Cosmic time dilation verification test

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Current practice calls for a time dilation correction factor to be added to SNe 1a data to create a rest-frame. A test has now been developed that proves or disproves time dilation by removing this added correction factor from published data. If
  Cosmic time dilation verification testRichard K. Love * a and Sean R. Love †b   a 2000 Clara Mae Ct. Springfield IL 2!"" b "#" $ast $l Camino Real% &"2' Mo(ntain )ie* C+ #'0'0,-ated (l/ "% 20"1 PACS numbers: 0.0. 3p #.0.Sf% #4.40.5 .3d% #.4. 36% #..7e%   #4.40.bp , #4.40.85% #4.409: $lectronic address; richlove< $lectronic address; seanlove< +=S>R+C>C(rrent practice calls for the correction factor ","1  z  +  to be added to S?e "a data to create a rest8frame. + test has no* been developed that proves or disproves time dilation  b/ removing this added correction factor from p(blished data. If cosmic time dilation does e6ist% then removing the added correction factor *ill disturb  e6pected ph/sical correlations beca(se the correction *as needed@ ho*ever% if cosmic time dilation doesnAt e6ist% then removing the added correction factor from the data *ill restore  correlations  beca(se the correction *as (nneeded. >he form(la%"","1  z  − + % *hich removes the addedtime dilation correction factor from p(blished data *as developed and s(ccessf(ll/ testedon data from =londin et al ,20041% >he first act(al application of the form(la *as to remove the time dilation correction factor added to the >/pe  Ia  s(pernova data (sed b/ Riess et al ,"##41 and 7erlm(tter et al ,"###1 in the landmar5 st(d/ establishing dar5 energ/. :hen the added time dilation factor *as removed from the S?e "a data% the acceleration% *hich had been attrib(ted to dar5 energ/% *as completel/ eliminated and the e6pected good correlation bet*een redshift distance and effective M= from the s(pernovae *as restored. >his proves that the addition of the time dilation correction factor dist(rbed an e6pected correlation beca(se the correction *as not needed. +ltho(ghthis is strong evidence against the e6istence of cosmic time dilation% more st(dies are needed to confirm this res(lt. I.-$)$LB7M$?> B >IM$ -IL+>IB? R$MB)+L BRMDL+ Redshift  z   relates the frequency of light emitted from a distant source to that detected by a local observer. An expected consequence of redshift is that the observed rate of any time variation in the intensity of emitted radiation will be proportional to a factor of ","1  z  + . [! >he factor ","1  z  +  is (sed to compensate for the e6pected time dilation of the light8c(rve shape d(ring the time of meas(rement% *hich is 5no*n as creating the Erest frameFfor the readings. G2H"  If there is cosmic time dilation% then removing this added correction factor from  p(blished data sho(ld dist(rb e6pected ph/sical correlations beca(se the rest8frame *as needed@ ho*ever% if there is no cosmic time dilation% then the observer8frame *o(ld be the correct data and removing the time dilation correction factor *o(ld restore ph/sical correlations *ith other data.>o emplo/ this test on p(blished data% it is first necessar/ to develop a form(la that *ill remove the factor ","1  z  + that *as added to the data to compensate for the effect of time dilation. >he follo*ing form(la is demonstrated in +ppendi6 " to remove the added time dilation correction factor from S?e "a aging data."","1  z   − +  :hether the form(la is added or s(btracted from the data depends on the form that time dilation ta5es in the partic(lar st(d/; +s *ill be seen in +ppendi6 I% *hen the data is the form of an aging rate of S?e"a% the removal form(la m(st be added   to the data to cancel the time dilation factor. >herefore *hen the aging rate e(als the time dilation factor% as it does in +ppendi6 I *ith data from =londin et al ,20041% adding the form(la to the aging rate gives a res(lt of one. >his is beca(se one is the aging res(lt e6pected *ith no time dilation. GH9o*ever% *here the time dilation correction factor is added to the effective pea5 magnit(des eff  B m  of S?e "a Gs(ch as it is *ith the data (sed b/ Riess et al ,"##41 and 7erlm(tter et al ,"###1H then the removal form(la m(st be  subtracted   to cancel the time dilation factor added to create a rest8frame. G'H% GHII. +C>D+L DS$ B >IM$ -IL+>IB? R$MB)+L BRMDL+In order for the removal form(la to test for the e6istence of time dilation% the data m(st meet t*o re(irements; ,"1 the factor ","1  z  +  m(st have been added to the data to createa rest frame and ,21 a correlation m(st e6ist *ith other data. >he anomalo(s acceleration of the high redshift s(pernova fits both these re(irements and *as the top candidate for the follo*ing reasons;".+ dist(rbance in the e6pected good correlation bet*een S?e "a l(minosit/ distance and redshift distance has been observed. In a st(d/ *here the standardiJed pea5 magnit(des of s(pernovae ,S?e "a1 *ere plotted against redshift velocit/% Riess et al ,"##41 reported that altho(gh the observed l(minosit/distance of the lo*8redshift s(pernovae met e6pected val(es% the high8redshift s(pernovae l(minosit/ distance *as greater than e6pected val(es. >his 2  observation is c(rrentl/ attrib(ted to an increase in ph/sical e6pansion ca(sed b/ an (n5no*n and invisible ,dar51 energ/ so(rce. GH% G!H2.:hen the time dilation factor of ","1  z  +  *as (sed b/ Reiss et al to create a rest frame% it added a factor of a s(pernovaAs o*n redshift  z  to its l(minosit/. >his means that the l(minosit/ of a s(pernova *ith a small redshift ,0.0"'1 is not visibl/ affected b/ the addition of redshift% b(t the l(minosit/ of one *ith a large redshift ,0.#!01is significantl/ increased. >he difference ca(sed b/ the addition of the correction factor therefore increases non8arithmeticall/ *ith redshift and appears as acceleration. .In the /ears since dar5 energ/ *as first proposed in "##4% the mechanism for its e6istence has not been proven. + st(d/ b/ =asila5os and Sola ,20"'1 demonstrated that the e(ation of the state of dar5 energ/ can sim(late a (intessence field% or even a phantom field% *itho(t being one in realit/% casting do(bt on an/ s(pporting data from :M+7% 7lanc5 or other instr(ments.   >herefore% beca(se of the limiting nat(re of dar5 energ/% this test co(ld provide the best e6perimental evidence on the e6istence of dar5 energ/ that is  possible  to ac(ire. G4H>he follo*ing t*o log graphs provide a clear pict(re of the effect of the (se of the time dilation factor and the effect of its removal. >he sample set incl(des # lo* and high redshift S?e "a samples that *ere modified to be Erest frameF b/ Riess et al ,"##41 and 7erlm(tter et al ,"##41. $ach sample incl(des an added time dilation factor of ","1  z  +  inthe form of corr  ∆ to compensate for ph/sical e6pansion. G#H G"0H ig(re " sho*s the 9(bble log diagram of the S?e "a  before  s(btracting "","1  z  − +   fromthe l(minosit/ of each S?. >he dotted line is the best fit of the high redshift samples alone. ?ote that the slope of the high J S?e "a ,2."1 is significantl/ greater than the slope of the lo* J S?e "a,2."1. >his disr(ption in the correlation of redshift and effective M= is c(rrentl/ attrib(ted to dar5 energ/.  I. 2 sho*s the 9(bble log diagram  after   s(btracting the form(la"","1  z  − +  fr  om the each sample to remove the time dilation factor. ?ote that the acceleration of the high redshift s(pernovae% *hich *as the evidence (sed to (stif/ the dar5 energ/ theor/% has  been completel/ eliminated% restoring the e6pected good correlation bet*een redshift andeffective mb .In s(mmar/% the removal of the added time dilation correcting factor from the e6isting l(minosit/ data restored the correlation *ith redshift data and th(s proved that the data didnAt re(ire correction for e6pansion increasing *ith time. 'I. "; 9(bble log diagram of # S?e "a *ith the acceleration in high8J S?e "a. >he effective mb  incl(des   the added correction factor ,"3  z  1 in the form of corr  ∆ I. 2; 9(bble log diagram of S?e "a *ith the added time dilation factor no* removed from each sample% sho*ing no evidence of acceleration c(rrentl/ attrib(ted to dar5 energ/.  >able " compares statistics of the uncorrected   data before the s(btraction of the added time dilation factor *ith the statistics of the corrected   data after the s(btraction. I.-escriptionS? b/t/pe SlopeIntercept":ith time dilation9igh J2."2'.#factorLo* J2.22'.+ll J2.'"2'.42:o time dilation9igh J2."2'.'factorLo* J2.242'.'+ll J2.2#2'.' >able 2 sho*s the effect of the s(btracting the added factor from the data of the closest ,"##2al1 s(pernova and most distant s(pernova ,"##!c51 in the st(d/. Riess et al ,"##41 and 7erlm(tter et al ,"##"1 G""H% G"2H. =eca(se this error is non8linear% it has been interpreted as (alitative% rather than (antitative. >he nonlinearit/ ma5es it appear that the acceleration begins at a certain redshift% *hen it is act(all/ contin(o(s and *hat EbeginsA is its visibilit/. S?  mb  z   [ ] "","1  z  − +  mb 8  [ ] "","1  z  − + "###B".20.0"'0.02#".2#"##!c52'.!40.#!00.'#22'.2# >able  contains the # data points (sed in I. " and I.2. G24H Col. ";  ( ) Source  Literat(re referenceCol 2;  ( ) Study  ?ame of s(pernovae st(d/ providing dataCol. ;  ( )  Name  I+D name assigned to s(pernova ,from so(rce1Col ';,  z  1 Redshift velocit/ of s(pernova ,from so(rce1Col. ;, mb 1 Stretch l(minosit/8corrected =8band pea5 magnit(de ,from so(rce1Col. ; "","1  z  − +  >ime8dilation factor ,calc(lated1 >able "; +fter the time dilation factor *as removed% the slopes and intercepts of both the high and lo* redshift S?e "a are not significantl/ different% sho*ing that the acceleration *as removed and eliminating need for the dar5 energ/ e6planation.>able 2; >able sho*s s(btraction of [ ] "","1  z  − +  factor from mb for highest and lo*est s(pernovae.
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