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Halc

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- TL;DR Summary
- Looking for material on a coordinate system relative to an event rather than to an inertial frame

I have been using a coordinate system that is anchored on an event (rather than a speed reference) in Minkowskian spacetime. This makes it sort of a special case (no gravity or dark energy, just like special relativity) of the cosmological (or CMB-isotropic) coordinate system used to foliate the entire universe, with the big bang being the reference event.

The reference event can be any event. It becomes the origin of the coordinate system.

So imagine the event in question being an explosion in existing space (boundless in all 4 dimensions) with infinite material expelled at evenly spaced speeds. By evenly spaced, I mean the typical separation between a piece of inertial ejecta and its neighboring piece is a uniform amount of proper velocity difference. In this way, from the viewpoint of any bit of ejecta, it appears to be the center of material that is stationary in expanding spacetime. This is the special-relativity version of expanding space coordinates.

I'm not speculating the possibility of the big bang being an explosion of material in space. If that were so, the concentrated mass would have gravity that would never allow any expansion at all, but this is just a mathematical model with no consideration of gravitational mass.

Some properties that I've worked out:

The coordinate system only foliates spacetime within the light cones of the reference event, sort of similar to Rindler coordinates only foliating a light-cone of spacetime. I think the coordinates work fine with past events, but events without time-like separation from the reference event are not part of the coordinate system.

Any inertial object whose worldline intersects the origin of the coordinate system is said to be stationary. Any motion relative to this stationary line is peculiar velocity, a vector. Velocities add the relativistic way, but recession rates (which are not vectors), being proper speeds, add linearly, hence can exceed c. Peculiar velocity decreases over time, so absent proper acceleration, all objects will eventually approach being stationary.

A pair of objects that are stationary relative to each other in an inertial frame (say at either end of a rigid object with no proper acceleration) are, in this coordinate system, always moving apart. In other words, rigid objects are always growing towards (but never reaching) their proper length. Likewise, the time it takes for light to travel from one end to the other is always decreasing, approaching but never reaching the time it takes light to travel the object's proper length. I've not worked out formulas for the above effects.

The rate at which clocks run is a function of the clock's peculiar velocity and not a function of any observer frame. No value seems observer dependent. There are thus no frame rotations, but there are still conversions to inertial coordinates relative to any selected inertial worldline.

Light will eventually reach any point in space from any other point in space. This is another big difference with the actual universe where the acceleration of expansion due to dark energy forms event horizons similar to Rindler horizons, beyond which emitted light can never reach portions of space.I am mostly asking for references since lacking a name, all my searches have turned up nada, and also feedback if any of the properties I've listed are nonsense. I'm speculating no new physics, just assigning different abstract coordinates to ordinary Minkowski spacetime.

The reference event can be any event. It becomes the origin of the coordinate system.

So imagine the event in question being an explosion in existing space (boundless in all 4 dimensions) with infinite material expelled at evenly spaced speeds. By evenly spaced, I mean the typical separation between a piece of inertial ejecta and its neighboring piece is a uniform amount of proper velocity difference. In this way, from the viewpoint of any bit of ejecta, it appears to be the center of material that is stationary in expanding spacetime. This is the special-relativity version of expanding space coordinates.

**Is there a name for such a coordinate system?**I would appreciate a link to some material on it.I'm not speculating the possibility of the big bang being an explosion of material in space. If that were so, the concentrated mass would have gravity that would never allow any expansion at all, but this is just a mathematical model with no consideration of gravitational mass.

Some properties that I've worked out:

The coordinate system only foliates spacetime within the light cones of the reference event, sort of similar to Rindler coordinates only foliating a light-cone of spacetime. I think the coordinates work fine with past events, but events without time-like separation from the reference event are not part of the coordinate system.

Any inertial object whose worldline intersects the origin of the coordinate system is said to be stationary. Any motion relative to this stationary line is peculiar velocity, a vector. Velocities add the relativistic way, but recession rates (which are not vectors), being proper speeds, add linearly, hence can exceed c. Peculiar velocity decreases over time, so absent proper acceleration, all objects will eventually approach being stationary.

A pair of objects that are stationary relative to each other in an inertial frame (say at either end of a rigid object with no proper acceleration) are, in this coordinate system, always moving apart. In other words, rigid objects are always growing towards (but never reaching) their proper length. Likewise, the time it takes for light to travel from one end to the other is always decreasing, approaching but never reaching the time it takes light to travel the object's proper length. I've not worked out formulas for the above effects.

The rate at which clocks run is a function of the clock's peculiar velocity and not a function of any observer frame. No value seems observer dependent. There are thus no frame rotations, but there are still conversions to inertial coordinates relative to any selected inertial worldline.

Light will eventually reach any point in space from any other point in space. This is another big difference with the actual universe where the acceleration of expansion due to dark energy forms event horizons similar to Rindler horizons, beyond which emitted light can never reach portions of space.I am mostly asking for references since lacking a name, all my searches have turned up nada, and also feedback if any of the properties I've listed are nonsense. I'm speculating no new physics, just assigning different abstract coordinates to ordinary Minkowski spacetime.