"Henry Haapalainen" wrote in message
...

"Bill Hobba" kirjoitti viestissä
...

"Henry Haapalainen" wrote in message
...

"Tom Roberts" kirjoitti viestissä
t...
fuzzlogic wrote:
I find all the textbooks showing spacetime as a 2D plane and the
heavy
objects bending it.

That is a mere ANALOGY. For instance, it cannot possibly "explain"
gravitation, because it requires gravity to make the heavy objects
bend
the "rubber sheet".


but how does this be interpreted in the real 3D world?

It needs to be applied in 4D spaceTIME. The word "curvature" is really
a
metaphor, or rather, a technical word with a specific meaning not
applicable to our everyday lives (unless you are a physicist (:-)).

The justification for using this term is that mathematically what is
called "curvature" in N-dimensional manifolds has a direct
relationship
to the local radius of curvature for a 2d surface.

To understand this requires some modest amount of study. I suggest:

Geroch, _General_Relativity_from_A_to_B_. This is a
non-mathematical introduction to the concepts of GR.

Tom Roberts

Curvature of space is not a metaphor. It is a correct description of
reality. But space time is a metaphor. It is a wrong explanation.

http://www.wakkanet.fi/~fields/

Henry Haapalainen

Since it is fully in accord with all experimental evidence your claim
lacks
any foundation.

Bill

Don't you ever get tired on that? HH

No.

Bill

To Einstien's theory of curved spacetime which is "concave" inward I
add my :convex" spacetime outward. Einstien took care of
attraction,and I took care of repulsion. We exist in a concave
"Einstien" spacetime,but about 7.5 billion light years distance space
takes a "Glazier" twist and space bends to convex. Thus at great
distances space accelerates away from us,and the greater the distance
the greater its inflating speed. Both inward or outward spacetimes
means they flow in opposite directions however they still have this in
common. They both keep the same relative rate of time. Bert

"G=EMC^2 Glazier" wrote in message
...
To Einstien's theory of curved spacetime which is "concave" inward I
add my :convex" spacetime outward. Einstien took care of
attraction,and I took care of repulsion. We exist in a concave
"Einstien" spacetime,but about 7.5 billion light years distance space
takes a "Glazier" twist and space bends to convex. Thus at great
distances space accelerates away from us,and the greater the distance
the greater its inflating speed. Both inward or outward spacetimes
means they flow in opposite directions however they still have this in
common. They both keep the same relative rate of time. Bert

You forgot, as usual, to take into account the ultimate principle, stew
paints isomorphism.

Bill

Tom Roberts wrote:
Mahmoud In My Dinner Jacket wrote:
[...]

All your values for the dimensionality of an embedding space are wrong.
For instance, not all 2-d manifolds can be embedded in a 3-d space --
the Klein bottle is an explicit counterexample (and it is flat).

That sounds like an awkward case.

In fact, to isometrically embed an arbitrary 3,1-dimension spacetime
manifold in a FLAT manifold requires a manifold of k,m dimensions (k
spacelike and m timelike). The tightest limits on k and m I know of a
k=88, m=2 -- that is ENORMOUS compared to your guesses.

Interesting.

Could spaces be split up in more ways than space-and-time, I wonder?
E.g., a seven-dimiensional "space" with 3 spatial dimensions, one
temporal, one treacle tart, one rock candy and one egg-mayonnaise salad

?

Mahmoud In My Dinner Jacket wrote:
Tom Roberts wrote:
Mahmoud In My Dinner Jacket wrote:
[...]

All your values for the dimensionality of an embedding space are wrong.
For instance, not all 2-d manifolds can be embedded in a 3-d space --
the Klein bottle is an explicit counterexample (and it is flat).

That sounds like an awkward case.

In fact, to isometrically embed an arbitrary 3,1-dimension spacetime
manifold in a FLAT manifold requires a manifold of k,m dimensions (k
spacelike and m timelike). The tightest limits on k and m I know of a
k=88, m=2 -- that is ENORMOUS compared to your guesses.

Interesting.

Could spaces be split up in more ways than space-and-time, I wonder?
E.g., a seven-dimiensional "space" with 3 spatial dimensions, one
temporal, one treacle tart, one rock candy and one egg-mayonnaise salad

?

Or even an eight-dimensional one with one fruitcake. :-D