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)
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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
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“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
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“Since the mathematicians have invaded the
theory of relativity, I do not understand it
myself anymore”.
Albert Einstein
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Güneş Flare Olayında
Manyetik Erkenin
Korunumu
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Küçük tınıs açılı parçacıklar ilmiğin ayakuçlarında Sert X-Işın Bölgeleri oluşturur.
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 + 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
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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 


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∂  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
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KORUNUM / SÜREKLİLİK / TAŞINIM
EŞİTLİKLERİ
How to extract the Physics from them
and/or
How to bury the Physics into them
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f evre – uzay yoğunluğu (phase-space density)
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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
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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
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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
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Korunum eşitliklerinin ‘standart’ biçimi
∂
( Fiziksel niceliğin yoğunluğu ) + ∇ ⋅ ( Fiziksel niceliğin akısı ) = Kaynak − Batık
∂t
∂Q
+ ∇ ⋅ ( Qv ) = S − L
∂t
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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
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2
 me (u + u0 )2  
me   me (u − u0 ) 
1
Fe0 (u ) =
+ exp −
exp −

2 2π kTe  
2kTe 
2
kT
e


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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
+ ...
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☺ Peter’s Taylor Expansion! ☺
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