Why Faster-Than-Light Travel Leads to Time Paradoxes

Why going faster than the speed of light leads to time travel paradoxes explained in less than 3 minutes. To get to this, we first have to quickly build up some understanding of space-time diagrams like this one. Here the horizontal axis represents one dimension of space and the vertical axis is time. So from the perspective of the Earth, in other words, Earth's reference frame, it isn't moving in space, but simply moves forwards in time like this. To make it more interesting, let's add a spaceship moving away from the Earth at 10% the speed of light C. From Earth's perspective, the ship moves both through space and time like this. The ship's path through spaceime is known as its world line. And the angle between its line and that of the reference frame here, the Earth is the arc tangent of the velocity over C. So here that gives 80° as depicted. So that rule implies an interesting limit. What happens if V equals C? In other words, something is moving at the speed of light. But the angle now equals 45° and we call that a null line. This is what light does. Anything steep in this line would be traveling faster than the speed of light or FTL. Perhaps the most extreme case is something that is anible which means instantaneous. It takes zero time to move a given distance here and thus it follows a horizontal line. Note how anible world lines are always parallel to the sender space axis which is here at the Earth. We need to know one last rule. Space and time distort in relativity. Not everyone agrees on where these axes live. The new axes can be calculated using so-called Laurent transformations. But the end result is that the ship's space axis will be mirrored about the null line. This is sometimes known as the reciprocity of axes rule. And hopefully this makes sense because as the ship slows down to zero, these axes will thus return to their same position as that of the Earth. Okay. Finally, we're ready to see the paradox. First, consider a faster ship, one moving, say, 70% the speed of light. After a certain amount of time, the Earth sends an FTL message to the ship. In fact, an anible one. After the message is received by the ship's crew, they spend a bit of time thinking about what to say back and they finally come up with a reply and send it towards the Earth again using an Anible transmitter. Now remember our key rule. Answable messages are parallel to the space axis of the sender here the ship. So the reply message has to be parallel to this line. Okay. So coming back to our diagram and sending the reply, it returns back to Earth. But look what happened. The reply was received by Earth before the initial message was even sent. This is a time paradox. Causality has been violated. This also demonstrates why observers can't agree on simultaneity in relativity. So, this was a special case of an antible message, but check out our longer video over at the Cool Wars channel where we prove this happens for any FTL message and the bizarre consequences that ensue.