I've always had serious trouble understanding why FTL travel will break causality.
Do you know of any good layman-level explanations?
Like, if I FTL from point a to point b, 10 light years apart, in my super duper warp vessel. It takes me, for the sake of argument, 10 minutes to make that journey. Now say I set off a big comms laser at point a, sending a message to point b, before I left. I don't see that laser until 10 years later.
What am I missing? I know I'm missing something, but that seems straightforward to me. It's weird to butt up against that seemingly incomprehensible.
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.
>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.
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.
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.
>From the ship's reference frame, Earth is in the past; from Earth's reference frame, the ship is in the past.
no. The "when it's 6:00 on the spaceship, it's 3:36 on Earth" doesn't mean "From the ship's reference frame, Earth is in the past". It is just different speed of time. The 3:36 of "slow time" isn't "less" than ("past" of) the 6:00 of "fast time". Say you have 2 clocks, and took one on a spaceship ride. When brought back it will be showing say 6 why the twin clock which didn't left the Earth would be showing 10 - the ship clock wouldn't be in the "past" as both clocks are on the table in front of you in the "present".
> The "when it's 6:00 on the spaceship, it's 3:36 on Earth" doesn't mean "From the ship's reference frame, Earth is in the past". It is just different speed of time.
It amounts to the same thing. From the perspective of Earth, time travels slower on the ship than on Earth. From the perspective of the ship, time travels faster on the ship than on Earth. Superluminal communication allows you to abuse the difference in reference frames to break causality.
Put it another way: when it's 6 on the ship, what time is it on Earth? It depends who you ask. Mission control would say it's 10. The people on the ship would say 3:36. Both are correct.
> Say you have 2 clocks, and took one on a spaceship ride. When brought back it will be showing say 6 why the twin clock which didn't left the Earth would be showing 10 - the ship clock wouldn't be in the "past" as both clocks are on the table in front of you in the "present".
In your example, the ship needs to change velocity in order to get back to Earth and compare the clocks. The ship is not always at rest in any reference frame; it either needs to stop and turn around, or accelerate to catch a retreating Earth.
It just so happens that in this scenario, whatever reference frame you choose, the ratio between the time on the ship and the time on Earth works out to be the same.
But this changes if the ship doesn't need to alter it's velocity. If the ship is travelling at 0.8c away from Earth, then it's equally valid to say that the Earth is travelling 0.8c away from the ship. It is therefore equally true to say:
* For every 10 hours on Earth, 6 hours pass on the ship
* For every 10 hours on the ship, 6 hours pass on Earth
In some reference frames Earth's time progresses faster than the ship; in other reference frames it progresses slower. If you're able to pass around information between reference frames instantaneously, then you can pass information backward through time.
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!
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.
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.
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.
Oh wow, this was fascinating! I was vaguely made aware of some of these concepts by a friend who studies quantum physics, but on he's never been able to explain it so "simply" (that's not doing the explanation any justice, it's not simple and some of it still went over my head, but "it clicked").
We see that matter and energy and all their fields and stuff move through time and space continuously. They don't spontaneously relocate themselves a million light-years away, and they don't generally relocate themselves a million years into the past. They trace a continuous path through time and space. (Oh, sure, for individual particles there's some quantum weirdness about exactly where it is along the way, but I think we're dealing with larger systems here?)
Now, physics have told us that space and time are glued together into a four-dimensional spacetime. So pick any two given points in spacetime — in whatever reference frame you like, doesn't matter if you're on Earth or in a space or next to a black hole — and take measurements of the distance between them, and the time between them. Ask yourself, "can some matter or energy travel along a path from the one point in spacetime to the other?" This is what it means to say, "are these points casually connected?" Because causes and effects have physical carriers, and they must move through time and space.
We found experimentally that there is generally a special speed limit — the "speed of light", though other things also are affected by this limit. We also found that this speed is constant in all reference frames. Some reference frames will disagree on how much space and time there is (your usual twin paradoxes and the like) but it all works out so that all observers agree on how much spacetime is between the points. (The mathematical objects for representing spacetime are quaternions, and the space and time vectors are just particular projections of the underlying quaternions, onto a set of measurements for a reference frame. But I don't know how to operate quaternions, and the specifics don't matter here.)
Now here's the thing:
If you are able to go faster than the speed of light (as measured in any reference frame of your choosing) it is geometrically equivalent to the power to go back in time. It doesn't really matter how you go faster, how you connected those two points — teleport there, open wormholes, warp space — there is some reference frame where you have travelled back in time. If you perform your maneuvers right, and take the right path, that reference frame could be Earth.
There's no other barrier: the speed of light itself was the barrier, and you just broke it. And if you have done so successfully, that means that the way cause-and-effect actually happens is ... something weird we only understand poorly.
observers moving relative to each other agree on what “the speed of light” is, but disagree about what “2 x the speed of light” is. Specifically, they disagree about which superluminal trajectories are forward in time vs backwards in time. Therefore, if you have a device that accelerates you to 2x the speed of light, it must accelerate you to 2x the speed of light in your own reference frame. As a result, you can accelerate to .99 c relative to earth using conventional means, activate the device, and then be travelling at 2x the speed of light in the .99c frame, which is backwards in time in the earth frame. You could then stop, turn around, and repeat the procedure to arrive at earth before you left.
The Alcubierre solution avoids this by being symmetrical, so that observers don’t have to agree on which direction is the destination and which is the origin
Do you know of any good layman-level explanations?
Like, if I FTL from point a to point b, 10 light years apart, in my super duper warp vessel. It takes me, for the sake of argument, 10 minutes to make that journey. Now say I set off a big comms laser at point a, sending a message to point b, before I left. I don't see that laser until 10 years later.
What am I missing? I know I'm missing something, but that seems straightforward to me. It's weird to butt up against that seemingly incomprehensible.