If the universe started as a point (BigBang) and is expanding symmetrically then it would result in an expanding 4 Dimensional sphere.
Consider the universe to be a 4 Dimensional sphere with time as the radial Dimension. Then all of space at “present” would be represented by the “3D Surface” of the sphere. Thus each point in space at “present” would be a boundary point. Now the expanding universe would correspond to an increase in the radial dimension or time. If the sphere is to remain a sphere then it would have to be accompanied by an equal increase of the surface or space.
Let us take a 2D cross section from this 4D sphere containing its centre. This would be a familiar circle with the radius representing time and the circumference 1D of space. Thus the size of this 1D of space at any time t would be given by
1D space = Constant*2*pi*t
Thus d(space)/d(time) = Constant*2*pi = CONSTANT.
Could this CONSTANT = C = Speed of light?
That is the circumference is increasing at the speed of light? Getting back to the 4D sphere this would mean that each point in space at “present” expands out into a sphere of radius C.
Speculating further, if around matter this expansion is changed, that is
d(space)/d(time) is not equal to C. It could well be that matter is none other than those areas in which this constant is made less than C. Thus matter would be seen to attract each other or gravity would be proportional to the extent that matter has altered this constant C around it. The increase in entropy or disintegration of matter would be a direct result of the rate of expansion within matter tending towards the rate C which is the rate of empty space Time. This would also explain why the Hubel Constant, the rate of expansion of the visible universe, is far less than C, as it has much matter.
In the above model , if space is a 3D spherical surface then a space ship heading in one direction should come back to the starting space coordinates, having travelled the circumference, just like going round the world. However the hitch is he has to travel faster than the speed of light as the circumference is increasing at this rate.
Objections.
The curvature as measured via cosmic microwave radiation suggest that the universe is flat. However this is also consistent with a rate of expansion = C as if it expanded for 14 Billion years at that rate, the distances measure in back ground radiation measurements , will only be that of a tangential surface, which will always be flat.
Consider the universe to be a 4 Dimensional sphere with time as the radial Dimension. Then all of space at “present” would be represented by the “3D Surface” of the sphere. Thus each point in space at “present” would be a boundary point. Now the expanding universe would correspond to an increase in the radial dimension or time. If the sphere is to remain a sphere then it would have to be accompanied by an equal increase of the surface or space.
Let us take a 2D cross section from this 4D sphere containing its centre. This would be a familiar circle with the radius representing time and the circumference 1D of space. Thus the size of this 1D of space at any time t would be given by
1D space = Constant*2*pi*t
Thus d(space)/d(time) = Constant*2*pi = CONSTANT.
Could this CONSTANT = C = Speed of light?
That is the circumference is increasing at the speed of light? Getting back to the 4D sphere this would mean that each point in space at “present” expands out into a sphere of radius C.
Speculating further, if around matter this expansion is changed, that is
d(space)/d(time) is not equal to C. It could well be that matter is none other than those areas in which this constant is made less than C. Thus matter would be seen to attract each other or gravity would be proportional to the extent that matter has altered this constant C around it. The increase in entropy or disintegration of matter would be a direct result of the rate of expansion within matter tending towards the rate C which is the rate of empty space Time. This would also explain why the Hubel Constant, the rate of expansion of the visible universe, is far less than C, as it has much matter.
In the above model , if space is a 3D spherical surface then a space ship heading in one direction should come back to the starting space coordinates, having travelled the circumference, just like going round the world. However the hitch is he has to travel faster than the speed of light as the circumference is increasing at this rate.
Objections.
The curvature as measured via cosmic microwave radiation suggest that the universe is flat. However this is also consistent with a rate of expansion = C as if it expanded for 14 Billion years at that rate, the distances measure in back ground radiation measurements , will only be that of a tangential surface, which will always be flat.