Can Spaceship A Destroy Spaceship B at 99.99% the Speed of Light?

[hubble_bubble]

Are you aware that a thrust that you experience as 1 g, the same force you feel standing on earth, will quite quickly accelerate you to 99.99999% the speed of light relative to earth? The fuel needed would depend on your elapsed time. At any 'moment', the requirements to accelerate at 1g relative to an instantly comoving inertial frame are the same as when you started from earth.

That sounds reasonable. How will that relate to the increase in dilation? What happens when we get into the 90% plus range as we approach c? From the external observer's point of view time is almost standing still. However we are still using the same amount of fuel at the same rate in our reference frame. How can we resolve this? Is it the compaction of space that matters in this case?

 

[PAllen]

That sounds reasonable. How will that relate to the increase in dilation? What happens when we get into the 90% plus range as we approach c? From the external observer's point of view time is almost standing still. However we are still using the same amount of fuel at the same rate in our reference frame. How can we resolve this? Is it the compaction of space that matters in this case?

I don't see much to resolve. Let's say you accelerate at 1 g (your experience) for 1 year of your time. You use up 1 million tons (rest mass) of fuel in one year to accomplish this. To an Earth observer, you have still used up exactly 1 million tons (rest mass - invariant) of fuel, but you have done so over, say, 1000 years (this isn't the real number - I haven't computed it, but it is some large multiple), and traveled nearly 1000 light years.

 

[Dale]

See the graph here. http://www.thebigview.com/spacetime/timedilation.html

"As it can be seen from the above function, the effect of time dilation is negligible for common speeds, such as that of a car or even a jet plane, but it increases dramatically when one gets close to the speed of light. Very close to c, time virtually stands still for the outside observer."

The outside observer see no change close to light speed. This applies to the propulsion mechanism if the mass dos not increase.

"Can we travel at the speed of light?

The hope that one day mankind will be able to travel at near-to-speed-of-light velocities seems farfetched, because of the incredible amounts of energy needed to accelerate a spacecraft to these speeds. The forces are likely to destroy any vehicle before it comes even close to the required speed."

The page does not demonstrate nor even claim to demonstrate any paradox related to fuel consumption or power. Please post your derivation of the paradox you mention in post 25.

 

[hubble_bubble]

I don't see much to resolve. Let's say you accelerate at 1 g (your experience) for 1 year of your time. You use up 1 million tons (rest mass) of fuel in one year to accomplish this. To an Earth observer, you have still used up exactly 1 million tons (rest mass - invariant) of fuel, but you have done so over, say, 1000 years (this isn't the real number - I haven't computed it, but it is some large multiple), and traveled nearly 1000 light years.

First thanks for all the replies. Take the time dilation to be one thousand fold, then would the space compaction be to this same percentage? Also, if we take the moving spaceship's frame to be stationary and the universe moving past at speed, can the spaceship ever launch a missile that from his perspective would be traveling away from him at 99.99% the speed of light?

 

[Dale]

Also, if we take the moving spaceship's frame to be stationary and the universe moving past at speed, can the spaceship ever launch a missile that from his perspective would be traveling away from him at 99.99% the speed of light?

Yes.

http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html

 

[Doc Al]

Also, if we take the moving spaceship's frame to be stationary and the universe moving past at speed, can the spaceship ever launch a missile that from his perspective would be traveling away from him at 99.99% the speed of light?

Again, the fact that the spaceship is moving (with respect to something) is irrelevant to its being able to launch a missile at any particular speed.

 

[PAllen]

First thanks for all the replies. Take the time dilation to be one thousand fold, then would the space compaction be to this same percentage? Also, if we take the moving spaceship's frame to be stationary and the universe moving past at speed, can the spaceship ever launch a missile that from his perspective would be traveling away from him at 99.99% the speed of light?

Yes, the universe going by would appear to have short distances in the direction of motion. The rocket would consider they had traveled only 1 light year in one year. To an observer stationary relative to the stars, the rocket seems compressed in its direction of motion. The length/distance contraction factor is exactly the same as the time dilation factor:

γ = 1/(√(1-v^2/c^c)

For an accelerating rocket, γ would by time varying, but still only depends on current relative speed.

 

[hubble_bubble]

The page does not demonstrate nor even claim to demonstrate any paradox related to fuel consumption or power. Please post your derivation of the paradox you mention in post 25.

Yes sorry I am thinking about several things at once. Just trying to make sense of the concepts.

 

[hubble_bubble]

Yes, the universe going by would appear to have short distances in the direction of motion. The rocket would consider they had traveled only 1 light year in one year. To an observer stationary relative to the starts, the rocket seems compressed in its direction of motion. The length/distance contraction factor is exactly the same as the time dilation factor:

γ = 1/(√(1-v^2/c^c)

For an accelerating rocket, γ would by time varying, but still only depends on current relative speed.

So if I have this right then a centre point between two objects moving away from each other should balance out the time dilation as in the frame of reference from the perspective of this centre position both objects behave in the same way. Is this right?

If so then what about this. Two solar systems at differing points in the universe each see the other moving away at a set speed. Let's imagine they have some unknown way of traveling instantly to any position in the universe. They both calculate the position that the other would be in their frame based on calculations of direction and acceleration. They then jump to that point in space. They would both arrive at a world that has the same reference frame as their own. Is this right or would an observer need to jump from this centre point for this to work?

 

[Dale]

Yes sorry I am thinking about several things at once. Just trying to make sense of the concepts.

understood. Just don't be so ready with the word paradox or contradiction. There aren't any. Also, IMO, the best way to learn relativity is to actually work some problems, draw some spacetime diagrams, solve some equations, etc.

 

[HallsofIvy]

Hubble bubble, you posted this under "relativity" and Doc Al's first question was "99% the speed of light relative to what?" which you never answered. You don't seem to be clear that speed always has to be measured relative to something and that is what the physics depends upon. In your first post you set up a situation in which spaceships A and B were motionless relative to each other. The situation is exactly the same as if you had said that A and B had speed 0 relative to whatever frame of reference you intended in your first post.

 

[hubble_bubble]

Hubble bubble, you posted this under "relativity" and Doc Al's first question was "99% the speed of light relative to what?" which you never answered. You don't seem to be clear that speed always has to be measured relative to something and that is what the physics depends upon. In your first post you set up a situation in which spaceships A and B were motionless relative to each other. The situation is exactly the same as if you had said that A and B had speed 0 relative to whatever frame of reference you intended in your first post.

I am currently digesting information and will have to defer an answer until I work out a few things. But thank you for your reply.