A Paradox

[Qfwfq]

Take two large masses far from other large ones, just to make things simpler. Fix them to each end of a rigid rod with a device for measuring attractive force between the two. Make sure the axis a running through both centres of mass has a stable direction, referred to the fixed stars, let things settle nicely and then measure the attractive force, f. Knowing the two masses and the distance r between them, f should match up the well known calculation, proportional to both masses for given r.

Now, surely there are many things wizzing along at velocities approaching c and in various directions. From these frames of reference the pair of masses will be wizzing at that velocity, the opposite way. For some directions, r will be contracted, while it won't for directions at right angles to a. For such observers, what should the attractive force between the two masses be?

Think carefully...

[FREYA021]

hehehe, look in books for atomic phisics... or IR spectroscopy... harmonic and unharmonic oscilators... if that is elastic or not bond... blablabla
sorry but its done ages ago!

[bumab]

Hmmm....

won't the masses appear to change in proportion to the change in r, thus making no difference?

[Qfwfq]

Originally Posted by bumab

won't the masses appear to change in proportion to the change in r, thus making no difference?

Think so? Try working that out.

[Bo]

as lomg as the observers aren't accelerating, they length contraction etc. is constant, so the system is in equilibrium and they measure a net force of 0 i suppose.

Bo

[Qfwfq]

I'm not sure what you mean by a net force of 0, are you sure you followed the description right? It isn't quite so simple.

Of course, I did mean inertial observers!

[Qfwfq]

Obviously, there will be equal and opposite forces between the parts and the system will be in equilibrium. For clarity, by "the attractive force between the two masses" we can understand the compressive strain on the rod.