2
$\begingroup$

The scenario I'm envisioning is this: A spaceship ("the ship") departs from a rest position ("Point A" or "the planet"), and travels at a relativistic speed towards Point B. At point B lies a wormhole, which topologically connects to a position right next to the planet. The wormhole does not translate the ship in time, relative to the observer (the planet).

By my understanding of the symmetry of velocity-induced time dilation, both the planet and the ship should regard the other as having aged unusually slowly during the trip. As soon as the ship arrives at Point B, it can pass through the wormhole and arrive next to the planet (still travelling at full speed).

What are the relative dates/ages at the moment of this event? It seems like the ship should see itself entering the wormhole at an earlier date than the planet sees it enter. I can't wrap my head around the specifics well enough to make a prediction.

Below is a diagram that assumes that the ship departed in 2000 CE, and that time dilation slowed clocks by 50% over a 2 year (planet time) journey.

enter image description here

$\endgroup$

1 Answer 1

4
$\begingroup$

The wormhole does not translate the ship in time, relative to the observer (the planet).

This is the key point. In the frame of the ship, the wormhole does translate the ship in time. This is because simultaneity is relative. The two events "ship enters wormhole" and "ship exits wormhole", which are simultaneous in the planet frame, are not simultaneous in other frames.

In the planet frame, your ship travels for 2 years and then emerges from the wormhole 2 years after it departed.

In the ship frame, it travels for 1 year, and only half a year passes on the planet. However, the wormhole moves the ship "into the future" in its frame, so that it emerges to a find a planet on which 2 years have passed.

$\endgroup$
2
  • 1
    $\begingroup$ But the mouth of the wormhole (and the planet seen through it) has the same relative velocity to the ship as the planet, so it would also have aged half a year since departure, in the ship's frame. Wouldn't that require that the planet through the wormhole started out being 1.5 years older? Or am I failing to grok part of the simultaneity behavior? $\endgroup$
    – Arkathorn
    Aug 3, 2023 at 13:31
  • 1
    $\begingroup$ @Arkathorn Transforming into the ship frame, from the planet frame, is what makes the wormhole ends become desynchronized. The transformation (a "Lorentz boost") is like a rotation in spacetime. An analogy is to imagine that two objects are at the same height, but then you change your reference for what "up" is -- the objects are then no longer at the same height. It's similar in spacetime: the Lorentz boost changes "which direction time is". $\endgroup$
    – Sten
    Aug 3, 2023 at 14:09

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .