Harmonic Quantum Integer

Transcription

1 Harmoic Quatum Iteger The hypothesis of this paper is that there is a quatum iteger umber system that is aalogous to the umbers associated with the elemets, the isotopes, or the differet eergy states of hydroge. The quatum umbers i this ew model are istead associated with differet fudametal costats (i.e. the ormalized properties of hydroge, or masses of particles ad bosos) rather tha to a specific isotope or hydroge eergy state. This hypothesis is supported by may empirical observatios ad secodary predictios. A secod hypothesis is that all of the fudametal costats are related to the eutro. The third hypothesis is that associated costats (i.e. the electro ad Z) are related by commo harmoic umber products typical of harmoic systems. These quatum properties become obvious whe appropriately plotted ad aalyzed. All costats are ormalized to their aihilatio frequecy equivalets, idepedet of their primary uits. The aihilatio frequecy of the eutro is the uiversal frequecy to which all other costats are mathematically liked. All of the costats are evaluated as couplig costats, with the deomiator equal to the aihilatio frequecy of the eutro ad the umerator equal to the other physical costat s frequecy. The aihilatio frequecy of the eutro (expressed as a dimesioless umber) is raised to a expoet, ad that value is equal to each couplig costat. Classic quatum umber/spectral properties are demostrated, icludig the property that the oly possibilities are those of a cosecutive iteger series, ad that there is symmetric lie splittig i the presece of a force field (for electromagetic or weak forces). These poits for each expoet are plotted o a l-l plae. The eutro is plotted at the (0, 0) poit. The oly possible quatum x-axis poits are related to iteger fractios (±/). The degeerate actual frequecies are all early equal to ±/ expoet values for the aihilatio frequecy of the eutro. The y-axis values are the mior differeces of the kow expoets ad quatum fractios ( ± /), aalogous to Zeema s splittig. These quatum iteger patters are oly related to liear relatioships of the fudametal costats. The l-l poits associated with the properties of hydroge are liked to all costats by two liear relatioships, oe for weak kietic forces (Bohr radius, mass of the electro) ad oe for electromagetic forces (Plack s costat, hydroge ioizatio eergy). The uclear etity poits all fall solely o lies betwee these hydroge poits, symmetrically plotted across both axes for quatum umbers 8 ad the eutro oly. The uclear particles ad bosos that are logically associated demostrate their umber lieage by harmoic itegers which are related to hydroge iteger poits ( = 8). Some uclear quatum umbers (i.e. muo, 24) represet the product of a associated hydroge iteger (i.e. eutrio, 2) ad a lower associated lieage uclear iteger (i.e. Z, 2). Derivatios of the actual frequecy equivalets, icludig the muo, tau, W, Z, pios, kaos, ad the quarks, are possible from the properties of hydroge oly to a accuracy of may expoetial digits, supportig the hypothesis. This model represets a ew ad powerful meas of aalyzig the relatioships of the fudametal costats, geeratig uifyig relatioships betwee hydroge ad uclear properties previously ot described. Keywords: harmoic systems, fudametal costats, uificatio model, fudametal particles ad bosos, weak force, electromagetic force

2 Itroductio The hypothesis is that the eutro represets the fudametal harmoic frequecy that is liked to all etities of physics by a simple quatum umber expoetial system Quatum physics is based o the hypothesis that there are oly discrete possible eergy levels for specific related physical systems ad states. 3 These eergy levels ca be defied ad predicted utilizig equatios based o a iteger or iteger quatum fractio series ad a fudametal frequecy. The periodic chemical ad isotope tables represet some of the earliest examples where two itegers, the umber of protos ad eutros, defie the oly possible elemetal/ isotope states. Later, the properties of the quatum eergy states of hydroge were defied by four quatum umbers. These properties were described by Bohr, Rydberg, ad Schrodiger. 2 7 The possible electro cofiguratios accoutig for the chemical properties of the elemets are defied by four quatum umbers. Moseley s law is aother quatum property that is also aalogous to this model. 8,9 Moseley s law relates the spectral-like properties betwee differet elemets, ot just of oe sigle elemetal spectrum. The model preseted here is idetical i cocept ad applicatio to these classic quatum systems. This paper presets a aalogous hypothesis, but expads the set of properties ecompassed by a uified quatum umber system. The hypothesis assumes that there is a simple cosecutive iteger quatum fractio umber system that uifies all of the fudametal costats of physics. All of these differet physical properties are examied i a maer similar to that of a sigle spectrum. The secod hypothesis is that all of the fudametal costats are directly mathematically related to the eutro. The eutro represets the most commo fudametal etity that is essetial to every aspect of physics ad the uiverse. 0 The eutro is potetially the mother of all other etities i the uiverse, so this is a logical choice for a fudametal frequecy. The aihilatio frequecy of the eutro (as a dimesioless umber) is the umerical foudatio of this hypothesis. The third hypothesis is that associated costats (i.e. the electro ad Z, or the quarks ad mesos) are related by commo harmoic quatum umber products. This is a classic property of may harmoic systems.,2 These hypotheses are supported by may empirical observatios ad accurate predictios. This paper iitially focuses o the relatioship betwee the properties of hydroge ad the eutro. The the properties of hydroge ad their associated uclear etities ad harmoic umber relatioships are aalyzed. These relatioships become obvious whe the fudametal costats are plotted ad aalyzed utilizig a ew method first described i this paper. The first step of the method is the trasformatio of the fudametal costats associated with the beta decay products of hydroge to a quatum iteger fractio system. The they are plotted o the l-l plae. Next, the poits for related uclear etities are plotted. The simple liear relatioships ad their simultaeous harmoic quatum umbers become apparet. The values for the uclear properties are the accurately predicted from the hydroge data, which supports the hypothesis. Fially, a brief summary of other fudametal properties that ca be potetially aalyzed usig these methods is preseted. Iitial summary ad support for this hypothesis The quatum umber properties hypothesized i this paper are ot apparet util the fudametal costats, icludig the eutro beta decay properties (eutrio ad the properties of hydroge), are first all coverted to aihilatio frequecy equivalets idepedet of their origial uits (Tables, 2, 3). It is a straightforward process to covert kow aihilatio eergies, masses, ad distaces of differet fudametal costats to their aihilatio frequecy equivalets. All of the calculatios are plotted o a l-l plae related to dimesioless umbers, the couplig costats. 3,4 The deomiator is the aihilatio frequecy of the eutro ad the umerator is the kow frequecy equivalet. The plotted expoets of the aihilatio frequecy of the eutro correspod to the kow ratios of the two frequecy values, represetig iverse mathematical fuctios. The actual kow expoet for each physical costat with the expoet base is equal to the aihilatio frequecy of the eutro, which is equal to

3 Table. Costats evaluated, their classic uit values, ad their frequecy equivalets. Costat Kow value stadard uits v k equivalets Hz electro bidig J Hz gravitatioal eergy Plack s (h) J Hz Rydberg (R) m Hz Bohr radius (a 0 ) m Hz electro mass (e) ev Hz up ev Hz top ev Hz Hz dow ev Hz Z ev Hz Hz W ev Hz muo ev Hz pio ev Hz pio ev Hz strage ev Hz bottom ev Hz tau ev Hz kao ev Hz kao ev Hz charm ev Hz proto ev Hz eutro ev Hz This table lists the costats evaluated, their classic uit values, ad their frequecy equivalets. The frequecy equivalets are calculated as the aihilatio frequecies of the masses or eergies, ad the frequecies associated with the wavelegths. the plotted value plus oe. Ispectio shows that the x-axis l-traslated costat s values are empirically related solely to ±/ values, where = to ± (Tables, 2, 3). The actual expoets of the kow costats are related to ±/. These are referred to as quatum fractios (qf ), ad the is aalogous to the pricipal quatum umbers of atomic spectra. For example, the kow qfs for the gravitatio bidig eergy of the electro i hydroge, the ioizatio eergy, the Bohr radius, ad the mass of the electro are all early equal to -, 2/3, 4/5, ad 6/7, respectively. A graphic traslatio the kow expoets is plotted o a l-l plae, where the poit (0, 0) is associated with the eutro. The x-axis is related to the qf- or ±/. The oly possible x-axis values are ±/±, ad are related to the qf values. The y-values represet the differece betwee the kow expoets ad the qf values similar to a split spectral property. 5 A total of four poits for each kow value are plotted, similar to imagiary umber properties (complex cojugate ad iverses) because the system is empirically symmetric. 6 8 The eutro is the oly etity at the ceter, (0, 0), poit. The poits associated with the properties of hydroge (the Rydberg costat R, the Bohr radius a 0, ad the mass of the electro e) represet the foudatio for all other fudametal costats idepedet of force. By plottig a lie related to the weak forces of hydroge, the mass of the electro ad the Bohr radius, all of the weak force costats ca be derived, icludig uclear oes such as tau, muo, Z ad W. By plottig the lie related to Plack s costat (-, 0) ad the ioizatio eergy of hydroge, all of the electromagetic force costats, such as the quarks, pios, ad kaos of the electromagetic force, ca be derived i a similar fashio.

4 Table 2. Quatum fractios ad δ values for the evaluated costats. Costat Abbrev. ± / qf, / or ( + /) gravitatioal bidig electro, H H exp k # rage δ, ± (exp k -qf) (calculated) Gbe Plack *s h eutrio, H v ave 2 -/2 ½ (3/2) 2 ~0.5 ( ) Rydberg, H R 3 -/3 2/3 (4/3) Bohr radius, H a 0 5 -/5 4/5 (6/5) electro, H e 7 -/7 6/7 (8/7) up u 0 -/0 9/0 (/0) * # ( ) top t 0 +/0 /0 (9/0) * # (0.0024) dow d -/ 0/ (2/) * # ( ) Z Z 2 +/2 3/2 (/2) W + W + 2 +/2 3/2 (/2) Muo µ 24 -/24 23/24 (25/24) pio + π /28 27/28 (29/28) pio 0 π /28 27/28 (29/28) strage s 30 -/30 29/30 (3/30) * # ( ) bottom b 36 +/36 37/36 (35/36) * # ( ) tau Τ 83 +/83 84/83 (82/83) kao 0 K /84 83/84 (85/84) kao + K /85 84/85 (86/85) charm c 39 +/39 40/39 (38/39) * # proto p / / eutro ± 0 0 This table lists the kow costats evaluated, the abbreviatios, the pricipal quatum umber, /, the hydroge quatum umber, the quatum fractio ad their iverses, the kow expoet (exp k ), ad the δ values. The H otes that these are the hydroge values. Note that all of the δ values are very small, but ot zero as predicted. The* sigifies that the quatum umber values are ot kow sice their masses are ot accurately measurable. The values i paretheses are calculated. The values labeled with # are the published rages.

5 Table 3. Couplig costat ratios ad expoets for the evaluated costats. Costat Abbrev. ±/ v k /v s (rage calculated) v s (±/) gravitatioal Gbe bidig electro, H Plack *s h eutrio, H v 2 -/ Rydberg, H R 3 -/ Bohr radius, H a 0 5 -/ electro, H e 7 -/ up u 0 -/0 ( ) top t 0 +/ dow d -/ ( ) Z Z 2 +/ W + W + 2 +/ muo µ 24 -/ pio + π / pio 0 π / strage s 30 -/30 ( ) bottom b 36 +/36 ( ) tau Τ 83 +/ kao 0 K / kao + K / charm c 39 +/39 ( ).4724 eutro ± 0 This table lists the kow couplig costat ratios evaluated, the abbreviatios, the pricipal quatum umber, ±/ values, ad the v s values raised to the ±/ values. Note that the degeerate ratio values derived from itegers oly are quite close, but ot exactly idetical to the kow values. This is supportig evidece of the hypothesis. The harmoic umber properties of logically associated etities lieage are also empirically demostrated oce each qf ad pricipal quatum umber are idetified. For example, Z is associated with oe of the l-l poits of the electro. Aother example is that the quatum umber of the muo is associated with the quatum iteger product of the eutrio ad the W boso quatum umbers. The derivatio of the actual uclear frequecy equivalets from hydroge properties oly is possible sice all of the associated etities are liearly liked betwee the eutro ad the hydroge poits oly by logical harmoic umbers, ad simultaeously they oly exist o lies coectig the hydroge poits to the eutro. This model is uequivocally supported by demostratio of multiple liear relatioships o the l-l plae betwee logically associated physical costats, ad is therefore tested ad supported. There is o speculatio i the calculatios or results. It will be show that this method displays l-l properties betwee logically associated costats, evaluated as frequecy equivalets, such as symmetry poits (i.e. the up quark, ad top quark). A aalysis of the costats as a l-l system ca be utilized to make predictios of fudametal costat values beyod what ca be experimetally made, icludig predictios of uclear high eergy physics costats from properties of hydroge oly (i.e. calculatio of

6 the mass of Z from the Bohr radius ad the masses of the electro ad eutro oly). Methods ad Results Aihilatio frequecy equivalets All of the costats, idepedet of uits, are coverted to aihilatio frequecy equivalets (Table ). This is a simple classic uit coversio, but it should ot be cofused with a kietic eergy process. This is ot a typical method to compare fudametal costats of differet uits, but it is oetheless completely valid. This is idetical to the logical method used i Moseley s law. 8,9 It allows for a ormalizatio of differet etities, sice they are all liked to the eutro, its beta decay products, ad a sigle uit (expressed i Hz). Sice the calculatios are related to dimesioless ratios (couplig costats), the actual physical uit is ot importat sice the ratios are idepedet of uit. The data used for the calculatios was acquired from ad Couplig costat aihilatio frequecy equivalets All of the kow fudametal costats, whe expressed as frequecy equivalets (v k ), are evaluated as dimesioless couplig costats spectra, where the umerator is related to each costat, ad the deomiator is related to the trasitioal aihilatio frequecy, v, Hz, frequecy of the eutro (Equatio ). Couplig costats deote the stregth of a iteractio ad are dimesioless. There are may other ratios that represet couplig, such as ratios related to the fie structure costat, α. 3,9 v frequecy couplig costat domai () k v Coversio of the couplig costat aihilatio frequecy equivalets to a expoet base of v All of the fudametal costats are coverted (trasformed) to expoet equivalets with the dimesioless base equal to v Hz divided by oe Hz, which equals v s. This is Equatio 2. Equatios 2 ad 3 are iverse mathematical fuctios. 20 The kow expoet value (exp k ) is calculated as the ratio of the l of each etity, divided by the l of v s. Table 2 lists the costats evaluated abbreviatios, quatum fractios (qf ), ±/, δ, pricipal quatum umber (), ad exp k values used i the calculatios. Table 3 lists the ratio values of the couplig costats ad the ±/ expoet values plotted o the l-l plae (Equatio 4). k exp k l( vk ) = = log vs( vk ) expoet domai (2) l( v ) log e ( vs)expk expk v = e Hz = v s Hz frequecy domai (3) v v k vs k - = ( v s) exp ratio couplig costat domai (4) The fudametal costats evaluated as a uified spectrum of the eutro The gravitatioal bidig eergy of the electro i hydroge is assumed to be equally as importat to the properties of kietic forces (icludig gravity) as the ioizatio eergy is to the spectral (Rydberg series) ad chemical properties of the elemets (Mosley s law), ad atomic spectra. This paper focuses first o the relatioship of the aihilatio frequecy of the eutro to the products of beta decay, icludig hydroge. Next the relatioship to the other particles ad bosos is iterrogated usig similar methods. Gravitatioal, electromagetic, ad strog eergies as a iteger series expoetial fuctio of the aihilatio frequecy of the eutro The relative eergy (or frequecy) values of the eutro (spectral trasitioal, aihilatio frequecy, v, Hz, ad Plack s costat times oe secod, s, (v h = Hz) equal the fudametal dimesioless couplig costats of this hypothesis, v s (Equatio 4). The hypothesis is based o the empirical physical fact that the couplig costat ratio v s, the ratio of the eutro ad Plack s time equivalet, is early equal to the ratio of the umerator, (product of Plack s costat (h) ad Hz) ad the deomiator (the gravitatioal bidig eergy of the electro i hydroge).

7 This calculated value is , 23 early equal to v s (Equatio 5; Tables, 2). The iverse of v s Hz is Hz ad the kow calculated frequecy equivalet of the gravitatioal bidig eergy of the electro is Hz. If the frequecy equivalet of the gravitatioal bidig eergy of the electro is associated with the frequecy of the eutro, it should logically be equal to approximately oe half the iverse of v s, sice it is a kietic force, which is show to be true. It is possible to eve more accurately derive the gravitatioal bidig eergy of the electro i hydroge usig this model, but that is ot the focus of this work ad will ot be further discussed. The aalysis above shows that there is a simple iteger expoetial relatioship betwee the couplig costats v s for the eutro, Plack s time, ad the gravitatioal bidig frequecy of the electro. This is a expoetial fuctio (Equatio 5), where is associated with the eutro, 0 with Plack s time, ad - with the bidig gravitatioal eergy. The eutro is the liear uit value for the elemets. Plack s costat is the liear uit for electromagetic properties. The gravitatio bidig eergy i hydroge follows the idetical patter, with a ratio spacig equal to early v s. v v h Hz = ( vs) Hz for = -, 0, (5) I classic harmoic systems, the oly possible steps are related to iteger fractios (a stadig wave patter).,2,2 It is logical that the actual properties of hydroge (ioizatio eergy, Bohr radius, ad the mass of the electro) ad may of the fudametal particle rest masses ad bosos should be associated with iteger quatum fractio ( ± /) expoets as well. This is aalogous to the orbital properties of hydroge, where there is a series of four quatum factors that are predictive of the properties of the elemetal orbitals (Tables, 2; Figs. 7; Equatios 25). Four quatum umbers, icludig a pricipal quatum umber, ca be used to defie all of the evaluated fudametal values i this mathematical system. These factors used i this hypothesis iclude: a hydroge pricipal quatum umber ( 8), a secodary (sec) quatum umber ( 9, for those etities that are ot directly related to hydroge, such as uclear properties (uc)), a factor related to whether the etity is associated to a kietic or electromagetic force, ad the symmetry sig value (±) for the l-l plae. These sigs defie i which quadrat the traslated poits lie. The degeerate frequecy values of the fudametal costats are related to the expoets ± / (Equatio 6). These values should be approximately equal to, but ot idetical to the kow values of all fudametal costats, which is true (Tables, 2). The same is true for the ±/ values ad the kow couplig costats (Table 3; Equatio 4). ± vk ( vs) Hz the oly possible approximate degeerate frequecy values (6) Traslatios of the fudametal costats to a ±/ expoetial relatioship plotted o a l-l plae The l-l plae is associated with the expoetial ad quatum umber domai of the costats. These poits are described as z poits, (x, y), that equal the total value (exp k mius oe values) (Equatio 7 4). The mius oe ceters the eutro at the (0, 0) z poit for symmetry. Therefore, the zero x-axis poit is associated with equalig both - ad + (Fig. ). exp = log v = + z = + x + y = ± + y (7) kvs vs k z symmetry possibilities = the four symmetry poits + + y or + - y or - + y or - - y where equals itegers to ± (8) ± δ = ± ± z δ represets the differece betwee the degeerate ±/ values ad the (exp k -) values (9) qf ± = x axis compoets (0) = ± quatum fractios ()

8 z (poit) = exp k = qf ± δ = x + y = ±/ ± δ = ±/ ± a/ ± b y = ± δ = ±(exp k qf) y = a/ + b l-l y axis ratio = ν ( /+δ) /ν z = / + δ z = / δ ratio = ν (+/+δ) /ν z = +/+δ z = +/ δ ratio = ν ( / δ) /ν ratio = ν (+/ δ) /ν x axis, x = ± / x = /± /2 /3 0 /3 ½ 2 3 ± 3 2 ±/, (qf) 0 ½ 2/3 4/3 3/2 2 hz ν s (2/3) /s ν s/s ν s (4/3) /s ν s (2) /s qf ν /ν /ν s (2/3) ν /ν ν /ν (2/3) ν /ν ν s/ costat h R eutro r + h Figure. Traslatio of the frequecy equivalet couplig costats to a l-l plae. This figure displays the l-l plae for the z poit values for the kow v k /v ratio expoets (exp k -). The uique eutro cetral symmetry poit, (0, 0), (/± ) is related to v s i the frequecy domai. All poits represet the expoets of v s that are related to ratios. The oly possible quatum () compoets of z, ±/, are plotted o the x-axis as small cross hairs (two for each ±). This is similar to a classic stadig wave patter. As approaches ± there is cofluece of poits that caot be displayed. The differet mathematical uit values associated with the x-axis are listed below, icludig: x, (/),, qf, Hz, frequecy ratios, ad the associated costats. This demostrates that a sigle actual frequecy associated with a specific costat ca be related to differet x-axis uits. The four possible symmetry splittig compoets δ are plotted o the y-axis. The otatio of each potetial z poit is related to its quadrat (top right +/+δ, bottom right +/-δ, top left -/+δ, ad bottom left -/-δ). The eutro is associated with a x-value of 0, R with ±/3, ad h with ±. exp k δ = ± (exp qf ) y axis compoet kow expoet splittig (2) = ± ± δ = qf + δ kow expoet (3) v v k vs ± ± δ = ( v s) kow ratio (4) The kow expoet value is usually traslated to the earest quatum iteger fractio value ad a δ. The y-axis values are the plotted o a l-l plae (Tables 2, 3). The associated itegers ad quatum fractio values are usually obvious. The distace from the (-, 0) z poit (Plack s costat) to the etities is idetical to their kow expoet value. This creates a symmetric stadig wave patter (Figs. 4). The oly valid possible poits are related to ±/ x-axis values. The differece ad its iverse (δ) betwee the kow expoets ad their quatum fractio are plotted o the y-axis for each costat at the x-value ±/. This represets the symmetric split spectrum property. The sum of the orthogoal distaces betwee two poits o the l-l plae is related to the ratio of two frequecies i the frequecy couplig costat domai (Table 3). The larger the sum of the distaces from a z poit to the eutro poit (0, 0), the greater the ratios. Movig to the right ad up is associated with multiplyig v s by each orthogoal factor. Movig to the left ad dow is associated with dividig v s by each factor. For example, twice the orthogoal distace o the l-l plae is associated with the square of the factor i the frequecy domai. For each kow l-l plae poit there are three other associated z poits, oe i each quadrat. This is assumed to be related to the iheret symmetry of the system, ad is supported by empirical fidigs. These are defied as symmetry poits associated

9 4 x (-/7, -/7h, +wk) e (+/7, +/7 h, +wk) e δ = ±(exp k -qf) = a/ + b (0, 0) (-, 0) h (, 0) h 3 (-/7, -/7h, -wk) e x = ±/ (+/7, +/7h, -wk) e Figure 2. Traslatio of the electro to the l-l plae. This figure displays the l-l plae ad the four traslated symmetry poits related to the electro. The eutro value is at the z poit (0, 0). The quatum iteger value of the electro is 7. The qf value of the electro is 6/7 or ( /7). These poits are plotted at a x-axis value of ±/7. The y-axis value is the differece betwee the exp k of the electro ad 6/7. Sice this is a l-l plae system, there are three other associated symmetry values, oe i each quadrat. These poits must fall o a circle. The thick arrows show the symmetry poits mirrored off the x-axis (dashed ad solid). The thi arrows demostrate the iverse symmetry poits mirrored off the y-axis (dashed ad solid). Ay of these values are valid ad may be associated with the electro directly or other logically associated lieage etities of the electro such as the Z boso (Fig. 6). Oly oe is the actual value associated with the electro though. with the four possible sig combiatios of the δ ad the / values (±/ ± δ) (Equatio 8). Each poit must demostrate mirror symmetry with the x- ad y-axes (Figs. 4). The δ value is equivalet i the frequecy domai to the factor that the degeerate quatum fractio frequecy is multiplied or divided by to arrive at the kow value (Equatio 6). A liear relatioship o the l-l plae meas that the couplig costat betwee etities is directly related to the quatum umber fractio axis. I other words, the couplig costats of a force are equally scaled per / chage. The differece i the slopes defies the stregth of the force. This model represets a classic mathematical iverse fuctio trasformatio from the frequecy ratio couplig costat domai to the quatum fractio expoetial domai. This is aalogous to K space ad real space i magetic resoace imagig 22 or Fourier trasform. 23,24 Both domais describe the same physical reality, but utilize completely differet mathematical forms. The atural log e v s value is To describe each specific costat s z poit for each kow physical costat, the followig otatio is used. This is aalogous to the defiitio of the electro orbitals usig quatum umbers. 6 This represets the traslatio of the kow costats to the l-l plae. The otatio icludes three sigs, two / pricipal quatum umber fractios (the first for hydroge or o-hydroge ad the secod for the associated hydroge umber), ad whether the etities are associated with a electromagetic or weak kietic property of hydroge. There are three sigs to defie the differet possible quadrats i which the poit falls. Directly followig the associated costat value is a abbreviatio (i.e. h for Plack s costat, a 0 for Bohr radius) (Tables, 2). For the hydroge values, the two pricipal quatum values are degeerate. For the electro, the otatio would be (-/7, -/7 H, +wk) e (Fig. 2). For the ioizatio eergy, the otatio would be (-/3, -/3 H, -em) R (Figs. 3, 4,). Usig Z for example, the otatio is (+/2, +/7 H, +wk) Z. Italics idicate this is the kow value, ot aother

10 4 x (-/7, -/7H, +wk) e (-/5, -/5 H, +wk) a 0 δ = ±(exp k qf) = a/ + b (-, 0) h (0, 0) 3 (-/3, -/3H, -em) R x = ±/ Figure 3. Traslatio of the electro (e), R (ioizatio eergy), ad Bohr radius (a 0 ) to the l-l plae. This figure displays the l-l plae ad the three traslated poits related to the electro (e), ioizatio eergy (R), ad Bohr radius (a 0 ). The eutro value is at the z poit (0, 0), ad Plack s costat at z poit (-, 0) by defiitio. The associated quatum iteger values are electro, 7 (6/7, -/7), the Bohr radius, 5 (4/5, -/5), ad R, 3 (2/3, -/3). These values are respectively plotted at x-axis values of -/3, -/5, ad -/7. Their associated δ y-axis values are related to the differece betwee the exp k, kow expoet values ad their qf values. All of the derivatios are primarily related to these five poits. symmetry possibility (Fig. 6). Therefore, the quatum fractio value of Z is + /2 or 3/2. Z is associated with the weak kietic positive sig for the hydroge poit associated at the electro at the +/7 x-axis poit. I most cases the / value for the pricipal quatum umber is a obvious traslatio. The exp k ad their correspodig v s raised to a specific qf are early idetical. The differece betwee the kow ad the qf is plotted as the δ directly above ad below the / value. Each poit is listed i paretheses (Table 2). Each z poit is first characterized by the / value ad its sig. Each / value i the described l-l otatio deotes its locatio o the l-l plae. Hydroge z poit lies, weak kietic ad electromagetic forces The properties of hydroge ca be defied by two primary logical lies o the l-l plae. The possible quatum umber poits associated with these lies have bee foud to be associated with all other etities. There are three other symmetric lies associated with each primary lie, just as there are three poits associated with each kow z poit (Equatio 8). The first lie is called weak kietic (wk), ad is defied by the z poits for the Bohr radius ad the mass of the electro. These poits are logically related to weak ad kietic etities, ad will be show to be related to the eutrio, tau, muo, Z, ad W. The other lie, electromagetic (em), is defied by the z poit for Plack s costat at (-, 0) ad the Rydberg costat poit (ioizatio eergy). These poits will be show to be related to the mesos ad quarks. The slopes ad y-itercepts of these two lies ca be used to calculate all of the possible z poits, ad are importat i the derivatio process. For example, the weak kietic poit for -/8 is liearly associated with the frequecy equivalet of the muo, while -/3 is liked to the pios ad kaos. The equatios (5 22) used for the lie calculatios are show. These equatios are related to the liear relatios of the two hydroge lies ad their uclear etities. Equatio 5 is derived from multiple poits

11 δ = ±(exp k -qf) = a/ + b x 0 3 / /3 /2 (, 0) h /7 /8 /6 /5 /4 (0, 0) (, 0) h 3 / x = ±/ Figure 4. All of the traslated possible iteger z poits of hydroge to the l-l plae. This figure displays the l-l plae ad all of the possible iteger z poits for hydroge with ragig from to 8. The eutro value is at the z poit (0, 0). The other possible z poits are dots while the kow values are black solid circles. These poits fall o the lies coectig the Bohr radius ad electro for oe, ad h, ad R for the other. These poits are i the idetical patter as those show i Figure 3. From these limited hydroge poits all of the fudametal couplig costats will be derived. They have a diamod patter because of the l-l dual axis mirror symmetry. The values larger tha 8 are ot plotted, but are all valid. o the hydroge lies. Equatio 6 is derived from the perspective of the slope from the eutro (0, 0) poit to the hydroge poits. Equatios 5 ad 6 are equivalet. The expoet domai equatios are show, where v k is the kow frequecy equivalet of a fudametal costat. H a H δ = ± ± b = ± a - ± ( b - a) sec H sec H [( H - ) b ± ( b - a)] δ = ± sec or [( H - ) b ± ( b - a)] δ = ± H (5) (6) where a em or wk (slope) ad b em or wk (y-itercept) defie a liear relatioship betwee associated hydroge fudametal costats ad x (/) for hydroge H,_em is related to electromagetic properties, ad wk is related to weak kietic properties slope from (0, 0) to ay z poit = δ (7) slope from (0, 0) to ay z poit = ± ( H ) b ± (b a) (8) slope from (0, 0) to ay z poit = ( ) [ (exp k )] for exp k (9a) or slope from (0, 0) to ay z poit = [( ) exp k ]- for exp k (9b) slope - ( b - a) + = H value associated with ay z b poit etity (20) a alterate form defiig the liear relatioship from the y values at x = 0 ad x = - of the hydroge factors related to specific quatum fractios ( ± y at 0) - ± y at - it ercept it ercept ( ) = exp k for hydroge (2)

12 x (-/5, -/5 H, +kw) a 0 (-/7, -/7 H, +wk) e (-/, -/8 H, +wk) lost δ = ± (exp k -qf) = a/ + b kietic weak hydroge lie (-/, -/3 H, +wk) (0, 0) eutro) muo eutro uclear lie (-/24, -/8 H, +wk) muo (+/2, +/3 H, -wk) W W eutro uclear lie 3 (+/8, +/8 H, -wk) (+/3, +/3 H, -wk) x = ±/ Figure 5. The kow z poits relatig the muo ad W with the eutro ad hydroge. This figure displays the l-l plae for the z values for the kow values of the masses of the electro, Bohr radius, eutro, muo ad W (solid black circles). The diamod patter at the periphery is the liear relatios of the / values derived from the mass of the electro ad the Bohr radius (wk H) (Fig. 4). The other white circle values are calculated. This liear arragemet of z values are logically assumed to be related to the kietic weak forces. Note that the kow z values of the muo ad W are related to the itersectio of radii of the iverses of -/8 ad -/3 wk H poits respectively ad the vertical pricipal quatum umber ±/ lie of -/24, ad +/2, respectively. This demostrates the geometric ad quatum umber lieage relatioship betwee hydroge ad the uclear properties. The quatum umber of the muo is 2 times the quatum umber of W. Two is the quatum umber associated with the eutrio. W ad Z are associated with the quatum umber 2. ( ± y at - ) ± ( - )( ± y at 0) it ercept it ercept = exp k for the o-hydroge factors (22) Below are the frequecy domai equatios expk + z v = ( v s ) Hz = ( v s ) Hz k qf vk = ± ± δ vs Hz vs Hz ± = ( ) (23) (24) H a ± ± ± b uc H vk = vs Hz (25) Nuclear z poits ad the weak kietic ad electromagetic lies The etities with quatum umbers larger tha 8 are associated with two pricipal quatum umbers, oe related to hydroge ( H ), ad oe secodary sec quatum umber. The lie splittig is liearly proportioal to / (x-axis). For the small values of, the oly possible qf values associated with each costat are those qf that are mathematically larger or smaller tha the exp k, so there is o speculatio i their assigmet whe they are accurately kow. This is ot true whe values are larger (greater tha 40), sice the / differeces become smaller tha the δ values. Logical assigmets are made (Table 2). More tha oe symmetry poit ca demostrate a liear relatioship to the other fudametal costat z values (Figs. 5 7). For example, the iteger 2 is associated with both the W ad Z bosos. Harmoic liage relatioship betwee hydroge values ad their uclear related etities By empirical ispectio there are oly 6 possible idividual symmetry poits i each l-l plae

13 quadrat associated with hydroge that defie all of the possible radii from the eutro (0, 0) poit. Eight poits are derived from the kietic weak etities ad eight from the electromagetic etities. For the whole l-l plae, there are 64 possible hydroge z poits related to values from to 8. Every uclear etity falls o oe of these radii coectig the eutro ad the other potetial hydroge poits. These 64 poits are based o oly two lies for the lowest pricipal quatum umber values oly ( = 8) ad properties of hydroge (Fig. 4). There are eight z poits per lie for weak kietic (wk) etities, or eight z poits per lie for electromagetic (em) etities that are liearly related to each other o the l-l plae (Figs. 3 7). Therefore, the actual expoets of a group of associated hydroge properties are all related to a specific lie where a ad b defie each specific lie slope (a wk), (a em) ad y-itercept (b em), (b wk) (Equatios 5 22). The eight weak kietic poits are solely derived from two z poits (the Bohr radius ( H, 5) ad the mass of the electro ( H, 7)) (Figs. 3 7). These two poits defie the lie slope: (a wk) , y axis itercept: (b wk) All of the eight electromagetic z poits are defied solely by Plack s costat ad the ioizatio eergy ( H 3) z poits (Figs. 3 7). These two poits defie the lie slope: (a em) ad y-itercept: (b em) Nuclear weak force etities relatioships betwee hydroge z poits ad the eutro z poit The mass values for the three eutrios are ot accurately kow, but are i the rage utilized i the calculatios. The reasoable, but ot precisely kow values of 7 0-6, 0., ad 0.5 ev were used as estimates for the calculatios of the electro eutrio, the muo eutrio ad the tau eutrio respectively. The approximate exp k for the average value is Therefore, the quatum fractio of ½ is assumed. It is ot completely clear if this is a valid value based o experimetal data, but it does appear to logically support the hypothesis. Tau, muo, Z ad W are all related to z iverses (radii) of the hydroge weak kietic lie poits (Figs. 5, 6). The predictios of tau, muo, Z ad W are made from the calculated weak kietic hydroge lie z ( = 2 8) iverse values ad their uclear / (qf) oly (Table 3; Equatios 5 22). W is associated with the z poit (+/2, +/3 H, -wk). The quatum umber 3 is associated with currets, i this case eutral currets. Z is associated with the z poit (+/2, +/7 H, +wk). The quatum umber 7 is associated with the electro. The muo is associated with the z poit (-/24, -/8 H, +wk). Tau is related to the z poit (+/83, +/6 H, -wk). The quatum umber for the muo is 24, ad the associated harmoic product is 2 * 2. Two is associated with the eutrio, ad twelve is associated with Z ad W. Tau is associated with the pricipal quatum umber 84. It is also associated with the harmoic product 7 * 2. These umbers are associated with the electro ad Z or W. Therefore, the weak etities represet product harmoic umbers of the beta decay masses, 2 for the eutrio, ad 7 for the electro with 2 for W ad Z. Electromagetic etities relatioship betwee hydroge ad the eutro z poit The z poits associated with electromagetic properties are derived from the em lie (Figs. 4, 7; Table 4). All of the quarks ad mesos are also related to a radius itersectig the eutro poit ad the electromagetic poits. This is idetical i patter to the weak force uclear etities. The z poits for the quarks iclude: up (-/0, *H, *em), dow (-/, *H, *em), strage (-/30, *H, *em), charm (±/39, *H, *em), bottom (+/36, *H, *em), ad top (+/0, *H, *em). The *sigifies that the values for the quarks are ot defied well eough to associate them with specific values. The experimetal accuracy for the actual quark masses is poor, so the exact calculatios are ot possible. The top quark is best kow. All of the quark predictios from this model are cosistet with the kow estimated values. The quarks quatum umbers follow harmoic umber properties as well, with the up quark umber 0, dow, strage 30 (3 * 0), charm 40 (2 * 7 * 0), bottom 36 (3 * 2) ad top 0. Therefore the harmoic product for strage is related to 3 for R ad 0 for up quark. Charm is associated with the harmoic product of 2 for the eutrio, 7 for electro, ad 0 for the up quark. Bottom is associated with the harmoic product of 3 for R, ad 2 for the W or Z. All of the hydroge

14 x (-/5, -/5, +wk) a o (-/, -/3 H, +wk) (-/, -/8 H, +wk) (+/7, +/7 H, +wk) e δ = ±(exp k -qf) = a/ + b kietic weak hydroge lie (-/, -/4 H, +wk) (0, 0) eutro Z eutro uclear lie (-/7, -/7 H, +wk) e (/2, +/7 H, +wk) Z (+/83, +/6 H, -wk) tau tau eutro uclear lie 3 (-/, -/ H, -wk) e x = ±/ (+/6, +/6 H, -wk) Figure 6. The kow z poits relatig the tau ad Z with the eutro ad hydroge o the l-l plae. This figure displays the l-l plae for the z values for the kow values of the masses of the electro, Bohr radius, eutro, tau ad Z (solid black circles). The diamod patter at the periphery is the liear relatios of the / values defied by the mass of the electro ad the Bohr radius (wk H lie) (Fig. 4). The other white circle values are calculated. Note that the kow z values of the tau ad Z particles are related to the radii of the / H values /6 ad /7 poits respectively. The actual expoet kow value is at the itersectio of the eutro radii ad their associated vertical / uc itersectio lies of +/83, ad +/2, respectively. The predicted values of the tau ad Z are withi the maximum experimetal measurable ucertaity. This demostrates the geometric ad quatum umber lieage relatioship betwee hydroge ad the uclear properties. The quatum umber of the tau is 7 times the quatum umber of Z (2) or 84, 84/83. quatum umbers are associated with the harmoics of these etities. The pio ad kao values are more accurately kow ad also oly occur at the itersectio of electromagetic hydroge z poit δ H radii ad their pricipal quatum umber values (Table 5). Each kao ad pio value also falls o radii from the eutro z poit to em δ H poits. The pio + is related to the z poit (-/28, -/3 H, +em). The pio 0 is associated with the z poit (-/28, -/4 H, -em). The kao 0 is associated with the z poit (-/84, -/3 H, +em). The kao + is associated with the z poit (-/85, -/6 H, -em). There is a product harmoic umber property betwee the pio ad kao as well. The product of 3 for R ad 28 for the pio is 84, the quatum umber of the kao. All of the uclear etities i this paper demostrate logical simultaeous associatios of the hydroge z poit to uclear values usig harmoic umber properties ad liear relatioships o the l-l plae. Discussio A preposterous hypothesis This paper presets a preposterous hypothesis that the fudametal physical costats of hydroge ad the fudametal rest masses (bosos) plotted i their actual frequecy equivalet couplig costat expoetial values are similar to a classic quatum stadig wave spectrum. This model i o way follows the maistream thoughts related to sophisticated uified theories presetly circulatig today. 25 O the other had, this model i o way represets the slightest departure from classic quatum mechaics ad harmoic systems.,2 The validity of this model

15 5 x (-/,-/8 H, +em) (-/, H, em) d (+/8, +/8 H, +em) 3 (-/, -/3H, +em) δ = ± (exp k -qf) = a/ + b (-/0, H, em) u (- /28, - /3 H, +em) pio + (-/28, - /4 H, -em) pio 0 (-/0, H, em) s (+/3, +/3 H, +em) R ( - /84, - /3H, + em) kao 0 (+/36, H, em) b (0, 0) eutro (-/85, - /6 H, - em) kao + (+/0, +/8 H, - em) t 3 ( - /, - / H, - em) ( +/3, +/3 H, - em) R (-/3, -/3H, -em) R (- /, - /H, -em) (+/39, H, em) c x = ±/ Figure 7. Plot of the quarks ad mesos z poits ad their relatioship to the hydroge z em poits. This figure displays the l-l plae for the z values for the kow electromagetic H poits, kaos, pios, ad the quarks. The * represet the fact that these values are ot accurately kow, ad caot be assiged. The solid black lies are the radii from the eutro to the electromagetic hydroge poits (ope circles) associated with the quarks ad mesos. The solid black circles are the kow values for the pios, kaos ad the eutro. The ope circles ad rage gray arrows are related to the estimated kow values for the quarks. The solid gray lies are rage of the calculated values for the quarks usig the values of 0 up-top, dow, 30 strage, 36 bottom, 40 charm. Note that all of the pios fall o electromagetic radii similarly to the weak force factors. The six quarks kow rages fall withi the predicted possible rages betwee the 8 δ rages. This demostrates the geometric ad quatum umber lieage relatioship betwee hydroge ad the uclear properties. Note that oe each of the pios ad kaos falls o the lie coectig the ucleus ad the R z poit. The lieage quatum umber is 3. The quatum umber of the pio is 28. Three times that value is the quatum umber of the kao, 84. eeds to be systematically evaluated to be prove wrog (because it does ot work to geerate accurate predictios), or prove correct (because it does). The power of the hypothesis The power of a hypothesis is its ability to predict kow physical facts that presetly caot be derived, or to logically explai uifyig relatioships of pheomea utilizig a simple method presetly ot uderstood. A few of these uresolved fudametal issues i physics iclude: the logical origis for the values for the fie structure cotstat, α, 4,9 ruig α, electro spi g factor, g e, Newto s gravitatioal force costat G, 4,26,27 the other force costats, ad the masses of the fudametal particles (bosos). 2,27 33 This model ca derive all of these costats, but this paper focuses solely o the values for the quarks, Z, W, the leptos, ad some of the mesos. This hypothesis geerates a simple supportable quatum ratioale for the actual values of the fudametal costats across all of the forces with o mathematical impossibilities or usolvable sigularities. It does ot require advaced math calculatios, hypotheses that caot be proved, or the ecessity to defie extra physical dimesios. Properties of classic harmoic systems ad the relatioship to music There are a umber of classic mathematic properties that are expressed i physical harmoic pheomea.,2 These are commoly see i musical systems ad will be used as prototype models that

16 Table 4. Predicted-calculated expoet values for the muo, tau, W, ad Z from hydroge z poits. Weak force etities ad qf ( H, uc ) Predicted expoet (kow) Relative error predicted (kow) 2/3 ad W (3/2) (4, 2) ( ) ( ) 5/6 ad tau (84/83) (6, 83) (.08493) ( ) 6/7 (electro) ad Z (3/2) (7, 2) ( ) ( ) 7/8 ad muo (23/24) (8, 24) ( ) ( ) The predicted-calculated values of W, tau, Z, ad the muo from the itersectio poits of the radii of the z values associated with the kietic weak hydroge lie ( = 2 8 poits) ad the vertical pricipal quatum umber lie ±/ are listed (Figs. 5, 6). This is idetical to the calculatio usig equatios The eutro poit was assumed to be liearly related to the iverse of the properties of hydroge ad the high-eergy weak forces expoets. The weak kietic hydroge values were used. Note that predicted values are i excellet agreemet with kow expoet values ad are early all withi the relative measurable ucertaity rages. The kow values are i italics ad the predicted values are ot. have idetical properties to this paper s hypothesis. For example, whe a strig is plucked, it geerates oe domiat fudametal frequecy. Simultaeous toes of iteger multiple frequecies are also produced. This is a form of a spotaeous quatum pheomeo. This is associated with a stadig wave geometric patter, such as that see i this model, ad is aalogous to Plack s law (Figs. 3). It was discovered eve i aciet times that harmoic toes were related by iteger fractioal relatioships of the fudametal frequecy. For example, humas recogize harmoy betwee two musical toes at iteger fractio steps idetical i character to the quatum fractio series i this model, where repeatig product umbers are see with the iteger values. Our stadard Wester harmoic toe system is largely based o the frequecy toe ratio of 3/2 ad a series of (3/2) times a frequecy. These iclude the series 9/8, 27/6, ad 8/64. The deomiator chages to maitai each toe i the same octave. This is related to the Pythagorea harmoic scale. Therefore harmoic toes are related to commo iteger products of two umbers. I this model, this patter is see i the iteger product relatioships of the iteger values for hydroge that are related to uclear properties. These modes are aalogous to the physical distributio of electros aroud the atom ad their associated quatum umbers. Despite the fact that this is a model focusig o quatum pheomea, essetially all of the basic mathematical properties are well-kow to occur i all periodic physical systems. Cofirmatio of the hypothesis This paper uequivocally cofirms the hypothesis that the fudametal costats evaluated follow classic quatum spectral characteristics. Though this is a classic experimetal spectral aalysis method, it represets a totally ew perspective o the previously ususpected quatum relatioships betwee the fudametal physical costats. This model is ot i coflict with ay existig physics values or laws, but oly plots the kow values by first ormalizig them to frequecy uits characterizig hydroge, the traslatig them to a log uit system o a l-l plae. This makes the liear ad quatum iteger fractio relatioships obvious. Almost all of the predictios are withi the rage of measurable relative ucertaity. Oe outlier is the muo, but this may be due to its g-spi factor. The mior differeces of predictios for a few of the kow values (i.e. the muo) may reflect classic mior highresolutio spectral shifts similar to the Lamb shift. For example, it is possible to calculate the exp k of the Z particle usig oly the pricipal quatum umbers 7 ad 2 ad the exp k of the electro (Equatios 5 22). The same is true for the pio + usig oly the pricipal quatum umbers 3 ad 24 ad the exp k of

17 Table 5. The kow ad predicted values of the quarks, pios ad kaos. Costat ±/ qf, / or +/ H values exp k # rage qf ± δ (predicted) # rage up -/0 9/0 * # # top +/0 /0 * # # dow -/ 0/ * # # strage -/30 29/30 * # # bottom +/36 37/36 * # # charm +/39 40/39 * # # pio 0 -/28 27/ pio + -/28 27/ kao 0 -/84 83/ kao + -/85 84/ The kow ad rage of predicted values of the quarks (Fig. 7) are listed. The values for the pios ad kaos are predicted usig the same liear relatioship as well as those related to em hydroge z poits ( = 2 8 poits) (Fig. 7). The hydroge values for the calculatios are listed. These calculatios were derived usig equatios 5 22 which is equivalet to the itersectio of the z hydroge electromagetic poits ad the uclear pricipal quatum umber. The eutro sigularity poit was assumed to be the ceter of the quark values similar to the kietic weak factors (Table 3). The associated / vales are listed for each etity. Note that predicted values are i excellet agreemet with kow expoet values. Note that the top quark is equivalet to the iverse of the up quark, 0 ad. The bottom quark is the iverse of the strage quark. The dow quark is the ext cosecutive iteger after the up value. The up, top, dow, strage, bottom, ad charm quarks are related to equals 0, 0,, 30, 36, 40. The pio ad kao values follow similar patters to the weak force factors (Figs. 5, 6) except they are related to the em hydroge lie-derived z poits ot the weak kietic hydroge z values. The *sigifies that the hydroge quatum umber values are ot kow sice their masses are ot accurately measurable. the Rydberg costat. This would be impossible usig ay other existig model. The calculated expoet differeces from the kow values are well withi the rage of subtle differeces see i other quatum spectral patters. Some of the kow values are simply ot accurately kow, icludig the quarks. The value for the top quark is most accurately kow ad does follow a predicted hydroge ad qf value (Fig. 7). The other quarks fall withi the predicted values. All of the particles should be associated with a iteger H value that ca be easily calculated (Equatio 20). Physical maifestatios of symmetry properties o the l-l plae The hypothesis is supported by documetatio of may accurate liear calculatios, predictios followig classic symmetry properties o the l-l plae. I fact, every value plotted represets a symmetric poit cetered o the eutro. A symmetry poit represets a value of idetical scale, but opposite sig. This is aalogous to complex umber properties. Other physical examples iclude positive ad egative charges, matter ad atimatter, attractive ad repulsive forces. There should be examples of symmetric poits represetig actual physical etities. The quarks top ad up represet symmetric iverses (Fig. 7). The uclear o-hydroge etities fall o iverse lies coectig the hydroge qf values. Similarities of quatum spectra characteristics, atomic model aalogy, ad this hypothesis This model is also based o the classic mathematical format defiig atomic spectral series. I these series the eergy values are related to the product of h, a fudametal frequecy, ad a fuctio based o dimesioless quatum itegers. The oly substative differece is that the equatio used i this model represets a expoetial iteger relatioship. May physical pheomea (magetic resoace relaxatio times, radioactive half lives) are related to expoetial relatioships. This property ca oly be true if the ratios of the actual values for the primary liear force equivalets are equal (Equatio 5). Therefore, this model represets a classic quatum system based o expoets ad stadig wave patters (/). There are multiple repeatig lie patters see i this model, similar to those see i all classic quatum spectra. I the Rydberg series, each group is based