# Orthochorous? Don't think I've heard that term before

• Fredrik
In summary: Perseus:text:1999.0011.0008&colid=:C1F740The noun isochor and the adjective isochoric are derived from the Greek words ἴσος (isos) meaning "equal", and χώρος (choros) meaning "space."
Fredrik
Staff Emeritus
Gold Member
An arbitrary Lorentz transformation ##\Lambda## in 1+1 dimensions can be written as
\begin{align}
\Lambda=\frac{\sigma}{\sqrt{1-v^2}}
\begin{pmatrix}1 & -v\\ -\rho v & \rho\end{pmatrix}.
\end{align} Here ##\sigma=\operatorname{sgn}\Lambda_{00}## and ##\rho=\det\Lambda##. I learned today that ##\Lambda## is said to be orthochorous if ##\sigma\rho=1##. I don't think I've ever heard that term before. (I found it in Streater & Wightman...which by the way is the second hit if I google the term). Can someone explain this term? Is it standard? What does the "chorous" part refer to? Now that I think about it, I realize that I don't even know what "ortho" means, so I wouldn't mind getting that explained too.

And no, I'm not misspelling "orthochronous". This is a different word.

In thermodynamics, an 'isochoric' process is one where the volume remains constant, so I'm guessing 'chorous' in orthochorous means volume. And ρ = det Λ is the factor by which the transformation changes volumes.

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Orthochorous is another subgroup where orthochronus preserves the direction of time. Orthochorus preserves the sign of the volume of space (Lorentz transformations)

this link has some of the various subgroups and mathematics involved

edit : its kind of strange that one can find dozens of links describing the subgroups orthochronous, proper, and restricted but finding coverage of orthochorous is almost non existant.

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Mordred said:
section 6.3 of this article covers some of the sub groups, took a bit to find it hope that helps
It might, but I think I understand the subgroups well enough. I'm mainly concerned with the terminology right now.

Based on what you guys said, it seems likely that some form of the word "chorous" means "volume". Thanks both of you.

Well, as per original ancient Greek, it doesn't

<Etymology

The noun isochor and the adjective isochoric are derived from the Greek words ἴσος (isos) meaning "equal", and χώρος (choros) meaning "space."> (from here).

Also χῶρος LSJ, Middle Liddell, Slater, Autenrieth 2.422 0 a definite space, piece of ground, place
χώρα LSJ, Middle Liddell, Slater 15.125 2 space

http://www.perseus.tufts.edu/hopper/definitionlookup?type=begin&q=volume&target=greek

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## 1. What is orthochorous?

Orthochorous is a term used in biology to describe an organism that has a straight or direct development path from embryo to adult stage.

## 2. How is orthochorous different from other modes of development?

Orthochorous is different from other modes of development, such as metamorphosis or indirect development, because it follows a linear and direct path without any significant changes in body structure.

## 3. Are all organisms considered orthochorous?

No, not all organisms are considered orthochorous. Many invertebrates, such as insects and crustaceans, undergo metamorphosis and are not considered orthochorous. However, most vertebrates, including humans, follow an orthochorous development pattern.

## 4. What are some advantages of orthochorous development?

Orthochorous development allows for a more efficient use of resources and energy, as there are no major changes in body structure. It also allows for a faster development time, which can be advantageous for survival in certain environments.

## 5. How is orthochorous development studied in scientific research?

Orthochorous development is studied through various methods, including observations and experiments on different species. Researchers also use molecular and genetic techniques to understand the underlying mechanisms and evolutionary history of orthochorous development.

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