Einstein provided us with Special Relativity, which taught us about inertia and motion, and then General Relativity which linked Gravity and Inertia
as being one and the same. As such, there should be obvious and glaring parallels in the equations for gravity and inertia, as well as in
philosophies. However, I do not believe, in their current form, the equations provide the full proof of Einstein's staggering claim. (Just to be
clear: I 100% support both special and general relativity, the only issue I have is with the equation for gravity).
The first parallel we should recognize is between (gravity) black holes and the speed of light (inertia). Both dilate time infinitely (or stop it,
whichever your fancy). On the other end of the spectrum we have (inertia) two object at rest relative to one another and (gravity) a completely empty
universe (which, doesn't exist, but still the idealism provides a parallel and does nothing to discredit the idea). There are also shades of gray,
where we can relate a neutron star with a speed close to that of light. What is parallel about these things is 1) Time Dilation, 2) an increase in
relative mass, 3) length contraction (these things have similar characteristics between inertia and gravity, however may not necessarily be exactly
The second parallel SHOULD be in the equations themselves, there should be a recognizable pattern in the philosophies which explain them.
Inertia: sqrt (1 - v^2 / c^2)
Gravity: t sqrt (1 - 2 G M / R c^2)
Instead of going into an in-depth discussion about the variables used, I will only briefly discuss why I believe the equation for inertia is correct
and the gravity equation not.
The equation describing inertia can be summed up quite simply as a measure of the occupation of spacetime over the maximum allowable occupation of
spacetime. The equation for gravity is some kind of hybrid mix of various, potentially legitimate, variables (to be honest, I think we need to dump G
all together, my apologies to Mr. Newton).
Mass is, essentially, a measure of the occupation of spacetime, HOWEVER, it is wholly inadequate for measuring gravity and the effects thereof.
If we look at the equation for inertia, we find that there is a LIMIT on the amount of spacetime matter can occupy, so the same must be true for
gravity (they are THE SAME).
Mass can, potentially, reach infinity, there is no cap to the amount of mass any single black hole can have, so there is SOMETHING MISSING from the
equation for gravity. Density should be included in the measure of gravity. Think of it this way: density is a measure of the depth of time dilation
(how much time is dilated) whereas mass is a measure of the breadth of time dilation (how far away from the origin time is dilated and how much).
Using density, mass, distance (I have NOT created any equation to describe this, I am NOT a mathematician, there may be more to the equation, I do not
know) and realizing the occupation of spacetime, you can truly align inertia and gravity as being one and the same.
You will begin to realize that black holes are not infinitely dense, they are 100% dense. The 100% occupation of spacetime causes there to,
essentially, be no time - as the TIME aspect of spacetime is completely filled with matter, thus causing the "infinite" dilation. Space and mass
are results of the dilation of time, and thus, as time dilates to 0, relative space shrinks to 0 and mass approaches infinity.
This means that gravity and inertia are NOTHING more than the occupation of and curvature of four dimensional spacetime. (It might help you to
understand if I told you to think about all types of motion in terms of time dilation and not distances... or it might just confuse you). A quick
note: space is 3 dimensions, time is a fourth - HOWEVER - time is NOT a dimension of space, so we aren't talking about some funky abstract,
impossible to imagine structure.
I'm sorry if this seems crude or quickly explained. I was never very good at writing papers or reports and this is something I have been meaning to
write up for many months, but kept putting off (I've probably written and re-written this a dozen time, it's just so much information that its
difficult for me to properly encompass everything - that and my hundreds of pages of notes ... oy). Maybe I'll come back in a few more months and
explain this better and continue further... Maybe not
And for those curious about the title: en.wikipedia.org...