Symmetry breaking from Lorentz transformation

Transcription

1 Abstrt Symmetry brekig from Loretz trsformtio Bi-Gg M Emil: bgm@sdt.ed. Symmetry brekig is disssed i this pper hih omes from the Loretz trsformtio of speil reltiity d hges or ie tht to reltiely moig bodies lys he the reltie speed eql i mgitde d opposite i diretio. A ppel s mde for the test of Loretz trsformtio i mltimedi eiromet hih hs the fdmetl sigifie tht it my reel the origi of symmetry brekig i my physil pheome. I 195, Albert Eistei pblished his speil reltiity tht hged or ie bot spe d time here Loretz trsformtio is the fodtio of its formlism. I Loretz trsformtio, ierti frme idepedet eloity sle s itroded hih sered by the light speed i m 1. Hoeer, bodies re ot lys moig i m. If to bodies re reltiely moig i to differet medi, sh s fish simmig i lke d bird flyig i the sky, ht ill hppe? As sho i Fig. 1, sppose ter is restig reltie to ir, d tke the ter/ir system s referee frme. There is bll moig i ter d other bll moig i ir. No e osider the reltie speeds betee bll 1 d bll.

2 Figre 1 To reltiely moig blls i to differet medi. The pper hlf is ir d the loer hlf is ter; ir d ter re restig reltie to eh other d tke s referee frme; bll 1 is moig tords right ith eloity reltie to ter; bll is moig tords left ith eloity reltie to ir. Right is ssiged s the positie diretio. Firstly, e osider the eloity of bll reltie to bll 1. To mesre the eloity of bll, bll 1 mst reeie the light from bll. Sie bll 1 is moig t eloity reltie to ter, eqiletly, tht is to sy, ter is moig t eloity reltie to bll 1. Therefore, the eloity sle i Loretz trsformtio shold be the speed of the light from bll mesred by bll 1. Aordig to Fresel s drg forml, the speed of the light from bll mesred by bll 1 is 1 = + 1 (1) here is the light speed i m d is the refrtie idex of ter. Cosiderig the refrtiity of medim, the eloity mesred i ter is ot eql to tht mesred i ir, there is = = () here is the eloity of bll if mesred i ter, is the light speed i ir, is the light speed i ter, is the refrtie idex of ir. Ths, =. (3) Aordig to Loretz eloity dditio forml, e get the eloity of bll reltie to bll 1 is 1 + = 1+. (4) Sbstitte (1) d (3) ito (4), e get

3 1 + + = = (5) Seodly, e osider the eloity of bll 1 reltie to bll. To mesre the eloity of bll 1, bll mst reeie the light from bll 1. Sie bll is moig t eloity reltie to ir, eqiletly, tht is to sy, ir is moig t eloity reltie to bll. Therefore, the eloity sle i Loretz trsformtio shold be the speed of the light from bll 1 mesred by bll. Aordig to Fresel s drg forml, the speed of the light from bll 1 mesred by bll is 1 1 = +. (6) Cosiderig the refrtiity of medim, the eloity mesred i ir is ot eql to tht mesred i ter, there is = = (7) here is the eloity of bll 1 if mesred i ir. Ths, =. (8) Aordig to Loretz eloity dditio forml, e get the eloity of bll 1 reltie to bll is 1 + = 1+. (9) Sbstitte (6) d (8) ito (9), e get

4 (1) Bese, therefore 1 1, i.e., to reltiely moig bodies i to differet medi brek the symmetry tht to reltiely moig bodies lys he the reltie speed eql i mgitde d opposite i diretio. If the to blls he the sme rest mss m, the ordig to Eistei s mss-eergy reltio, there re E 1 m m (11) d E 1 m m (1) The former is the eergy of bll from the iepoit of bll 1, d the ltter is the eergy of bll 1 from the iepoit of bll. Bese, there is eergy differee betee them tht E = E E. (13) 1 1

5 Sppose m = 1 kg, = m/s, = 1.3, = 1.333, = 5 m/s, = 8 m/s, the E = E E = J (14) 1 1 No the qestio is: Is it possible tht experimet is desiged to test this differee of eergy? This ill be e test of Loretz trsformtio i mltimedi eiromet. Whteer the reslt is, it ill led to e omprehesio of Loretz trsformtio. Someoe my rge tht the eloity sle i Loretz eloity-dditio forml (mely, forml (4) d (9)) shold lso be the light speed i m. Ee so, the symmetry brekig still exists. If e reple i (4) ith, e get = =. (15) Similrly, if e reple i (9) ith, e get (16) The, ordig to Eistei s mss-eergy reltio, e get E 1 m m (17) d

6 E 1 m m (18) Bese, there is eergy differee betee them tht E = E E. (19) 1 1 Sppose m = 1 kg, = m/s, = 1.3, = 1.333, = 5 m/s, = 8 m/s, the E = E E = J. () 1 1 Althogh forml (11) d (1) re differet from (17) d (18), respetiely, the resltt E ( = (11)-(1) or (17)-(18) ) oly hs ery slight differee: J. This reslt my me tht symmetry brekig mily origites from the refrtiity betee medi rther th Loretz trsformtio. Bt refl thikig ill reh tht the refrtiity betee medi d the differet eloity sles i Loretz trsformtio mot to the sme thig i tht the refrtiity betee medi jst origites from the differee of light speeds i them. The symmetry brekig from Loretz trsformtio hs fdmetl sigifie tht it my be the origi of symmetry loss e re lookig for i or fdmetl physis. Sie mtter osists of differet kids of prtiles gge bosos, fermios (leptos d qrks), gritos, or ee Higgs prtiles d these prtiles eer rest d their reltie motios keep to Loretz trsformtio (s ht e ko by fr), the heterogeeity of mtter or m (sh s m polriztio or so) ill brek symmetry spoteosly de to the rie of eloity sle i

7 Loretz trsformtio, hih mes tht symmetry brekig my origite from prtiles eiromets d their mtl reltios, i.e., symmetry brekig my be systemti emergee. Reet orks by Gpt he reeled tht grity my be the Seod-Order Reltiisti-Mifesttio of Eletrostti-Fore 3. Bsed o the reltiisti eloity dditio forml, Gpt deded et ttrtie fore betee to bodies omposed of toms, hih spports the possibility tht symmetry brekig my or spoteosly s systemti emergee de to Loretz trsformtio. Referees: 1. Eistei, A. A. Phys. 17, (195).. Wilzek, F. Ntre, 433, (5) Akoledgemet My thks to Prof. Gpt for helpfl disssios. This ork s prtilly spported by Ntiol Key Projet for Bsi Reserh (3CB1144) d Ntiol Ntrl Siee Fodtio of Chi (Grt No. 3135). Affilitio: 1 Shdog Proiil Reserh Ceter for Bioiformti Egieerig d Tehiqe, Ceter for Aded Stdy, Shdog Uiersity of Tehology, Zibo 5549, P. R. Chi Telephoe: ; Fx: ; Deprtmets of Physis, Tiji Uiersity, Tiji, 37, Chi