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Conservation of Energy in Einsteinian Gravity
One issue that confuses many people is a question what is the real world equivalent of the old Newtonian potential energy (a.k.a. "gravitational energy").
Some of us may remember from high school that we were told that (according to Newtonian gravity) when we lifted a weight, we did work against attractive gravitational force with which the earth attracted the weight. That the work we did got converted into potential energy of "gravitational field". This potential energy was thought to be able to be recovered when this lifted object was falling down either doing work or just acquiring kinetic energy.
Now we learn from this article that there is no such thing in the real world as gravitational attractive force. The attractive gravitational force turned out to be a mathematical fiction. And so there is no physical field. "Field" is only a name of the space where the phenomena under consideration occur. And obviously a name can?t absorb any energy.
Seemingly there is nothing that could be transformed into kinetic energy or absorb the kinetic energy converting it in "potential energy of the field". And yet all lifted objects need energy to be lifted, and when they fall they acquire kinetic energy and this kinetic energy is of course real as we can verify if the object falls on our foot. So where this kinetic energy comes from if no force acts on a free falling object? Obviously it can't be created out of nothing since the principle of conservation of energy prohibits such extravagance.
Those of you who read this article carefully might have guessed already where the energy comes from. Those who didn't might be still baffled by the fact that despite that no forces act on a freely falling object it falls faster and faster and so its energy is seemingly increasing. But where is this energy coming from? Those baffled people need some simple explanation.
The explanation is of course simple as most things in nature. It is only people who make them complicated, mostly because they learn mathematical descriptions of those things without understanding physics behind this math, and the math that describes simple physical phenomena is often extremely complicated.
So when a gravity physicist is asked how a falling object acquires kinetic energy that seemingly is coming from nowhere, he might say: "don't worry, energy is automatically conserved since divergence of stress-energy tensor vanishes identically at any event" (?!).
It might be good explanation to some but most likely won't be understood at all by poets and not even by some science teachers. Interestingly enough even many gravity physicists who deliver such "explanation" do not understand it and more or less privately think that this energy is created from nothing.
They don't understand it because it is just a mathematical description of what's really going on and the whole education of gravity physicists in physics is limited to memorizing the math. I'm not kidding this time. This is what's really going on in gravity physics. So let's explain in plain English what Einsteinian gravity says about how it works.
The thing that you could guess already is that total energy of any object is, as Einstein discovered, its inertial mass multiplied by the speed of light squared (the famous E=mc2). When the object is in free fall, e.g. falls straight "down", its velocity "v" increases and so its kinetic energy increases even faster than its velocity (when velocity doubles the kinetic energy quadruples as one may see from the formula for kinetic energy mv2/2, where m is the mass of the object, if one still remembers it from school).
It also happens that inertial mass of the falling object increases since energy has mass (again the same E=mc2) and so mass of the object depends on its velocity. Yet while falling down, the object gets into space where, as we already know, the time runs slower, and there is also more space (the famous Einsteinian "curvature of space"). This slower running time, and increasing amount of space that the light has to cover, causes the speed of light being slower in relation to a remote observer who is observing what happens and calculating energy of the falling object by multiplying its mass "m" by the speed of light "c" squared.
And so the observed speed of light drops by a tiny bit. Obviously it does not drop "locally" (as seen by the object itself) where it is always the same "c" as required by the basic principle of relativity that local speed of light, one that is measured by the object itself (if it could do such a thing) is always the same "c". But of course the object does not see its own kinetic energy neither so for the object (locally) its mass and speed of light, and therefore its energy is always the same (E=mc2). Only the remote observer is wondering what's going on and where the kinetic energy comes form if there is no force attracting the falling object to the earth.
It must be that increased mass has the same influence on energy as decreased speed of light so the amount of the energy of the falling object (as observed by all observers) stays the same while the object is falling. Actually it stays the same whichever way the object goes unless the object is pushed by some force. It only looks like it changes its energy when it?s in a free fall because we don't notice the changes in rate of time nor changes in the amount of space and so the tiny change in the speed of light. So the fact that total energy of this object remains constant is difficult to notice.
Being difficult to notice it?s not impossible to calculate and the calculations show that "lost" (due to smaller speed of light) internal energy of the object, and its "gained" (due to increasing inertial mass of the object) kinetic energy, are equal. There is no net change of the total energy of a object in a free fall as observed by any observer. The principle of conservation of energy is still working as it has always been and the mysteriously disappearing Newtonian "potential energy" is found as a part of the total energy of the falling object. It is hidden there in the falling object, perfectly localized, contrary to ideas of those who still explain the world with Newtonian gravity with its "universal gravitational attraction" and for whom the energy is "somewhere", in some unspecified limbo (called "field").
It turns out that energy is in a limbo only in mathematical theories like Newtonian gravity or Maxwell's electromagnetic theory. In the real world however since energy has mass (as E=mc2 shows) this energy has to be in a concrete point in space at any concrete time because this is where this mass is located. So it is located within the free falling object itself. And so the "potential" energy is not "gravitational". It is just the internal energy of the object itself.
So we see that according to Einsteinian gravity the "gravitational energy" does not exist at all.
It turns out to be the same kind of mathematical fiction as "gravitational force", and many other mathematical fictions that are slowly explained as such by physical theories like Einsteinian gravity.
The magic of fictitious entities working (almost) as predicted by mathematical theories that only say what is going on and when, is being slowly replaced by science, by physical theories that not only explain what is going on and when, but also why.
For mathematically oriented poets and science teachers there is an appendix showing how Newtonian potential energy is recovered from the internal energy of the object while the object is falling. When the object is rising the process works of course in the other direction: the disappearing kinetic energy is accumulated as internal energy of the rising object.
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