In mechanics, one often uses the model of a perfectly rigid body to model and determine the moti

In mechanics, one often uses the model of a perfectly rigid...

Key Concepts

Propagation of Forces

In reality, forces and deformations propagate at finite speeds (for example, as stress waves in materials), ensuring that no part of an object can respond before the effect has had time to reach it. This concept directly conflicts with the rigid body assumption, highlighting the incompatibility between classical rigidity and relativistic constraints.

Rigid Body Model

In classical mechanics, a perfectly rigid body is assumed to deform not at all under the influence of forces, meaning that any applied force causes an instantaneous acceleration across the entire object. This assumption simplifies analysis in many mechanical problems but inherently relies on the idea of instant propagation of internal forces.

Special Theory of Relativity

Einstein’s special theory of relativity establishes that no information or physical effect can travel faster than the speed of light. This limitation means that any change, such as a force or deformation, must propagate at a finite speed, contradicting the notion of instantaneous effects throughout a rigid body.

Transcript

00:01 In this problem, we want to discuss why the concept of rigid body is inconsistent with the special theory of relativity.

00:10 So here is a disc, rigid disk, and two points a and b.

00:14 Rotation axis is out towards you perpendicular to the screen.

00:19 And now, if it was a rigid body, that means that if you make point b start to move, a must move the same exact time.

00:31 But what does that mean in terms of communication information that means that a must have been communicated to with infinite speed that b is moving and that it must move but the special theory of relativity limits the speed to the speed of light nothing can be propagated nothing can be sent faster than the speed of light so a cannot know instantly that b is moving so a and b and b he will be moving.

01:04 A will not until a little bit later.

01:06 It may be a short period of time later, but it cannot move with b.

01:12 Because there is a limitation.

01:15 You cannot be, you cannot know anything instantly.

01:20 Cannot know anything instantly.

01:22 So there's going to be, so that, and remember with a rigid body, one part cannot be moving so that it changes the position, relative positions of all the pieces.

01:32 If b is moving and a is not, if a is delayed in its motion, then this is not a rigid body anymore.

01:38 It be a, are changing their position relative to each other.

01:43 So that makes it non -rigid.

01:45 So the concept of rigid body, special relativity are inconsistent because we have a limitation on how fast we can communicate information and that limitation is the speed of light.

01:59 Nothing can be faster than that.

02:02 For a and b to move when b does, that means we'd have to be effectively, we'd have to, the speed of light, if you want to use that as the limitation, would have to be infinite.

02:15 So you could have instant communication, but that's not the way it is.

02:19 Now, let me give you another example of how things really work in this concept.

02:24 It's not a rigid body in the classic sense, but it gives you the idea of this finite propagation, maybe a situation you've seen in a demonstration, maybe not.

02:33 Think of a collection of coils to stretch out.

02:39 Somebody's holding it at the top.

02:41 Usually a person's on a chair, and they're holding it off the ground.

02:46 So somebody's holding it up.

02:48 These are calls.

02:49 It would have been called.

02:50 You may know a slinky, but you're a collection of coils, and they spread out, if you don't know what a slinky is by name.

03:00 Now, a person's holding it, releases it.

03:05 Many will think, oh, it's just going to fall, even thinking that it's going to fall like a rigid body.

03:10 Because if it did, it would.

03:12 It was stretched out because everybody would have the same acceleration.

03:16 Gee, and everything would fall until anything hit the ground.