PLANCK MASS PLASMA ROTON SOLUTION OF THE COSMOLOGICAL CONSTANT PROBLEM

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1 PLANCK MASS PLASMA ROTON SOLUTION OF THE COSMOLOGICAL CONSTANT PROBLEM F. WINTERBERG UNIVERSITY OF NEVADA, RENO T: (775) , Fax: (775)

2 ABSTRACT The failue by the lage hadon collide to detect suesymmety and the Higgs aticle, suggests to elace suesymmety with anothe fundamental symmety, fo examle the symmety of the Planck mass lasma whee the vacuum is made u by an equal numbe of ositive and negative Planck mass aticles. The Planck mass lasma has fo each mass comonent a honon-oton sectum and it can exlain the obseved small ositive cosmological constant. The masses of the elementay aticles ae hee exlained by the gavitational field enegy of ole-diole aticles, which exlain Diac sinos as comosed fom gavitationally inteacting ositive and negative masses. 1. INTRODUCTION Fo the minimally suesymmetic standad model (MSSM) to agee with the exeimental facts equies a miaculous fine-tuning of the cosmological constant by about 56 odes of magnitude to comensate the zeo oint vacuum enegy. If the cosmological constant would be zeo, the easiest way to avoid this oblem would be to assume that the zeo oint enegy is exactly cancelled by some still unknown incile. Howeve this idea does not wok because the obsevational evidence obtained fom distant suenova exlosions shows that the cosmological constant is not zeo, but athe vey small and ositive [1, ]. But a ositive cosmological constant leads to an acceleated univesal exansion. Futhemoe, if the cosmological constant is set equal the enegy density of the dak enegy, this enegy density is about of the same ode of magnitude as the enegy density of the matte in the univese at ou moment in the histoy of the cosmic exansion. This aeas to be a highly accidental coincidence, because the matte density deceases duing the exansion unlike the cosmological constant which should emain constant. It is the Planck mass lasma hyothesis [3, 4, 5] which not only can give a lausible exlanation fo this coincidence, but this hyothesis also emits to obtain a value fo the cosmological acceleation aamete q RR / c, whee R is the wold adius and R its acceleation. The Planck mass lasma hyothesis elaces suesymmety by the assumtion that sace is densely occuied with an equal numbe of ositive and negative Planck masses. Following the Zittebewegung analysis by Schödinge of the Diac equation [6, 7], it was shown by Hönl and Paaeton [8, 9, 10, 11] that with the assumed existence of negative masses 1

3 one can deive the Diac equation. Accodingly, all femions would be comosed of bosons, and suesymmety would not be fundamental. With the mathematical aaatus by Bo [1], to obtain bound state solutions of ole-multiole mass configuations, I was able to deive fo the ole-diole mass configuation a maximum of fou excited states, making u a maximum of fou families in the standad model [4,5]. With an equal numbe of ositive and negative Planck masses the cosmological constant is zeo as in suesymmetic theoies and the univese euclidean flat. In its goundstate the Planck mass lasma is a two comonent ositive-negative mass suefluid ossessing a hononoton enegy sectum fo each comonent. Assuming that the shae of the honon-oton sectum measued in suefluid helium is univesal, this would mean that in the Planck mass lasma this sectum has the same shae, with the Planck enegy elacing the Debye enegy in suefluid helium. Rotons can be viewed as small votex ings with the ing adius of the same ode as the votex coe adius. A fluid with cavitons has a negative essue, and the same is tue fo a fluid of votex ings [13, 14, 15]. It is the centifugal foce which ceates a vacuum in the votex coe, making a votex ing to behave like a caviton with a negative essue, which in accodance to Einstein s gavitational field equations causes an outwad acceleation.. PLANCK MASS PLASMA HYPOTHESIS With the Planck length G / c 3 and the Planck foce F c 4 / G, the Planck mass lasma hyothesis makes the following assumtions [3, 4, 5]: 1. The ultimate building blocks of matte ae Planck mass aticles which obey the laws of classical Newtonian mechanics, but thee ae also negative Planck mass aticles.. A ositive Planck mass aticle exets a shot ange eulsive and a negative Planck mass aticle a likewise attactive foce, with the magnitude and ange of the foce equal to the Planck foce F and the Planck length. 3. Sace is filled with an equal numbe of ositive and negative Planck mass aticles, with each Planck length volume in the aveage occuied by one Planck mass aticle.

4 This hyothesis makes the following edictions: 1. Nonelativistic quantum mechanics as an aoximation with deatues fom the aoximation suessed by the Planck length.. Loentz invaiance as a dynamic symmety fo enegies small comaed to the Planck enegy. 3. A sectum of quasiaticles vey much like the aticles of the standad model, and beyond the standad models honons and otons. It futhe leads to a solution fo the oblem of quantum gavity, with a finitistic (Non- Achimedean) fomulation. It was eviously shown that the honon-oton sectum can exlain the honons as the dak enegy and the otons as the nonbayonic cold dak matte [14]. And it will hee be shown that it can even exlain the magnitude of the cosmological acceleation. 3. SPINOR ROTONS Fom the exeimentally established honon-oton sectum in suefluid helium one obtains fo the oton enegy a value about 0.16 times the Debye enegy. Relacing the Debye enegy with the Planck enegy m c, whee m is the Planck mass, the mass of the otons in the Planck mass lasma should be m 0.16m. In the two-comonent suefluid Planck mass lasma, thee ae ositive and negative mass otons m 0.16m. We now conside the gavitational inteaction of a ositive mass oton with a negative mass oton, seaated by the distance. Fo this (ositive-negative) mass diole the enegy of the gavitational field is ositive and with m m given by Gmm E Gm (1) Accoding to the mass-enegy equivalence, this field has the mass 3

5 E Gm m c c () A second equation is given by the uncetainty elation m c (3) Eliminating fom () and (3) one obtains 3 Gm m (4) c o because of Gm =ћc, m m m m 3 (5) With m 0.16m, one finds that m/ m , o mc GeV. If the ositive gavitational field mass is added to the ositive mass of the mass diole, one obtains a olediole mass configuation fom which one can deive the Diac equation. It is the small esidual mass m of the gavitational field which is the mass of a Diac aticle. While without the mass of the gavitational field a mass diole would lead to selfacceleation, a ole-diole configuation leads to a helical motion, along the helix eaching the velocity of light. It is fom this configuation that one can deive the Diac equation. We theefoe call this configuation a sino oton, and suggest that the non-bayonic cold dak matte is made u of it. The much lighte elementay aticles of the standad model ae in a likewise way made u fom much smalle ole-diole configuations of lowe enegy quantized votex configuations of the Planck mass lasma [3, 4, 5]. 4

6 4. COSMIC ACCELERATION The cosmic exansion can be comaed with the exansion of a hot gas in a Laval nozzle. If at the beginning of the exansion the temeatue of the gas is T, and its secific heat at constant essue c, the exansion velocity is given by [16] v ct (6) With the secific heat atio γ=c /c v we can wite fo (6) v ct v (7) whee f f (8) and whee f is the numbe of degees of feedom fo the molecules of the exanding gas. If the molecules of the exanding gas have only thee tanslational degees of feedom, one has with f=3, γ=5/3. But if they have in addition thee otational degees of feedom, one has with f=6, γ=4/3. Theefoe, if duing the exansion the gas gives off some of enegy stoed in the thee otational degees fo the benefit of the tanslational degee of feedom, the exansion velocity is inceased. But though the excitation of intenal degees of feedom in the molecules, by the excitation of electonic enegy levels, f can become much lage. Fo f=, one would have γ=1, and the exansion velocity would be inceased even moe. Fo a gas of sino otons, whee many Planck mass aticles take at in the double votex configuation the numbe of the intenal degees of feedom is likely to be vey lage, and we take f=, wheeby γ=1. Afte all the intenally stoed enegy in the sino otons is consumed, the acceleated exansion comes to an end. It is this temoay acceleation which can mimic a small ositive cosmological constant. The convesion of otational in tanslational enegy is uled by the second law of themodynamics and can go as in a Canot ocess at constant temeatue. Hee is it how it woks: We diffeentiate (7) with egad to time keeing T constant: 5

7 va cvt v (9) whee a the acceleation of the exanding flow of otons, hence 1 a v (10) in (10) we may ut / (11) whee Δγ is the diffeence fo if f=3 and f=, and R/ cthe age of the univese. Fo we take the aveage duing the time τ: ( 1) / (1) With =5/3 and setting v=c we find that c 1 1 c a R 1 4 R (13) Fo the non-dimensional acceleation aamete q=1/4=0.5. q RR / c, we find by setting a R, that We comae this value with the measued values of q given by Caldwell and Kamionkowski [17]. Fo the edshift z=, in the distant ast, these authos obtain q=0.4, and fo the esent time q=-0.5. Fo z=1, somewhee in the middle, they find that q=0.5, as in ou simle model. 5. CONCLUSION Accoding to Weinbeg [18], the dak enegy - small ositive cosmological constant oblem is the most imotant unsolved oblem facing elementay aticles hysics. Sting theoies can accommodate a small cosmological constant only with geat difficulty [19]. With a stinglandscae of about ossible univeses, it means that ou univese would have to be one of 6

8 them whee all the aametes of minimally suesymmetic standad model have the ight value to make ou existence ossible. This seems vey imlausible. The Planck mass lasma model, whee suesymmety is elaced by a lasma of ositive and negative masses, and whee hysical eality is in the thee sace and the one time dimension as fo all hysics laboatoies, has no difficulty to exlain the dak enegy and the small ositive cosmological constant. The density of the honos and otons of this lasma decease duing the cosmic exansion in the same way as the density of odinay matte. Howeve, fo the total amount of all the enegies to add u to zeo, equies that in the fomation of the ositive mass Diac sino otons, and to a lesse degee the Diac sinos of odinay matte, negative enegy must be caied away. This leads to the question, whee did this negative enegy go? One ossibility is that it is located in the lage voids seaating the cluste of galaxies in the metagalaxy. REFERENCES 1. A.G. Riess et al. Aston. J. 116, 1009 (1968).. S. Pelmutte, Astoh. J. 517, 565 (1999). 3. F. Wintebeg, Z. Natufosch.-Physical Sciences 43a, 1 (1988). 4. F. Wintebeg, The Planck Aethe Hyothesis, C.F. Gauss Pess, Reno, Nevada, nd Edition F. Wintebeg, Z. Natufosch.-Physical Sciences 58a, 31 (003). 6. E. Schödinge, Beline Beichte No. 416 (1930). 7. E. Schödinge, Beline Beichte No. 418 (1931). 8. H. Hönl Ann. D. Physik 33, 565 (1938). 9. H. Hönl and A. Paaetou, Zeitsch. Physik 11, 51 (1939). 10. A. Paaetou and H. Hönl Zeitsch. Physik 114, 478 (1939). 11. H. Hönl and A. Paaetou, Zeitsch. Physik 116, 153 (1940). 1. F. Bo, Z. Physik 15, 615 (1949). 13. F. Wintebeg, Z. Natufosch.-Physical Sciences 47a, 117 (199). 14. F. Wintebeg, Z. Natufosch.-Physical Sciences 57a, 0 (00). 15. G.E. Volovik, Physics Reots 351, 195 (001). 16. L.D. Landau and E.M. Lifshitz, Fluid Mechanics, Pegamon Pess, London, 1959,

9 17. R.R. Caldwell and M. Kaminonkowski Annu. Rev. Nucl. Pat. Sci : S. Weinbeg, Lake Views, The Belkna Pess of Havad Univesity Pess, Cambidge, Massachusetts, London, England, 009,. 46ff. 19. R. Kallosh, A. Linde, S. Kachu, S. Tivedi Phys. Rev. D 68 (003),

On Quantum Gravity and the Interpretation of Quantum Mechanics. F. Winterberg University of Nevada, Reno

On Quantum Gravity and the Interpretation of Quantum Mechanics. F. Winterberg University of Nevada, Reno On Quantum Gavity and the Inteetation of Quantum Mechanics F. Wintebeg Univesity of Nevada, Reno 1 Abstact It is shown that classical geneal elativity can be obtained as the limit of fully quantum mechanical