Advances in Fluid Mechanics by E. Krause

By E. Krause

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The wave equation (22) for the new description is ∂ν χ λνσ κ ∂σ Aκ = Cλ , (26) where the isomer form6 χ λνσ κ = χ˜ µρ λν E˜ µρσ κ (27) of the constitutive tensor relates to the Levi–Civita tensor. The isomer form of the constitutive tensor is weighted with the determinant’s absolute value as per χλ ν σ κ = |∆|−1 Aλλ Aνν Aσσ Aκκ χ λνσ κ , (28) whereas the nonisomer form transforms with the sign of the Jacobian determinant as follows: χ˜ λ ν σ κ = ∆ λ ν σ κ A A A A χ˜ λν σ κ . , reflections and inversions), it is essential to take these distinctions into account.

Present knowledge seems to indicate that, in an inertial frame, the constitutive tensor of vacuum in a Cartesian basis can be written as a 6×6 matrix as follows in Table 1. The numerical invariance of the configuration shown in Table 1 defines the conformal group [14]. The Lorentz group is the invariance group of the spacetime metric tensor and is a subgroup of the conformal group. It is instructive to view these matters through the telescope of history. After Maxwell’s formulation of the macroscopic field equations, Lorentz—in his electron theory—postulated their validity in the microscopic domain and established their invariance under transformation now known as the Lorentz group.

The reader may open many a book on quantum field theory and will find the convenient substitution c = 1 and sometimes, even worse, an imaginary time x0 = ict. Some people just felt that spacetime should have a positive definite metric. These measures were motivated by a false aesthetics. With hindsight, they merely contributed to the drift of theory away from physical reality. Additionally, the Giorgi rationalization was not popular among the creators of the special and general theories of relativity either.

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