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What does general relativity say about the relative velocities of objects that are far away from one another? Nothing. … Answer: They don't have any well-defined velocity relative to us. The relativistic speed limit of c is a local one, not a global one, precisely because velocity isn't globally well defined. …

Within the context of Newtonian mechanics, there's a simple answer: velocities are not absolute, but differences in velocities are. So you can state that acceleration occurs unambiguously. … In special relativity, this is a bit more complicated because of relativistic velocity addition, but all observers can unambiguously compute a "proper" acceleration for every object, which is the acceleration …

It was found that the velocity profile of the central 20 pc of the gas disk possessed a Keplerian profile (i.e., $v \propto r^{-1/2}$) as expected if the gas was orbiting in the gravitational potential … Note that the measured gas velocities on opposite sides of the central body differ from each other by roughly 1000 kilometers per second. …

difference between Galilean and relativistic velocity addition starts in the fourteenth decimal place. … For example, a satellite in low-Earth orbit has a speed of $$ v = \frac{2\pi R_\oplus}{90\rm\,minutes} \approx 7500\,\mathrm{m/s} \approx 2\times10^{-5}c $$ and so has relativistic corrections $(v/c)^ …

The net momentum of the light will match that of an equivalent mass moving at the speed of the resonator, the net energy will match the relativistic total energy of that mass at that speed, and the net … they are the same as the energy and momentum of an equivalent rest mass with the velocity of the enclosing resonator. …

In terms of relativistic physics: whatever experimental setup you are using: there is no such thing as attributing a velocity vector of the experimental setup with respect to the relativistic Ether. … [Later addition] The underlying point is that relativistic physics attributes physical properties to spacetime. John Wheeler expressed that as follows. …

Next he intends to prove that when the observer locates himself in the frame of the moving test charge, he will see, in addition to the regular electrostatic Coulomb (repulsion) force acting on the test … charge, an additional repulsion in the $+x$ direction whose origin is entirely relativistic. …

Speed has a definite meaning, i.e. , the absolute value of the velocity vector, which is given as $({\rm d}x/{\rm d}t,~{\rm d}y/{\rm d}t,~{\rm d}z/{\rm d}t).$ There is no mathematical meaning in the phrase … In addition recent studies show that an arrow of time exists just because of gravitational interactions . …

In addition, one assumes conservation of momentum. We do a thought experiment involving a closed box containing two objects of mass $\mathtt{M}$. … Due to the recoil of the light, the masses will move, but the velocities will obviously be very small (for macroscopic objects). …

[See Figure 1-(b)] The weird point is that $B$ measures a resultant velocity $w$ for the charge which complies with the relativistic velocity addition as: $$w=\sqrt{(\alpha_uv)^2+u^2},$$ where $\alpha_u … as reaching a terminal velocity of $v$. 2- The experiment is carried out away from any gravitational field. …

The other big misunderstanding was that the x,y and z-components of the velocity operator do not commute while they do so in the non-relativistic theory and therefor the operator must be wrong, they thought … If the inherent M and P values change because of external B and E fields (by addition) then the electron accelerates. Chiral representation Now what about the c in the velocity operator. …

Although made up of non-relativistic atoms, the low-energy excitations of superfluid, i.e. the phonons, are said to be "relativistic". … I believe this should be a fundamental feature of relativity, but I do not see how to prove it. The velocity addition formula for sound is not the same as that for light. …

1-\beta v^1)},\quad \overline{v}^3~=~\frac{v^3}{\gamma(1-\beta v^1)}, \quad\text{(rel. velocity addition)}\tag{14} $$ and $$ \overline{x}^1_0~=~\frac{x^1_0}{\gamma(1-\beta v^1)}, \quad \overline{x … G. van Weert, Relativistic kinetic theory, 1980. …

The relativistically correct speed addition rule is the following: $$s=\frac{v+u}{1+\frac{vu}{c^2}}$$ When $\frac{vu}{c^2}$ is close to zero (in other words when the velocities invloved are much less … As you approach the speed of light, the energy given to you by the force causing the acceleration basically contributes more and more to the increase of your mass and less and less to the increase of your …

This turns out to be true only on a riemannian manifold; the fact this is almost always true in classical mechanics is an "accident" due to the postulates of classical (non relativistic) mechanics. … Because newtonian mechanics postulates state that the state of a system is completely determined by the knowledge of all positions and velocities of its constituents at a given instant. …