My maths is shaky but I can follow your formula OK. But it does seem you assume a value for 'a' at the beginning of time to give the answer you want.

But whatever the scientific basis for 'a', my problem lies with the phylosophy because I find it difficult to grasp the concept of 'nothing' in a 3+1 dimensional world, where 'a' seems to be a value occuring at a point just after 'nothing' ends. Which then puts us into beginning of 'infinity' where 'forever' is another difficult concept to grasp.

I do not expect an answers as such. I just wondered.

Quoting horace40: ". . .But it does seem you assume a value for 'a' at the beginning of time to give the answer you want. . . . But whatever the scientific basis for 'a', my problem lies with the philosophy because I find it difficult to grasp the concept of 'nothing' in a 3+1 dimensional world, where 'a' seems to be a value occurring at a point just after 'nothing' ends."

The expansion factor 'a' is not really a dimension. It just says that if a = 1 today, then long ago, 'a' must have been very much smaller than 1. The smallest 'a' that has been measured is in fact about: a = 1/1100 (one-eleven-hundredth) which represents the time when (at least our part of) the universe first became transparent.

Further, the hypothetical case of "a=0" simply means "before expansion started", about which can only be hypothesized - so try not to develop a headache about it!

Jorrie

Jorrie,

This question a not related directly to the immediate post but one that has come up for me several times. It has to do with what a geodesic is.

Is a geodesic the shortest path between two points in a given space. In other words, would the geodesic of a region of space with no gravity (flat space) just be a straight line? Is it more complicated than that (not just the shortest distance).

Sorry if this is a bit off topic,

Roger

Hi Roger, you asked: "Is a geodesic the shortest path between two points in a given space."

Not necessarily. See below.

"In other words, would the geodesic of a region of space with no gravity (flat space) just be a straight line?"

In this case, yes.

A geodesic is really the path of least action and not the shortest path in general. In a gravity-free environment, it is a straight line and in a gravitational field it is not. An inertial orbit around Earth follows a space-time geodesic and it is easy to see that it is neither a straight line in space, nor the shortest spatial distance between two arbitrary points lying on the orbit.

Remember that in relativistic gravitation theory, what is normally considered is space-time, so what matters there is space-time geodesics, but they follow the same basic principle of least action.

Hope it helps. Jorrie

Jorrie,

where does this equation come from? Is it derived from something fundamental in relativity?

Hi Roger, no it is not a specific relativistic requirement. The equation you refer to is loosely described in the eBook on page 177, coming from:

which is the square root of an energy divided by a 'distance'. The Einstein-de Sitter model deals with a universe that is precisely balanced between collapse and 'escape' (expanding forever), much like an escape velocity.

That really gave me a lot of insight. Thanks Jorrie. I'll have to think about this a bit.