A Puzzle,

I apologize for being so slow at posting this but it was the weekend and I do have other things I had to do and I wanted to be as clear as possible. It’s a problem I dreamed up some 40 years ago when I was first learning about General Relativity. It is made very clear in most presentations of General Relativity that it is impossible to define a rigid object. Seeing how most physics laboratories make a lot of use of so called “rigid” equipment, the inherent difficulty of the suggested conflict aroused my interest.

Let us suppose that you are completely familiar with special and general relativity. You are in charge of programming the navigation computer on a ship which is a member of a large intergalactic fleet of fighting ships. Now I am sure most of you are well aware of the existence of idiots in command positions who have no idea of what constraints control your work (if you don’t know what I am talking about, see most any Dilbert cartoon). It turns out that your commander (in charge of the entire fleet) does not believe in relativity at all. He is aware of the finite speed of light so he is aware of the fact that there are distortions in what he actually sees during a maneuver, but beyond that, he is ignorant of the entire phenomena and has no interest in learning.

Your problem is that the commander doesn’t care about the fact that you cannot define a rigid object; as far as he is concerned, his entire fleet is to maneuver as if it is a rigid object. Now he may not be able to check things during an actual maneuver, as his fleet is far too large, but he can certainly review the computer logs of what your ship did during the maneuver. What he can do is to make sure everyone is in formation after their rockets are shut down, and, he can tell from the computer logs if anyone made any changes in position after the maneuver was completed.

The rules you have to obey are as follows: first, everyone in the fleet must start their rockets simultaneously (this is well defined as, prior to the maneuver, they are all in the same inertial frame), and second, everyone in the fleet must shut down their rockets simultaneously (this is also well defined as, after the maneuver, they are all in the same inertial frame).

When any maneuver is finished, the commander may tour the fleet and examine the computer logs as to when the rockets on a given ship were fired, in what direction they were fired and exactly how long they were fired. Since he has been the commander for several thousand years, he is quite familiar with the firing logs for most every position in the fleet and for every common maneuver performed. He will notice something unusual immediately. If he thinks you allowed your ship to get out of position during the maneuver, the punishment is the death penalty.

Now we know the other navigators have managed to fake the guy out for a thousand years or so we ought to be able to figure it out too. Restating the problem, given our initial position in the fleet (relative to the flag ship - set up a coordinate system with the flagship at the origin) and the intended maneuver to be followed (expressed in the commanders instantaneous local coordinate system) find the best relativisticly correct path which your ship should follow.

What you need to come up with is an algorithm which will carry you from your start position to your finish position for each and every maneuver the commander may specify. Hint: you will clearly have to include adjustment of the times on your computer clock during the maneuver as the clocks will not read the same as the commanders clock during that phase. (All clocks on board your ship are synchronized with the computer so you don’t have to worry about any other clocks.) On the other hand, no adjustment on the time can be made after the maneuver is completed (let’s say that is just thrown in to keep you honest).

Start with some simple maneuvers and see if you can figure out what your ship should be doing. Try a straight line acceleration first. You all should be able to work that one out. Once you get that worked out, try a simple turn with no acceleration for the flagship; that gets a tad more complex. If you get that worked out, you can try a moving turn: i.e., a turn with acceleration in the direction of the turn (centripetal force on the flagship) actually a rather trivial complication.

Now an accelerating turn gets difficult (at least for me). I did it 40 years ago but it wasn’t easy and I am not entirely sure it was without error. I had some major timing problems. At any rate, I think this ought to keep you all busy thinking for a while and I think it will show some significant insights into the dynamics of general relativistic motion. I am curious as to what kind of results you guys can come up with.

Have fun -- Dick

Oh lord, help us!

J.W. is in command!

[img]/phpBB/images/smiles/icon_smile.gif[/img]

I think your puzzle has gone beyond my ability to suspend disbelief.

Just frag the feakin' admiral and be done with it.

How does one manage to make it to Fleet Admiral without knowing that a fleet of ships cannot move as a rigid object? You'd think he would have met his Peter Principle promotional rank limit long before the rank of Admiral.

I do not understand where I have asked anyone to suspend disbelief. That the circumstance described in the puzzle is not apt to happen is of no real consequence at all as it is no more than a story to set up the boundry conditions on the puzzle; there exists no violation of any law of physics there at all.

Or are you referring to the statement that you are familiar with Special and General relativity. I am of the opinion that a number of people on this forum are sufficiently educated to solve the puzzle. You ought to at least try it anyway, it's a lot of fun.

Yes, the part I quoted said "completely familiar"...

I'll go home now.

The only way to get familiar is to think about situations and how they work out. The issues are really not that difficult. The rope problem you guys were playing with essentially brings up all the problems with straight line acceleration. Why don't you try your hand at it?

Have fun -- Dick

Me thinks my original post in this space was taking up too much bandwidth.

The unintended crux of the puzzle lies in its confusion of a Newtonian worldview, (valid in the zone of middle dimensions,) applied over the implied relativistic speeds in space-time.

(Me thinks.)

Chip

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"A commander doesn't need intelligence, just a good loud voice." -- Dr. Morbius from Forbidden Planet


<font size=-1>[ This Message was edited by: Chip on 2001-12-12 02:23 ]</font>

Am I missing something? Say this fleet of ships all has the same maneouver programmed into its Guidance computer. They all 'go' at the same time. They all stop at the same time. They will still be in formation at the end of the maneouver. There we go, problem solved. The end.

Or did I miss a big huge whopping chunk of physics out there somewhere? If so, please explain.

As for the rocket and rope trick, it only looks like the rockets are further apart to the outside observer, and the rockets and ropes look stretched. The outside observer won't see the rope snap because it wouldn't snap. The rockets are the same distance apart relative to each other. What's the mystery?

Are you talking about the problem posed in this thread? In that problem, the rope does snap.

Yes. The we assume it would snap because the outside observer would observe that the two rockets are further apart than they actually were. If the rockets themselves always seem to be the same distance apart form inside the rockets, then this local condition must call for the space itself to be stretched, or some other factor based upon the unreliable nature of observations taken at such high velocities. The observation that the rope is longer would be purely an optical illusion so close to the speed of light. I'm not questioning why the rope would do two different things depending upon the frame of reference, I'm questioning the accuracy of the statement that the outside observer would see the rope snap.

I understand, but it appears that that is not the case. If you have a question about the arguments presented in that thread, address them specifically. Probably should do that there, no? Or email, if you want. mentock@mindspring.com

Cheers. Sorry to go off on one in the wrong thread, but thet thread seemed to be going off on a huge tangent, or so my limited understanding thought. I'll re read it to try and make some sense of it.

John,

That was my initial response to the post when I first read it as well. However, it doesn't allow for turning.

Consider a simple maneuver where all the Commander's ship does is rotate on an axis 180 degrees. If another ship simply rotated on its axis 180 degrees, then it would end up in front of the Commander's ship when it started out behind it. To remain "in formation," the other ship would need to sweep through space in an arc so that it always remained behind the Commander's ship.

If the Commander were able to spin his ship sufficiently rapidly, and the other ship were sufficiently far away, the other ship could need to move through space faster than the speed of light in order to stay in its correct formation position . . . yuck!

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"Ask to understand, but don't challenge unless you have the knowledge."--NEOWatcher

The contents of this post are ©2009 by SeanF and may not be copied or retransmitted in any form without the express written consent of SeanF

You are absolutely correct! If you are too far from the commander and the commander decides to rotate the flagship you are, what do they say? "SOL" and better run for it! So let us say the commander never rotates his ship faster than one degree/second (slow rotation gives him a feeling of power) just how far away can you be and still maintain your position (presuming that your only problem is not exceeding the speed of light)?

However, you seem to miss the point that the proposed plan even fails in straight line acceleration. If every ship follows the same acceleration plan, on acceleration from the original inertial frame to the final inertial frame, their separation in the second frame will be larger than their separation in the first frame (see the "Rope" thread).

True, but in the original post, you said:

Which I would take to mean that it doesn't matter if you're further away (and accelerating more slowly) during the maneuver, just so long as you're where you should be when he stops and your computer says you were "where you should have been" the whole time . . . Of course, that way, all you need to do is figure out where you should end up, go there, and fake the computer records while he's flying around! [img]/phpBB/images/smiles/icon_wink.gif[/img]


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SeanF

<font size=-1>[ This Message was edited by: SeanF on 2001-12-10 12:46 ]</font>

Sorry but you made one bad assumption. You assumed that at the finish of the manuver the fleet was in the same inertial frame as it was when the manuver began. I understand why you jumped to that conclusion; however, it was not intended to be implied.

So long as the fleet is in an inertial frame, the commander has all the time he desires to check the position of each ship. If you understand that the constraint is the fact that he does not have time to check anything during a manuver, then the only requirement becomes "the fleet must be in an inertial frame", not "the fleet must be in the original inertial frame.

If you choose the constraint to be the second, then the problem is completely trivial and your solution is totally valid.

Have fun -- Dick

What's an inertial frame?

[spelling!!! And only four werds!]

<font size=-1>[ This Message was edited by: johnwitts on 2001-12-12 19:24 ]</font>

An inertial frame is one that is not accelerating.

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