This discussion must remain confined to a SR, as within the context of GR and the presence of gravitational fields, the shape or curvature of space is dynamic and thus distances also become dynamic and proportional to the local curvature of space.
I am again surprised by this type of a statement. I hope you realize that you are setting up a prefered reference frame. A LY is not a LY if you like. From difference reference frames a light year can be very different.
If we accept;
- That the velocity of light is constant
- And that the velocity of a moving object does not affect the velocity of light
Then the distance that a photon travels between any two points in space, must be the proper distance between those two points, as defined from within their common rest frame. This assumes two points or objects which share an inertial or accelerating frame of reference. (While we may have difficulties with accelerations, light does not.)
Where two objects are in motion relative to one another, the same photon moving between the two objects, whether they are inertial or accelerating, will also travel the proper distance between the two, as defined by the location of each object in space, at the instant of emission and absorption or reflection, by each of the objects.
This does not establish a preferred frame of reference, all it does is establish that as far as a photon is concerned it always travels the proper distance between two points in space. The photon's velocity is unaffected by the velocity of its point of origin or destination.
origin said:
If 1 twin flys to a planet 4.6 light years away a 0.975c he will have a very different measurement of the a light year than the stay at home twin. the traveling twin will say the planet is about 1 light year away and the stay at home twin will say the planet is 4.6 light years away. Even if the flying twin were to flash a pulse of light he would measure the speed of light a c AND it would take about 1 year to reach the planet.
This is accurate, but it assumes that the traveling twin measures distances with his/her length contracted ruler. However, that same twin would have known the proper distance to his/her destination, before beginning the trip. And the only practical way for the twin to measure the distance is with light, and his/her calculations must account for the fact that the length contraction he/she experiences in the ship, has no affect on the light he/she uses to measure the proper distance to the destination.
Remember we are limited here to flat space. While there is good reason to accept that objects in motion do become length contracted. Planets and stars don't get closer together just because we are moving. Though there are times that may appear to be the case.
In the twin paradox, time dilation becomes reconciled when the twins meet after the trip and compare clocks. Unfortunately, their rulers do not retain a memory of having been length contracted. So the returning twin must accept that he/she did just travel, the proper distance between the two planets.
Remember we are staying in flat space and space does not change shape or curvature.
origin said:
Saying proper distance is confusing because you are talking about the proper distance from in one reference frame. It is not possible for a space ship in one reference frame to somehow know the proper distance of another reference frame and use that in a calculation to determine the speed of an object.
Proper lengths and distances are agreed on from all frames of reference, and any observer in a spaceship with a relativistic velocity would have to understand time dilation and length contraction sufficiently that even without bouncing a laser off of their destination they could transform distances between frames. The only time this would be untrue is where the traveler was unaware of "who" or "what" was actually moving.
The fact that the traveler knows his/her own velocity relative to his/her starting point and/or destination, provides the only information required, in addition to the round trip time of light between the ship and it's destination to determine the proper distance between the two.
Though there remain questions about empirical proof of, length contraction of objects is well supported by proof of time dilation. There is nothing outside of GR and the curvature of space/spacetime, that supports and similar contraction of "distances". Even the length contraction of objects is indirect.