All of which was already explained by Laue in 1911:
https://en.wikisource.org/wiki/Translation:Two_Objections_Against_the_Theory_of_Relativity_and_their_Refutation
Hopefully we don't have to wait another 110+ years before everybody understands this.
Probably similar to the old suggestion of Clifford (1871), according to which matter is just Riemannian curvature of space. Even Einstein said something in that direction. See the following paper that gives a sketchy overview of that idea in relation to general relativity...
I guess you describe the same events A and B from the viewpoint of two different frames: In the first frame (upper image), the light clock moves to the right, in the second frame (lower image) it moves to the left. If that's the case, then event B on the lower image is located in the middle of...
As far as I know from reading Einstein's collected papers, there is only one published paper of Einstein in which he used the EP to discuss the twin paradox (besides some letters from 1917-1918 in which he also sketched that solution). It's in his popular article (without equations) from 1918...
When people refer to spacetime as hyperbolic, they usually mean that parts of spacetime can be described by certain models of hyperbolic space. For instance, relativistic velocity space inside $$u_{x}^{2}+u_{y}^{2}+u_{z}^{2}=1$$ can be described in terms of the Beltrami–Klein model or Poincaré...
That's the emission (or ballistic) theory of light. While it is consistent with the Michelson-Morley experiment, it was refuted by many other experiments that use moving light sources.
The theory says that only "inertial" motions are relative (or symmetric), whereas accelerated motions - as indicated by comoving accelerometers - are "absolute".
They don't need anything to know about their past movements, they only need an accelerometer - an indication of zero means they can...
He apparently refers to the series of twin paradox articles in the Physics FAQ written by Michael Weiss:
https://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html
Yes. Let's say that both start at the same time with same acceleration profile (i.e. same proper acceleration in opposite directions and same proper times). So they accelerate away from each other from t=0 to t=5 (with t being the times measured on the rockets), then reverse acceleration from...
On p. 26 we find the inverse of formula 5.17:
(5.18) ##q=(1-J)q'(1+J^{\ast})##
and the most familiar form of the Lorentz transformation:
(5.19) ##x'=\gamma(x-vt),\ y'=y,\ z'=z,\ t'=\gamma(t-vx),\ \gamma^{-2}=1-v^{2}##
which is shown to be included in 5.16 on p. 25 by setting ##I=e_{1}##...
Unfortunately, in order to produce hyperbolic rotations (i.e. Lorentz transformations), ordinary quaternions don't suffice. You have to use complexified quaternions, better known as Biquaternions.
A good introduction was given by the great mathematician John Lighton Synge:
"Quaternions, Lorentz...
Yes, I should have added that DeSitter's vacuum solution is related to Einstein's modified field equations that include the cosmological constant. Anyway, the point is that GR solutions such as this contributed, at least in the long term, to Einstein's abandonment of his idea quoted above...
This is somehow related to Mach's principle (at least in Einstein's reading): Are all forms of gravitational fields, the spacetime metric, and the inertia of bodies, fully determined by the masses of the universe? A nice historical description of this problem was given by Janssen...
As the electromagnetic field tensor consists of six independent components, three electric (##E_x##, ##E_y##, ##E_z##) and three magnetic (##B_x##, ##B_y##, ##B_z##) ones, it was initially represented by Sommerfeld as a “six vector” in terms of Plücker (or Grassmann) line coordinates in order to...
Another example: The Fitzgerald-Lorentz contraction hypothesis was initially introduced in order to save the "stationary" aether from being refuted by MMX.
This should remind us that one experiment (such as MMX) alone can never be the reason for adopting a theory. Indeed, the strength of special...