Time Dilation

Lord Skimper wrote:Also wondering about missiles as they fly passed at fairly high rates of speed they must be having time dilation on their systems, computing, and responding to commands etc.... Even with Apollo FTL comms the message to the missile would have to be very short and the response time of the missile would be tiny. I'm surprised missile can hit anything at all, rather than the Manticorian missiles missing or hitting two ships when they meant to all miss is astounding. And before Laser heads even more astounding. Counter missiles even more so.

SWM wrote: Yes, missiles do experience time dilation. The text even mentions this! But this does not have any deleterious effect on the accuracy of the missiles. From the point of view of the missile, the rest of the universe slows down, so the missile has lots of time to take it's sensor readings and adjust course. Messages which are received time-dilated can be easily slowed down in processing. It doesn't cause a problem.

BobfromSydney wrote: I would think a missile flying at a high fraction of c would experience a 'slow down' of its own internal clock.

To me it would seem like this would be a disadvantage in terms of 'reaction speed' to anything happening in the rest of the universe, since the missile would get less computing time to respond and its responses would be slower. (Overall I don't think its a big deal during approach, but may make the firing solution harder at the end).

Well, nobody experiences a slowdown of their own clocks; they see it on the clocks of objects moving relative to them.
For instance, if a missile is coasting at 4/5 c relative to the ship that launched it, the Lorentz factor 'gamma' is 5/3 (= 1/sqrt{1 - [0.8]^2}). So if its target is 4 light-seconds ahead, it'll take 5 seconds to reach it, but people on the ship will see that the missile's computer effectively has only 3 seconds worth of clock cycles left (= 5 s / [5/3]). Meanwhile, in the missile's rest frame, the target is only 2.4 lt-s ahead (= 4 lt-s / [5/3]), so again it'll take 3 sec to get there (= 2.4 lt-s / 0.8 lt-s/s).

I misspoke.

What I meant might be better illustrated by this example. There is a missile and a point defence system. Both system have identical processors.

The point defence system (target) is the 'stationary' frame of reference. I'm going to specify that the missile was originally 'fired' by the 'target', has travelled away, looped back and accelerated to 0.95c.

The missile starts 95 light seconds away and is travelling at 0.95c toward the target. The point defence system does not move.

EDIT: The distance of 95 light seconds is established using a pre-positioned marker. A big mirror is positioned so that it takes 190 seconds (according to the target) for a beam of light to bounce back from the mirror. The missile's flight path takes it adjacent to the marker/mirror.

So it seems to me that the point defence system will have 100 seconds to track the missile and calculate the best response. (Well, slightly less than 100s, since the missile needs to be stopped before it impacts the target)

The missile itself only experiences ~31.2 seconds of subjective time. Hence the missile's computer will only have ~31.2 seconds to refine its attack profile.

So it seems to me that the computer on the defending side gets to make three times more calculations than the attacking computer.

That's what I meant by saying a 'slow down' of a moving 'internal clock'. Perhaps instead of the loaded word 'clock' I should substitute the phrase 'flow of time'?

I'm not sure I agree with SWM's assertion that from the missile's perspective the rest of the universe slows down. It would seem to me that the rest of the universe has sped up (from the missile's perspective)!

Am I missing something? Doesn't the 'response time' advantage rest with the side that is less time dilated?

BobfromSydney wrote:I misspoke.

What I meant might be better illustrated by this example. There is a missile and a point defence system. Both system have identical processors.

The point defence system (target) is the 'stationary' frame of reference. I'm going to specify that the missile was originally 'fired' by the 'target', has travelled away, looped back and accelerated to 0.95c.

The missile starts 95 light seconds away and is travelling at 0.95c toward the target. The point defence system does not move.

EDIT: The distance of 95 light seconds is established using a pre-positioned marker. A big mirror is positioned so that it takes 190 seconds (according to the target) for a beam of light to bounce back from the mirror. The missile's flight path takes it adjacent to the marker/mirror.

So it seems to me that the point defence system will have 100 seconds to track the missile and calculate the best response. (Well, slightly less than 100s, since the missile needs to be stopped before it impacts the target)

The missile itself only experiences ~31.2 seconds of subjective time. Hence the missile's computer will only have ~31.2 seconds to refine its attack profile.

So it seems to me that the computer on the defending side gets to make three times more calculations than the attacking computer.

That's what I meant by saying a 'slow down' of a moving 'internal clock'. Perhaps instead of the loaded word 'clock' I should substitute the phrase 'flow of time'?

I'm not sure I agree with SWM's assertion that from the missile's perspective the rest of the universe slows down. It would seem to me that the rest of the universe has sped up (from the missile's perspective)!

Am I missing something? Doesn't the 'response time' advantage rest with the side that is less time dilated?

That's what gets weird is that both frames of reference are equally valid. As I understand it, both the missile and the defense get the 100 seconds to compute things. They both see the other as having less time.

Kizarvexis wrote:

BobfromSydney wrote:I misspoke.

What I meant might be better illustrated by this example. There is a missile and a point defence system. Both system have identical processors.

The point defence system (target) is the 'stationary' frame of reference. I'm going to specify that the missile was originally 'fired' by the 'target', has travelled away, looped back and accelerated to 0.95c.

The missile starts 95 light seconds away and is travelling at 0.95c toward the target. The point defence system does not move.

EDIT: The distance of 95 light seconds is established using a pre-positioned marker. A big mirror is positioned so that it takes 190 seconds (according to the target) for a beam of light to bounce back from the mirror. The missile's flight path takes it adjacent to the marker/mirror.

So it seems to me that the point defence system will have 100 seconds to track the missile and calculate the best response. (Well, slightly less than 100s, since the missile needs to be stopped before it impacts the target)

The missile itself only experiences ~31.2 seconds of subjective time. Hence the missile's computer will only have ~31.2 seconds to refine its attack profile.

So it seems to me that the computer on the defending side gets to make three times more calculations than the attacking computer.

That's what I meant by saying a 'slow down' of a moving 'internal clock'. Perhaps instead of the loaded word 'clock' I should substitute the phrase 'flow of time'?

I'm not sure I agree with SWM's assertion that from the missile's perspective the rest of the universe slows down. It would seem to me that the rest of the universe has sped up (from the missile's perspective)!

Am I missing something? Doesn't the 'response time' advantage rest with the side that is less time dilated?

That's what gets weird is that both frames of reference are equally valid. As I understand it, both the missile and the defense get the 100 seconds to compute things. They both see the other as having less time.

No, BobFromSydney is correct. I had misspoken earlier. Well, I was correct that the clocks of the rest of the universe slow down as seen by the missile. But the rate at which the target and the missile are closing the distance is the same; that is, the missile will see the ship approaching at the same 0.95 c that the ship sees the missile approaching. But the missile will see a different distance between the ship and itself. The missile will calculate that the ship will impact the missile in 31.2 seconds, which is exactly the amount of time that the ship will see the missile's clock move.

But this really isn't as big an advantage for the defender as you might think. First of all, missiles do not travel at 0.95 c. They only travel at 0.8 c, which gives a gamma of 1.666; the missile clock moves at 0.6 times the ship clock rate. That is quite noticeable, but since the missile can accelerate at tens of thousands of gees, it does not help PDLC aiming all that much. Counter-missiles end up with their own time dilation, so they have the same problems as the missiles they are attacking.

So there is some advantage, but not enough to guarantee point defense accuracy.