Spaceship A and spaceship B

1. Aug 2, 2012

hubble_bubble

Spaceship A and spaceship b are travelling at 99.99.... % the speed of light. Spaceship A is behind spaceship B. Spaceship A wants to destroy spaceship B and fires a missile. Will spaceship A succeed for any velocity the rocket is launched at and at a variable distance?

2. Aug 2, 2012

Staff: Mentor

Traveling at 99.99..% c with respect to what? Are they both moving at the same speed?

3. Aug 2, 2012

hubble_bubble

Both moving at the same speed and in the same direction.

4. Aug 2, 2012

Staff: Mentor

OK. So why wouldn't ship A's missile hit ship B? The fact that they happen to be moving with respect to something else doesn't matter.

5. Aug 2, 2012

hubble_bubble

If they are traveling at 99.99...% the speed of light of course it matters. Say you fired your missile at 5% the speed of light (yes I know it is impractical) then you have a problem unless time dilation has skewed yourview of the universe enough to make you think the wrong velocity is 5% c.

6. Aug 2, 2012

hubble_bubble

Let's put it another way. In all frames of reference light is at a constant speed. So anything measured with regard to the speed of light should be constant. So if spaceship A fires a missile at 5% the speed of light then that is the speed it should travel at from the observers perspective unless his measurement of the speed of light is wrong.

7. Aug 2, 2012

Staff: Mentor

The missiles are firing at some speed with respect to the ships. Say I am in ship A and you are in ship B. You and I are at rest with respect to each other--we are moving together. If I fire a missile at you, then it will eventually hit you regardless of its speed. The fact that we happen to be moving with respect to something else is irrelevant.

8. Aug 2, 2012

Staff: Mentor

Right. The speed of light (in vacuum) is the same for all observers.
No. Something moving at less than the speed of light will appear to move at a different speed in different frames.
Say A and B are traveling at 0.99c with respect to the earth. A fires a missile at B at 0.05c with respect to the ships. As far as A and B are concerned, that missile is moving at 0.05c.

Of course, as seen by earth observers, the speed of the missile is much greater, a bit faster than 0.99c. So earth observers will see the missile eventually catch up to B.

9. Aug 2, 2012

hubble_bubble

OK. If I Were to fire a photon from ship A to a target on ship B and measure its speed in relation to the missile would I get correct results? If at the same time I fired a photon at a target that was stationary with respect to the earth and measured its speed would that result agree with spaceship Bs result. If so how? It would mean that the first photon would have to slow dramatically and be time dilated so its speed appeared right to the observer in spaceship B. Otherwise it would simply not be detected at all as time dilation changes spaceship Bs view of the universe.

10. Aug 2, 2012

Staff: Mentor

An observer on A would measure the speed of the photon as c, as would an observer on B (obviously), an observer on the missile, and any other observers (e.g. on earth). Similarly with photons fired from B, the missile, the earth, or anything else.

Please show your work. You made a mistake somewhere, but it is not clear what that mistake is from this description.

11. Aug 2, 2012

hubble_bubble

Sorry I was being a little flippant. Of course there is no time dilation of the photon. This however still raises the question as to how that individual photon would be perceived. Would it be seen as in a lower energy state? Something has to change due to the time dilation.

12. Aug 2, 2012

phinds

WHAT time dilation? The people on the ships aren't experiencing any time dilation. Do you understand that or not?

The fact the someone in a DIFFERENT frame of reference sees them time dilated is irrelevant to them.

You do realize, I assume, that you personally are moving at 99.9% of the speed of light from some frame of reference and that frame of reference sees you as time dilated. Do you notice anything?

13. Aug 2, 2012

hubble_bubble

Frames of reference are useful tools but the paradoxes abound. I am speaking with reference to the earlier poster who included earth into the scenario so from the point of view of an earth observer there would be time dilation.

Spaceship C is traveling in exactly the opposite direction to A and B but not on a collision course. Spaceship C is traveling at the same speed as A and B but in the opposite direction. As C passes space ship A, A fires one photon at ship B and one photon at ship C. Both ships B and C are at equal distances from A at that time. Will both photons be detected at the same time?

14. Aug 2, 2012

Staff: Mentor

A second frame had to be introduced to give meaning to your statement that the ships were moving at 0.99c. (Moving at 0.99c with respect to what?) The fact that earth observers will need to consider time dilation (and other relativistic effects) in interpreting the observations of the ships is irrelevant.

I assume you meant "as C passes ship B".
At the same time according to whom?

15. Aug 2, 2012

Staff: Mentor

That is given by the relativistic Doppler equation.

http://en.wikipedia.org/wiki/Relativistic_Doppler_effect

Paradoxes abound only in the sense that there are a lot of things which are confusing to students of relativity. None of the things which confuse students are actual paradoxes representing logical inconsistencies of the theory.

16. Aug 2, 2012

Staff: Mentor

Once again, all observers will measure the speed of that fired photon as being c with respect to their own frame. To understand how those observations can all be consistent, you must apply several relativistic effects, not just time dilation. You must include length contraction and the relativity of simultaneity as well.

17. Aug 2, 2012

Staff: Mentor

The easiest way of getting through this problem is imagine yourself actually on one of the spaceships. From the perspective of someone is spaceship A... You are in a spaceship that is floating motionless in space. Spaceship B is also floating motionless in space somewhere in front of you, right in your gunsights. The rest of the universe is rushing past you at .9999c, but that doesn't change the fact that you and your target are floating motionless. You have an easy shot at your target, and there are no relativity effects involved at all.

Last edited: Aug 2, 2012
18. Aug 2, 2012

hubble_bubble

That is interesting and explains a few things.

19. Aug 2, 2012

darkhorror

99.9% of the speed of light with respect to something else doesn't matter at all.

The speed of spaceship A and B is 0 in the example you are talking about.

20. Aug 2, 2012

hubble_bubble

As time dilation basically slows down all activity in the two spaceships with reference to an earth based frame of reference then that also means that propulsion is also slowed down. How does this square with theoretically being able to produce near light propulsion? If all processes slow with relation to the surrounding universe the propulsion would weaken in effect the nearer to light speed one got.

Also as to the expansion of the universe this effect would also be true of any galaxies accelerating away from each other. The special relativistic view of hubble's law would then be nearer the mark than anything else as light speed would be impossible even for a dark energy driven expanding universe.