[AntonioLao]

If H signifies the n-dimensional volume of a local infinitesimal quantized curvature of spacetime events and if C is a linear contact transformation matrix then the ratio of the transformed volume over the original volume is equal to the Jacobian of the transformation.



Consequently, if the Jacobian is unity then the volume is an invariance of the transformation. Topologically equivalent volumes do not necessarily indicate length and angle invariance. However, geometrical similarity of volumes (e.g., spheres into spheres) implies length and angle invariance.

Many modern cosmologists strongly believe that the universe is expanding implying that its volume is increasing. Furthermore, inflation models suggest that the rate is accelerating or decelerating meaning that it is nonlinear contrary to Hubble’s original prediction. The question is how this variable rate of expansion affects the relative angular distances of its time axis and the time axes of all particles within. One workable hypothesis is that the mean curvature of the universe is not a constant. This can only implies the dynamical configurations (in configuration space of n-dimension) of its two principal minimum and maximum curvature and . As determined by astronomical observations, the mean curvature of the present epoch is almost equal to zero. Since mean curvature is the sum of the principal curvatures, zero mean curvature implies that one of the principal curvatures is negative. Moreover, a negative principal curvature suggests a negative time axis. As a final note, a negative time axis implies a negative volume or negative time axes for all virtual volumes of virtual particles and virtual antiparticles.

[mkirkpatrick]

If we are then expanding,as most seem to think,the volume is already present to permit
this,is it not?





regards michael.

[AntonioLao]

Originally Posted by mkirkpatrick If we are then expanding

Contrary to popular belief, we are not expanding in the cosmological sense of the word. What is expanding according to standard big bang theory is the spacetime continuum and not the 3D space continuum of our physical existence.

[mkirkpatrick]

Originally Posted by AntonioLao Contrary to popular belief, we are not expanding in the cosmological sense of the word. What is expanding according to standard big bang theory is the spacetime continuum and not the 3D space continuum of our physical existence.

The continuum is relative is it not?The space time I mean.





regards michael.

[AntonioLao]

Originally Posted by mkirkpatrick The continuum is relative is it not?The space time I mean.

Both special and general relativity is trying to tell us that the continuum is absolutely relative. But if we take out the time part then it becomes absolutely absolute.

[mkirkpatrick]

Originally Posted by AntonioLao Both special and general relativity is trying to tell us that the continuum is absolutely relative. But if we take out the time part then it becomes absolutely absolute.

Then if that were to happen,the bottom would fall out of volume?


regards michael.

[AntonioLao]

Originally Posted by mkirkpatrick the bottom would fall out of volume

In zero gravity, it appears just like a real hole.

[mkirkpatrick]

Originally Posted by AntonioLao In zero gravity, it appears just like a real hole.

And the exit of this hole?Would that be in this universe,or prehaps another?



regards michael.

[AntonioLao]

Originally Posted by mkirkpatrick Would that be in this universe,or prehaps another

If the universe is a Klein bottle then outside and inside could not be distinguished.

[mkirkpatrick]

Originally Posted by AntonioLao If the universe is a Klein bottle then outside and inside could not be distinguished.

Well then I would guess that it is not a Klein bottle,and that there is another universe
beyond a dimensional portal.



regardsmichael.