Space has no time. No beginning No end.

[MigL]

Consider a torus, studiot, where the two dimensional surface is a simplification of our 4D space-time. We can picture this 2D surface in our 3D space as a doughnut shape. So this 2D surface needs embedding in a higher dimension.

We note however that this surface is not simply connected, ie. a loop around a certain section of this space cannot be drawn down to zero radius ( around the inner 'hole' and normal to the outer diameter ). This implies certain directions are favoured. We also note that around the outside of the doughnut the curvature is positive and triangles have more than 180 deg., while on the inner surface the curvature is negative and triangles have less than 180 deg. such that there are also preferred rotations. This means an embedded torus lacks translational as well as rotational symmetry.

 

Now consider a flat torus which we can picture as a map where the top is identified with the bottom and the right side is identified with the left. We note that even in 3D we cannot picture it because its curvature is intrinsic, ie. it doesn't need to be embedded in a higher dimension. We also note that in this case, translational symmetry and rotational symmetry is preserved. This is a good thing because if they were not, according to Amy Noether, we wouldn't have conservation laws for momentum and angular momentum.

 

Keep in mind that I'm certainly no expert in topology, so some of my reasoning may be flawed.

[mattrsmith88]

maths can't solve everything. If there is a equation for an unbounded universe, it will be an endless one

[studiot]

Thank you for this information, MigL, I was not aware of this work. Isn't there a lot of work going on in many directions?

 

However I don't see that a flat torus provides a manifold that does not require a higher dimension to exist in. This is certainly acknowledged in the analyses I have seen, eg

 

http://math.univ-lyon1.fr/~borrelli/Hevea/Presse/index-en.html

 

Such an object is only locally flat, in the sense that a straight line is an arc of a circle of infinite radius. You need to find a globally flat universe, otherwise the triangulation exercise I described will still show discrepencies.

 

All 3D objects possess 2D surfaces, you cannot have the surface without also having the object.

 

However there is a more promising approach as a candidate for Strange's manifold requirement, which is essential a desire for the surface without the object.

 

If you choose a space filling curve you have a manifold but no object, although the 'curve' occupies 2D or 3D space. The curve can be considered an ordered list of points in the space.

 

http://www.dcs.bbk.ac.uk/~jkl/BNCOD2000/slides.html

 

An interesting consequence of this is that 2 points can be adjacent in 2D or 3D space, but not be neighbouring points in the manifold.

 

(Plenty of scope for scifi here)

 

go well

[machapungo]

Time is a mental construct not a physical reality..

 

As a mental construct time can only exist in a brain and it is used to measure motion.

 

As a mental construct, it can have a beginning and an end.

 

Current physics has time starting at the moment of the big bang because at that moment there is nothing to use as a clock but, of course, there are no thinking entities either.

 

What we use as a clock is arbitrary and a clock is just something that moves at a relativly consistent speed and repeats at a relatively consistent rate.

 

We thinking entities should not confuse the observer wih the observed..

Edited November 3, 2013 by machapungo

[BusaDave9]

Time is a mental construct not a physical reality..

 

As a mental construct time can only exist in a brain and it is used to measure motion.

 

No, time is the 4th dimension of the universe. But it is true that our mental image may not match what time really is. Einstein helped us understand time as a dimension of our universe.

 

Red is a real color. It's wavelength is about 700 nanometers. Now our mental image of red is a vibrant exciting color. On the other hand our mental image of blue is a cool, soothing color.

Edited November 3, 2013 by BusaDave9

[studiot]

There are several articles in this week's New Scientist about the existence (or non existence) of time.

 

http://www.newscientist.com/section/physics-math

[Endy0816]

I think as long as there is causal trail backwards, from point A to B, then the moment was real even without a living observer.

 

Our observation of the present is the sum total of everything that has happened in the past.

 

There are events that could end up out of reach, unknowable. When spacial expansion outpaces light speed, or if there is a "period" of nonlinear time. Tricky things to try and discuss :/