Interstellar Travel Without Propulsion or Time Dilation

[Yemmy]

I hope this is the right forum for this question.
Imagine alien tech allows them to travel 1 million light years to Earth instantaneously.
No thrust, vector, propulsion was involved. They didn't have to approach the speed of light, with its attendant increase in mass.
Having arrived at earth, in the same Earth minute they left home, they look back at their point of origin and the light they see is 1 million years old.
Where in time is our alien?

 

[Orodruin]

You forgot to specify the following:

1 million light years to Earth instantaneously.

In what frame?

Where in time is our alien?

In what frame?

 

[Ibix]

To expand slightly on Orodruin's answer, "instantaneous" doesn’t have a unique meaning in relativity. It's rather like describing a shelf as being "at the same height" without specifying what it's the same height as.

Depending on who defines "instantaneous", then "the same time as the alien left,on Earth" could mean anything in a two million year period, the time when a radio pulse that will reach the alien as he leaves left Earth to the time when a radio pulse sent by the alien as he leaves reaches Earth.

It's also worth noting that faster than light travel can lead to causal paradoxes. You may wish to google for the tachyonic antitelephone, which is a formal version of the go-back-in-time-and-shoot-your-grandfather paradox.

 

[DrStupid]

Where in time is our alien?

As the jump is defined to be instantaneously, it would be in the same time in the frame of reference the definition refers to.

 

[DaveC426913]

Having arrived at earth, in the same Earth minute they left home, they look back at their point of origin and the light they see is 1 million years old.
Where in time is our alien?

Right. So he can see himself leaving his home planet.

And now you see why a magic faster-than-light drive results in a paradox.

 

[jbriggs444]

Right. So he can see himself leaving his home planet.
And now you see why a magic faster-than-light drive results in a paradox.

Seeing something in the past does not entail a paradox. One can look into a mirror and see the past quite easily. It takes a bit more framework before one can turn faster than light travel into a paradox, e.g. https://en.wikipedia.org/wiki/Tachyonic_antitelephone

 

[Jonathan Scott]

Travel or communication faster than light in a specific frame does not necessarily cause causality paradoxes, although any preferred frame which allows this (like the common science fiction concept of "subspace") violates the principle of relativity. It is only if communication a finite amount faster than the speed of light is possible in all directions in all frames that causality problems like the tachyonic antitelephone arise.

 

[DaveC426913]

Hm. I'll try to defend that.
In my readings somewhere, there is an assertion that, as soon as you have a wormhole that can make an instantly traversible trip between two points, it is tantamount to having a time machine.

Essentially, if you can put the exit at a different spot in space, it is just as easy to put the exit at a different spot in time.

I don't think it should matter how you get from A to B faster than c, just that you do. And therefore a spaceship should have the same ability as a wormhole.

I'll have to go looking for it. Pity you can't do Ctrl-F on dead-tree books.

 

[PeterDonis]

In my readings somewhere, there is an assertion that, as soon as you have a wormhole that can make an instantly traversible trip between two points, it is tantamount to having a time machine.

This is true, but a wormhole is not the only way to have FTL travel, and the reason the wormhole has this property is not that it allows FTL travel. It's something stronger: a spacetime with a wormhole in it has a different topology from a spacetime that doesn't. It's the different topology that creates the conceptual problems with wormhole spacetimes, not just the enabling of FTL travel.

 

[DrStupid]

I don't think it should matter how you get from A to B faster than c, just that you do. And therefore a spaceship should have the same ability as a wormhole.

I don't think that there is any doubt about that. The point ist, that the violation of causality doesn't happen in the frame with v>c but in another frame, moving with the speed u with u·v>c².

 

[Yemmy]

So much great material in these answers! Thank you.
My idea was making the move outside of our universe, outside of Eisteinian space time. So no wormholes.
Thanks again, all.

 

[phinds]

So much great material in these answers! Thank you.
My idea was making the move outside of our universe, outside of Eisteinian space time. So no wormholes.
Thanks again, all.

There is no such thing as "outside of our universe"