Unsophisticated, theoritical implications of time dilation between 2 worlds

[CastorRuss]

Putting all practical implications aside, I was thinking about the idea of another planet that travels around the sun faster than Earth. I know that some planets do, but let's say that some day in the future we were able to create another planet, called Earth 2, that traveled around the Sun at a speed near the speed of light. Let's also say that somehow it was fairly easy and quick to move between Earth and Earth 2. So in this scenario, could someone from Earth 2 travel to Earth, spend a few years, and then go back to Earth 2 to find that only a few weeks had passed? The implications of this are amusing and interesting to think about and I was wondering if it is either wrong, correct, or simply possible or probable.

 

[hamster143]

It would work the other way around. If Earth 2 is moving sufficiently fast, you could spend a few weeks on Earth 2 and discover that a year has passed on Earth 1.

You'd need some extremely powerful engines to keep it in orbit, of course.

 

[JesseM]

It would work the other way around. If Earth 2 is moving sufficiently fast, you could spend a few weeks on Earth 2 and discover that a year has passed on Earth 1.

That's actually equivalent to what CastorRuss said--the idea was that if you were a native to Earth 2 but you took a vacation on Earth 1, then when you returned you'd find that less time had passed on Earth 2. Either way you put it, the idea is the same: time goes by slower on Earth 2 than on Earth 1.

You'd need some extremely powerful engines to keep it in orbit, of course.

Right, you couldn't have a natural (free-fall) orbit at relativistic speed around an ordinary star. Maybe you could have a natural relativistic orbit if the planet was just outside the photon sphere of a black hole, though (though I don't know if such an orbit could be stable, I know photon orbits on the photon sphere are unstable).

 

[CastorRuss]

Thank you for the responses. I have a follow-up question, though I recognize that it probably has to do with my lack of understanding of Einstein's relativity so it may not be easy to explain to me.

In this hypothetical where there are 2 Earths, and Earth 2 moves at a speed near the speed of light, let's say it is nonetheless very close to the Earth. Perhaps it would be easier to just imagine a rocket ship rather than a second Earth, but anyway...

My question is about how Earth 2 would receive signals from Earth 1. Because, for example, what is 1000 years relative to Earth 1 may be only 1 year relative to Earth 2. So say that Earth 2 is picking up radio signals from Earth 1. If they are right near each other, you'd think they would pick up the signals only moments after they are being sent. So then... would Earth 2 somehow pick up 1000 years of radio signals in 1 year? Or would it get the radio signals at the same rate they were sent, somehow?

To ask the question another way- let's continue to say that the distance from Earth 2 to Earth 1 is not far, and a person can easily travel between them via a transporter. Let's say that the travel time between the two Earths, in Earth 1 time, is 1 day. So, a person on Earth 2 is on their transporter, about to leave, and the last radio signal they hear from Earth 1 correctly states "It is now January 1 of the year 10,000!" When this person arrives on Earth 1, will it be January 2, year 10,000 there? Or will it be more like the year 11,000?

Essentially, I am confused about the rate at which Earth 2 would receive Earth 1's radio signals.

 

[CastorRuss]

Any takers on that one?

 

[JesseM]

My question is about how Earth 2 would receive signals from Earth 1. Because, for example, what is 1000 years relative to Earth 1 may be only 1 year relative to Earth 2. So say that Earth 2 is picking up radio signals from Earth 1. If they are right near each other, you'd think they would pick up the signals only moments after they are being sent. So then... would Earth 2 somehow pick up 1000 years of radio signals in 1 year? Or would it get the radio signals at the same rate they were sent, somehow?

If Earth 2 is rotating around its sun (or black hole) at relativistic speeds so that its clock is ticking 1000 times slower than Earth 1 in the common rest frame of both suns (assuming the suns themselves are at rest relative to one another), then if Earth 1 sends out a signal once per year according to their clock, observers on Earth 2 will get 1000 signals a year according to their own clock's definition of "a year" (since it actually takes 1000 years for their clock to tick forward by 1 year in the common rest frame of the two suns).

To ask the question another way- let's continue to say that the distance from Earth 2 to Earth 1 is not far, and a person can easily travel between them via a transporter. Let's say that the travel time between the two Earths, in Earth 1 time, is 1 day. So, a person on Earth 2 is on their transporter, about to leave, and the last radio signal they hear from Earth 1 correctly states "It is now January 1 of the year 10,000!" When this person arrives on Earth 1, will it be January 2, year 10,000 there? Or will it be more like the year 11,000?

I don't know how a "transporter" is supposed to work, but let's just assume the person travels on a spacecraft moving at relativistic velocity and that it takes 1 day to travel between the two systems. Then if they leave Earth 2 when Earth 2 gets a signal saying it's 10,000, in the common rest frame of their two suns less than a day will have passed since Earth 1 sent that signal, so it'll still be 10,000 on Earth 1 in this frame at the moment the traveler leaves. Then if the traveler takes 1 day to reach Earth 1 in this frame, it'll still be 10,000 on Earth 1 when they arrive.

 

[CastorRuss]

Makes sense, thanks.