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seen Mar 27 at 20:45

Jul
28
comment Why is the Ritz combination principle incompatible with Classical Mechanics?
+1 Thanks. It was a very clarifying answer.
Jul
28
accepted Why is the Ritz combination principle incompatible with Classical Mechanics?
Jul
28
revised Proving that interval preserving transformations are linear
added 35 characters in body
Jul
28
comment Proving that interval preserving transformations are linear
+1 Nice proof..
Jul
27
revised Physics-oriented books on fractals
edited tags
Jul
27
comment Proving that interval preserving transformations are linear
@Qmechanic: Yes, it does help. The question I posed in my comment above now becomes: How do you prove that a Lorentz matrix can always be brought into the form $\delta _{\mu }^{\rho }$ using Lorentz transformations? This is equivalent to asking whether the Lorentz matrices are invertible, which they are, by definition. I hope I'm making more sense now.
Jul
27
answered Proving that interval preserving transformations are linear
Jul
27
comment Why is the Ritz combination principle incompatible with Classical Mechanics?
I understand how the Ritz combination principle comes about naturally in Quantum Mechanics... You say: "This relationship is impossible to understand classically". This is what I don't understand. What's the justification for claiming that the Ritz combination principle cannot fit with classical mechanics?
Jul
27
asked Why is the Ritz combination principle incompatible with Classical Mechanics?
Jul
27
comment Proving that interval preserving transformations are linear
@Qmechanic: How does one prove that a tensor $a_{\mu }^{\rho }$ that satisfies $\eta ^{\mu \nu }a_{\mu }^{\rho }a_{\nu }^{\sigma }=\eta ^{\rho \sigma }$ can be put in the form $\delta _{\mu }^{\rho }$ through Lorentz transformations? If this is supposed to be elementary, at least point me to some website or something that explains it, since I'm self-studying this stuff. Thanks.
Jul
27
comment Proving that interval preserving transformations are linear
@Qmechanic: I'm not clear on the 3rd step. Specifically, the part that says "By possibly performing an appropriate "rotation", we will from now on assume without loss of generality that the constant matrix ..." Can you elaborate? Thanks.
Jul
26
asked Physics-oriented books on fractals
Jul
26
awarded  Critic
Jul
25
comment Proving that interval preserving transformations are linear
@Ben Crowell: Edited the question.
Jul
25
revised Proving that interval preserving transformations are linear
deleted 55 characters in body
Jul
25
comment Proving that interval preserving transformations are linear
@Ben Crowell: I think I was wrong to put it that way. Spacetime is homogeneous, isotropous, and flat, with the Minkowski metric. What I don't want to assume is any properties of homogeneity or isotropy in the coordinate transformation $\left\{y^i\right\}\leftrightarrow \left\{x^i\right\}$. All I want to assume is that the interval is preserved, and from that prove the linearity. I hope it's clearer now.
Jul
23
asked Proving that interval preserving transformations are linear
Jul
18
awarded  Supporter
Jul
18
accepted Rotations in space-time
Jul
16
asked Rotations in space-time