited to the diamete of the indivisible atiles leads to a maximum veloity fo matte as desibed by Haug in a seies of aes is given by v max This maximum veloity gives a maximum elativisti obability of one: l (4) ale P ale v max ale P ale (5) Thus, unde atomism the obabilities ae always inside what ae onsideed valid obabilities. The inteetation of this should be that if we ae obseving a known elementay atile an eleton, fo examle, then this is the obability that the atile is in a mass state in a obsevational time window of one Plank seond. With the tem known atile I simly mean that we know its edued Comton wavelength. Pobabilities in ou theoy ae moe than mee abstations; they always have to do with distanes and veloities. And sine veloity is distane divided by a time inteval, we an say that ou uantum obabilities ae always elated to sae and time at the uantum level. 6. Heisenbeg-tye unetainty inile and the link to atomism Thee seems to be a vey inteesting elationshi between Heisenbeg s [] unetainty inile and atomism. The Heisenbeg unetainty inile is given by x (6) whee is the unetainty in momentum and x is the unetainty in osition. Now, the unetainty in the length of the edued Comton wavlength of an indivisible atile in the atomist model inside a given elementay atile is

8 8 so unde atomism we have x v () E x E t v E (8) v Ou inteetation is simly that the unetainty in enegy is a funtion of the unetainty in veloity. Unde atomism the minimum veloity fo a atile we assume is v 0andthemaximumveloityisv max l. This means we must have s E vmax l! l E E E v min 0 m E m (9) Thus, ou unetainty inile gives a ange fo the total enegy in a atile. Moden hysis has nothing like it, as thee is then no limit on v, exet fo v<,andinthisase,oneanalwaysmovev lose to, something that basially leads to a situation whee we an get as lose to infinite enegy as we want. Unde atomism, the maximum enegy is the Plank mass enegy, and the minimum is the est-mass enegy. So, if I know the atile is an eleton, then I know its enegy must be between m e and m. The Plank mass enegy is eahed when it is aeleated to its maximum veloity. In tems of time-seed we get E vmax E v min E m E m (30) We edit that thee also is anothe tye of maximum unetainty in the osition of the indivisible atile (atiles) making u an elementay atile elated to the maximum length tansfomation (not the length ontation) of the edued Comton wavelength of the elementay atile in uestion at its maximum veloity. This is given by

9 9 x max x max. s x max x max v max l! (3) we use hee bax athe than x as thee in ou view is two tyes of unetainty in the osition of the indivisible atile, one is elated to length ontation of the edued Comton wavelength, the othe esetive is fom a length tansfomation. Fo an eleton this gives a maximum unetainty in its osition of x max e 9, 6, 53, 48 m. This is a vey lage distane, but still makes moe sense than infinity, whih is given by moden hysis. This is also the distane light tavels in aoximately 30.8 seonds. So, what does this mean? The maximum unetainty in osition simly means we ae dealing with an eleton taveling at its maximum veloity v max l. Then, fom the lab fame to measue the oint whee the two indivisible atiles in the eleton ollide, one has to wait u to 30.8 seonds, and in this time the eleton will have taveled 9,6,53,48 m. In othe wods, thee is nothing mysteious about it. The unetainty inile is atually losely linked to elativity theoy, but an only be fully undestood when one undestands the atomist idea of elementay atiles. Anothe way to see this is that the time between eah ounte-stike in the eleton is, as measued fom its est fame, simly the edued Comton time, that is.9 0 s. Howeve, at its maximum veloity as obseved fom the laboatoy fame (the fame the eleton moves elative to at this seed) we have a time inteval of t t vmax s l! 30.8 s (3) Again, this means aoximately 30.8 seonds between eah ounte-stikes in the eleton just befoe the eleton eahes its maximum veloity, as obseved fom the laboatoy fame. Sine the maximum veloity is vey lose to the seed of light, this means that the eleton has taveled aoximately ,, 6, 85m, between two ounte-stikes. Table 4 summaizes the unetainty limits in elementay atiles fom the esetives of atomism and moden hysis. The moden hysis esetive is natually moe omlex than illustated hee. In moden hysis many uestions emain on the existene and natue of the mass ga, fo examle, and futhe, the natual units of Max Plank, inluding the Plank length and Plank time is also not undestood well fom moden hysis, but have lea elations and exlanations unde atomism. Max Unetainty atomism Momentum ale ale l Position unetainty ale x ale Mass ale m ale Max Unetainty standad hysis 0 ale ale 0 ale x ale 0 ale m ale Mass ga ale m ale Unknown Redued Comton wavelength ale L ale 0 ale L ale Table 4: The table shows fomulas fo elativisti mass. Assume fo a moment that a oton was an elementay atile, then the maximum unetainty in its osition would be x max P 36.6 m

10 0. This in stong ontast to moden hysis ditum that says to know the momentum of a oton exatly means thee will be infinite unetainty in the osition of the oton. 6.3 All elementay atiles ae a obabilisti funtion of the one and only ue mass Unde atomism the only eally ue mass, and in eality the only mass, is the Plank mass atile. All othe elementay atiles an be seen as a obabilisti funtion of the Plank mass atile. The exeted elativisti mass of any atile is simly E[m] m P m ale m (33) v This is the exeted mass ove a long time eiod. A long time eiod is a time eiod that is long elative to the edued Comton time. Inteestingly, this also means that we an ewite the uantum obability as m v m v m v E k + m m m P E k + m m (34) The uantum obability is eual to the kineti enegy lus the atile est-mass enegy divided by the Plank mass. Again emembe that the maximum veloity of the Plank mass atile is zeo. This means that Plank mass atiles annot have kineti enegy and all thei enegy is est-mass enegy, so we must have P 0+m m (35) Again, we see the Plank mass atile uantum obability always must be one. Tuning to the maximum elativisti uantum obability fo othe atiles, we get, at thei maximum veloity P max E k + m m P max E k + m m m m + m v max P max m P max (36) When v<v max, we must have a uantum obability of less than one. The Plank mass atile, howeve, is uniue as v v max; beause the the maximum veloity fo the Plank mass atile is zeo. In ou view, this simly means the Plank mass atile only exists fo one Plank seond befoe it busts into ue enegy (light). Redued Comton Time A vey useful onet to undestand and develo theoies fo subatomi atiles involves the time inteval that the seed of light uses to tavel a distane eual to the edued Comton wavelength of the atile we ae onsideing. We assume the seed of light as measued with Einstein-Poinaeé synhonized loks. Fo examle, the edued Comton time of an eleton will then be t e seonds (3) When obseving subatomi atiles at time intevals lose to the edued Comton time, stange uantum e ets will aea, but they will be fully undestandable, even at a logial level, though atomism. We will look at this in the next setion.

11 8 Elementay Patiles Beome Time Deendent at Obsevational Time Windows Close to Thei Redued Comton Time Again, an eleton has the following numbe of intenal ollisions e seond ollisions e seond (38) and we have defined one kg as aoximately ollisions e seond. The mass of the eleton in kg is simly its intenal ollision feueny divided by the kg feueny. This gives us kg (39) Fo most time intevals, the mass of an elementay atile, suh as an eleton, is obsevational time indeendent. Fo examle, if we obseved the atile fo half a seond we would get ollisions e seond (40) And one kg has the following numbe of intenal ollisions e half seond , so the atio of ollisions in the eleton deided by the ollisions in the mass we have defined as one kg is still the same. Again, unde atomism the kg definition is a ollision feueny elative to an amount of matte that we alled a kg. That the ollisions and theefoe the building bloks of an elementay atile omes in uantum fist beomes visible when we wok with (obseve) a atile at time intevals lose to the edued Comton time. Assume we ae obseving an eleton ove a time inteval of only.5 its edued Comton time, that is a time inteval of t.5 t e.5 The mass fo elementay atiles unde atomism is dietly linked to the numbe of ounte stike between indivisible atiles making u the elementay atile and these ollisions only haen evey edued Plank time. This means that in this ase we not will have.5 ollisions, but only one ollision. The numbe of ollisions in the one kg ove this time inteval is n (4) The mass of the eleton is the ollision atio feueny in that time inteval and it now is m e kg (4) 30 This we see is onsideably lowe than the known eleton mass. This mass is atually aoximately 33% lowe than the known mass of the eleton. Again, this is beause we ae woking with suh shot time intevals that uantum e ets ae stating to lay a ole. If we measue it exatly ove one edued Comton time inteval, then the mass of the eleton would be its known mass. The mass simly gets unstable when obseving the mass at lose to the edued Comton time inteval. Figue shows the eleton s deteministi mass as a funtion of the obsevational time window. We ae using time stes of 0. edued Comton time, that is 0.. As we an see the mass uite aidly gets vey stable aound the known eleton mass. The fat that the mass is time deendent at vey shot time intevals has seious imliations. It means that if we ae oeating on shot obsevational time intevals and thee is an unetainty in what exatly time window is, due to measuement eos, fo examle, then we will get vey inteesting obability distibutions in the mass. What would the exeted mass be if we inluded z Comton intevals (whih also gives ollisions e obsevational time window in the atile one is obseving, whee z is an intege) + a andom time inteval between and. Hee we ae basially woking with a known time inteval of z + a andom time inteval between l and (unifomly distibuted). The exeted mass is then E[m] n Z b a f(x)dx n Z b a z z In the seial ase whee a andz b E[m] we get ln + ln + dt z(ln(b + z) ln(a + z)) (43) n ln + e ln + e me (44)

12 Figue 3: This figue illustates the obsevation that the mass of an eleton beomes time deendent at time intevals lose to the edued Comton time of the eleton. The blue oints ae time oints we have alulated fo. The time intevals used ae 0. edued Comton time intevals. Numbe of Obsevational time Exeted eleton Obsevational time Exeted oton Comton times window eleton Mass kg window oton mass kg.568e E E-4.593E E-.380E E E E-.868E E E E E E E E E E-4.548E E E-3.66E E E E E E E E-3.0E-.69E E E-3.05E-0.66E E E-3.056E-9.66E- Table 5: The table shows the exeted mass of an eleton and a oton. we have a unifomly-distibuted andom time inteval between l and, in addition to a known at of the obsevational time window of z. Table 4 shows the obsevational time window deendent mass of an eleton and a oton. Hee we have hosen the time inteval so that the mass is undeestimated to the maximum extent, so this is basially the aoah desibed above. Even then the exeted mass is uikly onveging to its known mass, as the obsevational time window ineases. 9 Gavity When Mass is Time-Seed Haug has suggested that Newton s gavitational onstant is a omosite onstant of the fom; see [9?, 5] G l m 3 kg s (45) MCulloh 04 [6] has deived a simila fomula fo big G based on Heisenbeg s unetainty inile; see also []. Haug [9] has deived this fomula fom dimensional analysis, as well as fom Heisenbeg s unetainty inile, using his newly-intodued maximum veloity fomula fo matte [8]. See [3] and[4].

13 3 Suisingly, we an efom all of ou Newton gavitational alulations based on the esetive of mass as time-seed and a new gavitational onstant. The Haug gavitational onstant is based on time-seed (athe than kg) and is given by G H m 4 s 3 (46) The gavity foe, when oeating with mass as time-seed e mete, is given by This we an deomose F G H ˆm ˆm (4) F ḠH ˆm ˆm F ḠH n ˆm n ˆm F 3 l (48) whee n and n simly ae the numbe of Plank masses in the two masses. The obital veloity fo a Plank mass is given by v o GH ˆm s 3 l (49) The obital veloity fo any mass lage than a Plank mass is given by v o GH ˆm GHN ˆm s N l3 N l (50) These ae all the same fomulas as given by standad Newtonian gavity, when deomosed into a deee level. This is not so stange, as kg is simly a feueny atio, and mass an also be exessed in othe foms. We will etun to the subjet of gavity late on. We will laim thee ae a few ommon misundestandings aound the inteetation of Newtonian gavity that ush sientists to think big G is essential, when in fat, the Plank length is most likely the key to undestanding gavity fom a fesh esetive. Table 5 shows the deomosed gavitational fomulas, that is the gavitational fomulas fom a deee esetive, both when we stat with Newton s gavitational onstant and mass as kg, and when we stat with Haug s gavitational onstant and mass as time-seed. We see that all of the fomulas ae exatly the same fo things elated to gavity that we atually an obseve. And we see that only fo the gavitational foe itself is thee a di eene in the fomulas, and that foe annot be obseved dietly. Howeve, both ae oet fom a theoetiaoint of view: one is linked to kg and the othe to time-seed, and to go fom time-seed to kg we an simly multily by. What we an obseve: Fom mass as kg Fom mass as time-seed: Obital veloity v o v o Gavitational aeleation field g n l g n l Gavitational ed-shift lim!+ z() n l. lim!+ z() n l. Gavitational defletion n4 l n4 l. Gavitational time dilation t 0 t f n l t 0 t f n l What we annot obseve: Fom mass as kg Fom mass as time-seed: Gavitational foe n l F n n n l F n n Table 6: The table of a seies of measuements that atually an be obseved/measued in elation to gavity, and also the gavitational foe that we annot obseve and measue.

14 4 0 Fundamental Eletiity as Time-seed The well-known fundamental eletial units suh as the Plank hage and Plank voltage an be ewitten in the time-seed fom. This an be done simly by multilying the taditional exessions of these units with. Fo examle, the Plank hage is given by in the time-seed fom this is 0 (5) l 0 (5) That is to say, the hage is the suae oot of the Plank time multilied by 0. This leads to an invaiant Plank hage aoss any efeene fame. This beause unde atomism when we ae all the way down to the Plank length, thee an be no length ontation. The light atiles only have a hage at ollision; this hage is half of the Plank hage i l 0 (53) The eleton hage is based on time-seed e l 0 (54) Also, the eleton hage must be invaiant and the same as obseved fom any efeene fame, if the fine stutue onstant is not a eted by veloity. When it omes to eleton voltage, we have Conveted to time-seed fom this gives V e 0 (55) V e l 0 (56) In othe wods, the eleton voltage is a eted by veloity, as the edued Comton wavelength of the eleton will ontat at high veloity. And we know that the eletial enegy is given by E V ee l l 0 0 l l (5) Sine the veloity is vey low ( ), we atually have to wok with kineti eletial enegy hee, and atually we should have a in font of this euation. Howeve, ou oint is simly that we an just as well oeate with time-seed system athe than the taditional units. We an also ewite the standad hage fomula simly by deomosing the Plank onstant into what it is in atomism. The Plank hage is then s (58) The units of the numbe is ollisions e seond. So is metes e ollision, so the hage is now the suae oot of metes e ollision, in ontast to the hage in the time-seed fom that is the suae oot of the time between eah ollision in a Plank mass is less than the Plank length, so at fist sight this sounds absud if the shotest length is one Plank length. Howeve, it is deived fom the Plank onstant and it is elated to kg. As exlained unde setion 3, thee ae aoximately 45,945,9 Plank masses in one kg, so is simly the Plank length divided by numbe of Plank masses in one kg. The Plank Units All of the Plank units an be witten in thei nomal fom o thei time-seed fom. Fom Table 4 we see the di eene is only in Plank units, whee the standad fom has the Plank onstant. Thee is no Plank onstant in the time-seed fom. The standad fom using the gavitational onstant is the most onfusing one, with suh things as, 8,andeven 9. It is vey had to get any intuition out fom the seed of light oweed to anything

15 5 above. The fat that moden hysis has not undestood that big G is vey likely a omosite onstant leads to a lot of onfusing fomulas that ae muh easie to undestand one one undestands that the gavitational onstant is a omosite onstant. Units: Nomal fom: Deee fom: Time-seed fom: Gavitational onstant G G l 3 G H 3 Max veloity Plank mass atile Plank length Plank time t G G 3 5 t l t l Plank mass m G m m Plank enegy E 5 G E E l Relationshi mass and enegy E m Redued Comton wavelength m Plank aea l G 3 l l l l Plank volume l 3 3 G 3 9 l 3 l 3 l 3 l 3 Plank foe F 4 G F F Plank owe P 5 G P Plank mass density 5 G l 3 Plank enegy density E G E l 3 Plank intensity I 8 G I Plank feueny! Plank essue l 3 5 G! G Plank hage 4 0 e Plank uent I Plank voltage V G Plank imedane Z Eleti enegy E V Plank aeleation Plank gavitational aeleation field 4 4 0G a F m g Gm l I l 3 V 0 P l 3 E 0 0 l 3 I l 3! l 3 0 I 0 V l 0 Z V I 0 Z V I 0 G E V E V a F m a F m g Gm l g G Hm l Table : The table shows the standad Plank units and the units ewitten in a simle and moe intuitive fom. Summay of Key Numbes and Convesion Fatos Hee we will summaize some key numbes and onvesion fatos To go fom time-seed (ontinuous seonds e mete) to kg, multily by This is also the momentum of a Plank mass atile. To go fom kg to time-seed (ontinuous seonds e mete) to kg, divide by To go fom time-seed (ontinuous seonds e seond) to kg, multily by This onvesion fato is also the mass of a Plank mass in kg. And natually we also have the undestanding that the Plank mass is one ontinuous seond e seond One kg is 0.5 ontinuous seonds e mete, and 45,945,9 ontinuous seonds e seond. The numbe 45,945,9 is also the numbe of Plank masses in one kg. Any mass that is moe than one ontinuous seond e seond must ontain moe than one elementay atile.

16 6 Aoximately 6.5 kg is ontinuous seonds e mete, and 99,9,458 ontinuous seonds e seond. 99,9,458 is also the numbe of Plank masses in 6.5 kg. When it omes to mass as time-seed, we know only the Plank mass without knowing the Plank length. Fo mass in tems of kg, we only need to know the Plank length to know the Plank mass; we do not need to know the Plank length fo othe masses. The standad mass is easie wok with and measue; the time-seed mass seems to give deee insight, but it is muh moe di ult to obseve and euies, fo examle, that we have aleady found the Plank length fom gavitational exeiments. The mass of elementay atiles in fom of kg is atually obsevational time deendent, but the obsevational time-deendene aidly gets so small that it hadly is obsevable as soon as the obsevational time window is onsideably lage than the edued Comton time of the atile we want to study. Unde atomism this would mean we need to use obabilisti models at the uantum sale, and it also exlains why this uantum andomness aidly gets negligible as we aoah the maosoi wold.. 3 Conlusion We have shown how we an desibe mass as both time-seed (ollision time) and as kg, and how to go fom kg to time-seed o fom time-seed to kg. We have also shown that we an do gavity alulations just as well fom the esetive that mass is time-seed (time sent on ollisions). We then need to use a di eent gavity onstant. This suots the view that Newton s gavitational onstant is abitay in the sense that it is a omosite onstant needed to tun a etain esetive on mass into the oet and deee fomulas fo gavity. Both the time-seed way of looking at gavity and the nomal way lead to exatly the same fomulas at a deee level. Refeenes [] E. G. Haug. Unified Revolution: New Fundamental Physis. Oslo,E.G.H.Publishing,04. [] E. G. Haug. The Plank mass atile finally disoveed! The tue God atile! Good bye to the oint atile hyothesis! htt://vixa.og/abs/ , 06. [3] E. Shödinge. Übe die käftefeie bewegung in de elativistishen uantenmehanik. Sitzungsbeihte de Peuishen Akademie de Wissenshaften. Physikalish-mathematishe Klasse, 930. [4] M. Plank. Natulishe Masseinheiten. De Königlih Peussishen Akademie De Wissenshaften,. 49., 899. [5] M. Plank. Volesungen übe die Theoie de Wämestahlung. Leizig: J.A. Bath,. 63, see also the English tanslation The Theoy of Radiation (959) Dove, 906. [6] E. G. Haug. The mass ga, kg, the Plank onstant, and the gavity ga. htt://vixa.og, 0. [] A. Einstein. Zu elektodynamik bewegte köe. Annalen de Physik, (), 905. [8] A. Einstein. Relativity: The Seial and the Geneal Theoy. Tanslation by Robet Lawson (93), Cown Publishes, 96. [9] E. G. Haug. The gavitational onstant and the Plank units. a simlifiation of the uantum ealm. Physis Essays Vol 9, No 4, 06. [0] E. G. Haug. The ultimate limits of the elativisti oket euation. the Plank hoton oket. Ata Astonautia, 36,0. [] E. G. Haug. Can the Plank length be found indeendent of big G? Alied Physis Reseah, 9(6),0. [] W. Heisenbeg. Übe den anshaulihen inhalt de uantentheoetishen kinematik und mehanik. Zeitshift fü Physik, (43): 98,9. [3] I. Newton. Otiks: O, a Teatise of the Reflexions, Refations, Inflexions and Colous of Light. London, 04. [4] H. Cavendish. Exeiments to detemine the density of the Eath. Philosohial Tansations of the Royal Soiety of London, (at II), 88,98.

17 [5] E. G. Haug. Newton and Einstein s gavity in a new esetive fo Plank masses and smalle sized objets. Intenational Jounal of Astonomy and Astohysis, 08. [6] M. E. MCulloh. Gavity fom the unetainty inile. Astohysis and Sae Siene, 349(), 04. [] E. G. Haug. A modified Newtonian uantum gavity theoy deived fom Heisenbeg s unetainty inile that edits the same bending of light as GR , 08. [8] E. G. Haug. A suggested bounday fo Heisenbeg s unetainty inile. htt://vixa.og/abs/0.049, 0.