# Questions on World Enough And Space-Time

Discussion in 'Physics & Math' started by Anti-stupidity, Oct 19, 2017.

1. ### Anti-stupidityRegistered Member

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So i was reading my new book from amazon.com, World Enough And Space-Time: by John Earman, when I came across a chapter that I looked forward too when reading through the contents page. The book is a simple introduction to many of the common philosophical, historical, perspectives or arguments professed in the Substantialist-Relationist debate on the ontological status of space-time (Does it inhere in the objects we use to distinguish space or time or is there a substratum of Spatio-Temporal points independent of objects & their properties).

This chapter was dipping into some of the various classical spacetime structures and used few but still enigma rich mathematical notation.

The first is Machian Space-Time, as he put it.

Here are a few equation questions i'm wondering:

In defining the nature of Machian Space-Time he decides to introduce a symmetrical contravariant tensor field,

.

What is the purpose of a symmetrical contravariant tensor field? When would you decide to use it and how? What is its purpose?

I have seen this kind of device before used in special relativity,

with a signature of either (-,+,+,+) or (+,-,-,-).

Than he mixes the simultaneity of time structure with

which forces it to be this:

, this I understand.

Later, to make an appropriate metric over instantaneous spaces, he defines a covector

coressponding to a space-like vector

by,

What is the difference between a covector and a regular vector? What makes a vector a space-like vector? Does it mean space-like because its components are only

or is there some other mathematical reason?

Then he wrote that

was not unique since it solves the above equations so this does also solve it,

for an arbitrary

.

What is exactly similar between these two,