2.1 A hint to gravityLet us imagine we have a sphere of radius R filled with energy E. The sphere initially would have an energy density of:
then we start compressing the sphere in all
directions making the radius R of the sphere smaller, and hence
the energy density greater. Now let us assume that there is a maximum
energy density that spacetime can have, and let us assume that we
reached that density by compressing our sphere to its limits. What we
would have is simply a very dense sphere of energy as shown in Figure
2.1, that would be impossible to shrink further. But I am not done
with assumptions, and I will assume that I have a much greater force,
even greater than the force that spacetime has to keep it from
shrinking. Well, if I compress the sphere even further, and spacetime
cannot stand more energy than that, the only thing that spacetime can
do is to shrink with the energy it contains, hence producing something
as shown in Figure 2.2. This figure is the same as Figure 1.5e which
was derived from General Relativity as discussed in paragraph 1.3.2.
Hugh D. Young in his book University Physics states "all nuclei have approximately the same density". The idea that comes to mind now is; what if what we have described so far is the nucleus of an atom? What if there was a fight between the nuclear force that compress the nucleus together and spacetime that limiting its density prevents it from collapsing into a dimensionless point? Obviously one nucleus on its own would not have enough force to distort spacetime considerably, but many atoms put together as in large masses might just have that force. In this case we would still be able to measure the stiffness of spacetime as we know the force of the nucleus and the displacement. The force is simply the sum of all the forces of all the nuclei that make up the mass, the displacement would be the gravitational redshift (Dl/l) caused by the mass/energy itself, something like:
where N is the number of atoms present in the mass. |
Fig 2.1 - Sphere of energy compressed to the limit. Fig 2.2 - Same as Figure 1.5e, but this time it shows a sphere full of energy compressed with a force greater than the stiffness of spacetime. The volume of the two sphere is the same, and so is the density. |