Source: http://members.tripod.com/li_chungwang0/physics/unify-me.html
Timestamp: 2019-04-22 19:24:35+00:00

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How to unify two concepts: Locating soft spots (like g(u) in [Rob, p.7, l.11]) for possible development.
Both the Galilean transformation and the Lorentz transformation come from the same theory [Rob, p.6, l.9-p.8, l.8]. Only their additional assumptions are different: The former assumes that the speed of light is infinite [Rob, p.8, l.9], while the latter assumes that the speed of light is a constant<+¥ [Rob, p.8, l.19].
The same idea with different interpretations. [Gol, p.257, l.4] relates the Poission bracket of functions to the Lie bracket of vector fields [Spi, vol.1, p.212, l.-3].
The same phenomenon viewed from different reference frames. Example. [Cor, p.293, l.-2-p.294, l.2].
Invariance under different reference frames. Example. Maxwell's equations: The first pair [Cor, p.314, l.-16] & the second pair [Cor, p.314, l.-14].
Unification [Go2, p.554, l.9-l.-15] often requires that we adopt a revolutionary viewpoint to smooth the transition. Examples: [Sym, p.313, l.-14-l.-12] & [Go2, p.553, l.-12-l.-10].
To unify Halmilton's principle, Fermat's principle and Maupertuis' principle of least action requires broad knowledge [Born, p.719, Appendix I].
These principles are theorems [Born, p.129, §3.3.2] rather than axioms.
[Born, p.127, (1)] is the optical version of [Born, p.736, (85)].
Fermat's principle is the optical version of the principle of least action [Born, p.742, l.5].
The methods in optics are more effective than those in mechanics. For example, the concept of the Fresnel zones provides an effective algebraic method to calculate the electric field [Hec, p.488]. However, in the general electromagnetic theory we have to use the analytic method of solving Maxwell's equations.
For any formulation in mechanics there corresponds a significant equivalent in optics [Born, p.734, l.8]. However, for a certain formulation in optics, the corresponding equivalent has no significant meaning in practice [Born, p.739, l.5]. However, in the case of diffraction, the concept of diffraction in optics does lead to the discovery of electron diffraction [Born, p.744,l.-2].
Correctness and clarity are key for impressing a true student of physics. If a reader has to spend a lot of time clarifying the confusion and correcting the mistakes of a book, then any honor that the book's author received will not help increase the value of his work.
Here by "transversality" we mean that the direction of the normal field (U, V, W) of the surface S(x,y,z)=S1 coincides with the direction (dx, dy, dz) of the extremal of the field.
Only through comparing various forms of a cross section may we understand the essence of the concept. That is, only after shedding the nonessential parts may the key point reveal itself.
(A fixed solid angle; one scatterer) A beam of identical particles passes through a central-field [Coh, p.906, (A-3)].
(A fixed angle of deflection; one scatterer) A beam of identical particles pass through a central-field [Lan1, p.49, (18.15)].
(A fixed angle of deflection; many scatterers) A beam of charged particles is shot through a thin foil [Sym, p.138, (3.273)].
The collision between two beams [Lan2, p.34, l.-7].
Although the various forms make one dizzy, the essential message is the same. (A) and (B) are the same. (B) is a special case of (C). (D) can be considered the total cross section of (C).
[Eis, p.N-3, (N-20) & (N-21)], we may write the solution of [Eis, o.N-3,(N-19)] as [Eis, p.N-3, (N-22)]. By [Eis, p.I-2, (I-8) & (I-9)], we may write the solution of [Eis, p.I-2, (I-7)] as [Eis, p.I-3, (I-11)]. The idea behind the above method is similar to variation of the constants [Col, p.15, l.3].
Using the method of variation of the constants, we obtain the solution directly by integration. Using [Eis, p.I-3, (I-11)], we reduce [Eis, p.I-2, (I-7)] to [Eis, p.I-3, (I-12)], which is solvable by means of the power series technique. Using [Eis, p.N-3, (N-22)], we reduce [Eis, p.N-2, (I-19)] to [Eis, p.N-3, (I-23)], which is solvable by means of the power series technique.
Remark. The physical considerations [Eis, p.I-2, (I-8), | u| ® ¥ ; p.N-3, l.-15, r ® ¥ ] help us reduce the differential equations to the desired “homogeneous” form.
It seems that [Rei, §6.2] & [Rei, §6.4] deal with different problems. It turns out that we can use the system-reservoir approach [Rei, p.212, l.1] to solve both problems.
It seems that [Rei, §6.4] & [Rei, §6.10] study the same problem and derive the same canonical distribution [Rei, p.212, (6.4.2) & p.231, (6.10.13)] but via different approaches. [Rei, §6.4] separates the ensemble into two parts (a system and a reservoir) and then maximizes the entropy. In contrast, [Rei, §6.10] considers the ensemble as a whole and then maximizes the number of the possible configurations [Rei, p.231, l.10]. However, it turns out that the two approaches are equivalent [Rei, p.231, (6.10.15)].
Only a few summands contribute appreciably to the sum [Rei, p. 17, Fig.1.4.1; p.111, (3.7.17); p.222, l.14; p.347, (9.6.4)].
Only a small region of integration contributes appreciably to the integral [Rei, p.36, (1.10.4) & p.224, l.9].

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