Abstract
The hypothesis proposed in this article assumes modification of the function for gravitational time dilation,
. In this hypothesis,
is replaced by
. The result that follows from this is that galaxies have the same sign of binding energy as quarks.
Definition of Binding Energy
Before we go further, we must define binding energy in a fundamental way. The "binding energy" described in this article is the net energy of gauge bosons which is released during the formation of the object being considered. Conversely, a negative binding energy represents the net energy of gauge bosons which is
absorbed during the formation. Further we may assume that the binding energy to be considered is directly related to the binding energy of an atomic nucleus in that it involves mass defect. In this interpretation, we assume that
*c^2)
is the binding energy where
is the total mass of matter taken minutest piece by minutest piece (i.e. when they are not interacting or when they are distantly seperated), where
is the mass of the "whole" matter (i.e. when these minutest pieces are together), and where
is the potential. By defining binding energy in this way, we make the two following things equal: the total binding energy of the system and the
net energy of the gauge bosons released from the system during formation.
Mathematical result from these assumptions
Established formula:
Proposed formula:
c^2}{m_{parts} c^2}}})
Rearranging the formula:
^2=1-\frac{\left(m_{parts}-m_{whole}\right)c^2}{m_{parts} c^2})
^2=1-\frac{\left(m_{parts}-m_{whole}\right)}{m_{parts}})
^2=1+\frac{\left(m_{w hole}-m_{parts}\right)}{m_{parts}})
^2=1+\frac{m_{whole}} {m_{parts}}-1)
^2=\frac{m_{whole}}{m _{parts}})
This implies that:
as long as
, and that:
as long as
.
This leads to two categories of things:
1) If the mass of the whole is
less (not greater) than the mass of the parts, then the objects will experience a time dilation, and also, the fraction of binding energy to rest energy is positive.
2) If the mass of the whole is
greater (not less) than the mass of the parts, then the objects will experience a time acceleration, and also, the fraction of binding energy to rest energy is negative.
The first category corresponds to things whose formation (in net) has added a number of gauge bosons to free space (e.g. stars, pulsars, and white dwarfs).
The second category corresponds to things whose formation (in net) had subtracted a number of gauge bosons from free space (e.g. quarks, leptons, and other matter formed during the "cosmic" dark ages).
Where does the formation of a galaxy fit in? It could be said that galaxies have formed before stars have shined among them. If they were simply lanes and nodes of gassy light elements scattered sparsely across space and time it is concievable that much of the radiation they absorbed would not be released just as fast, provided that temperature outside them was greater. This is given if the result of radiation intake leads to a net increase in the angular momentum of the cosmic gas (i.e. more angular momentum leaves free space and enters into the realm of matter).
We see the opposite in the formation of stars, which occurs in a vastly different thermal enviroment. When stars form, the temperature outside is less than the temperature within. Naturally, heat energy from stars will leave the mass from which is produced and into free space. The only way a good fraction of that radiation could be absorbed is for there to be a good amount of regions at some place(s) and time(s) where the "cosmic" dark age reigns, otherwise, galaxies may only continue to form by mergers. Gamma rays with high enough energy can cause the formation of subatomic particles in regions exhibiting properties which were more dominant in the cosmic "dark age".
Possible experiments
1) The formula considered clearly suggests a different function for gravitational time dilation, which will have measurable effects in experimentation if true. The binding energy to be considered is not gravitational binding energy, but rather the change in radiation energy in free space that occurs due to the formation of the object whose time dilation is being considered. It is this special kind of binding energy divided by rest energy which is proposed to replace the role of
in the equation
.
2) By determining the net amount of radiation that a galaxy has absorbed since the original formation of the galaxies of the "dark ages" from which it is ultimately derived, one may make predictions to test so as to see if the ratio of "observed + unseen mass" to observed mass is in line with the predicted binding energy / rest energy (per the definition of binding energy given at the throughout this paper).
Re: "Binding Energy", Gauge Bosons, Galaxies, and Time
