Talk:Interstellar travel/Archive for 2004

Relativity questions

There's a couple of questions I've been wondering about on this subject:

1. What happens if something travelling near the speed of light is heading toward a source of Gravity? Given that gravity affects all masses equally regardless of how heavy they are (or how heavy they're made based on how fast they're going), could something break the speed of light via being accelerated by gravity as it was moving toward the gravity's source?
2. And if it could be accelerated to at least the speed of light, what would happen at the point that it was very close to the speed of light? There would theoretically be a point where the mass of the object would be greater than the rest of the universe. If that's the case, does it start exerting huge amounts of gravity on the rest of the universe, pulling it all toward the object?
3. As far as I can see, time wouldn't actually go backwards if you went faster than light. The equation for the perception of time with speed is t = t0 / sqrt(1 - (v^2 / c^2)). This would mean that at a speed greater than light, the 1 - (v^2 / c^2) part would go negative, meaning that the sqaure root of a negative number would be taken. Under complex number maths, this means that the number becomes imaginary, so beyond the speed of light the time would be some sort of imaginary number time.
4. So what sort of time would the 'imaginary number' time be? Hypertime?

Daveryan 12:53 28 Jun 2003 (UTC)

Things are not quite so simple. The real answer to your question is "understand relativity". But I'll try to be helpful.

First of all, general relativity (GR) is not a correct theory: we know of phenomena it can't handle. Various attempts at quantum gravity have not yet met with success. But for this kind of problem it is the best theory we havem and it seems to be fairly accurate. So everything else I'll say will be assuming general relativity holds.

Both special and general relativity require you to change how you think about basic physics in order for you to understand what's going on. This can be difficult, but good books exist. You have to be careful, though, because words like "time", "mass", "gravity" and "speed" don't mean what you think they mean.

The idea that gravity accelerates all objects equally, independent of mass, is more subtle than it looks. But perhaps the simplest answer to your first question is that gravity is not independent of velocity in GR. (It's very difficult to be precise here without talking about curvature of spacetime and so on). Just as a light beam gets no faster as it nears a heavy object (although it may experience redshift) an object very near the speed of light does not get much faster either --- although what seems to happen depends on how you measure its velocity. In fact, objects travelling very near the speed of light behave more and more like photons as they get faster.

If you decide to try to accelerate an object up to near the speed of light, you can definitely increase its mass. But it takes energy to do this - in fact, the increase in mass is exactly the same as the energy input divided by c². This holds true for all velocities, even very low ones, but when you throw a baseball, its kinetic energy is tiny compared to its mass times c², so the increase in mass is also tiny. So just by pushing an object faster, you could indeed significantly increase its mass - but that extra mass has to come from somewhere.

The formulas for time dilation and suchlike just don't make sense for objets moving faster than the speed of light. To understand what's going on, you need to look at spacetime as a whole. To simplify things, let's ignore the starship itself and look only at events: the starship leaves, and the starship arrives. Special and general relativity point out that the times of these two events are different for different observers. If you're moving quickly compared to me, a clock you carry with you will read a different time between the two events than a clock I carry. If we pick two arbitrary events, it might happen that you see one event happening first and I see the other happening first. But (in special relativity) if you can get from one event to the other without travelling faster than light, then we will always agree on the order. If you can't though, then we may disagree on the order in which the events happen. This is a problem if one of the events is supposed to cause the other, like starting the starship engines is supposed to cause arriving at their destination. If you see that spaceship happening faster than light, then some observer who's moving fast enough will see that spaceship arrive before it leaves. But the principle of relativity says that the same laws of physics work for this other observer, so the spaceship can't leave before it arrives.

General relativity still says that time travel and faster-than-light travel are the same, but it describes (purely theoretical) ways to do both. --Andrew 03:54, Apr 17, 2004 (UTC)

Best Place I could find to mention that I've removed the line which stated that upon return to Earth, time dialated travelers would experience the full duration (Earth relative) of the trip. This statement was at odds with the classic "twin paradox," wherein one identical twin will in fact age slower over the entirety of a round trip at c-fractional velocities. --Icelight 29 June 2005 21:59 (UTC)

Actually, what that sentence was referring to was that the traveller would arrive to find that more (local) time had elapsed than they'd perceived subjectively in-flight. I've modified that passage to make this clearer.--Christopher Thomas 29 June 2005 23:06 (UTC)

Okay, that's much clearer than it was. --Icelight 30 June 2005 00:18 (UTC)