Circles in Minkowski space: unknown notation

  • Thread starter nomadreid
  • Start date
  • #1
nomadreid
Gold Member
1,430
141

Main Question or Discussion Point

I am reading an article about Minkowski space (as a vector space, which is why I am putting my question in this rubric) which is poorly translated from the Russian, and have come across several notational curiosities, most of which I have been able to figure out. However, there is one that I do not know. Talking about positive and negative radii, the author refers to "m-m circles". (Apparently "m" is not significant, as he also refers to "n-n circles" and other letters.)
Specifically, he says:
"The invariant of the [Lorentz] transformations is
-x22 = R2 = inv
...
For R2>0 the orbits are n-n Minkowski circles with real radii R, for R2<0 the orbits are m-m circles with imaginary radii Ri."
Nowhere in the paper does the author indicate that he has coined these terms; apparently they are standard terms in Russia. But I don't know any Russian mathematicians or physicists. So:
(1) what do these terms refer to? (guesses also welcome)
(2) are these standard terms in English? If not,
(3) what are the corresponding standard terms in English?
Even a partial answer will be much appreciated. Thanks.
 

Answers and Replies

  • #2
pasmith
Homework Helper
1,740
412
I am reading an article about Minkowski space (as a vector space, which is why I am putting my question in this rubric) which is poorly translated from the Russian, and have come across several notational curiosities, most of which I have been able to figure out. However, there is one that I do not know. Talking about positive and negative radii, the author refers to "m-m circles". (Apparently "m" is not significant, as he also refers to "n-n circles" and other letters.)
Specifically, he says:
"The invariant of the [Lorentz] transformations is
-x22 = R2 = inv
...
For R2>0 the orbits are n-n Minkowski circles with real radii R, for R2<0 the orbits are m-m circles with imaginary radii Ri."
Nowhere in the paper does the author indicate that he has coined these terms; apparently they are standard terms in Russia. But I don't know any Russian mathematicians or physicists. So:
(1) what do these terms refer to? (guesses also welcome)
(2) are these standard terms in English? If not,
(3) what are the corresponding standard terms in English?
Even a partial answer will be much appreciated. Thanks.
"Space-like" and "time-like" spring to mind, although it may be that the author is using a different sign convention than that adopted by Wikipedia.
 
  • Like
Likes 1 person
  • #3
nomadreid
Gold Member
1,430
141
Many thanks, pasmith. That would make perfect sense in the context.

(I am curious why "m" and "n" . "Space" and "time" in Russian don't begin with those letters. And why repeated (n-n, m-m)? But these questions would be more "Trivial Pursuit" for etymology fanatics, not for a Physics Forum, so I won't lose any sleep over such details, as long as I can understand what physics the author is referring to.)
 

Related Threads on Circles in Minkowski space: unknown notation

Replies
6
Views
971
  • Last Post
Replies
2
Views
4K
Replies
10
Views
1K
  • Last Post
Replies
4
Views
5K
Replies
8
Views
813
Replies
6
Views
4K
  • Last Post
Replies
8
Views
884
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
3
Views
5K
Top