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I'm sure someone else must have come up with this (the description in the third paragraph), but I haven't seen it. Briefly, for those not familiar with it, radar simultaneity generalizes Einstein's simultaneity convention directly to arbitrarility accelerating observer. Dalsepam has posted a paper describing it.
A key issue with accelerating observers is that there is no natural way to construct a global coordinate patch. Different approaches map different parts of spacetime, but none can be global. For Fermi-normal, your patch is bounded by areas where extended hypersurfaces intersect, but it is able to cover extensive regions that are not yet causally connected to the observer. Radar makes a different compromise (as I view it): its coordinate patch only includes the prior lightcone of an event on an observer's world line. However, the bad areas for Fermi-normal are readily mapped once they are in an observer's prior lightcone. Radar simultaneity also is inapplicable in cosmology (Observer's world line must extend to prior lightcone of distant event. This is not generally possible for cosmological distances).
Ok, now my descriptive picture. Imagine attached to any object you can see a clock and a mirror (you, the observer, have a clock too). What you see on the object's clock shows proper time progress for the object. The image of your clock in the objec's mirror tells you how to map the event you are now seeing to your own history - back from now halfway to the time you see in the reflection. You choose to follow this information from clocks and treat doppler and aberration effects (leading to rapid changes in perceived distances, etc.) as purely optical artifacts of your changes in direction motion (which of course you can feel).
A key issue with accelerating observers is that there is no natural way to construct a global coordinate patch. Different approaches map different parts of spacetime, but none can be global. For Fermi-normal, your patch is bounded by areas where extended hypersurfaces intersect, but it is able to cover extensive regions that are not yet causally connected to the observer. Radar makes a different compromise (as I view it): its coordinate patch only includes the prior lightcone of an event on an observer's world line. However, the bad areas for Fermi-normal are readily mapped once they are in an observer's prior lightcone. Radar simultaneity also is inapplicable in cosmology (Observer's world line must extend to prior lightcone of distant event. This is not generally possible for cosmological distances).
Ok, now my descriptive picture. Imagine attached to any object you can see a clock and a mirror (you, the observer, have a clock too). What you see on the object's clock shows proper time progress for the object. The image of your clock in the objec's mirror tells you how to map the event you are now seeing to your own history - back from now halfway to the time you see in the reflection. You choose to follow this information from clocks and treat doppler and aberration effects (leading to rapid changes in perceived distances, etc.) as purely optical artifacts of your changes in direction motion (which of course you can feel).
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