#### DIRECTED BOTH AT PHYSICISTS CONVENTIONALLY ‘VERSED’ IN SPACETIME THEORY AS WELL AS AT KEEN SCHOOL-MATHS NOVICES, this new SPACETIME FUNDAMENTALS book unravels special relativity in one spatial dimension. Avoiding misnomers such as ‘proper’ (own-) and confusing presentisms such as ‘length contraction’, *Part I—T FOR TWO* and *Part II—SPACETIME TRINITIES* show how time dissimultaneities and spacetime sameness lead to a boundary speed identifiable *without postulation* as the speed of light. As also earlier detailed in a series of IOP’s *European Journal of Physics* papers, *Part III—FORCE MASS AND ENERGY* discards the populist ‘relativistic mass’ idea aptly branded ‘a pedagogical virus’ by Lev Okun, and uses two underrated equations to clarify and properly vindicate Newton’s reaction equals action principle which has been traditionally misrepresented and misinterpreted in relativity.

*Part IV—SPHERICAL GEOMETRY SURPRISES* offers innovative visual insights into relativistic acceleration. Tracing a rocket’s scaled ‘own-time’, a seemingly hitherto unknown spherical ‘HEMIX’ spiral’s colatitude sine reflects changing scaled velocity—a spacetime intrinsic ‘own-line’ curiously reminiscent of marine navigation’s 1537 loxodrome.

As expounded in 2016 in Elsevier’s *Results in Physics* journal, *Part V—AN OCCAM STEEPLECHASE* and *Part VI—THE RELATIVITY CURATE’S EGG* explore fixed-thrust twin rockets’ time dispersals and retro-separations, and oddly hitherto ignored radar formulae which bypass highly convoluted literature approaches and directly sort out the ‘rigor mortis’ (‘rigid motion’) acceleration issue shown to be epitomised by a simple ‘hand-held fan’ real-values metric ‘own-surface’.

*Part VII—ROLLER COASTING SPACETIME* solves the ‘Bell’s spaceships’ enigma: How does a co-accelerating medium between twin rockets ‘expand’ ? The hemix spiral *generates* the helicoidal solution—a real metric ‘HEMICOID’ own-surface hosting hemices which chart increment own-times. These hemices are crossed by expanding *non-inertial own-length* helices which are *extrinsically* validated by ‘cosmographic’ overlappings of shared velocity cylinders and ‘distances helicoid’ boundaries.

#### Basic geometry also *intrinsically* corroborates the apparently unprecedented hemicoid surface which, as shown in a sequel 2017 *Results in Physics* paper, itself uniquely emerges independently of relativity theory. Successive radar trajectories not only surf ‘horizon’ hemices as expected, irrespective of their original rear rocket emission times they also traverse each shared own-time medium expansion helix at identical angles and *nonzero* geodesic curvatures. A casualty where an accelerating medium is concerned, widely sacrosanct *Minkowski spacetime* is plainly exposed as *overgeneralised***—**even in special relativity. Also, as outlined in a further paper published in 2019, medium helices on the hemicoid manifest *nonzero* geodesic curvatures. General relativity literature’s kernel *diktat* that an acclerating medium’s ‘free particle’ paths *should be geodesics* is thus seriously questioned. Equivocating reactions of physicists and institutions unsettled by such seemingly indelicate conclusions are chronicled in the book’s *EPILOGUE—Minkowski spacetime’s ‘post-truths’* (linked above).

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