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IC/80/100 (Limited Distribution) International Atomic Energy Agency 1) 2) IC/80/100 Dirac's cosmology ia baaed on his large number hypothesis ' (L.N.K.) IT.^JRNAL REPORT which ia the assumption that if two large numbers are comparable there is some (Limited distribution) deep underlying physical reason and not a mere accident. It turns-out that the International Atomic Energy Agency ratio of the estimated age of the Universe, t , to e /me (m,e being the mass •'•• and and charge of the electron, and c the speed of light) Is 7 x ic^ . Also, the fJ '• 1% ^ United Nations educational Scientific and Cultural Organization ratio of the electric to gravitational force between an electron and a proton, e /G Ma (M being the proton mass and G the gravitational "constant") is 2 * 10^. INTERN AT! C'JAl CENTRE FOR THEORETICAL PHYSICS Further, the estimated number of nucleons in the Universe, N, is of order 10 . On the basis of his L.B.H. Dirac takes G to vary inversely with time and K to vary as the square of tiae. For total conservation of energy he invokes a "negative energy *ea" vhich is not observable. (Incidentally, this problem of matter creation does not arise in Diraq's revised theory .) DIrac then DO NEUTRON STARS DISPROVE MULTIPLICATIVE CREATION constructs tvo models depending on whether matter is created uniformly through all space (additive creation) or more where more matter is present (multiplicative III DIRAC'S LARGE NUMBER HYPOTHESIS? * creation). In the one case astronomical distances scale up while in the other 1) 2) case they scale dovn, with time " '. This fact provides a test of the theory Asghar Qadir " In principle by observing 3olar system distances over sufficient periods of time. International Centre for Theoretical Physics, Trieste, Italy, Unfortunately, the test Is not very "clean" as there could be many other factors and responsible for such effects at the type of accuracy required of 10 every two years. Asif A. Mufti Before going on to consider a "clean" test of multiplicative creation Jfattamatics Department, QviaId-I-Asa»,University, Islamabad, Pakistan. in L.M.H. let us consider the conclusions of the hypothesis. It can be argued 2 that e /G Mm ia fundamental as matter is composed of atoms vhose structure ABSTRACT depends on the forces between protons and electrons. However, there aeeras Dirac's cosmologyf based on his large number hypothesis, took the to be no reason to prefer t (me /e }~ to t (Me /e2) vhich is I * 10 or gravitational coupling to be decreasing vith time and matter to be created P giP , 2 -1 as the square of time- Since the effects predicted by Dirac's theory are the ratio of t to the Planck, time ^-10 , or (me /e ) to Planck time p very small, it is difficult to find a "clean" test for it. Here we show 21 that the observed radiation fron pulsars is inconsistent with Dirac's "^lO , etc. Considering the number of dimensionless quantities that can be multiplicative creation model, in vhich the matter created is proportional constructed in this way it Is Inevitable that two or three of them are to the density of matter already present. Of course, this discussion makes comparable to an order of magnitude. Whereas an exact agreement of two no comment on the "additive creation" model, or on the revised version of forty digit numbers i£ unlikely, an order of magnitude agreement has a Dirac's theory. probability of one in forty only. If more than forty such dimensionless constants can be found then there is a certainty that at least two will agree to an order of magnitude? For this reason one may have difficulties in MIRAMARE - TRIESTE accepting the L.H.H. as such, but this does not in any way disprove Dirac's July I960 cosmology with varying <J and creation of matter. To obtain a "clean" teat of the theory we need some phenomenon in a critical state where very small effects vould make a very big difference. • To be submitted for publication. For multiplicative creation such a critical situation Is provided by neutron •• Permanent address: Mathematics Department, Quaid-i-Azam University, ster*. They radiate away a small fraction of their mass, and the effect of Islamabad, Pakistan. -Z- t.hij nsaLis luiij can be ota^rved. If they wore also "secretJng" .a'.'.er due to Now, for the observed slowing down of pulsars to be consistent with Fc,(6), multiplicative creation, the xass la»s would be drastically altered. Relying i.e. the left-hand side to be negative we must have on the observed data ve can see what limits would be imposed on the neutron 2 star Bass. Let us ccr.sider this point in more quantitative detail. dE /dt| >, 2rcc /t . (7) rad " p Since multiplicative creation requires an increase of mass proportional This equation gives a limit of the mass of the pulsars to the mass and trie square of the time, ve must have M = (8) (1) for a given amount of radiated energy. Thus the mass at time t can be expressed in terms of the mass at the present time by Using the standard method of deducing the radiated energy from the observed energy flux 5' "o n '•'•the- '-''-data "~fo r ™2 0 "•—neutro* n ~*-™ we find that 2 2 t /t ) . (2) 18 of them are entirely incompatable with multiplicative creation, as we would require them to have masses less than ICf K& , and even down to 2 x 10" M^I Thus the ratio of change of the mass of a neutron star due to multiplicative Ofthe'Other two one has a mass less than 0.06 Mfi,while the other is only creation at the present time is limited by the Ruffini limit . We conclude that apart from other considerations multiplicative creation of matter is ruled out by the existence of neutron stars. (3) According to the "traditional" neutron star model of pulsars 6) their energy loss was due to dipole radiation. It.is well known now that there are also other mechanisms responsible for energy loss ACKNOWLEDGMENTS dE ,/dt » dE ,/dt + 4E/dt , (it) One of the authors (A.Q.) would like to thank Professor Abdus Salam, rad rot the International Atomic Energy Agency and UNESCO for hospitality at the where dE /it is the total energy radiated, dE ,/dt i3 the rotational rad rot International Centre for Theoretical Physics, Trieste. energy loss given by ^/ dErot (5) (I being the moment of inertia of the neutron star, u its frequency and to the rate of decrease of frequency) and AE/dt is the non-rotational energy that could be radiated. Putting multiplicative creation into the picture we get the total energy loss dE /dt being given by dE_/dT t = -dEra d./d t + 2mc /tp (6) 1) P.A.M. Dirae, Proc. Roy. Soc. (London) A 333. l*03-ln8 (1973). Diatue*.*'.. M/M Serial Pul&ar Observed energy M 21 2T 6 2) P.A.M. Dlrac, Proc. Rcy. Soc. (London) A 338, I|39-W (X9T3). Ho. P S R * 10 cats. flux x 10 egTH./sec, * 1O gnw. * 10" 3) P.A.M. Dirac, "The large number of hypothesis ana the Einstein theory 1 0328 3.1 2.0 3.3 1.6 of gravitation", preprint of the Physics Department, Florida State University, Tallahassee, Florida. 2 0527 5.0 0-3 0.5 0.25 H. Rufflnl, Physics and Contemporary Heeds, Vol.1, Ed. Hiazuddin 3 0532» 6.1 5 » 106 a.3 " 106 U.I * 106 (Plenum Publishers, 1977). k 0628 0.6 0.5 0.83 0.U E.J. Groth, Weatron Stara. Black Holea and Binary X-Ray Sources, 5 0808 O.lt 0.03 0.05 0.02 Eds. H. Gursty and R. Ruffini (D. Riedel Publishing Co., 19T9). 6 0323 2.8 0.3 0.5 0.2 6) A. Qadir, R. Huffini and L. Violini, Lettere al Huovo Cimento 27_, 7 0833* 5 5 381-381* (1980). 1.5 7 * 10 1.2 x 10 0.6 x 10 8 083^ 1.2 1.0 1.7 0.8 7) D. ter Haar, Phys. Rep. 57-125 (1972). 9 0950 0.2 10.0 17.0 0.08 10 1133 0.* 1.0 1.7 0.8 11 1237 1.5 0.2 0.33 0.16 12 1506 1.2 5.0 8.3 k.i 13 1642 0.5 3-0 5.0 2.5 ill 17^9 3.3 1.0 1.6 0.8 15 1919 0.8 0.2 0.33 0.16 16 1929 0.5 3.0 5.0 2.5 1? 1933 6.1 u.o 6.7 3.8 US 2015 3.0 0.02 0.03 0.016 19 201*5 1.2 0.05 0.0S • 0.01*1 20 2213 1*.3 ta.O 6.6 3.3 The distance and the observed energy flux of 20 pulsars is given. On the t>a*iB of Eq.(8) and this data, the calculated upper mass limit, M, Is given in grans and solar masses. The pulsars marked with a • are not In- consistent with multiplicative creation, but the others are—even if ve alloir neutron stars with mass as little as 10~5 M« : -5- -6- CURREHT ICTP PREPRINTS ASD IHTERHAL REPORTS IC/T9/163 0. GELMIHI: The s-vave Qc5c states. ic/80/16 AHfiD OSKAlf: Tour-body problem for four bound alpha particles in 0. IC/79/165 S. MARCULBSCU and L.
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