CHAPTER 2
Expansion Process Vs. Newton's Theory
The point of this book is to introduce a new meaning to our understanding of how gravity behaves that is in direct conflict with our present belief. That is rather than being an attractive phenomenon, "all masses are attracted to one another", instead. "all masses grow towards one another". In doing this I introduce a new and different paradigm into our thought processes and all of our instincts and beliefs fight against this change
The first key issue lies in the apparent negative statement against the GEQ concept comes from Newton's gravity law expressed with a plus sign on the right-hand side of the equation.
Acceleration = +GM/R2
The meaning in the GEQ interpretation of this is, " any object, say a sphere, gets larger in time in proportion to the mass (the M) so any spheres with different masses will become different sizes as they expand."
This of course is not what we see; all so-called rigid objects do not change sizes in time! So my first task is to show the above intuitive belief is not true.
To show this let me start by defining what we mean when we talk about the "dimension" of something. A useful definition is in terms of the velocity of light in a vacuum, usually symbolized by the letter "c". What is particularly useful about such a definition is that the velocity of light is the same for all observers so no matter what reference system an observer is in, how he is moving, he can always use the same definition. Furthermore, the peculiar and most useful property of light speed is that no physical object can go faster than "c".
A simple and valuable expression of this definition is:
Length = c*t
That should be read as; "the length of an object is defined by the lapsed time for a pulse of light to travel from one end of an object to the other end."
An example of this is if I measure the "time-length" of a meter stick I will find it is 13.28x10-9 seconds long; and if you, in a coordinate system moving at some large velocity relative to me, likewise measure a meter stick, you will get the same result. OK?
Now let me do a thought experiment according to two different points of view: First with the assumption "rigid rods" are really rigid, do not change length in time (and this of course is the standard view); the second experiment in accordance with the GEQ view that "rigid lengths" actually do change length in time.
Conventional view: Say I have a meter stick that I use to measure the radius of a sphere and find it to be 1 meter. A little time passes and I make a second such measurement and nothing has changed, the radius is as before, 1 meter.
Now let me repeat the same sequence of measurements in accordance with GEQ point of view using you: First measurement of radius, 1 meter. Second measurement a bit time later: What do you see?
That depends: If you are "in" the universe you are subject to its rules and see the same thing I do, but if you are "outside" the universe and not subject to its rules, what you see is the radius has gotten larger between the first measurement and the second! For the sake of argument let's say you see the radius has doubled so it now appears (to you) as 2 meters.
But what do you see? If you are inside the universe, subject to its rules, and what happens to the sphere, must also happen to you and the measurement stick. If you have doubled in size just has the sphere, then you will see no change in the sphere because your measurement stick still registers the same length for the radius. You cannot distinguish between a static situation (no change) and a dynamic situation (change but ratio of sizes unchanged). So, if you are "in" the universe you see the radius unchanged.
There is an important corollary to this and that is that wavelengths of light and frequencies must change in time to match the changes in physical objects and distances. Given the intimate relation between light energy and matter this requirement is a consequence of the expansion and of the observation that all observers see the velocity of light the same. I use light to measure the length of my meter stick in effect saying "it's so many wavelengths long at some particular frequency" so clearly it is so or there is no expansion and GEQ is dead.
On the other hand, Newton's gravity law written as the law of expansion has that nasty "M" on the right-hand side of the equation that implies objects with different densities (spheres or any other form) will expand at different rates and sizes will not be time invariant: A necessary requirement for GEQ to have legs. Looking at the GEQ expansion basis appears to assure us that this condition cannot be met.
Surprisingly, this turns out not to be true mainly because of the speed limit imposed on physical objects that they can never exceed the velocity of light.
As a metaphor consider two balloons expanding at different rates. Initially the balloon expanding faster gets larger because its radial velocity increases more rapidly, but as it nears the velocity of light, its growth rate becomes just below c and becomes nearly constant; the slower expanding balloon speeds up, catches up and from that time onward, they remain very nearly the same size even as they continue to grow in dimension. According to GEQ we are in that state of dimensions since in concept everything has been expanding for a very long time.
Because of this speed limit our intuition is wrong and this can be shown by the following sequences of equations using calculus to find the size of an arbitrary sphere as it expands in accordance with Newton's gravity law, as GEQ would have it, with a plus sign. Here is that derivation for those of you comfortable in the language of calculus: For those of you not comfortable, don't worry, I will explain what is going on here and provide you with the important results.
Equation (6) multiplied by C tells me the exact size of the sphere at any time and includes "M" buried in Rmin. Equation (7) tells me the approximate size of the sphere at any time
and note, the mass term M is missing in equation (7)!
So look what happened. I started with the GEQ version of Newton's law, calculated what the radius would be of an arbitrary sphere after some time had passed, and discovered it would be exactly given by the mess of equation (6), or approximately by the simple expression of equation (7), R =c*t, that looks the same as the definition above of length expressed as an elapsed time!
Neat result, but what does it mean in the context of GEQ?
First, I did this calculation for an arbitrary sphere, so the results would be the same for any sphere independent of its mass. So to the extent the sphere's size is determined by equation (7), all spheres do not change relative sizes as they expand!
Second, to the extent the sphere's size is determined by equation (6), there is a difference in the sizes of spheres of different densities. The fact is the difference is vanishingly small but can be measured under certain conditions, so GEQ can be falsified (or not) by measurement to see if the effect exists or not!
In other words, it is of the utmost importance that there is a very small difference in dimensions predicted by equations (6) versus the equation (7) prediction, that equation (7) has no M in it, and this difference can in principle be measured! The point is this provides me a way of determining by experiment if all matter really is expanding or not.
However, equation (7) has taken on a new meaning in this context, representing the size of the sphere as a function of time in the same way as the observer "outside" the universe sees it. That is, if he sees the sphere doubling in size, that is what is happening from his point of view. That is, the sphere's radius has gone from R to 2*R. But from our point of view we also have doubled in size (rule of this GEQ universe), so we continue to see the sphere unchanged in size and can claim, what remains time invariant in GEQ are sizes to the extent size is in accordance with equation (7)! In other words, any two spheres of different densities will remain the same relative sizes as time passes.
So, equation (7) retains its meaning in this strange ever-expanding universe governed by GEQ rules!
What all the above shows is that the expansion view of GEQ does not disagree with Newton's gravity law (no observer can distinguish between his law with a plus or minus sign) and this is a necessity since his law, within certain constraints is one of those "truths" in physics that holds even though General Relativity replaces it, providing us with a deeper understanding of gravity's behavior.
Another way of looking at this result is that to the extent what I say here is correct, I can replace the present paradigm, all rigid bodies are time invariant in size, with a new paradigm, rigid bodies in fact are not time invariant in size, they only appear that way from our point of view and this can be shown to be false or true under some measurement conditions. ."...
