Trolled much lately?

Here in Sweden, it's well-known that the workers' unions support the social democrats, and the employer's union supports the right-wing parties, either directly, or indirectly, through financing ad campaigns.

There're are also many cases where politicians are offered jobs by special interest groups in connection with advancing their agenda. E.g, a politician pushes for a law change a special interest group wants, and after the change goes through, he's offered a job as thanks. By systematically favouring special interest groups, a single member of parliament can lift several salaries at the same time (as chairman, consultant, board member, etc), besides the one he/she gets from the state.

Probably. But that doesn't have to be a bad thing. It means the most successful books will sell less, and people will have more money left to buy the lesser known books. At least that's how it works with music piracy - people who pirate music tend to spend their money on other music products instead.

There's no universal "now" in relativity theory. Which events are simultaneous, depends on the observer. Two events can be simultaneous for you, while being years apart for an observer moving close to the speed of light.

So when someone sends a message which arrives instantly in their reference frame, it MUST appear before it was sent in some other reference frame (and after it was sent in yet other reference frames).

The sense of "now" gets skewed at all speeds, but the lightspeed barrier is sufficient to slow down signals so they don't arrive before they were sent in any reference frame.

Hm... I think those're stars which were within the Hubble sphere when they emmited the light which now reaches us, and that light has been red-shifted by the expansion of space, not by the speed of the stars as such.

Is that what you mean by scale changing in flight?

With respect to you (the original sender).

But I phrased it wrong... I meant that you could send a faster-than-light message to a fast-moving object, who then relays it back to you, and it arrives before you sent it (in your frame of reference).

Oops, sorry. I meant that you could send a faster-than-light signal to an object which travels close to the speed of light, which then relays it back to you, and you get it before you sent it.

This is possible because in the fast-moving object's reference frame, the events of sending and receiving the return message are simultaneous, but in your reference frame, the event of receiving it can take place years before the event where the fast-moving object sends it.

Ah, but what prevents observers in different frames from relaying the message using ordinary, sub-light-speed transmissions?

Say you send an FTL signal from point A to point B, which are in the same reference frame.

At that moment, a fast-moving space ship (B') passes by B, and B relays the signal to B' using an ordinary, sub-light-speed transmission.

At the same time, another space ship, A', passes by A. A' moves with the same velocity as B', and is in the same reference frame, so it should be possible for B' to send an FTL signal back to A'. Moreover, depending on the velocity of A' and B', the signal can arrive back at A' before A sends it.

A' then relays the signal back to A using an ordinary, sub-light-speed transmission, and it arrives before A sent it.

Ah, but what if the recipient of the message was moving close to the speed of light? In their reference frame, the event where you leave Earth could be years *after* the event where you arrive at the destination.

Furthermore, if the recipient sent another warp ship back to Earth the moment they saw you arrive, it would take one second to get back to Earth in their reference frame, but in Earth's reference frame, it would arrive years before before you left the planet.

If you travel at 4 c you will find a 1.5 years old gas cloud. Travel at 8 c to find a 1.25 years old gas cloud. Travel there at 16 c to find a 1.175 years old cloud.

Travel as fast as you want. You shouldn't ever get earlier than a year after my departure let alone prevent it. Now, it could be that someone find out about this and tries to intercept you by going there at twice your speed. They'll get there before you and it will surely take you by surprise but that's still not time travel from your point of view.

You need a relay station to make the warning message arrive before it was sent. Ideally, the relay station should move close to the speed of light, in a direction parallell to a line between star system A and star system B.

When the explosion occurs at star system A, you send an FTL message to the relay station R. In A's frame of reference, the message travels faster than light, but still arrives after it was sent. However, if R moves sufficiently close to the speed of light, the message will arrive before it was sent in R's frame of reference.

R then sends out a message to star system B. In R's frame of reference, it sends out a signal that merely travels faster than light, but in A's and B's reference frames, it will arrive before it was sent.

So whether we look at it from R's, or from A's and B's, reference frame, one of the signals will be able to arrive before it is emitted. The closer to the speed of light we let R move, the more skewed its frame of reference will be compared to A's and B's, and the earlier its signal will arrive at B. We can also make the time-consuming portion of the trip arbitrarily short, by letting R pass close to one of the star systems when the message is relayed.

In total, the message will be able to arrive at B before it was sent from A, given sufficiently high speeds of R. And if we can do that, it's trivial to use a second relay station R' to send a message back to A and warn them before the star explodes.

Good point. But each observer has to deduct the time it took for light to reach them, when they observe events. According to an observer on Earth or Vega, the space ship left Vega at T=0, and arrived on Earth at T=5 years, so events happened in the right order for them. To see that events happen out of order, we at least need to consider an observer who is moving fast relative to Earth/Vega.

Different observers (reference frames) have different ideas of what events are simultaneous. For an observer R who moves relative to A and B, the "instant" message may arrive before or after it is sent, depending on which direction R moves in.

To actually send messages back in time, A and B can use R as a relay station. A sends an instant message to R, who then relays it instantly to B. But what is instant delivery in R's message frame, may actually mean the message is delivered before it is sent in A's and B's reference frames.

Actually, we don't. Only the expansion of the universe causes galaxies to recede from us faster than the speed of light - and they're unobservable for that very reason.

If a spaceship moves at a high speed relative to Earth, events will occur in different orders in the space ship's frame of reference. Specifically, if an event on Earth and an event on the space ship are simultaneous in Earth's frame of reference, in the space ship's frame of reference, the Earth event will happen after the local event. This is after all optical effects are adjusted for.

Now let's assume Earth sends an instant signal to the space ship. "Instant" means the signal is emitted on Earth and received by the spaceship simultaneously, where "simulteaneously" is defined by Earth's frame of reference.

However, in the space ship's frame of reference, the emission of the signal from Earth occurs after it is received by the space ship. If the space ship sends an instant message back, it will be emitted from the space ship and arrive on Earth simultaneously. However, in the space ship's frame of reference, "simultaneously" means *before* the message was emitted from Earth.

This doesn't violate causality... causality is violated when you (on Earth) send an FTL message to the moving spaceship, and the spaceship uses the same FTL technique to send a message back. In the space ship's frame of reference, the first message is received before it's sent out, so the space ship just needs to send an instant message back to Earth, to make it arrive before the first message was sent.