the big bang by kevin kennedy https://padlet.com/kkennedy180/91riiclfkr183bl3 en-us 2020-12-18 13:52:46 UTC 2020-12-22 01:10:56 UTC hello@padlet.com The key feature to bear in mind is that the gravitational potential energy is a negative quantity.You can see this by realizing that in order to separate two objects, one has to overcome the attractive gravitational force and this requires one to supply positive energy from outside.This is why launching satellites into space requires such huge amounts of positive energy supplied by fuel, in order to overcome the negative gravitational potential energy of the satellite due to the Earth’s attractive force. kkennedy180 https://padlet.com/kkennedy180/91riiclfkr183bl3/wish/1034772928 2020-12-20 22:03:39 UTC https://padlet.com/kkennedy180/91riiclfkr183bl3/wish/1034772928 This negative gravitational potential energy exactly cancels out the positive energy of the universe. As Stephen Hawking says in his book A Brief History of Time (quoted by Victor Stenger, Has Science Found God?, p. 148):β€œIn the case of a universe that is approximately uniform in space, one can show that this negative gravitational energy exactly cancels the positive energy represented by the matter. So the total energy of the universe is zero.” kkennedy180 https://padlet.com/kkennedy180/91riiclfkr183bl3/wish/1034773414 2020-12-20 22:04:19 UTC https://padlet.com/kkennedy180/91riiclfkr183bl3/wish/1034773414 Conservation laws are established in general relativity if there is a Killing vector πΎπ‘Ž, where for some values of the index π‘Ž there may be zero entries, so that for a momentum vector π‘π‘Ž = (𝑝𝑑, 𝑝⃗ ) the inner product π‘π‘ŽπΎπ‘Ž = π‘π‘œπ‘›π‘ π‘‘π‘Žπ‘›π‘‘. The Killing vector is then an isometry such that a vector along a parallel translation defines a conserved quantity relative to the Killing vector. kkennedy180 https://padlet.com/kkennedy180/91riiclfkr183bl3/wish/1037056519 2020-12-22 01:06:47 UTC https://padlet.com/kkennedy180/91riiclfkr183bl3/wish/1037056519 That conserved quantities are variables conjugate to the components of the Killing vector. How to find Killing vectors is somewhat involved, but as a rule, if a metric coefficient π‘”π‘Žπ‘ = π‘”π‘Žπ‘(𝑑) then there is no Killing vector with a component along that coordinate direction. The general line element for a cosmology involves a scale factor π‘Ž = π‘Ž(𝑑),𝑑𝑠2 = βˆ’π‘‘π‘‘2 + π‘Ž2(𝑑)(π‘‘π‘Ÿ2 + π‘Ÿ2𝑑Ω2which is a pretty good clue that this spacetime has not fundamental conservation of energy. kkennedy180 https://padlet.com/kkennedy180/91riiclfkr183bl3/wish/1037057939 2020-12-22 01:07:42 UTC https://padlet.com/kkennedy180/91riiclfkr183bl3/wish/1037057939 There is no timelike directed part of a Killing vector, therefore conservation of the energy conjugate variable can’t be established fundamentally.So is energy absolutely not conserved in our universe? The answer to this depends upon upon some other conditions; for it does turn out that our universe may have a unique condition which recovers energy conservation kkennedy180 https://padlet.com/kkennedy180/91riiclfkr183bl3/wish/1037060549 2020-12-22 01:09:23 UTC https://padlet.com/kkennedy180/91riiclfkr183bl3/wish/1037060549