Born rigidity is a concept in special relativity. It is one answer to the question of what, in special relativity, corresponds to the rigid body of non-relativistic classical mechanics.
This sentence is not clear. What is a rigid body? What is not a rigid body?
What is the physical difference.
As a result, Born (1910) and others gave alternative, less restrictive definitions of rigidity.
What you need is first of all a physical defintion.
1. Definition
Born rigidity is satisfied if the orthogonal spacetime distance between infinitesimally separated curves or worldlines is constant,or equivalently,
That is maybe true but the text is not clear what is really meant.
if the length of the rigid body in momentary co-moving inertial frames measured by standard measuring rods (i.e. the proper length) is constant and is therefore subjected to Lorentz contraction in relatively moving frames.
Also this sentence is not very clear.
My own first impression is that a moving rigid body, should not undergo length contraction.
Born rigidity is a constraint on the motion of an extended body, achieved by careful application of forces to different parts of the body.
Also this sentence is not very clear. You need more detail to understand.
See Reflection 1 - General
2. Stresses and Born rigidity
3 Born rigid motions
A classification of allowed, in particular rotational, Born rigid motions in flat Minkowski spacetime was given by Herglotz, which was also studied by etc.
If you want to understand this it must clear what the difference is between 'motions' in general versus 'Born rigid motions'. Has this something to do with the bodies studied (i.e. rigid versus non-rigid bodies) or with the motions of these bodies?
3.1 Class A: Irrotational motions
He concluded, that the motion of such a body is completely determined by the motion of one of its points.
This can only be true for round objects?
3.2 Class B: Rotational isometric motions
This whole paragraph is much too mathematical.
4 General relativity
Attempts to extend the concept of Born rigidity to general relativity have been made by Salzmann & Taub (1954).
Before you do that the concept "Born rigidity" should be clear. What does it physical mean.
5 Alternatives
Several weaker substitutes have also been proposed as rigidity conditions, such as by Noether (1909) or Born (1910) himself.
That maybe true. But what is missing are certain details
6. See also
Following is a list with "Comments in Wikipedia" about related subjects
If you want to understand the universe or shorter by home i.e. our local physical environment, than almost always: you have to perform experiments. This you can call the golden rule of physics.
Related to the behaviour of bodies apperently you can make a distinction between two types:
Bodies that are not rigid. These bodies experience length contraction when in physical movement.
Bodies that are rigid. These bodies do not experience length contraction when in physical movement.
The problem is that the article does not clearly indicate which materials belong the one or the other group.
What is worse the article also does clealy explain the experiment (setup and its details) how you can decide if a material is either rigid or not. In fact this experiment should demonstrate length contraction (as a function of the matirial used).
It seems that the whole concept of "Born rigidity" is treated as a thought experiment, which makes it rather unscientific, if it is not supported by real experiments.
Reflection 2 - (Thought) Experiment
The purpose of this experiment is to demonstrate the difference between non rigid and rigid material.
Non rigid material is supposed to experience length contraction.
Rigid material is not supposed to experience length contraction.
The Figure's 1, 2 and 3 show the possible outcome of an actual experiment. The question is which one is true?
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Figure 1
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Figure 2
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Figure 3
Each figure consists of two parts:
The top part is a train which stays at rest in the background.
The bottom part is a train which passes in front of this train in the front.
Each train consists of two "parts"
The bottom part is the actual train, which moves over the rails.
The top part is the cargo, a rod, which floats above the train and which is connected in the center with the train.
The length of the train and the length of the rod at rest are identical.
The three possible outcomes are:
In figure 1 the train contracts but not the cargo.
In Figure 2 both the train and the cargo contract. This means the concept of rigid versus not rigid material is not existing.
In Figure 3 the train does not contract but the cargo. If this answer is true than answer 1 should also be true.
There is also a fourth answer possible that neither one is true.
What makes this experiment simple is that clocks are required.
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Created: 16 February 2015
Updated: 20 September 2017
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