Since no one seemed to reply to my prior messages regarding this I must have not explained myself very well. I will try to restate my (mis)understandings of GR, and if no reply, I'll drop it and try to figure it our for myself.
Let’s say there is I, who is in an area of space that I will initially assume is removed from any significant curvature, meaning that the space around me is of uniform density. I walk thirty feet in the y direction and place a dog (point A) that stays stationary. I then return to my original position and walk 40 feet into the x direction and place a bone (point B). If I then return again to my original position and view both the dog and that bone at the same time there are a few things I can assume to be true.
Firstly I can rightfully assume that the distance between the two, from point A to point B is 50 feet, simply from PT. I can also assume that if the dog traveled at a constant velocity with respect to point A from point A to point B I would see it move at a constant velocity as well. I can finally assume that the time I would measure as the dog moves from point A to point B would be slightly more than the time measured by the dog (if it had a clock) according to the Lorentz transformation, and along with this, a calculation that would result in a slightly greater distance. Since I know this I can account for it and come to the conclusion that the 50 feet is correct.
I now watch the dog travel to the bone along a straight line at a constant velocity, say 5 feet per second, and admire its behavior. Unbeknownst to me there is an enormously massive object lying slightly off of the course that the dog must take to get to the bone. Because of this the space right in the middle of the path has severe curvature. This curvature will cause two things to occur.
1) The velocity of the dog will not appear to be uniform from my perspective.
2) The time I measure for the dog’s journey will be even greater than the time allotted for the Lorentz transformation.
This begins to trouble me and I begin to think that the dog didn’t go in a straight line at a constant velocity. I decide to take the trip myself by walking out to point A and traveling to point B. I will measure the distance I cover in space by using my constant velocity (still 5 feet per second) times the time I record.
I realize that what would actually be experienced is I would measure 10 seconds and assume 50 feet. In fact, I would actually travel more space per unit time in the severely increasingly curved volume and less space per unit time in the severely decreasingly curved volume. I wouldn’t “feel” any of this so I would still be justified in saying that I was in uniform motion. I will be surprised however, when I measure this distance using the same yardstick as before to be 60 feet instead of 50 since my motion was uniform (5 feet per second) initially with respect to point A.
This is where I am confused. Can I look from point A to point B and "see" 50 feet, but measure 60 feet? Am I justified when looking from the origin to assume 50 feet? I would assume not considering the true distance is 60 feet. Would it actually appear this way or am I confusing two issues here?
According to the dog that has gone to my original location (origin), my motion wasn’t uniform and the time it took me to traverse this space is longer on its clock (assuming it is wearing one) than on mine. Using this model though, how is it that the time measurements will differ? I understand that my motion through time will decrease while the dog’s remains the same (all motion is through time), but where is the physical representation of this occurrence? How is it that uniform motion through curved space actually increases, or decreases, your actual velocity with respect to another body? What is the element responsible for this? Do I even have an accurate understanding of this situation?
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