[weavejester]

Suppose you set off in a spaceship at 80% of lightspeed, or 0.8c, travelling away from Earth. At this speed, according to relativity, time is slowed to 60% of it's 'usual' value. So for every 10 hours that pass on Earth, only 6 will appear to pass on the spaceship.

However, this is only true from the perspective of someone on Earth. From the point of view of someone on the spaceship, the opposite is true. From their perspective, the spaceship is stationary, and Earth is travelling away from it at 0.8c. Therefore, for every 10 hours that pass on the spaceship, only 6 will appear to pass on Earth.

Suppose there was a way of instantaneously communicating between the two. On Earth, 10 hours into the mission, mission control sends a message to the spaceship. Because of time dilation, the spaceship receives the message only 6 hours into the mission, from their perspective. The spaceship then sends a message back, and due to the same time dilation effect, the message arrives on Earth 3 hours and 36 minutes into the mission (60% of 6 hours). In other words, the reply from the spaceship will arrive 6 hours and 24 minutes before mission control sends the original message.

[trhway]

>On Earth, 10 hours into the mission, mission control sends a message to the spaceship. Because of time dilation, the spaceship receives the message only 6 hours into the mission, from their perspective.

And from their perspective - "for every 10 hours that pass on the spaceship, only 6 will appear to pass on Earth." - the message was sent at 3:36 of the Earth time. They immediately send a response message which immediately arrives at 3:36 of the Earth time from their perspective. No paradox so far.

[AnimalMuppet]

There's a paradox if the message replies to the first message, because the reply arrives before the original message is sent.

[trhway]

>because the reply arrives before the original message is sent.

from which POV? From the ship's POV - the message is sent at 3:36 Earth time , and the immediately sent reply is received at 3:36 Earth time.

[AnimalMuppet]

From Earth's POV.

[trhway]

From Earth's POV - the message is sent at 10 of Earth time which is 6 of the ship's time from the Earth's POV, the reply sent and received immediately at 6 of the ship's time which is 10 of the Earth time from the Earth POV.

[weavejester]

There's no absolute reference frame here.

From the perspective of someone on Earth, when it's 10:00 on Earth, it's 6:00 on the spaceship.

But from the perspective of someone on the spaceship, when it's 6:00 on the spaceship, it's 3:36 on Earth.

From the ship's reference frame, Earth is in the past; from Earth's reference frame, the ship is in the past. If you have superluminal communication, the Earth can send a message to the ship's past, which can then send a response to Earth's past.

[drran]

If you use a mobile phone, you can reply to the second message (by network) before the first message will reach you (by air), so you can break causality and travel back in time!

[Sanguinaire]

I'm in the same boat as the person you replied to; breaking causality never made sense to me.

In the case of your explanation, what sticks out to me is the "Suppose their was a way of instantaneously communicating" part - it seems more intuitive to me that the warp bubble would not allow any communication across the threshold, effectively becoming a pocket universe.

[NoGravitas]

The ship you're in isn't what's traveling FTL, though; it's going at normal relativistic speeds. But say both you and Earth have an ansible (a faster-than-light communicator); then you get the problem in the previous comment.

[AnimalMuppet]

And, any FTL travel can be used as an ansible.

[weavejester]

Instantaneous communication makes the numbers easier because you don't have to account for travel time, but causality can be broken with any superluminal form of communication.

If you have a ship with warp speed, then you have superluminal communication, because you can just carry a message on board. Even if you can't communicate inside the warp bubble, as long as you can exit the bubble at some point, then you can travel via warp, pop out, and transmit your message conventionally.

In my earlier example, if the ship and mission control had messenger drones capable of travelling many times faster than light, then the ship's response drone could arrive on Earth before mission control's messenger drone was launched.