Nice try, but obviously the earth spinning, as well as rotating around the sun IS a giant clock, as was pointed out. It doesn't have to be accurate to an atomic clock, you can see that the earth return to the same position, in relation to fixed reference points, (though 3 million years makes that impossible), but as a thought experiment it is quite valid. Way more valid than accelerating a spaceship to close to the speed of light.
Because there are actually objects that have been going around the sun for 3 million years. And there is an object rotating around the earth, like a giant clock. And the earth spins, like a giant timepiece. In fact, we use them to talk about time, all the time.
Forget accuracy to the level of an atomic clock. You can use the moon, the earth, or the sun as time keepers. The point, which is obvious, is that the orbiting twin, or clock, experiences time in a different way.
But if you use an obvious giant clock, the earth, or the moon, they are not moving in the space ships orbit, so they are not effected by the speed, like a clock on board is. But you can still see them from a space ship in low earth orbit. So according to the orbiting clock, or twin, they are moving faster than they seem to the earth bound twin.
So the clock, or twin, in orbit, has a slow clock. Yet, they can see the earth spin, the earth go around the sun, so we have a wonderful paradox. The orbiting clock/twin sees time going faster, based on the clock on board. For all practical purposes, the moving clock/twin is experiencing time speeding up, watching the earth move. If we increase the velocity, (remember, this is a thought experiment, not reality), we can make it so the orbiting clock/twin goes much much faster (remember, we have really long lifetimes for our theoretical twins)
So by increasing the orbit speed, and ignoring the other problems that creates, (just like the original twin paradox thought experiment ignores acceleration and the energy involved), we can end up with the orbiting twin/clock has experienced 2,999,900 years, and the earth clock/twin shows 3,000,000 million orbits of the earth around the sun.
So the moving clock is now 100 years behind. It is the year 3 million, but according to the orbiting clock/twin, only 2,999,900 years have passed. Even when they could see all 3,000,000 years happen.
So from the orbiting clock/observer, time went faster. Obviously if we increase the velocity, we can imagine real time travel. Or reverse the motion, decrease the movement, relative to the earth, and time slows down, from the moving clocks point of view.
This is what science knows happens. Time doesn't change, (the earth goes around the sun, the earth spins, that motion does not change), but the moving observer, or clock, experiences time slowing down, or speeding up. So from this, we know time is a function of the observer, or if you will, a clock in the same motion as an observer.
So what is time? If it is variable, depending on how fast you are moving, or how much gravity you are experiencing, time is not how long something takes, it is how long you observe it takes. Which as we know, is variable, depending on your motion. So now time isn't how long it takes the earth to spin once, or anything really, it is what you measure it to be, based on your position and speed, relative to the earth.
Robinson first define day...
Or are we talking revolutions of the earth?
It doesn't matter how you define it. The atomic clock or the rotation of the earth, both events, observed from the moving space ship, seem to go faster.
So our moving twin sees the same number of rotations, or ticks of the clock, they just seem to go by faster. It doesn't matter if it is years, days, or seconds on an atomic clock, time goes faster, outside the space ship.
So they see 3,000,000 years go by, they just went quicker. 3,000,000 revolutions around the sun, or the same amount of time on a clock, it doesn't matter. Movement, and changes in gravity, cause the speed, or time, of rest of the universe to change, to that observer.
Time on board the space ship does not change. For them. We would see their clock running slower. If they were going really fast, they are traveling in time. Actually, even if you don't go that fast time changes. According to relativity, going up a mountain changes time, as does going deep in the earth, or flying in a plane, time is changing all the time.
So what is time then? Is there really time if it changes? Is the concept of "real" time even valid? If time is different for different clocks/observers, depending on where they are, and how fast they are moving, what does that mean?
You can't slow time down, or speed it up, in the sense that you can live longer. Because your clock, where you are, doesn't change. It only changes in relation to somebody else's clock. But you can time travel, if you go really fast, in the sense that you can speed up the rest of the Universe, by moving very fast.Or, according to experiments, slow the rest of the Universe down, by reducing your speed, in relation to somebody else's clock.
Which, if you think about it, is pretty cool.
Then there is the matter of light, which is another relative issue...