View Full Version : Relativity puzzle.

Mister Earl
2010-Oct-07, 06:52 PM
Ok. Let's say I got a rocket that utilizes an antimatter reaction engine for propulsion. Now, as I approach the speed of light, I get substantially more massive. However, the energy yielded by matter / antimatter annihilation is dictated by mass, correct? So, as I'm getting more massive and massive, so does the antimatter and matter I'm using for fuel. So my thrust would increase correspondingly.

Now, I realize that even this won't get me up to light speed... it's impossible... so sooner or later somehow the brakes gotta come on. I can't see this going into some kind of lightspeed-breaking runaway process.

There's something I'm missing here. What is it?

Mister Earl
2010-Oct-07, 07:29 PM
No response yet, so I'll take a stab at my own question. I'm guessing the effects on time would prevent the antimatter rocket from achieving lightspeed. I think what would happen is that while the increase of mass wouldn't be detrimental to the overall acceleration as the rocket gets closer to lightspeed, time would slow down enough so that yes, it would have eventually hit or even passed the speed of light, but time is now going so slowly for the rocket that it wouldn't hit the speed of light before the end of time.

I'm probably wrong here somewhere.

grant hutchison
2010-Oct-07, 08:01 PM
The energy and reaction mass you have aboard your rocket doesn't change from the point of view of the rocket itself: your fuel can only apply the usual acceleration to your ship, no matter what your velocity is compared to some outside observer.
But an outside observer sees that acceleration acting in the presence of length contraction and time dilation: the relativistic gamma factor (which scales the length contraction and time dilation) applies to the third power when converting shipboard acceleration to that measured by an external observer. As the ship approaches lightspeed relative to an external observer, its acceleration dies away towards zero, as measured by that observer: it can never reach c.

Grant Hutchison

Mister Earl
2010-Oct-07, 08:07 PM
Hrm. The whole frame-of-reference trips me up sometimes. The fuel I'm referring to, Grant, is matter-antimatter annihilation. The confusion on my part is that it is said that as one approaches c, mass increases. Energy output via matter-antimatter annihilation depends on mass, correct? While I don't think the rocket could ever match or exceed c, I'm wondering how the matter-antimatter annihilation would be effected as one closes in on c.

Length contraction is something else that I can't wrap my head around, yet. :)

grant hutchison
2010-Oct-07, 08:23 PM
The idea of "relativistic mass" creates more problems than it ever solved, I'm afraid. You won't find it in many modern textbooks.
The matter and antimatter are aboard the ship, being used to eject reaction mass (or photons) out of the back of the ship. The acceleration they produce is felt aboard the ship, and isn't influenced by what apparent mass the ship or its fuel has to an outside observer. (How could it?)

If you want to view it from the perspective of the outside observer, the larger relativistic mass of the fuel has to push the larger relativistic mass of the ship, and the resultant acceleration still scales through time dilation and length contraction.

Grant Hutchison

2010-Oct-07, 08:24 PM
The confusion on my part is that it is said that as one approaches c, mass increases.

The mass only increases as "seen" by a stationary (relatively speaking) observer. You and your fuel would not get any heavier from your point of view.

Energy output via matter-antimatter annihilation depends on mass, correct?

So the "stationary" observer would see more energy generated. But that energy has to accelerate a greater mass (from his perspective). So the acceleration he sees is the same you do.

2010-Oct-08, 12:08 AM
And even seen from the external reference you're forgetting that the ship itself is also heavier by the same amount, so they cancel out.

Ken G
2010-Oct-08, 12:31 AM
Yes, the first thing you always have to do in relativity is choose the reference frame from which you will analyze the problem. It's very important not to skip this step-- you fall into language that sounds like it is absolute (like "approaching light speed"), but in fact it only holds in some particular reference frame. Generally speaking, if there is an inertial (nonaccelerating, often thought of as stationary) frame available, it is wise to choose that. However, in this case the inertial frame has a lot of extra stuff happening, that grant hutchison and Strange referred to already. They also mentioned that there is less of that extraneous stuff going on in the frame of the rocket, so here it might actually be easier to use the noninertial frame of the rocket.

The advantage of using the rocket frame is, the one thing you know about this rocket is its engine, how it works in the rocket's own frame. This means you know the acceleration of the rocket in the rocket frame, which is called its "proper acceleration." So if you take the perspective of the rocket, you know what your accelerometer will read, and you can use that to figure out what is happening to the speeds of everything else around you. This is actually pretty straightforward if you know your own proper acceleration-- but your acceleration does not give you the rate of change of the velocity of everything else, it gives you the rate of change of c times the (believe it or not) inverse tangent of the v/c of everything else. That quantity is called the "rapidity" of everything else, and it is what accumulates in proportion to your proper acceleration. So using that little trick, you can take the proper acceleration from your matter/antimatter engine, convert it directly to a changing rapidity of everything else (which is allowed to increase without bound), and then convert that to the speed of everything else (which won't exceed c). To convert from your proper time to theirs, you just integrate your time dilation as seen from the others to match up their "nows" with yours, and you can figure out what they will reckon also, as well as when they will reckon it.