SPACETIME a. e. milne

 

Spacetime is Euclidian, and surfaces of simultaneity are flat. Gravity can affect time on a local level, and LT's rotate the flat surface of simultaneity.  

Milne's timescale problem is that it's hard to understand Special Relativity.  

SCM's timescale problem is that no one knows what the shape of the 3-surfaces are, and it is hard to understand how gravity could affect things on a global level.

Milne's Model.   

The Litmus tests of whether an idea is consistent or inconsistent with Milne's Model is to ask whether it attempts to apply Lorentz Transformations on a cosmological scale or whethery they primarily deal with the Friedmann metric.

Gravitation, Relativity and World Structure
Only Chapter's 1-7 and 16-Appendix are specifically referenced here. The content between chapters 8 and 15 are beyond the scope of this presentation.

The "Inflation-in-Milne-Model" animation presented is a non-calculus-based approach to the idea of motion in the Milne Model.  

In these chapters, Milne refers to particles traveling faster than the speed of light, which is ostensibly what the animation shows during periods of the instantaneous representation of the acceleration of the observer.

Milne takes a calculus based approach which treats uniform accelerations due to gravitational attraction instead of the instantaneous acceleration due to thermal collision. His approach is similar to that of Mike Fontenot (see CADO, below). Milne treats the change in the observed location of the particle with respect to the observer as an actual velocity, and so frequently describes "Faster than Light" motion of particles in chapters 8-15. This can be taken as the mechanism for cosmological inflation as presented by Milne, though this should be verified by better educated mathematicians and physicists.

This image shows an observer under non-instantaneous acceleration. It shows only events rather than the worldlines of objects, but it's not hard to imagine the animation with lines drawn between some of the events to represent worldlines of non-accelerating particles.

If they were, the intersection where these lines crossed the horizontal t=0 axis would move back and forth at rates higher than the speed of light. Distance between worldlines along a constant t is the definition of distance as used in Lorentz Transformation.) This might be called Faster Than Light Motion in some interpretation, though of course it is only faster than light in reference to the accelerating observer.

That is, there is no reference frame where any object is traveling faster than the speed of light, but the observer is not remaining in any single reference frame, so he can observe an object's position changing faster than the speed of light.

Lewis Carroll Epstein’s 1976 work, Relativity Visualized, presents many of the same concepts presented by Milne. Having not sat through numerous arguments with Eddington, Russell, Einstein,Theory of Relativity in a manner that was self-consistent and that *anyone* could understand. Even so, because of the difficulty of the two different coordinate systems presented, the Appendix should be skimmed before delving into the meat of the book. Epstein's use of a space-propertime diagram, distinct from a space-coordinate-time diagram is compatible with Milne's description of a mixed coordinate system.

The description and Illustration of the General Theory in Epstein's book is truly unique, and if the mathematics of the Schwarzschild Metric could be somehow illustrated by the nonmathematical models of Epstein, a great leap forward could be made in pedagogy.

Epstein views his own model as simply a self-consistent possibility, distinct from the concept of "expanding space," but has not made a careful critical analysis and comparison.

objects moving toward us near the speed of light.

The diagrams indicate that when the observer accelerates toward a stationary object, it appears further away. Extrapolation of this idea leads to the realization that this change in perceived distance is limited only by the acceleration of the observer.

This simultates how an object could be viewed to be moving "faster than the speed of light" and is consistent with Inflation of the Milne Model Universe.

Milne Model, (and in particular the explanation for Inflation.) He determined that by accelerating toward a distant receding object, you increase its coordinate distance until you've matched pace with it, and cause its current coordinate age to change rapidly by accelerating toward or Milne’s model.