Einstein, Lorentz i Euklid

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Scientific Paper
Title Einstein, Lorentz i Euklid
Author(s) Mustafa Sprecic
Keywords Lorentz, Einstein, Euklid, Lorentz-ove transformacije koordinata
Published 2013
Journal None

Abstract

Algebarsku i geometrijsku povezanost Einstein-ovih i Lorentz-ovih velč?ina u STR najlak?e je predoč?iti putem sljedećeg algebarskog iskaza

(f-1) <img border="0" data:image="" png;base64,ivborw0kggoaaaansuheugaaabqaaaaucamaaac6v+0="" aaaaovbmveuaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaad="" +8yhyvaaaaenrstlmaagedbaujbwyzcw0uchardghnbteeaaaaheleqvr4xnwrsxjdiqgeex1axd="" l="" q8bkcuuyozsohhxdzls25lsov2ulqdflgeiidu9kqiifilxxpeex2chxwdnknxugxc4dzbnfxjpufkp5h0nwtymq="" dltuiweny9qmxt08egyddz6+dt+9qh9aegenhrofi0fpjmachx6uilh9="" xbsjub3l0a="" 6jaaaaaelftksuqmcc");="" border-image-slice:="" 9="" 9;="" border-image-width:="" 9px="" 9px;="" border-image-repeat:="" stretch="" stretch;="" background-color:="" white;"="" style="border-style: solid; border-width: 1px; border-color: rgb(204, 204, 204) rgb(153, 153, 153) rgb(153, 153, 153) rgb(204, 204, 204); position: relative; height: auto; margin: 10px auto; max-width: 100%; padding: 7px;" src="https://sites.google.com/site/specijalnateorijarelativnosti/_/rsrc/1362950619174/Home/Einstein%20i%20Lorentz%20-%20zajedno.gif" />
Einstein vrijeme u kretanju (crtkano vrijeme t') iskazuje pomoću "izmjerene velič?ine" l0 = ct0
 Einstein-ovo vrijeme (t'A) =   <img border="0" data:image="" png;base64,ivborw0kggoaaaansuheugaaabqaaaaucamaaac6v+0="" aaaaovbmveuaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaad="" +8yhyvaaaaenrstlmaagedbaujbwyzcw0uchardghnbteeaaaaheleqvr4xnwrsxjdiqgeex1axd="" l="" q8bkcuuyozsohhxdzls25lsov2ulqdflgeiidu9kqiifilxxpeex2chxwdnknxugxc4dzbnfxjpufkp5h0nwtymq="" dltuiweny9qmxt08egyddz6+dt+9qh9aegenhrofi0fpjmachx6uilh9="" xbsjub3l0a="" 6jaaaaaelftksuqmcc")="" 9="" 9px="" 9px;="" height:="" auto;="" margin:="" 10px="" max-width:="" 100%;="" padding:="" 8px;="" color:="" rgb(51,="" 51,="" 51);="" text-align:="" justify;="" background-color:="" rgb(243,="" 243,="" 243);="" font-family:="" arial,sans-serif;="" font-size:="" 13px;="" line-height:="" 16px;"="" style="border-width: 9px; border-style: none;" src="http://latex.codecogs.com/gif.latex?t%27=%5Cfrac%7Bt_0%7D%7B%5Csqrt%7B1-%5Cfrac%7Bv%5E%7B2%7D%7D%7Bc%5E%7B2%7D%7D%7D%7D" /> ,  Lorentzova koordinata za vrijeme   (t'L) =   <img border="0" data:image="" png;base64,ivborw0kggoaaaansuheugaaabqaaaaucamaaac6v+0="" aaaaovbmveuaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaad="" +8yhyvaaaaenrstlmaagedbaujbwyzcw0uchardghnbteeaaaaheleqvr4xnwrsxjdiqgeex1axd="" l="" q8bkcuuyozsohhxdzls25lsov2ulqdflgeiidu9kqiifilxxpeex2chxwdnknxugxc4dzbnfxjpufkp5h0nwtymq="" dltuiweny9qmxt08egyddz6+dt+9qh9aegenhrofi0fpjmachx6uilh9="" xbsjub3l0a="" 6jaaaaaelftksuqmcc")="" 9="" 9px="" 9px;="" height:="" auto;="" margin:="" 10px="" max-width:="" 100%;="" padding:="" 8px;="" color:="" rgb(51,="" 51,="" 51);="" text-align:="" justify;="" background-color:="" rgb(243,="" 243,="" 243);="" font-family:="" arial,sans-serif;="" font-size:="" 13px;="" line-height:="" 16px;"="" style="border-width: 9px; border-style: none;" src="http://latex.codecogs.com/gif.latex?t%27=%5Cfrac%7Bt-%5Cfrac%7Bv%7D%7Bc%5E%7B2%7D%7Dx%7D%7B%5Csqrt%7B1-%5Cfrac%7Bv%5E%7B2%7D%7D%7Bc%5E%7B2%7D%7D%7D%7D" />
 dok je Lorencova velič?ina t' = x'/c vezana za vremenski interval t = x/c . 
<img border="0" style="font-family: arial, sans-serif; font-size: 13px; line-height: 16px; background-color: rgb(243, 243, 243);" src="http://latex.codecogs.com/gif.latex?t%27=%5Cfrac%7B%5Cfrac%7Bct-vt%7D%7Bc%7D%7D%7B%5Csqrt%7B1-%5Cfrac%7Bv%5E%7B2%7D%7D%7Bc%5E%7B2%7D%7D%7D%7D" />,           <img border="0" style="font-family: arial, sans-serif; font-size: 13px; line-height: 16px; background-color: rgb(243, 243, 243);" src="http://latex.codecogs.com/gif.latex?t=%5Cfrac%7B%5Cfrac%7Bct%27&plus;vt%27%7D%7Bc%7D%7D%7B%5Csqrt%7B1-%5Cfrac%7Bv%5E%7B2%7D%7D%7Bc%5E%7B2%7D%7D%7D%7D" />.
Formula (f-1) predstavlja opći izraz koji povezuje Einstein-ove i Lorentz-ove velič?ine u bilo kojem konkretno posmatranom primjeru relativnih kretanja po zakonu puta:
PC = x = ct  i  PB = x/n = vt . Izraz je korektan za sve skalarne vrijednosti brzina c i v i bilo kojeg međusobnog odnosa c/v = n >1. Dakle, brzina c nije nu?no da bude brzina svjetlosti u vakuumu. Mo?e to biti i bilo koja brzina <img style="font-family: Arial, Verdana, sans-serif; font-size: 13px; background-color: rgb(238, 238, 238);" src="http://fric8.files.wordpress.com/2011/08/brzine-v-i-c.gif?w=115&h=13" /> , bilo kolike skalarne vrijednosti. To nam omogućava neposredniji uvid u geometrijsko i fizičko znač?enje Einstein-ovih i Lorencovih formula na konkretnim sadr?ajima i primjerima dostupnijim neposrednom posmatranju, te tako lak?e uočiti Einsteinove zablude i pogre?na tumačenja fizičkih, algebarskih i geometrijskih istina koje se tim formulama opisuju
 
 Na slici imamo Lorencove du?ine:Ovaj crte? je crtan za ct/vt = n = 5/3 Na crte?u Lorencova du?ina x' = CL = LN, i vt' = BL = LT.
Iste te du?ine pomoću Lorencovog t'
 PC = PN = ct = x ,  PB = PT = x/n = vt , CL = LN = LF = LE = PD = x' = ct' , BL = LT = x'/n = vt'  ,  BC = NT = x - vt , BN = CT = x'+vt' . Najjednostavnija geometrijska i fizič?ka istina za Lorencovu velič?inu t' iskazuje sljedeća algebarska jednakost <img style="font-size: 9pt; font-family: Tahoma; line-height: 16.75px; background-color: rgb(243, 243, 245);" src="http://latex.codecogs.com/gif.latex?\\frac{ct-vt}{\\sqrt{c^{2}-v^{2}}}%3Dt%27=\\frac{t\\sqrt{c^{2}-v^{2}}}{c%2Bv}" />.
Među tima du?nama postoje i sljedeći relativni odnosi:
<img border="0" alt="" style="border: 1px solid rgb(242, 242, 241); padding: 4px; background-color: rgb(255, 255, 255);" src="https://sites.google.com/site/relativistickaalgebra/_/rsrc/1336840850603/uvod/lorentzove-transformacije/20%29%20Kvadrati%20Lorenc%20-%201.gif" /> i dalje    <img border="0" alt="" style="border: 1px solid rgb(242, 242, 241); padding: 4px; background-color: rgb(255, 255, 255);" src="https://sites.google.com/site/relativistickaalgebra/_/rsrc/1336840926690/uvod/lorentzove-transformacije/21%29%20Lorenc%20du%C5%BEine-2.gif" />. Lorentz-ovi vremenski intervali imaju sljedeću međuzavisnost (istu tu zakonitost slijede i odgovarajuće du?ine) <img alt="" style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 9pt;" class="bbc_img" src="https://lh5.googleusercontent.com/-JZC6KJuh7ZQ/Uas7FJOSZvI/AAAAAAAAGmg/PLeUhzbD990/w462-h44-no/photo.jpg" />.
Algebra je "srce" matematike, a Euklidova geometrija je njena "du?a"! Bez srca i du?e nema ?ivota ni matematici!

<img alt="" style="border: 0px none;" src="https://lh6.googleusercontent.com/-kdhTv0nSXUE/UAcDMwejt2I/AAAAAAAAEQU/lEOZyVDUS6A/s235/Lorenc%2520koordinate%2520x%2520i%2520t.jpg" /> Lorentzovo t' ima značenje <img alt="" style="border: 0px none;" src="https://lh5.googleusercontent.com/-UGPU_GkNY4c/UAcDC56OBeI/AAAAAAAAEPQ/iQJx0mxfotU/s388/26%2529%2520Lorencovo%2520t%2527%2520izvo%25C4%2591enje.jpg" /> .Ukoliko imate veličinu du?ina BN = CT i BC = TN onda veličinu Lorencovog vremenskog intervala t' mo?ete izračunati i n jedn od sljedećih načina: <img border="0" style="border: 9px none; border-image-source: url(data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAMAAAC6V+0/AAAAOVBMVEUAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///+8yHYvAAAAEnRSTlMAAgEDBAUJBwYzCw0UChARDghnBteEAAAAhElEQVR4XnWRSxJDIQgEEx1Axd/L/Q8bKCuuyOzsohHxdZLS25LSOV2ULQdflgEiIDu9KqiIFILXXpeEx2ChXwdnKNxUGxc4dZbNfXjPufkp5H0Nwtymq/dltUIweNy9qmXt08EgydDZ6+dT+9Qh9AeGenhROFI0fPjMaCHx6uIlh9/xBSJuB3l0A/6JAAAAAElFTkSuQmCC); border-image-slice: 9; border-image-width: 9px; border-image-repeat: stretch; position: relative; box-sizing: border-box; display: inline-block; height: auto; margin: 10px auto; max-width: 100%; padding: 8px; -webkit-border-image: url(data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAMAAAC6V+0/AAAAOVBMVEUAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///+8yHYvAAAAEnRSTlMAAgEDBAUJBwYzCw0UChARDghnBteEAAAAhElEQVR4XnWRSxJDIQgEEx1Axd/L/Q8bKCuuyOzsohHxdZLS25LSOV2ULQdflgEiIDu9KqiIFILXXpeEx2ChXwdnKNxUGxc4dZbNfXjPufkp5H0Nwtymq/dltUIweNy9qmXt08EgydDZ6+dT+9Qh9AeGenhROFI0fPjMaCHx6uIlh9/xBSJuB3l0A/6JAAAAAElFTkSuQmCC) 9 fill / 9px stretch;" src="http://latex.codecogs.com/gif.latex?Lorentzt'=\\frac{BN}{c&plus;v}=\\frac{BC}{\\sqrt{c^{2}-v^{2}}}" />

Potrebno je analizirati algebarske, geometrijske i fizič?ke istine dublje i temeljitije nego je to uradio A. Einstein. Naprimjer:    <img border="0" src="http://latex.codecogs.com/gif.latex?Lokalno%5C:&space;vrijeme%5C:&space;=%5C:&space;t-%5Cfrac%7Bv%7D%7Bc%5E%7B2%7D%7Dx=t-%5Cfrac%7Bt%7D%7Bn%7D=%5Cfrac%7Bct%7D%7Bc%7D-%5Cfrac%7Bvt%7D%7Bc%7D" /> .

Ni jedna od navedenih velič?ina nije suprotna klasič?noj fizici i Euklidovoj geometriji. Ono ?to je suprotno klasič?noj fizici i Euklidovoj geometriji je Einstein-ovo tumač?enje značenja navedenih algebarskih, geometrijskih i fizič?kih istina. To nas upućuje na Einstein-ovu pogre?nu logiku, Einstein-ovo povr?no i pogre?no razmi?ljanje i zaključ?ivanje, Einstein-ovo poistovjećivanje istina i mogućih istina.
Fizič?ari i matematič?ari nisu dovoljno duboko i temeljito analizirali povezanost i međuzavisnost Lorentz-ovih i Einstein-ovih velič?ina u STR: Jedna od va?nijih istina koju niu uočili "pametni" fizičari i matematičari S. Hawking, ili E.witten naprimjer je i sljedeća algebarska istina i transformacija <img border="0" style="border: 9px none; border-image-source: url(data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAMAAAC6V+0/AAAAOVBMVEUAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///+8yHYvAAAAEnRSTlMAAgEDBAUJBwYzCw0UChARDghnBteEAAAAhElEQVR4XnWRSxJDIQgEEx1Axd/L/Q8bKCuuyOzsohHxdZLS25LSOV2ULQdflgEiIDu9KqiIFILXXpeEx2ChXwdnKNxUGxc4dZbNfXjPufkp5H0Nwtymq/dltUIweNy9qmXt08EgydDZ6+dT+9Qh9AeGenhROFI0fPjMaCHx6uIlh9/xBSJuB3l0A/6JAAAAAElFTkSuQmCC); border-image-slice: 9; border-image-width: 9px; border-image-repeat: stretch; position: relative; box-sizing: border-box; display: inline-block; height: auto; margin: 10px auto; max-width: 100%; padding: 8px; -webkit-border-image: url(data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAMAAAC6V+0/AAAAOVBMVEUAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///+8yHYvAAAAEnRSTlMAAgEDBAUJBwYzCw0UChARDghnBteEAAAAhElEQVR4XnWRSxJDIQgEEx1Axd/L/Q8bKCuuyOzsohHxdZLS25LSOV2ULQdflgEiIDu9KqiIFILXXpeEx2ChXwdnKNxUGxc4dZbNfXjPufkp5H0Nwtymq/dltUIweNy9qmXt08EgydDZ6+dT+9Qh9AeGenhROFI0fPjMaCHx6uIlh9/xBSJuB3l0A/6JAAAAAElFTkSuQmCC) 9 fill / 9px stretch;" src="http://2.bp.blogspot.com/-YCZdf4X0EGM/Ua9yTKn025I/AAAAAAAAGnY/TMCdR1gJCyo/s1600/okomita+relativna+brzina.gif" /> , <img border="0" style="border: 9px none; border-image-source: url(data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAMAAAC6V+0/AAAAOVBMVEUAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///+8yHYvAAAAEnRSTlMAAgEDBAUJBwYzCw0UChARDghnBteEAAAAhElEQVR4XnWRSxJDIQgEEx1Axd/L/Q8bKCuuyOzsohHxdZLS25LSOV2ULQdflgEiIDu9KqiIFILXXpeEx2ChXwdnKNxUGxc4dZbNfXjPufkp5H0Nwtymq/dltUIweNy9qmXt08EgydDZ6+dT+9Qh9AeGenhROFI0fPjMaCHx6uIlh9/xBSJuB3l0A/6JAAAAAElFTkSuQmCC); border-image-slice: 9; border-image-width: 9px; border-image-repeat: stretch; position: relative; box-sizing: border-box; display: inline-block; height: auto; margin: 10px auto; max-width: 100%; padding: 8px; -webkit-border-image: url(data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAMAAAC6V+0/AAAAOVBMVEUAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///+8yHYvAAAAEnRSTlMAAgEDBAUJBwYzCw0UChARDghnBteEAAAAhElEQVR4XnWRSxJDIQgEEx1Axd/L/Q8bKCuuyOzsohHxdZLS25LSOV2ULQdflgEiIDu9KqiIFILXXpeEx2ChXwdnKNxUGxc4dZbNfXjPufkp5H0Nwtymq/dltUIweNy9qmXt08EgydDZ6+dT+9Qh9AeGenhROFI0fPjMaCHx6uIlh9/xBSJuB3l0A/6JAAAAAElFTkSuQmCC) 9 fill / 9px stretch;" src="http://1.bp.blogspot.com/-Ej30goLnEzw/Ua9yoSNDe1I/AAAAAAAAGng/tfp0RYawS_o/s1600/ct+i+okomito+2ct'.gif" /> ,u ovoj prethodnoj jednakosti radi se o Einsteinovom, a ne Lorentzovoj veličini t'.
Nema u navedenom algebarskom iskazu, niti u geometrijskom prikazu velič?ina u tim formulama, ni jednog detalja koji nije u skladu sa Euklidovom geometrijom i klasič?nom fizikom (Einstein pogre?no tumač?i značenja tih iskaza).
<b style="font-family: arial, sans-serif; line-height: 1.25; font-size: 10pt;">

</b>
<b style="font-family: arial, sans-serif; line-height: 1.25; font-size: 10pt;">
(f-5) 
</b>
<img border="0" style="color: rgb(0, 0, 0); font-family: Verdana, Helvetica, Arial, sans-serif; font-size: 13px; line-height: 16px; background-color: rgb(243, 243, 243);" src="https://sites.google.com/site/specijalnateorijarelativnosti/_/rsrc/1263655609186/relativisticka-algebra---uvod/lorencove-transformacije/Izvo%C4%91enje%20Lorenc%20x%20prim%20je%20x%20tg%20polovine%20ugla.gif" /> , (f-6) <img border="0" style="color: rgb(0, 0, 0); font-family: Verdana, Helvetica, Arial, sans-serif; font-size: 13px; line-height: 16px; background-color: rgb(243, 243, 243);" src="https://sites.google.com/site/specijalnateorijarelativnosti/_/rsrc/1263655745093/relativisticka-algebra---uvod/lorencove-transformacije/Izvo%C4%91enje%20Lorenc%20x%20i%20x%20prim%20je%20ctg%20polovine....gif" /> .

(f-7) <img border="0" style="color: rgb(0, 0, 0); font-family: Verdana, Helvetica, Arial, sans-serif; font-size: 13px; line-height: 16px; background-color: rgb(243, 243, 243);" src="https://sites.google.com/site/specijalnateorijarelativnosti/_/rsrc/1263656909887/relativisticka-algebra---uvod/lorencove-transformacije/Odnos%20x%20prim%20i%20x%20-%20frekvencija.gif" /> ,                                  (f-8)  <img border="0" style="color: rgb(0, 0, 0); font-family: Verdana, Helvetica, Arial, sans-serif; font-size: 13px; line-height: 16px; background-color: rgb(243, 243, 243);" src="https://sites.google.com/site/specijalnateorijarelativnosti/_/rsrc/1263656958203/relativisticka-algebra---uvod/lorencove-transformacije/Odnos%20x%20i%20x%20prim-frekvencija.gif" />.
Lorentz-ove velč?ine slijede sljedeću algebarsku i geometrijsku istinu: (f-9) <img border="0" style="border-width: 1px; border-style: solid; border-color: rgb(204, 204, 204) rgb(153, 153, 153) rgb(153, 153, 153) rgb(204, 204, 204); padding: 7px; background-color: rgb(255, 255, 255);" src="https://lh4.googleusercontent.com/-MrGckhoJYSA/UR-rLZmv_VI/AAAAAAAAGBc/XIPWE_1tDr8/s1600/Lorencovo%20x%27%2Bvt%27-%20boja.jpg" /> .
(f-10)
<img src="https://lh6.googleusercontent.com/-btFDWpARYzU/UUGh1Dj4MEI/AAAAAAAAGP8/5dtIblP8qx0/s511/2l_0%2520puta%2520x%2527%2520-%2520Lorenc.gif" />

 Einstein-ove velč?ine slijede tu istu algebarsku i geometrijsku istinu: (f-11) <img border="0" style="border-width: 1px; border-style: solid; border-color: rgb(204, 204, 204) rgb(153, 153, 153) rgb(153, 153, 153) rgb(204, 204, 204); padding: 7px; background-color: rgb(255, 255, 255);" src="http://latex.codecogs.com/gif.latex?%5Cfrac%7B2l_0%7D%7B%5Csqrt%7B1-%5Cfrac%7Bv%5E%7B2%7D%7D%7Bc%5E%7B2%7D%7D%7D%7D=2ct%27=ct%5Ccdot&space;%5Csqrt%7B1-%5Cfrac%7Bv%5E%7B2%7D%7D%7Bc%5E%7B2%7D%7D%7D" /> .
(f-12)   <img border="0" style="border-width: 1px; border-style: solid; border-color: rgb(204, 204, 204) rgb(153, 153, 153) rgb(153, 153, 153) rgb(204, 204, 204); padding: 7px; background-color: rgb(255, 255, 255);" src="http://latex.codecogs.com/gif.latex?2ct_0=%7B%5Ccolor%7BMagenta%7D&space;2ct%27%7D%5Ccdot&space;%5Csqrt%7B1-%5Cfrac%7Bv%5E%7B2%7D%7D%7Bc%5E%7B2%7D%7D%7D=ct%5Ccdot&space;(1-%5Cfrac%7Bv%5E%7B2%7D%7D%7Bc%5E%7B2%7D%7D)" />.

<img style="border: medium none; color: rgb(0, 0, 0); font-family: arial, sans-serif; font-size: 13px; line-height: normal; text-align: center; width: 512px; height: 62px;" src="https://lh6.googleusercontent.com/-ZAhDMdMbcfA/UXzMY_1ijoI/AAAAAAAAGYY/nvpR7priAeQ/s512/Einstein-ovo%2520t%2527.gif" />
Ajn?tajnove i Lorencove formule geometrijski i algebarski su korektne za sve moguće skalarne vrijednosti  brzina  <img width="115" height="13" alt="" title="brzine v i c" style="line-height: 1.25; font-family: arial, sans-serif; font-size: 10pt;" src="http://fric8.files.wordpress.com/2011/08/brzine-v-i-c.gif?w=115&h=13" />, i ne samo onda kada je c brzina svjetlosti. 
Albert Einstein povr?no i pogre?no tumači sljedeće geometrijske, algebarske i fizičke istine <img border="0" src="http://latex.codecogs.com/gif.latex?2l_0=ct(1-%5Cfrac%7Bv%5E%7B2%7D%7D%7Bc%5E%7B2%7D%7D)" />
Lorencove veličine baziraju se na sljedećoj algebarskoj, geometrijskoj i fizičkoj istini 
<img border="0" src="http://latex.codecogs.com/gif.latex?%5Cfrac%7B2l_0%7D%7B%5Csqrt%7B1-%5Cfrac%7Bv%5E%7B2%7D%7D%7Bc%5E%7B2%7D%7D%7D%7D=%7B%5Ccolor%7BMagenta%7D&space;x%27&plus;vt%27%7D=ct%5Csqrt%7B1-%5Cfrac%7Bv%5E%7B2%7D%7D%7Bc%5E%7B2%7D%7D%7D" />,<img border="0" src="http://latex.codecogs.com/gif.latex?%7B%5Ccolor%7BMagenta%7D&space;x%27&plus;vt%27%7D=t%5Csqrt%7Bc%5E%7B2%7D-v%5E%7B2%7D%7D" /> (to je Lorencova istina).
Algebra (i aritmetika) su "srce" matematike, a Euklidova geometrija je "du?a" matematike. Bez srca i du?e nema ?ivota ni matematici! Algebarski jezik i jezik geometrije su precizniji i objektivniji u prikazu i opisu fizičke stvarnosti od Einsteinovog govornog jezika!
<img alt="" class="bbc_img" src="https://lh4.googleusercontent.com/-FX984ogvrHk/SorA-1hGiMI/AAAAAAAAAag/1MBACg34vts/s429/sl43loromjeri.gif.jpg" />Jednakost ukazuje na relativne odnose Lorentzovih veličina.