# Is 100% rigid object theoretically possible?

1. Sep 15, 2011

### Abu Rehan

Can there be a 100% rigid object i.e., an object that cannot be compresses any bit? I believe that's not possible. The proof below-
Suppose there is one such object(cubic shaped). I have applied a force on that from two opposite or all six sides. From newton's third law the object is also applying back a force.
Suppose we seal the object from all the sides in the same state(i.e., the forces are still acting there).
Now take another identical object and seal that easily without wrestling much with that.
Now observe the two sealed boxes. If the object is incompressible then there would be absolutely no difference between the two sealed boxes. But in the first case forces are acting against the walls of the box and in the second case there are no or little forces acting between the object and the wall which means cases are not identical. Thus we arrive at a place of contradiction. Therefore there must be some compression that would distinguish the first from the second. Hence, 100% incompressible object is theoretically not possible. However I acknowledge that compression may be as little as one would want. That however little compression would result in the opposite force, compression given by, L= F/k. But 0% compression is not possible.

2. Sep 15, 2011

### HallsofIvy

A one hundred percent rigid object is (theoretically) possible in Newtonian physics, not Einsteinian physics. Imagine a long pole of a one hundred percent rigid material. If you push one end, the other moves instantaneously. You could use that rod to communicates (perhaps by Morse code) faster than the speed of light which is not possible in Einstein's physics.

3. Sep 15, 2011

### Andrew Mason

You are correct - a perfectly rigid body is a limit that can be approached but never reached in Newton's world. But why do you say that the two boxes have to be identical in terms of the forces between the walls? The definition of a rigid object would be simply that its volume and shape is constant, not that the forces between its parts are constant, would it not?

The last part your "proof" appears to be based on a premise that the forces between molecules obeys Hooke's law. What is the basis for that assumption?

AM

4. Sep 15, 2011

### A.T.

What happens when two perfectly rigid spheres collide, according to Newtonian physics?

5. Sep 15, 2011

### chrisbaird

They exchange momentum during an infinity small period of time. The instantaneous force at the collision becomes infinite, but in such a way that the total force is still the finite constant required to bring about the proper change in momentum, like a Dirac delta function. Yes, this is an idealization because there are no infinities in the real world, but physics is littered with idealizations. So I would say that we have never observed a 100% rigid object experimentally, but Newton's laws do not forbid it on theoretical grounds. Einstein's relativity does.

6. Sep 15, 2011

### Andrew Mason

A perfectly rigid body is not possible even in Newton/Maxwell physics either. All known forces between bodies depend on separation. Therefore, there can be no change in the forces between the fundamental constituent parts a body without some change in their separation.

Can the limit on how rigid (ie. how small a compression that a body can have) not be determined by Newtonian mechanics (using equations for Coulomb force/Lorentz force, gravitational force, nuclear force)? I expect this would be the same limit that SR would provide, based on the postuates of relativity.

AM

Last edited: Sep 15, 2011
7. Sep 15, 2011

### Redbelly98

Staff Emeritus
Or put another way: the speed of sound in a rigid body is not only faster than c (which would be bad enough), it is infinite.

8. Sep 15, 2011

### Stephen Tashi

It's difficult to judge the validity of an argument if you already believe it's conclusion. Abu Rehan's argument is based on statics rather than dynamics. The statics taught in elementary physics is rather mysterious. An object of 10 lbs rests on the ground in one place and and object of 20 lbs rests on the ground in another place. Somehow the ground knows to push up 10 lbs on the 10 lb objecta and 20 lbs on the 20 lb object. Does that really make sense without considerations of how bodies deform?

9. Sep 16, 2011

### Curl

The two boxes "proof" is rather weak. One can more easily show that "compressibility" must be present using quantum mechanical arguments.