Do you think you could argue that in court for failing to stop at a stop sign? It was reported by the defendant Ed Wood; "I wasn't accelerating or decelerating so I must have been at rest" "Rest is equivalent to stopped your Honour".
Everyone and everything is moving, in about 17 directions at once. That number could be maybe 13 or some other teen... I forget exactly... But no matter.
All motion is in relation to other motion from the tiniest difference to the speed of light. We're all moving relative to something else... We're all 'relatives' in one big relativistic family. When one is said to be at rest compared to what they can see of things around them.., it only means they are within the same gravity field. At least for all that counts... But that specific field is still in motion relative to everything else not moving at the same speed and direction as they... Their atomic speed of operation, or aging.., being dependent on that gravity field... The more gravity, the slower they age... And of course there are still minor differences within that over all field.., just as there are here on earth, according to direction and speed of movement within that local field... Mountain tops to sea level or between southern India and the NW Pacific both at sea level...
Earth in fact is a vehicle in space and it is undergoing the very same forces that any other vehicle would be incurring when traveling through space... It is earth's traveling at high speed through the gravity flux of space that brings on the 'feel' of gravity under our feet. Earth and humans are attracted to each other. Our own bodies are generating their own mass gravity too... Really inertia produced by the mass and velocity through the flux, exactly as with the spaceships... The two attract each other... What I see as clearly likely is that with enough velocity, through a no friction environment.., the ship's passengers will be able to carry some air with them and walk about on the outside of the spaceship without magnetic shoes, etc... They're own speed giving them their own gravity.., along with the ship creating it's own gravity too, the two will cling together, as we do with the earth.., and as the salt grains tended to do in the experiment carried out in the space lab... That salt of course not knowing what time it was... lol
Continuously applying acceleration will bring on continuing compression to the mass that is being accelerated. Acceleration does shrink things while it is on going... As with the elevator example... The elevator starts up and compresses the soles of the shoes you're wearing. They being held in place by the inertia of your body mass above. So your head doesn't start to move upward right away...
That upward moving compression of the shoe soles is then applied to your actual feet.., as even more acceleration and thus even more compression is applied to the soles of the shoe soles below... Continuing to accelerate, each bit of increased compression is applied to the soles of your shoes and works it way up through your body to your head.., which finally starts to move... And so of course the body is shorter... But there is more to it than that...
At this point the compression is released out the top of your head... So there is a limit to how much it can affect you.. Only compressing while contained within the body, working its way upward to the head. As the 'entire' body starts to move upward., the shoes will become more in tune with the previous acceleration and will be moving with it. The limit is that the more and more acceleration compression that is applied to the feet, the more and more is then released from the head. And it is only the difference that is being applied at any one time... So there is a limit to the amount of compression when using a linear rate of increasing acceleration... But there is more to it than that...
More compression can be applied to the body, making it even shorter.., if the rate of acceleration itself is increased... If the same maximum rate of speed was reached in only half the distance.., the body would be compressed that much more.., while traveling that distance.., but as the acceleration, in either case, stops.., 'whatever' compression that was contained in the body at the time will be dissipated out the top of the head, as it finally comes to be moving at the same speed as the floor... It all washes... The body is compressed by the rate of acceleration for the duration of the acceleration...
But there is more to it than that...

As the compression starts at the bottom of the shoe.., in reality there is nothing to keep the upward compression from expanding in all directions. It will actually radiate in all directions other than that from which it comes. Similar to a balloon you push your finger into... Or the photon traveling through successive slits...
The compression will start to dissipate almost instantly from the sides of the shoes.., and the tops of those shoes.., and outward laterally all the way up your body... It will compress outward to whatever point ceases to be called 'you' and then escape... Only the compression that is applied directly under the ankle will be transmitted upward. That then will be radiated out along the length of your legs.., the only part that will still be there is that which managed to retain it's upward direction and passes through the hips into the body itself. Where of course it does the same...
We're nothing more than containers of water... We're basically fluid and will behave more or less as fluid under various scenarios. While in many cases still maintaining the perspective of ourselves that we've always had in more usual circumstances... Because whatever is affecting our bodies is affecting everything else too. Keeping all the relatives together... It's nice to have family...
That stop sign of yours is one of the minor differences that occur within a gravity field... The law is written that your car must come to rest relative to the sign..., not your own rest within your vehicle...

I think relativistic mass must be relativistic because that's what it's called...? Some of us are really getting down to basics here... lol
There is the difference of gravity strengths which create the various rates of aging at the atomic level... Ergo each gravity field has it's own preferred frame of reference... When one is covering the same ground as another., but A is doing so seemingly faster than B.., there is what is called relativity... I say seemingly faster because when they both come together again.., their trip mileage planned on earth and executed in space is the same... What really happens is that they are simply aging slower in the increased gravity they incur while speeding through space... Their bodies age slower.., and their clocks run slower too... All is at rest withing the space ship... And they 'think' their year is an earth year... But only because they're not looking at earth.., and counting it's orbits around the sun... If they did.., they would *know* their clocks and minds are all being affected by the trip itself... They're not really taking less time to make the trip than was planned on before starting... They just aged slower than earth so it appears to them on return that gravity did them a favor by keeping them in partial suspended animation. Also helping to reduce the boredom of the trip... The gravity of the situation was being applied to their preferred reference frame... Like the steak in my freezer... It's been there for a year, all the time thinking it's still warm and cozy from just being cut from a steer a minute or two ago...
Nothing could control time even if it was there... How would they do that anyway...
It is gravity that does it.., and everyone knows it. They are not causing the earth do orbit faster... Because it doesn't orbit faster... Nothing is actually different except the rates of aging and therefore perceptions. There is no actual time to stretch or compress... If our perceptions are already slowed.., why would time need to adjust itself to match..? To make us well again..? How very considerate...
'Relativistic' mass never actually 'increases'... It only appears to increase to those who aren't really there... It's done with math.., using the confusion factor of 'time'...
If there are ten years between departure and return of a space ship.., and that space ship experiences only five years going by their slower perspective.., then as those on earth look at the spaceship.., it probably goes like this...
They will see in their math that all that space ship did had been compressed and 'shortened' into five years... That 'time' shrunk for them... That the distance they traveled had to be squeezed into five years.., and so the length of the ship also has to be shortened to half it's length... I mean.., if one were to continue time dilation which squeezes the distance.., and not shorten the ship..? Eventually the ship would be as long as the distance of the trip... Ya know..?
So.., when the ship and everything in it is shortened by so called 'time dilation'.., its compactness or density is supposedly increased and therefore mass is said to increase... Although inversely proportional to size so no net weight gain.
Is that about right..? Or exactly right... It's all an illusion, created by using imagined time.
Take you time and..., think about it. lol