# Lorentz Fitzgerald contraction

Does the lorentz fitzgerald contraction hypothesis contradicts the classical motion of rigid body?
I am not sure but i think it doesn't contradicts the classical motion of rigid body.

## Answers and Replies

Nugatory
Mentor
There is no such thing as a classically rigid body in relativity. Google and search here for "Born rigidity" for more.

vanhees71
There is no such thing as a classically rigid body in relativity. Google and search here for "Born rigidity" for more.
Born rigidity only applies when proper acceleration is involved it has absolutely nothing to do with relative motion without proper acceleration.

PeterDonis
Mentor
Born rigidity only applies when proper acceleration is involved

This is not correct. It is perfectly possible to have a Born rigid geodesic congruence. The simplest example is a congruence of parallel inertial worldlines in Minkowski spacetime.

This is not correct. It is perfectly possible to have a Born rigid geodesic congruence. The simplest example is a congruence of parallel inertial worldlines in Minkowski spacetime.
Ok then, what is the difference between a Born rigid and a non Born rigid congruence of parallel intertial worldlines in Minkowski spacetime?

If there is no acceleration it is totally useless to talk about something being Born rigid.

PeterDonis
Mentor
what is the difference between a Born rigid and a non Born rigid congruence of parallel intertial worldlines in Minkowski spacetime?

The first one exists and the second one doesn't. Every congruence of parallel inertial worldlines in Minkowski spacetime is Born rigid.

Meir Achuz
Homework Helper
Gold Member
"Does the lorentz fitzgerald contraction hypothesis contradicts the classical motion of rigid body?"
The classical definition of a rigid body, that it retains its shape when moving, is contradicted by special relativity. An SR definition of a rigid body is that it retains its shape in its instantaneous rest system, even while moving. You could look at
arXiv:1105.3899.

"Does the lorentz fitzgerald contraction hypothesis contradicts the classical motion of rigid body?"
The classical definition of a rigid body, that it retains its shape when moving, is contradicted by special relativity. An SR definition of a rigid body is that it retains its shape in its instantaneous rest system, even while moving. You could look at
arXiv:1105.3899.
What is your definition of moving?

In SR there is no such thing as absolute movement, all movement is relative.
What is not relative is proper acceleration.

PeterDonis
Mentor
An SR definition of a rigid body is that it retains its shape in its instantaneous rest system, even while moving.

This isn't a good definition as it stands, since, as MeJennifer points out, "moving" has no absolute meaning in relativity.

In relativity, there is no such thing as a "rigid body" in the classical sense, because internal forces between different parts of an object are not instantaneous; they can only be transmitted at the speed of light. The best that can be done in relativity is Born rigidity. The technical definition of Born rigidity is that the congruence of worldlines that describes the body (one worldline for each point in the body) must have zero expansion and shear. Heuristically, this means the distances between different parts of the body are constant. However, the conditions under which this is even possible are quite restrictive, much more so than in Newtonian physics, because of the Herglotz-Noether theorem (which you can look up for more info).