So I started to wonder about potential energy and gravity again. In mathematics you can say that it has a value depending on where you measure it relative the 'gravitational field'. And you measuring infinitely far away, the way it is set up mathematically, will give you a negative value for potential gravity, and so also for the potential energy.

"For the conservation of energy to work, the sum of the Kinetic energy "T" of a body pulled by gravity, and it's gravitational potential energy "U", must be a constant.

T+U=C

Kinetic energy is always positive, and will increase as the body falls faster and faster towards your source of gravity. To compensate, U is going to have to be zero. If it was positive, the total energy C would not be constant. Sort of a fudge, but necessary if you want the conservation of energy to work. You get around it by making the gravitational force equal to minus the gradient of the potential energy. F=-\nabla U.

A negative U makes sense in some way, because your gravitational energy, though always negative, increases as you move away from the body, i.e. upwards. You expect gravitational potential to do this, increase, as you move up, so that you'll gain energy as you fall. If U was always positive, but decreasing, it would mean that potential energy would decrease as you moved away from the body. Also, if you tried to make it always positive but increasing, though the potential energy would approach a maximium, your effort would be confounded as you moved close to the body, i.e. as x->0.

The choice of negative potential energy is really the best of a bad bunch. Try graphing the equation, then graphing it's negative. Move both graphs up and down by constants to get a feel for why the canonical option really is the lesser of many evils." By ObsessiveMathsFreak.

So, what is gravity then?

Maybe a better question would be. What is SpaceTime? Because that's the real question. In Einsteins relativistic universe you have four acknowledged dimensions. three that I sum up as creating 'distances' in a three dimensional space and.. This is where so many miss the importance, exactly because the way it is presented.. Time, or its arrow.

It's not correct to write it like this. SpaceTime is one thing physically and mathematically as I understands it. Represented by four dimensions together. You can lift them out and 'isolate them' in mathematics, but not in reality. Too many seems to think that because I can turn something around then that must represent a true solution too. Mathematically it might, but you need some sense of proportions to see if it is consistent with the world you live in.

So, potential energy, and Gravity, outside the text book does not 'cling off' into negative expressions as far as I understand. If they did we would have anti gravity

and ?? anti potential energy flowing all around us, whatever that would be? And disregarding fantasies, there are no such things observed in this universe, and no experiments validating it that I know of.

Potential energy is a relation, not something 'touch able'. Gravity is a relation too, expressed through accelerations (constant or variable 'inertia') invariant mass, also able to be converted into the notion we have of 'energy', that then might represents some ultimate quantity, or better seen, as transforming 'usable work -> into -> Work done. To imagine what 'energy' might be we either has to use a wave or a 'photon'. That's the cleanest expressions I know, allowing us to measure.

The SpaceTime we see is expanding. Using mathematical concepts, as differing from reality, of positive versus negative energy we then need a explanation to from where that 'expansion energy' comes from. In a closed universe you will expect a balance, we use the conservation laws to express that. So if the room expands the 'energy' for that has to come from somewhere. But it might be wrong. Maybe the room expanding has nothing to do with our notions of 'energy'. We might overreach in defining negative concepts that bears no mathematical resemblance to reality, not fitting what we see as we measure and experiment. Use my 'curtain of light' and imagine it to be a 'game' for a second. Then the 'discrepancies' we see in QM as related to SpaceTime becomes where the logic of the game points to something else.

People tend to believe in choices, QM is the 'truth', as it's describing the smallest constituents of our universe, and Relativity will need to adapt. Or Relativity is true, and it is QM that needs to adapt. QM does away with the notion of classical causality chains, or, QM is not describing it all (hidden parameters). How about a third one, neither QM nor Einstens relativity catches 'it all', but they both describe, the same universe? That' seems better to me. Both describe reality, from two perspectives, physics using 'scales' to find the differences. Both has a beautiful logic to them, although neither of them is what we see in our daily life. There we have a third description that works just fine, Newtonian mechanics.

But relativity does not state that conservation laws must hold. In fact it seems to depend on what you believe, not on Einsteins equations per se. You are the one bending them to your needs. I find conservation laws to make a enormous lot of sense myself, as describing interactions of various kinds. But I'm not sure if the universe is 'closed', and neither should you be. If it's not then Noether's theorem shouldn't be relevant for a SpaceTime geometry. That means that we don't have to look at 'energies' being shuffled around inside a closed 'box' as the geometry might have another definition. Space isn't there classically, and that one we can prove with any vacuum. So to expect nothing to grow into more 'nothing'? Becomes somewhat of a oxymoron looked at that way.

You only need to consider what different observers will define as being the 'energy' observed, to see that it is observer dependent. And that one is just like 'time' and 'distances'. Relativistically described your universe 'shrinks' with your relative motion, and mass. Your positional definition change both in time and in distance. And as you can measure it to be true for you, the question becomes what a measurement really should mean. There I prefer to define it from 'locality' instead from 'Lorentz transformations'. That actually makes me more in tune with what we deem a repeatable experiment, than placing myself and my definitions in a abstract 'mindspace' where nothing is 'true', before you made the necessary transformations. And as I see it it's not only relativistically time dilations and their complementary Lorentz transformations exist. They exist, as I expect, here and now. I don't need a relativistic 'speed' for it, although we may have trouble measuring it.

And yes, it can all be expressed in 'energy'. But what the he* does that mean? That we are 'energy'? Nope, we're 'matter'. Are we then, 'waves'? Nope, we're still 'matter'. 'Photons' then, we are the 'Photons', right? Nope, matter..

Matter is one thing, photons another, gluon s a third, Higgs bosons a fourth, etc etc, add infinitum. They are not the 'exact same'. If they were, we wouldn't be here arguing, well if you're not going to get mystical on me, telling me that we are the consciousness creating the 'world'? To say that we can follow a logic from 'matter' to 'energy' is not the same as stating them to be the exact same. And neither does it demand that all 'bosons' must be 'waves', or for that sake 'photons'. The wave particle duality still exist, and is not solved into being one or the other. And if you to that add all other presumed bosons existing, and why not add 'thoughts' to the mix? After all, without those we wouldn't even care.

Are thoughts 'bosons'