Originally posted by tony4
Could Time Just Be Caused By Mass ???
If we take the first approximation of Einstein's rate of time dilation caused by gravity we get
t is the equivalent time of an event at "infinity" of length t0
G is the gravitational constant
c is the speed of light
r is the distance from a big mass M
Now it can be shown that the sum for ...[text shortened]... bound to the fact that there is mass. Without mass the whole concept of time would disappear.
Your first equation is incorrect. Assuming everything is static it should read:
t = t_0 (1- a/r),
where a = 2GM/c² (the Schwartzschild radius).
Your second equation makes no sense. What is r(i) and why are you summing over masses. In the Newtonian approximation what you can do is write the potential energy of two point particles labelled i and j with masses M_i and M_j at r_i and r_j as:
V_i_j = - G M_i M_j / |r_i - r_j|
So that the total potential energy involves a double sum over i and j over the two particle potentials:
V = sum(i) sum(j < i) V_i_j
I have heard the statement that total field energy balances total mass/kinetic energy before. This is not a prediction of any theory I know of but based on observation.
When you replaced 1 with the dynamic term equal to one, you dropped the second term. You then write your third equation down and state that if the mass is zero then t = 0. True, but you´ve already relied on that sum being equal to 1 so you can´t then set it equal to zero.
Also your eventual conclusion is wrong. If there were no mass in the universe then in the General theory of Relativity time would pass at the same rate for all observers - it would not stop nor would it become infinitely fast.
At the Schwartzschild radius of a (static uncharged) black hole the completely time-like component of the metric vanishes. But that means that a clock at that radius takes an infinite amount of time to tick once when measured by an asymptotic observer - the observer at the Schwartzschild radius doesn´t notice anything unusual.