Negative Acceleration does not exista supplement to the paper, Time's Paradigm, stating that if nothing decelerates we are all continuously gaining mass 
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In a Universe governed by Special Relativity (SR), there can be no deceleration, we are all constantly increasing our velocities and our mass as we head towards the speed of light (c).
While mathematics requires negative acceleration and negative velocities to express clarity of motion surrounding a frame of reference such as our planet or sun, within any standard thought experiment involving spaceships and cosmic bodies in motion, where nothing is stationary and no observer knows true velocity, there can only be positive acceleration. Of course, the quick reply is "everything is relative", even acceleration, because a point of reference must be nailed down in order to contemplate motion of any kind  but hang on! Is it not fairer to suggest that only negative acceleration is relative, and that positive acceleration is, actually, absolute?
Here's why:
1. Two solar systems are moving away from our point of reference at about the same speed, one (A) to our left, the other (B) to our right. An astronaut accelerates her ship, in her view, departing from A towards her objective, B. We are near stationary from our perspective somewhere in between the two systems. As she approaches us and before her flyby she will at some stage appear to have decelerated to near stationary.
2. Firstly, it stands to reason that if the body from which she departed was heading away from us and she was heading towards us, then her accelerating departure would appear to be deceleration, as observed from our frame of reference.
3. From her frame of reference, however, she would consider she was accelerating to catch up with us. She would even pass right through this imaginary stationary point of ours without even knowing or feeling anything. So, is it relevant to anyone but us? Is it real at all?
4. The astronaut does not know (nor anyone for that matter) the actual speed of the inertial frame of reference she left, so she assumes she is heading towards (c). She does not factor in any possible deceleration, even though she can see our reference frame out there in space, because for her we are moving away. Does this mean that there is no such thing as deceleration in the Universe?. She added energy, and off she went. If so, then we are all accelerating, we are all gaining mass in whichever direction we travel. SR demands that we gain mass (albeit relativistic) as we accelerate, so we are constantly increasing in energy and so mass.
5. What is our astronaut, therefore, doing? Accelerating, decelerating, both or neither?
6. Deceleration is physically the same as acceleration. When you fire rockets to decelerate you feel the gforces. You are adding energy to the system. Relativity says that all motion is relative. Deceleration in one frame of reference can be acceleration in another. Therefore, we are all always accelerating; always adding energy; always gaining in mass.
7. If, as described above in point 1., there were only these four inertial frames of reference in the entire Universe, none would be stationary, not even ours. We would all together be a system with its own trajectory.
8. Deceleration, or negative acceleration, could then only be possible in this larger system's opposite direction. If only the Universe were that simple!
9. It could be suggested that, by returning to her point of departure, the astronaut might reduce the increase in mass associated with her original acceleration from system A, but this is a mere local event. Other observers might consider her speeding spaceship to be at rest from their point of view, so her return is simply more acceleration. For those who never return to their point of origin, clearly an increase in mass and velocity is inevitable.
10. Rockets and spaceships are necessary examples used to describe relative motion, but they have some 'realism issues'. To boost a rocket we fire particles out of an engine in the opposite direction to achieve acceleration. Newton's equal and opposite law evoked. Does that not mean that these particles are travelling in the reverse direction at the same speed or even faster than our rocket? What happens at relativistic speeds?
11. It has been argued many times before that the above paragraph does not really matter, as we are doing a thought experiment, not conducting a real flight. But it does matter!
12. Where is all this energy for acceleration coming from? If every body is accelerating then there is no way to receive energy by collision or propulsion, as such means would naturally produce deceleration in the opposite direction. Unless, that, too, is acceleration; in which case, no energy was transferred between bodies as they were both accelerating away from each other  and the 2nd law of Thermodynamics curls its toes.
13. At some stage in the distant future, then, we may all find ourselves travelling at near light speed. We would not consider this as such, due to our individual relative platforms, however, it raises another question: Where will this take us?
14. As we are and all other bodies are increasing in energy, mass and velocity, adinfinitum, we will eventually reach a moment where the Universe has no more space into which mass can expanded, it will have infinite energy and time will grind to a halt. Or, perhaps, it just goes on expanding forever, increasing in mass and energy  comepletely at odds with the Laws of Thermodynamics.
15. Alternatively, if time, space and velocity were cyclical progressions, rather than linear platforms on which SR is based, this paradox can be resolved. As proposed on the Home Page of this site, we are all in constant and gradual deceleration. Now, there is equilibrium. We are not all expanding forever towards (c). This hypothesis, Time's Paradigm, suggests that all bodies in the Universe are involved in cycles, that even the Universe must be, in its entirety, one grand cycle, without beginning or end.
Returning to your point of departure, see also: The Twins Paradox Did Twin B really travel in time?
Time's Paradigm is a philosophy of science paper discussing the reality of time. It argues that time is a cyclical fourth dimension, where zero and light speed are attributes of the same event and infinite progression is invalid.
Visit the Home Page for a summary of chapters. Or, Abstract for a more detailed overview.
TIME'S PARADIGM
A synopsis of a work in progress. Copyright: A. Graham, 1988  2016
No unauthorised use of the material published or the concepts described herein is permitted.