I really got great help from Grok, which make my formula from my initial S(f_1-f_2)=-GMm(1\/r_1-1\/r_2) to Sm(f_1-f_2)=mc^2{[1-2GM\/(c^2*r_1)]^(1\/2)-[1-2GM\/(c^2*r_2)]^(1\/2)}. <\/p>\n\n\n\n
{PS: f_1 and f_2 are frequency of the static time field wave at the point_1 and point_2 respectively, f_1 and f_2 are proportional to the time passing speed\/clock speed at the point_1 and point_2 . }<\/p>\n\n\n\n
Grok helped me done in two consective steps following.<\/p>\n\n\n\n
First, in the formula of last post for static time potential energy field I gave, Grok calculated out S = m c\u00b2 \/ f_\u221e according to my formula and general relativity as I requested, so S can be a constant without m.<\/p>\n\n\n\n
So I think that it’s better to make S as a constant to refine the static time potential energy field equation as:
Sm(f_1-f_2)=-GMm(1\/r_1-1\/r_2) or S(f_1-f_2)=-GM(1\/r_1-1\/r_2), where now
S = c\u00b2 \/ f_\u221e,
in which S is static time potential constant,
in which f_\u221e is the frequency of static time field waves measured at a point where the gravitational field strength is zero and Grok brough this f_\u221e to me in S = c\u00b2 \/ f_\u221e,
in which f1 and f2 are wave frequency of static time field at point 1 and point 2 in space, and r1 and r2 are distance from the two points to the center of the gravitational field.<\/p>\n\n\n\n
Second, Grok told me that -GMm(1\/r_1-1\/r_2) I used is only accurate in Newton’s weak gravitational field, and then I realize that this initial formula need to upgrade to GR, but to be honest, I havent learned to understand General Relativity to do calculation yet although I think I understand the spirit of GR. By the way, in fact I asked Gemini to give me formula of potential energy change in gravitational field, and Gemini gave me -GMm(1\/r_1-1\/r_2) which I didnt calculate by myself, haha.<\/p>\n\n\n\n
So I asked Grok to use GR’s gravitional potential energy change formula to replace my Newton one to recalculate the formula. Grok make it as S m (f\u2081 \u2212 f\u2082) = m c\u00b2 [ \u221a(1 \u2212 2 G M \/(c\u00b2 r\u2081)) \u2212 \u221a(1 \u2212 2 G M \/(c\u00b2 r\u2082)) ] which I copy here, and which can be simpler as
S(f_1-f_2)=c^2{[1-2GM\/(c^2*r_1)]^(1\/2)-[1-2GM\/(c^2*r_2)]^(1\/2)} .
And also Grok tell me S=c\u00b2 \/ f_\u221e as same here.<\/p>\n\n\n\n
Firstly, I let Grok read my post including my formula and prompt to use general relativity to check it is f or f^n or n^f, and then Grok gave me S = m c\u00b2 \/ f_\u221e according to my post.<\/p>\n\n\n\n
Secondly, Grok even helped me upgrade and finish the whole equation.<\/p>\n\n\n\n
By the way, I dont mean that my way in this case is the right way, because at least I should know the meaning of the equation of General Relativity completely. We can make AI and computer do math job for us but we shall know the basic principals of formula or programs, it’s like we can use calculator do arithmatic for us but we shall know exactly what it calculate. But I know just where -GMm(1\/r_1-1\/r_2) comes from but not how mc^2{[1-2GM\/(c^2*r_1)]^(1\/2) comes from where.<\/p>\n\n\n\n
It’s not surprising that human will transfer more and more math and other jobs to AI, just like we have transfered arithmatic to calculator and simulation to computer, and later we will transfer almost all calculation, most proof and derivation in math to AI.<\/p>\n\n\n\n
What will human keep in future out of AI? I believe that most valuable and essential nature of human which AI cant replace is spiritual stuff like inspiration, character, morality, feelings, connections between each other, etc.<\/p>\n","protected":false},"excerpt":{"rendered":"
I really got great help from Grok, which make my formula from my initial S(f_1-f_2)=-GMm(1\/r_1-1\/r_2) to Sm(f_1-f_2)=mc^2{[1-2GM\/(c^2*r_1)]^(1\/2)-[1-2GM\/(c^2*r_2)]^(1\/2)}. {PS: f_1 and f_2 are frequency of the…<\/p>\n