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Assuming completely empty space, does a spacecraft traveling at 0.5 C require continuous thrust to avoid deceleration?

If the spacecraft is traveling at 0.5 C, does it's relativistic mass act upon objects that it passes by?

It is understood that space is not truly empty. The question was designed to consider only relativistic effects.

On a continuing thought however, If the spacecraft is traveling at 0.5 C and starts to decelerate, does it need to decelerate it's relativistic mass or it's rest mass?

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"Completely Empty Space" and "Objects that pass by it" is a complete contradiction. –  Argus Jun 21 '12 at 21:55
    
I am pretty certain it decelerates velocity or specifically momentum is decreased relativistic mass is a very specific thing that is easily confused with total mass. –  Argus Jun 28 '12 at 22:13
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5 Answers

In completely empty space a spacecraft travelling at any speed does not need thrust to stay at that speed. It only needs thrust to accelerate or decelerate. Space isn't empty, so a spececraft would need a small amount of thrust to maintain it's velocity, but in most circumstances the thrust needed is tiny. This issue was discussed in Would a fast inter-stellar spaceship benefit from an aerodynamic shape?.

No matter how fast a spacecraft travels it doesn't develop a stronger gravitational field. This is because the source of the field is the stress-energy tensor not just the mass. For more discussion of this see reletivistic mass as seen by different observers.

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A fast moving spaceship has a much stronger gravitational field in a rest frame than a slow moving spaceship, it deflects stationary objects by more, precisely because the stress tensor is the source, and it has more "relativistic mass". This is the confusion caused by thinking that rest mass makes gravity. Energy makes gravity, relativistic mass makes gravity, not rest mass. –  Ron Maimon Jun 21 '12 at 15:17
    
I'm confused. Are you saying that the 'Gravity' effect caused by the high speed spacecrafts relativistic mass does have an effect on objects it passes? –  Walter Greene Jun 28 '12 at 13:50
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First, a quibble: in completely empty space, the speed of a spacecraft is ill defined. What would it be moving relative to? Empty space?

Now, let's say that the spacecraft is moving relative to the CMB at 0.5 c in otherwise empty space. I'd like to say that no thrust is required because there is no drag on the spacecraft to decelerate it. However, due to the blue shift of the CMB in the direction of travel, I suspect that there may actually be some radiation pressure decelerating the spacecraft.

Update:

Another minor quibble: Mass acting on other masses is a Newtonian conception of gravity. In the context of GTR, mass does not "act upon objects"; mass (energy) "acts" on (curves) spacetime. This curvature is related to the density and flux of energy and momentum which are frame dependent quantities (though they are expressed in a frame independent way via the stress-energy tensor).

The bottom line, as Ron points out, is that, in the coordinate system in which the rocket moves at 0.5 c, it is the relativistic energy and momentum of the spacecraft that relate to the spacetime curvature as "seen" in that coordinate system.

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Nope. In fact the principle of inertia implies that once something get's going in empty space it will keep going at that speed forever. Although for your second question yes the presence of other bodies would accelerate you toward them since you would follow a geodesic (following a geodesic being the appropriate generalization of the principle inertia). The speed doesn't really matter (although obviously it changes the degree to which you are pulled and if you are moving fast enough you can escape the pull of the planet but NOT if you don't accelerate). So no in COMPLETELY empty space you would not need continuous thrust (or any additional thrust) but if there are other bodies around you will need a bit of thrust to avoid them but if they are far away this thrust could be somewhat negligible.

Edit: (As was pointed out by another answer if you were moving in empty space you wouldn't even "know" you're moving but I think it's still a reasonable question if space is "almost empty" like if you're between the Andromeda and the Milky Way (pretending nothing else is floating between them). Then you could "see that you're moving" but the bodies wouldn't require you to really thrust at all to keep going along a constant velocity (although strictly speaking you'd be following a geodesic with a minute curvature).

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I've nothing to add to the kinematics and relativity of the situation, which others have properly addressed. But if you're interested in the topic of interstellar travel more generally, this article by a former NASA scientist is great reading: http://arxiv.org/abs/1101.1066

Abstract below:

Energy, incessant obsolescence, and the first interstellar missions

Marc G. Millis

Projections for the earliest interstellar mission possibilities are calculated based on 27 years of data on historic energy trends, societal priorities, required mission energy, and the implications of the Incessant Obsolescence Postulate (Where newer probes pass prior probes). Two sample missions are considered: launching a minimal colony ship where destination is irrelevant, and sending a minimal probe to Alpha Centauri with a 75 year mission duration. The colony ship is assumed to have a mass of 10^7 kg, and the probe 10^4 kg.

It is found that the earliest interstellar missions could not begin for roughly another 2 centuries, or 1 century at best. Even when considering only the kinetic energy of the vehicles without any regard for propellant, the colony ship cannot launch until around the year 2200, and the probe cannot launch until around 2500. Examination of the Incessant Obsolesce Postulate shows that it becomes irrelevant under several conditions.

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Presumably this "Incessant Obsolesce Postulate" would be the observation that you might get there soon by launching later if your technology or access to energy resources is growing fast enough? –  dmckee Jun 22 '12 at 3:04
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For the drag caused by the CMB see http://prao.aps.org/story/v12/st22 and the references there.

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Mind that this is defined in terms of the speed relative the CMB. Which means I can choose a "rest" frame from which the "fast" spacecraft is at rest relative the CMB and experiences no drag. –  dmckee Jun 21 '12 at 20:18
    
@dmckee Could you explain that a bit more? The speed relative to the CMB should be truly objective. The CMB reference frame in one location is moving relative to the CMB in another location (like one local cluster compared to another, they move away), but we can predict the CMB reference frame near the edge of the visible universe and evaluate is a galaxy is moving relative to it. Or so I thought. –  AlanSE Jun 28 '12 at 14:54
    
@AlanSE: Sure the CMB frame is well defined. But the question places no restrictions on the rest frame. So for some rest frames the "fast" space craft could be at rest relative the CMB and experience no drag. In that case, of course, the observer at rest does experience an thrust from the CMB. –  dmckee Jun 28 '12 at 14:59
    
-1 Answers should be more than just a link –  endolith Jul 17 '13 at 14:36
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