# Tensors may be considered a special class

1. May 14, 2004

### Janitor

I once read that tensors may be considered a special class of a more general class of entities called 'holors.' It was just a parenthetical comment; no further information was supplied.

Can anybody fill me in on this topic? In what sense is holor a generalization of tensor? What branches of mathematics or physics make use of holors?

2. May 14, 2004

### MathematicalPhysicist

i myself dont know anything about holors but from what i found in google there is a book about this very specific issue you might find it usefull:
https://www.amazon.com/exec/obidos/ASIN/0521245850/weisstein-20/104-7769069-9375115

one of the authors is Domina Eberle Spencer (i posted about her article on her interpratation of HAFELE-KEATING experiment you can find it here:
http://www.physical-congress.spb.ru/english/spenser1/spencer1.asp the post itself is in theory development forum).

3. May 14, 2004

### Janitor

Thanks for the links, LQG. The price of that book at Amazon scares me. The review of the book at least gives me an inkling of what holors are about.

4. May 15, 2004

### MathematicalPhysicist

for this we have libraries.

5. Jun 21, 2004

### Tommunist

The Theory of Holors

I have recently purchased The Theory of Holors, which I have been looking to do for quite awhile during my study of Tensor Analysis. A holor is basically a generalization of tensors, spinors (which include quaternions), twistors, et cetera. It generalizes the object to such an extent that a holor can be produced for about anything that can be described by a matrix of integral dimensions (almost every property of any physical entity can be described by a holor). It introduces the holor without the need for a specific transformation rule; in fact, some examples include holors which have no transformations at all.

The book tries to merge vector and tensor analysis by generalizing notation for a tensor. The new notation is extremely strict; however, it has much more upsides than down. At first I felt a bit weary about using the new notation since most books are written in the older, more ambiguous notation (including boldface vectors and tensors), but later I realized it is best to know both of these languages -- one should use the holor notation in applications that require more generalized objects than tensors or in applications that require strict notation.

The book was published in 1986; as far as I know, it is the only work on this topic. The older notation has, obviously, not given way to the newer form; probably because the less mathematically strict physicists and engineers dominate the applied mathematics world. However, I strongly encourage anyone interested in general relativity, quantum gravity, or quantum field theory to read this book and become familiar with its mathematical language. The information from it is definitely worth the price.

6. Jun 21, 2004

### Janitor

Hmmm, maybe the same sort of people who like category theory would find the holor idea attractive.