Special Relativity Electromagnetic and Gravitation combined Into one theory

Transcription

1 --5 Speial Relatiity Eletromagneti and Graitation ombined Into one theory Mourii Shahter ISRAE, HOON Introdution In this paper, I try to ombine Eletromagneti and Graitation into one theory, using hidden parameters of Speial Relatiity. Assumption he eletron harge annot be separated from the eletron mass. Both are "onneted "to the same partile. his is true for all other "elementary partiles". In eletriity and eletroni we an aumulate harge only on apaitors, so I assume that partile mass is the apaitor mass that hold the partile harge. Of ourse, suh an assumption must agree with all other theories like Relatiity Graitation Eletromagneti et I paid attention that "ransmission lines" behae mathematially aording to Speial Relatiity, (3D eletromagneti aity also), hene I used the ransmission line to explain why "Spae ime" is the "apaitor" of partile harge. he final onlusion was that the entire unierse is an eletromagneti aity. he eletromagneti waes reate A urrents in the "mass apaitane" and the mass moe aording to professor Einstein equations. But Graitation waes does not exists. _ //7 - mourii@gmail.om, mourii@walla.o.il Israel tel

2 Definitions m, m Rest mass and moing mass µ Vauum permeability µ Relatie permeability ε ε R R β X Vauum permittiity Relatie permittiity he speed of light in auum he speed of light in matter he mass eloity relatie to the lab slip apaitane α apaitor quality fator Elementary partiles he table below ontains a lot of information about known elementary partiles, but one important olumn in this table is missing. And I am going to explain what olumn is missing and why. he harge of an elementary partile (see the elementary partiles table aboe) an be ±, ±, or eletroni harge. he harge is limited in range and 3 3 quantized. he mass range is arying wide. How we an explain it. hose who learn eletrial engineering know that harge is always kept on the plates of a apaitor. If so, elementary partiles hae also apaitane. he missing olumn in the table aboe is therefore the apaitane of eah elementary partile. Eletrial engineers know also that exept harge there is also indued harge. In the piture below [] we see a single apaitor. Suppose its mass is m and its apaitane is E. A good apaitor is a apaitor with a big E E m ratio. So the apaitor quality fator an be defined as but My definition is entirely different m and strange and the reasons will be explained later. I define the apaitor quality fator α as follow α m So, the quality fator for the apaitor in ase [] is α //7 - mourii@gmail.om, mourii@walla.o.il Israel tel

3 E m α E 4 4m α 3 6m E α E 8m 4 α 3 Suppose all the apaitors in the piture aboe are the same. In ase [] the harge between two apaitors is indued harge. he equialent apaitane of 4 apaitors 3//7 - mourii@gmail.om, mourii@walla.o.il Israel tel

4 E onneted in series is and the total mass of 4 apaitors is 4m so the apaitor 4 quality fator for ase [] is α ase [3] and ase [4] are soled in a similar way. What we an learn from these examples? ase [], desribe an eletron. We sense the negatie side of its apaitor. he eletron has the best apaitor quality α We know that the proton is positiely harged and its mass is 834 times the eletron mass. So the proton is a ery long hain of 834 apaitors onneted in series and we sense its positie side. For the proton m α ( 834 m ) E 834 Proton's apaitor quality fator is law ompared to eletron apaitor quality fator If two protons ollide in an aelerator like the H the apaitor series onnetion is broken. What we get is other apaitors series parallel onnetion. Eah ombination of apaitors from our point of iew is a different partile. Elementary partiles that hae no harge are two hains of harged partile in suh arrangement that the total harge appear to be zero (ring). For example positron plus eletron appears together as γ photons. Intermediate onlusions All the partiles are made from one blok of "ego" suppose it is the eletron with mass m and unknown apaitane E and basi harge of eletroni harge. All other partiles are hains, strings and rings made from the basi blok (here is eidene that the basi "ego" blok is the uark's blok not the eletron's) So the unierse is muh simpler then we think. And the number of different partiles is muh lower. Step he Eletrial Equialent iruit for Relatiisti Mass And hidden parameters in Speial Relatiity Aording to Speial Relatiity, elementary partiles hae a rest mass m. When the partile moes with a "slip" β it's mass m is growing aording to m.a] m β Beause of the square root in the equation, the "slip" β is limited to < β < whih means that the partile eloity is always less then the speed of light 4//7 - mourii@gmail.om, mourii@walla.o.il Israel tel

5 Now I multiply both side of eq. by α αm.b] αm β Now I am going to make a brae hange in eq..b he square of eq..b is α m α m α m ] α m + β ( β)( + β) β + β Eq. in ontrary to eq., is a "ontinuous funtion" with only two "bad" points β ± Aording to eq. we an pass the speed of light, Step Deriing an Eletrial Equialent iruit that helps understand Speial Relatiity et go bak to eq. and write it as follows 3] m m m m α α α + α + + β + β Now I diide the last equation into two parts that now on must be treated separately α m α m β 4] α m α m+ + β he total relatiisti mass is omputed using Pythagoras 5] α m α m + α m + I gie two numeri examples. Pay attention to the seond example, in whih the mass eloity is higher then the speed of light ( β > ) Suppose; m m and β.8 then, m m β.8 β m+ m m β + β 555 In the following example, If the mass eloity is higher then the speed of light, we get an astonishing result.he mass m is a omplex number. 5//7 - mourii@gmail.om, mourii@walla.o.il Israel tel

6 m m and β.4 higher then the speed of light m m.5.46 β.4 β m+ m m β + β ( ) m.48 j.43 j omplex number mass he following graph is for m against β Step 3 Making the equation a bit more physial In eq. or eq. we dont see any familiar physial phenomena. And the idea that speed of light is the same in all diretions is not intuitie So, I am going to turn those equations into onentional not weird and intuitie physial equation that eery student meets during his studies. et define π j, f to be any frequeny, ω π f,, k f λ 6] α m, α m, α m, α m + + Now let substitute those definitions in eq. 4, (eah equation is diide by jω ) And I define some new terms suh as: Z,,, Z Z+ Z and put them in eq. 3 and eq. 4 6//7 - mourii@gmail.om, mourii@walla.o.il Israel tel

7 7] α Z α Z α m β m α m α m jω jω jω β jω β m+ + ( ) ( ) α m + β α m α m jω jω jω β jω β ( + ) ( + ) + What we get is something more familiar to eletrial engineers 8] α m α m α m + α m+ + β + β α m α m α m Z Z+ + Z+ + jω jω jω Z Z+ + Z+ + + jω jω jω jω ( β ) jω ( + β ) + Eery eletrial engineer will say that,, +, are eletrial apaitors. And it is well known that the alternating urrent (A) impedane of a apaitor is: 9] Z jω Before ontinuing with the explanation, let sole one more example Milliken Experiment In 99 Robert A. Milliken and Harey Flether performed an oil drop experiment to measure the elementary eletri harge of the eletron oday we know that for the eletron or positron 3 m 9.9 kg.5mev and the eletron harge is E 9.6 oloumb We know from eletriity that harge equal apaity time oltage Using E E VE and α m We an define a new kind of oltage that we will all "Rest Mass Voltage" m V Sine 7//7 - mourii@gmail.om, mourii@walla.o.il Israel tel

8 V m V E m E α m.6 (9.9 ) E α α 6.64 oloumb kg he same proedure an be used to find the "Rest Mass Voltage" for other harged elementary partiles suh as Protons and quarks (Pay attention to the physial units) Partiles that hae no harge are omposed from harged partile with opposite harges. he neutron for example, is a positie proton plus a negatie eletron (old model) or harged quarks (new model). et see now if the experiment at H (arge Hardon ollider) are made properly. In all olliders, elementary partiles suh as protons eletrons and so on, make ollisions near the speed of light therefore; β < but β, he part of the equation that is responsible to mass grow is m m m m m m beause, m+ β β β β + 4 From eq. 8 Step 5 Now I am going to explain why the speed of light is the same in any diretion ] Z Z + Z + Suppose the urrent that flow through the series of impedanes is I [] V + V Z I + Z I I + I I + I jω jω + jω ( β ) jω ( β ) he question is how the urrent depended on frequeny?. o find the answer we must remember that for a apaitor d ] i dt In the ase of A et use those definitions in eq. I Ie I Ie I Ie jωt jω ( β ) t jω ( + β ) t 3] + And from eq. j( ω ( β ) t) j( ω ( + β ) t) 4] V + V+ Ie + Ie jω ( β ) jω ( + β ) he reason for that is that the frequeny of the urrent and oltage must be the same and the same frequeny must also appear in the impedane of the apaitor 8//7 - mourii@gmail.om, mourii@walla.o.il Israel tel

9 5] V Z I Ie jω ( β) V+ Z+ I+ Ie jω ( + β) ( ω ( β ) t) j ( ω ( + β ) t) he onlusion is that when the mass is moing and β we hae two frequenies So 6] V V + V+ Is a superposition of two different oltages with different frequenies and amplitudes? Suh a phenomena desribed aboe our in "wae guides", "transmission lines", and "aities". onlusion: we lie in a 3D eletromagneti aity, only eletromagneti waes and harges are responsible for eletri urrents. apaitane and mass are passie elements. Step 6 A short introdution to ransmission lines o understand what happens in a "transmission line" let exam; Relatie Galilean Moement Suppose a hopper fly aboe a highway. If the hopper eloity is to the right, the pilot laim that the eloity of the ars moing to the right is and ars moing to the left are at a higher eloity +. hoppers an moe faster then ars. If >, the pilot obsere that all the ars moe to the left. j x 9//7 - mourii@gmail.om, mourii@walla.o.il Israel tel

10 Step 7 Wae Moing in Opposite Diretions and Standing Waes (hopper and Vehiles desribe mathematially) z y x w( t, x) A os( k( x t)) t x z y x x w( t, x) A os( k( x + t)) he following equation w( t, x) A os( k( x t)) Desribe a osine wae moing along the x diretion from left to right While w( t, x) A os( k( x + t)) Desribe a wae moing in the opposite diretion from right to left In order to find the wae diretion, we know that os( ϕ) when ϕ So for the wae moing along the positie x diretion w( t, x) A os( k( x t)) ϕ means x t or x t For the wae moing along the negatie x diretion w( t, x) A os( k( x + t)) ϕ means x + t or x t A standing wae is a wae in whih its amplitude is formed by the superposition of two waes of the same frequeny propagating in opposite diretions. w( t, x) w( t, x) + w( t, x) w( t, x) A os( k( x t)) + A os( k( x+ t)) Aos( kx) os( kt) Aos( kx)os( ωt) //7 - mourii@gmail.om, mourii@walla.o.il Israel tel

11 Step 8 Waes under Galileans ransformation Now, suppose that an obserer O (the pilot of the hopper) is moing with eloity in the positie diretion of x. his position relatie to the x axis is gien by (look again on the piture aboe) x x + t he moing obserer O will see the osine wae as follow w ( t, x) A os( kx t)) A os( k( x + t) t)) A os( kx k( ) t)) w ( t, x) A os( kx+ t)) A os( k( x + t) + t)) A os( kx + k( + ) t)) ω Now, if and β we an write the aboe equation from the point of k iew of the obserer, as follow; w ( t, x ) A os( kx k( ) t)) A os( kx k( ) t)) A os( kx ω( β ) t)) w ( t, x ) A os( kx + k( + ) t)) A os( kx + k( + ) t)) A os( kx + ω( + β ) t)) he moing obserer sees two waes with different frequenies he standing wae is the sum of the waes that moe to the right and to the left w( t, x ) w( t, x ) + w( t, x ) w( t, x ) A os( kx ω ( β ) t)) + A os( kx + ω ( + β ) t)) w( t, x ) A os( kx ω t+ ω βt) + A os( kx + ω t+ ω βt) Aos( kx + ω βt)os( ω t) w( t, x ) Aos( kx + kβt) os( ωt) Aos( kx + kt)os( ωt) Aos( k( x + t)os( ωt) But, x x + t herefore, w( t, x ) Aos( k( x + t)os( ω t) Aos( kx)os( ω t) w( t, x) What we see is that the obserer moes to the right, from his point of iew. he standing wae exists and moes to the left beause x x + t x t //7 - mourii@gmail.om, mourii@walla.o.il Israel tel

12 he transmission line model of Relatiity oaxial ables are transmission lines, used to transmit eletrial information at ery high frequenies in able V and Internet he simplest transmission line is win-lead is a form of parallel-wire balaned transmission line. he separation between the two wires in twin-lead is small ompared to the waelength of the radio frequeny (RF) signal arried on the wire. I use the twin lead transmission line to explain S.R A λ ( t kx) j ( t, x) Ve ω x B j( t kx) ( t, x) Ve ω + x In the piture aboe (piture A) a transmission line is onneted to a sinusoidal oltage soure. the transmission line is terminated with an adequate resistor. and a standing wae is reated along the transmission line. It was proed that a standing wae is a superposition of two waes moing in opposite diretions, eah wae with eloity. So instead of one ransmission-line I use two. One for the wae going //7 - mourii@gmail.om, mourii@walla.o.il Israel tel

13 from left to right, (piture B). and one, for the wae going from right to left. (piture ) Now I onnet a apaitor to the transmission line. In suh a way, that the apaitor an slide along the transmission line. he apaitor onneted to the transmission line hange the distribution of urrent and oltage along the whole transmission line (eery star or elementary partile disturbs the entire Unierse) the apaitor an moe to the right with eloity while keeping an eletrial onnetion with the transmission line (see piture B and ). he apaitor is the obserer O (the pilot of the hopper) When the apaitor whih desribe rest mass in the S.R model α m moe to the right the impedanes Z aboe. he urrent in eah apaitor is gien by I V Z ( ω t) j Ve jω and Z + hange as was explained I ( ω ( β ) ) ( ω ( + β ) ) j t j t V Ve V+ Ve I+ Z Z + ( ) ( ) jω β jω + β his urrent through the sliding apaitor hange the oltage and urrent in eery point along the transmission line. A transmission line without any disturbane is a homogeneous transmission line. When the apaitor is added or hanged from one alue to a greater alue all the oltages and urrent hange but the hange goes through the transmission line at the speed of light or less so if two blak holes ollide (eah blak hole is represented by a apaitors the first blak hole is represented by the seond by. their moement hange the urrent and oltage along the entire transmission line and IGO ath the eent after some millions of years, beause information on a transmission line goes a bit "slowly" In the ase of eletron positron annihilation the eletron represented by and the positron by are annihilated and the mass anish, what we get is a γ ray. In this ase, a transmission line that was disturbed by two partiles and then the disturbane disappeared. Mathematially, we hae to pay attention to the fat that when the mass don t moe the urrent is only I 3//7 - mourii@gmail.om, mourii@walla.o.il Israel tel ( ω t) Ve jω And when the mass moes the urrent is a superposition of two urrents j

14 ( ω ( β ) ) ( ω ( + β ) ) j t j t Ve Ve I I + I+ + jω β jω + β ( ) ( ) At the speed of light( β ) I and I + I What make mass to moe he amplitude of V, V, V + in the transmission line, are the same, so it is easy to show that I I + I+ In eletriity the power is gien by * S P+ j V I So we an ompute the Power delierd to the apaitors * S j V I S S + S j + j V I + V I * * But S < S + S + so mass may prefer not to moe (the law that a system prefer to hae minimum energy) Aording to the rules of eletriity, the apaitor is a passie element the apaitor power is Reatie ( j) the apaitor store energy taken from the "ransmission line". If the eloity is higher then the speed of light. he apaitane turns into resistane. he urrent through it appears as heat. 4//7 - mourii@gmail.om, mourii@walla.o.il Israel tel

15 Examples µ ε Homogeneous ransmission line Homogeneous Unierse near star ( + ) µ µ ε ε R R far from star µ ε Point star far from star near star µ ε R µ µ ε ε R between planets? near star R µ µ ε ε R far from star µ ε ransmission line behaior between two planets 5//7 - mourii@gmail.om, mourii@walla.o.il Israel tel

16 far from star ( r) ( + ( r)) ( r ) Near a Star or Blak Hole he mass is distributed as a funtion of distane from star enter to the end of the unierse onlusions. Eletron harge stay on a apaitor, the apaitor has mass, mass and apaitors are passie element and an't transmit graitation waes. We an notie only when mass moe and make the "ransmission ine" oltages and urrents to hange alue.. he " ransmission ine" inluding mass distribution is what we all "Spae time" 3. Mass beomes omplex at eloity higher then the speed of light 4. Unierse in one dimension behae like a transmission line, in three dimensions the unierse behae as a spherial aity, all the stars and galaxies are in that aity. 5. Our unierse is almost empty so it is almost homogenous. 6. No suh thing: here are four onentionally aepted fundamental interations graitational, eletromagneti, strong nulear, and weak nulear. May be all elementary partiles are hains, strings and rings of eletrons. 7. Sine the speed of light is the same for all this fores. hey behae aording to the same rules herefore the unierse is simpler than we think 6//7 - mourii@gmail.om, mourii@walla.o.il Israel tel

17 _ 8. Appendix he analysis of ime Dilation, ength ontration and orentz ransformation are similar to mass hange. Beause all the equation look the same. he analysis of time dilation is similar to the analysis of mass hange τ m τ and m β β he analysis of length ontration is similar to the analysis of mass hange beause they look the same. λ m λ and m β β and orentz boost ransformation (x diretion) t β x m m t ' similar to m ' β β x t m m x ' similar to m ' β β y ' y z ' z Speial Relatiity Eletromagneti and Graitation ombined into one theory 7//7 - mourii@gmail.om, mourii@walla.o.il Israel tel