# Expansion as stretching

PeterDonis
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2019 Award
You could distinguish between cylinder and plane
By sending out a probe around the curved dimension of the cylinder...
It would come back to you from the other direction
This is extrinsic curvature, not intrinsic curvature. bapowell was talking about intrinsic curvature.

PeterDonis
Mentor
2019 Award
The fabric of space-time is static and unchanging in some sense
I already addressed this in post #7. The concept of "change" requires time as an external parameter. With reference to spacetime, time is not an external parameter; it's one of the dimensions of spacetime. So spacetime is not "changing" or "unchanging"; it just is.

The space-time of the past and the fabric of the future already exist
This would be fine if you left out the word "already". That word implies time as an external parameter. The "past" and "future" are just different parts of spacetime, like the southern hemisphere is a different part of the Earth's surface.

We occupy a thin spatial slice of the fabric
No, we don't; "we" are not points. We are worldlines (or world-tubes if you take into account that all objects have a finite size). The instant of "now" for each of us is the intersection of our world-tube with a particular spacelike slice of spacetime. But that intersection is not what "we" are, because time is a dimension of spacetime, and "we" occupy that dimension as well as the spatial ones.

And it so happens that the slices are becoming bigger
The word "becoming" is not appropriate here, because it implies time as an external parameter. See above.

It is NOT ONE STAGE stretching...

But rather a series of sequential stages which happen to be becoming bigger
You're headed in the right direction, but there's that word "becoming" again. A better way to put it would be the way I put it in post #7:

the spacetime geometry of our universe is such that "slices" cut out of it a certain way have a spatial scale factor that increases along a timelike direction orthogonal to those slices

TEFLing
This would be fine if you left out the word "already". That word implies time as an external parameter. The "past" and "future" are just different parts of spacetime, like the southern hemisphere is a different part of the Earth's surface.

No, we don't; "we" are not points. We are worldlines (or world-tubes if you take into account that all objects have a finite size). The instant of "now" for each of us is the intersection of our world-tube with a particular spacelike slice of spacetime. But that intersection is not what "we" are, because time is a dimension of spacetime, and "we" occupy that dimension as well as the spatial ones...

:
What is philosophically special about" now "

Such that we are aware of now

In a very different way from the past and future?

What is special about the present?

Can something sensible be said?

PeterDonis
Mentor
2019 Award
What is philosophically special about" now "

Such that we are aware of now

In a very different way from the past and future?
A quick side question: why are you putting extraneous line breaks in?

If you mean this a a philosophical question, it's off topic here; this is a physics forum.

If you really mean it as a physics question, then the answer is that there is nothing special, physically, about "now". It's just a particular set of events that get picked out when you choose coordinates.

As far as what we are aware of, we are not aware of "now" because of the finite speed of light. We are only aware of our past light cone. (Actually, in practical terms, the nerve signals in our brains that instantiate our awareness travel a lot slower than light, so what we perceive as "now" is actually a time interval of something like 10 to 100 milliseconds, which is a very long time in fundamental physics terms.)

What is special about the present?
Physically speaking, nothing. See above.