Theoretical Problem

[wedjat]

I've been told that because this situation would not be able to be created in our Universe, the laws we abide to would not apply to the problem, and therefore it has no solution. But, I believe the question is still valid.

 

If there was a rod [width does not matter, but length does] that was 1 light-year in distance, as in it is 1 light-year long, and you were to move it one foot in either direction, would a person on the opposite end see that shift instantly, or would the information of its position take the speed of light to reach the other end?

 

Let's say that, in order to avoid the relativity and speed-factors of getting that person to the other end, there was a timer, and it was calibrated for travel-dilation to be precisely the exact time of the person on the other end.

 

If I'm mixing terminology, or if this question isn't valid, please tell me.

 

I look forward to your answer(s)!

[Little Bang]

The information would take one year to reach the observer.

[Moontanman]

what looks like us to be instant movement is actually a pressure wave traveling along the rob, the longer the rod the more obvious the wave becomes. a rod a light year long would not move at both ends instantly, the movement would be a wave traveling at around the speed of sound in the material.

[modest]

Indeed.

 

Imagine person A pushing the rod and poking person B on the other end. A pushes it and sees B get poked 2 years later. Considering how long light takes to get from here to there, person A concludes that it took 1 year after the push for B to get poked.

 

Person B gets poked and sees A push at the same time. After considering how fast light travels he concludes that the push happened one year before the poke.

 

For the purpose of thought experiments it is sometimes necessary to assume a rod "a rigid rod" is... rigid... or that it has "born rigidity". To do this you would have to assume that every atom of the rod is accelerated instantly from some person's perspective. You would need lots of person-A's along the rod who have all agreed to push it at some time T where all their clocks are synchronized, by some means like Einstein synchronisation.

 

~modest

[Southtown]

It would probably take as much energy as accelerating a yardstick to the speed of light, no?

[modest]

It would probably take as much energy as accelerating a yardstick to the speed of light, no?

 

No, it really wouldn't take any more energy to accelerate a born-rigid object. Each person along the object only needs to accelerate a single atom. There are as many people pushing atoms as there are atoms (quite a few), but the net energy they spend pushing the rod would add up to being the same as person A pushing it all on his own—he is pushing every atom.

 

~modest

[modest]

I'm sorry, Southtown. I believe you are correct:

 

It sometimes puzzles people when they consider a physical rod of some arbitrarily great length L, initially at rest, and then subjected to forces so that the leading end of the rod accelerates in the positive x direction with constant acceleration a > 1/L. What happens to the rest of the rod? Needless to say, if we accelerate the leading end simply by pulling on that end, the effect will propagate down the length of the rod at roughly the speed of sound in the rod material, and the rod will not maintain Born rigidity. However, it is theoretically possible to apply coordinated forces to each section of the rod in unison, so we can imagine trying to accelerate the entire rod to maintain Born ridigity with the leading end. The problem is that the acceleration which each section must undergo increases, and is inversely proportional to the distance from the pivot event. As a result, it will be necessary to exert arbitrarily large forces, and eventually the required acceleration goes to infinity. Another way of saying this is that the acceleration must be accomplished in less and less time as we approach the pivot event, and it must be instantaneous at the pivot event. On the other side of this event, the acceleration must be accomplished in negative time, i.e., those sections of the rod would need to have been accelerating (in the opposite direction) prior to the time t = 0 when the leading end began its acceleration.

 

Born Rigidity and Acceleration

 

~modest