# Time Dilation and Interplanetary Migration

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1. Jan 2, 2016

### SharkySharp

In various documentaries they bring up the argument that we wont be able to visit other stars because even if we would travel with the speed of light, it would take xxx years, since the next habitable planet is xxx lightyears away.
BUT: What about time dilation? If an object approaches light speed, time from its point of reference moves very slow. At lightspeed time stands still.
My conclusion: If we can travel fast enough (but still SLOWER than lightspeed), we should be able to travel for example 1000 lightyears in just 10 minutes (in the meantime on earth, more than 1000 years pass).
Where do i go wrong here? Or are these documentaries just wrong?

2. Jan 2, 2016

### phinds

No, it its own frame of reference time moves for EVERYTHING at one second per second. You are thinking of length contraction.
No, to say that time stands still at light speed is extrapolating the math into unphysical territory and implies that there is such a thing as a reference frame for a photon, which there is not.
This part is correct. You didn't go wrong anywhere. Pop science is dreadfully wrong much of the time. It is extremely unlikely that we will ever achieve anything like a sizable fraction of lightspeed. In fact pop sci tends to be overly optimistic in that regard, while ignoring length contraction.

3. Jan 2, 2016

### Ibix

10 minutes is rather optimistic unless you intend to arrive smeared all over the back of the ship, but you are basically correct (with the exception phinds noted). The energy requirements are quite horrific, though, enough to be prohibitive even if you use the most efficient possible fuel.

4. Jan 2, 2016

### SharkySharp

Thank you phinds and Ibix, for clearing that up. <3

5. Jan 2, 2016

### pervect

Staff Emeritus
For some figures on travel times, take a look at http://math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/rocket.html. A continuous acceleration of 1g is assumed. The energy cost is neglected -

The main article also has the rather discouraging numbers about the fuel/payload ratio requirements for an ideally efficient photon drive rocket. The best theoretical designs for a beamed-core matter/antimatter rocket I'm aware have a projected effective exhasut velocity of perhaps .69c. See http://arxiv.org/abs/1205.2281 "Beamed Core Antimatter Propulsion: Engine Design and Optimization". Assuming you could get 1g out of such an antimatter drive without it melting (which is rather unlikely), you'd need over 38 kilos of antimatter for every kilo of payload and structure to reach the nearest star and stop, 10 kilos of antimatter per kilo of payload to do a flyby.

So if one doesn't care about Earth time anyway, I've always thought that some form of suspended animation or perhaps life-extension would be the preferable choice, a biological solution rather than trying to get to relativistic speeds. Of course, there are some rather severe problems with keeping a closed spaceship system operating for centuries, not only in the power generation (though it would take significantly less power than achieving relativistic speeds), but preventing loss of material (atmosphere and such) from the system. Not to mention the 100% recycling needed.