naeric taylar
Transkript
naeric taylar
Einstein’ın Bilimsel Yöntem açısından “Günahı” •“I have not succeeded formulating boundary conditions for spatial infinity” •“The curvature of space is variable in time and place, according to the distribution of matter, but we may roughly approximate to it by means of a spherical space. At any rate, this view is logically consistent, and from the standpoint of the general theory of relativity lies nearest at hand; whether, from the standpoint of present astronomical knowledge, it is tenable, will not here be discussed” Albert Einstein, Cosmological Considerations on theGeneral Theory of Relativity, Dover Pub., 1923, p. 183&188 50 51 “Einstein’s asumption of homogeneity had three profound effects on cosmology. First, it introduced the idea of a finite universe, which resuscitated the medieval cosmos – previously considered obsolete and antithetical to science itself (continued). Eric Lerner, The Big Bang Never Happened, Times Books, Random House, 1991 52 Second, the aesthetic simplicity of the assumption of homogeneity, combined with Einstein’s prestige, embedded this assumption in all future relativistic cosmology (continued). (agy) 53 Third, and perhaps most significant, it set a precedent by allowing the introduction of assumptions contrary to observations, in the hope that further observations will justify the assumption. In the case of Einstein’s cosmology it was the hope that, on scales larger than clusters and superclusters of galaxies, the universe would become smooth” Eric Lerner, The Big Bang Never Happened, Times Books, Random House, 1991 54 ‘We replaced scientific certainty with scientific progress’ Richard Feynman 55 “The Concordance Model (ΛCDM) is based upon the general theory of relativity (GR) and so it is important to ask just how well that theory is supported by observations and experiment. For example, how good is Einstein Equivalence Principle?” (Questions of Modern Cosmology, p. 319) Malcolm Longair 56 Accelerated expansion of the universe ‘It is yet unclear whether the explanation of the fact that gravity becomes repulsive on large scales should be found within general relativity or within a new theory of gravitation’. Alain Blanchard, Evidence for the Fifth Element, Astronomy and Astrophysics Reviews (2010) 18:595–645 57 “Modesty is the best policy” “Evidently”, writes Einstein himself in a letter addressed to the Magazine Science, “evidently, if Dr. Miller’s results should be confirmed, then the special relativity theory, and with it the general theory in its present form, fails. Experiment is the supreme judge.” “But”, adds Einstein, “we must take into account the fact that no theory exists outside the theory of relativity and the similar Lorentz theory which, except for the Miller experiment, explains all the known phenomena up to date”. And he concludes: ”Under the circumstances, nothing remains but to await a more complete publication of Miller’s results. Then it is to be hoped that a correct decision will develop”. Emile Borel, Space & Time, Dover Pub. Inc., N.Y., 1960, p. 189 58 59 60 “Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore”. Albert Einstein 61 62 Güneş Flare Olayında Manyetik Erkenin Korunumu 63 Küçük tınıs açılı parçacıklar ilmiğin ayakuçlarında Sert X-Işın Bölgeleri oluşturur. 64 65 66 + B0 B ( x ,0 ) = − B0 x>0 x<0 ∂B ∂2B =η ∂t ∂ x2 B(x , t) = B0 erf ( ξ ) ξ = x / ( 4η t )1/2 erf (ξ ) = 2 π ξ −u e ∫ du = 2 0 2 1 1 5 ξ − ξ 3 + ξ − ... 3 2! 5 π 50 40 30 20 10 0 -10 -20 t=0,25 B0 t=0,5 t=0,75 -30 -40 -50 67 68 MB Eşitliğinin Üçüncü Momenti(3) ∂ B2 + ∇ ⋅ ( E × H ) = − µ 0η j ∂ t 2 µ 0 E×H = B2 µ 2 − v ⋅ ( j × B) v B2 ∂ B2 + ∇⋅ = − µ 0η j 2 − v ⋅ ( j × B ) v µ ∂ t 2 µ 0 69 ∂ B2 + ∇ ⋅ ( E × H ) = − µ 0η j ∂ t 2 µ 0 E×H = B2 µ 2 − v ⋅ ( j × B) v B2 ∂ B2 + ∇⋅ = − µ 0η j 2 − v ⋅ ( j × B ) v µ ∂ t 2 µ 0 PASJ, 51, 161-71, 1999 70 KORUNUM / SÜREKLİLİK / TAŞINIM EŞİTLİKLERİ How to extract the Physics from them and/or How to bury the Physics into them 71 f evre – uzay yoğunluğu (phase-space density) 72 Maxwell Boltzmann Eşitliği F ∂f ∂ f (r , u , t ) + (u ⋅ ∇ r ) f (r , u , t )+ ⋅∇ u f (r , u , t )= ∂t m ∂t • • • • Durgun durum (steady state) Eşdağılımlı (homogeneous) Çarpışmasız (collisionless) Yönbağımsız (isotropic) çarp ∂f / ∂t = 0 u .∇rf = 0 (∂f / ∂t )çarp = 0 (F .∇u) f = 0 73 Maxwell Boltzmann Eşitliğinin Hız Momentlerinin Türetilmesi • g(u) = m u 0 = m • g(u) = m u 1 = m u • g(u) = m u 2 = m u2 • g(u) = m u 3 = m u3 • ... ∫ g(u) ∂f ∂ F f (r, u, t ) du + ∫ g(u)(u ⋅ ∇r ) f (r, u, t ) du + ∫ g(u) ⋅ ∇u f (r, u, t ) du = ∫ g(u) du ∂t m ∂ t çarp 74 MHD Eşitlikleri ∂ρ + ∇ ⋅ (ρ v ) = 0 ∂t ∂ 1 B2 B 2 − ρ ∇Φ + ρ + (v ⋅ ∇ ) v = −∇ P + ρν ⋅ ∇ B + ∇ v + ∇ ( ∇ ⋅ v ) 8π 3 4π ∂ t 1 − 2ρ Ω × v + ρ ∇ Ω × r 2 2 +ρr× dΩ dt ∂s ρT + v ⋅∇ s = −∇ ⋅ q − Lr + j 2 / σ + ρ ε nuclear + Hν + H w ∂t E.R. Priest, Solar Magnetohydrodynamics, D. Reidel Pub. Co., Dordrecht, 1984 75 Korunum eşitliklerinin ‘standart’ biçimi ∂ ( Fiziksel niceliğin yoğunluğu ) + ∇ ⋅ ( Fiziksel niceliğin akısı ) = Kaynak − Batık ∂t ∂Q + ∇ ⋅ ( Qv ) = S − L ∂t 76 Maxwellian 1/ 2 mi −m u e Fi 0 = 2π kTi i 2 / 2 kTi Drifting Maxwellian 1/ 2 me −m (u −u ) e Fe 0 = 2π kTe 2 e 0 / 2 kTe 1/ 2 mi −m u e Fi 0 = 2π kTi i 2 / 2 kTi 77 [ f 0 e = β exp − α (v − u ) 2 ] α = m / 2T Warm electron stream drifting with a speed less than its thermal speed through a cold-ion distribution 78 2 me (u + u0 )2 me me (u − u0 ) 1 Fe0 (u ) = + exp − exp − 2 2π kTe 2kTe 2 kT e 79 80 81 82 83 Doğrusal (Linear) & Doğrusal Olmayan (Non-linear) Sonsuz kez diferansiyeli alınabilen gerçel veya kompleks bir f (x) işlevinin gerçel veya kompleks bir ‘a’ sayısı komşuluğunda güç serisine açılımı (Taylor açılımı) f ( x) = f (a) + f ′(a) 1! ( x − a) + f ′′ ( a ) 2! ( x − a) 2 + ... 84 ☺ Peter’s Taylor Expansion! ☺ 85