NewDescartes said:
Objects are definitely relative to one another. If I am moving towards an object that is moving towards me, it looks like the object is getting closer.
When did I say otherwise? My point was that there is no absolute truth about which of two objects is moving at a greater speed, whereas there is an absolute truth about whether a given object satisfies the definition of a black hole, it's not a frame-dependent thing (see below).
NewDescartes said:
If I am accelerating toward an object that is moving away from me at V< A, it also appears that the object is moving closer to me.
V < A doesn't even make sense as an equation--are you unfamiliar with
dimensional analysis? You can't have an inequality where one side involves a velocity and the other involves an acceleration, because which side is bigger will depend on what choice of units you happen to make. For example, would you say V < A if V=60 meters/minute and A=360 meters/minute^2? But wait, 60 meters/minute translates to 1 meter/second, whereas 360 meters/minute^2 translates to 0.1 meters/second^2. So are you going to say V < A if we use units of meters and minutes, but V > A if we use units of meters and seconds? That doesn't sound very physical.
And even if we settle on a particular system of units like meters and seconds your statement isn't true. Suppose in some frame at time t=0 I am at rest (v=0) and another object is moving to the right at 5 m/s. If I am accelerating to the right at 10 m/s^2, then my velocity as a function of time will be v(t) = 10*t, so my velocity will match that of the other object at t=0.5 s when my velocity will be 5 m/s to the right. Between t=0 s and t=0.5 s, my velocity will be less than 5 m/s, so since the other object is moving to the right at a constant speed of 5 m/s, prior to t=0.5 s the distance between me and the other object is increasing, not decreasing. Only after t=0.5 s am I getting closer to the object as time passes.
NewDescartes said:
An object moving away from Earth @ .999999% the speed of light creates a massive redshift in the light rays, effectively making the information from Earth irretrievable on that object, a black hole.
No, part of the definition of the term "black hole" is that it's an object with an "event horizon" such that it is
impossible for light emitted from events inside the event horizon to escape to the outside, whereas you're talking about a situation where the light from an object can reach us but it's just so redshifted that it'd be very hard to detect in practice. And you didn't reply to my more recent post where I pointed out you can always use a network of local observers who measure the object as it passes right next to them.
NewDescartes said:
Your comment "practical difficulties aren't relevant to a description of a theoretical problem" is a totally ignorant statement. Solving practical difficulties is the sole purpose we do physics.
Theoretical physics involves taking results of practical experiments and abstracting them into a general set of mathematical rules. As long as a given experiment would be possible
in principle it can be a topic for a theoretical discussion about what these mathematical rules would predict for the results, regardless of the practical difficulty of actually carrying out the experiment (we can always hope that better technology would make previously-impractical experiments practical). You should be aware that the very concept of a "black hole" is something that originally arose purely from the theory of general relativity rather than any actual observations at the time, and that even today we can't verify with any great certainty that any real astrophysical objects have all the properties predicted by the theory (including the event horizons which are part of the definition of black holes).