You may think you've seen this before, since I've seen similar discussions in the archives of this, but I think I've distilled the thoughts down to a couple of facts that contradict the common beliefs regarding relativity. Let me preface this with a basic observation: Lorenz invariance does not apply between things that change their inertial frame of reference. The transforms state that all frames are equivalent, not that there is no difference between them, or that experiments that cross between frames will always produce the same results. The contradicting statements are as follows. If either of these is mistaken, please let me know where I can find a reference. 1. Velocity is always relative, not absolute. 2. When an object decelerates, time dilation decreases. For the second statement to be true, there must be a difference between acceleration that increases time dilation and acceleration that decreases time dilation (a.k.a. deceleration). When thinking about this, please remember that we aren't talking about two objects and their relative movement, but also talking about the typical speed of the rest of the universe in relation to those two objects. For General Relativity, we know that moving things out of a gravitational field will decrease time dilation. It's pretty obvious that, just by measuring microscopic differences in time dilation, we could identify the direction of the gravitational gradient (even if we couldn't feel it) and follow that arrow to a point of minimal gravitational dilation. An absolute zero might not be possible simply because there is nowhere in the universe that doesn't feel the effects of other gravitational bodies, but you could still follow the gradient. Similarly, it should be possible to follow such a gradient towards an absolute zero velocity. Again, no more achievable than absolute zero temperature, but if you can measure a gradient, you can follow it. If you can follow it, then it must lead somewhere. My conclusion is that there must be an absolute zero velocity, even if such a thing is meaningless for the purpose of Lorenz invariance. Thoughts?