Recent content by PAllen

No, as measured locally by an accelerometer, or by design with preprogrammed propulsion systems. The aim is to demonstrate: 1) There exist simultaneity conventions having nothing to do with light that are equivalent to the Einstein convention. 2) You only get to make one choice for...

Yes, fixed now.

At time t, clock 1 sends a signal to clock 2, triggering clock 2 to send its time reading to clock 1. We are assuming the clocks mutually stationary after having separated with identical acceleration profile. Also, that they started out in synch before separation. At some time on clock 1: t+k...

Note, an invariant fact is that if you move the clocks away and then back together with identical acceleration profile, they will be in synch. The part subject to choice is whether or consider them synchronized while apart. There is no way to check this without some other convention. If you...

Something worth noting in these discussions is that isotropy can be assumed for some physical process unrelated to light, and this will then force the consequence of one way light speed isotropy. For example, suppose you assume that moving two collocated identically constructed clocks away from...

I'll sum up my position: A given detector can measure KE of a test body (relative to that detector, of course) with no recourse to coordinates, clocks or conventions. Among coordinate systems which place that detector 'at coordinate rest', the formulas for predicting that measurement in terms of...

What matters is the relative motion of detector and body, not the details of frame construction (in particular, clock synchronization plays no role).

Then my point is proven: KE is a directly measurable local quantity that does not depend on clock synch (you don't even need one clock, let alone two). It depends only only on the relative motion of detector and test body. The formula for it may be synchronization dependent, taking the...

But that directly measured local quantity is the only thing that can sensibly be called KE. So perhaps you should say the Newtonian formula only equals KE with conventional synchronization. That would support @pervect ’s point of view that Newtonian physics (e.g. the Newtonian KE formula...

KE is dependent on relative velocity between detecter and particle. However, it not dependent on synchronization convention. It is, in fact, the inner product of the detector’s 4 velocity and the particles 4 momentum. This is a local invariant.

I still see no explanation of how different synchronization convention can cause otherwise identical sand beds to result in different crater depth.

Sure it does. And if particles with identical motion are measured with 2 different calorimeters moving relative to each other, they will measure different KE. Calorimeters are the main way particle accelerator experiments measure KE in the lab frame.

Really? How does a calorimeter depend on clock synchronization? Or, simpler, if crude, crater depth in 'standard sandy ground' ?

The sectional curvature as described can be directly related to the Riemann tensor as written in terms of the metric. BUT, for connection different from the Levi-Civita connection, this would not be the 'right' curvature tensor. So the reliance is there, but rather hidden. If you consider the...

Note, there are other ways to define intrinsic curvature constants. For example, consider the area of a small circle on the surface of a sphere. Measure its area and take the difference with the plane area formula for the same radius as measured on the sphere. Divide by the plane area to get a...