The "Gravitational Potential Energy is not real" Myth
Written: 1998.11.08
Last Revised: 1999.04.25
Some fans don't understand why Conservation of Energy dictates that the lower limit for Death Star energy yield is 2.2E32 joules. One of the most common complaints is that potential energy is not real energy (although this basic sentiment is often covered up with so much technobabble that it is not easy for someone to realize that this is what they're truly saying). This is simply incorrect. Potential energy is just as "real" as any other form of energy. Some trekkies refuse to accept this kind of statement, and commit a classic act of "bad science" by conjuring up explanations which they hope will confuse laypeople, even if they don't move people who know better. The following is an example, taken from the post of a trekkie (identified only as "Chris") which was e-mailed to me (it was posted in an AOL discussion group, where I imagine that science pretenders retreat so that they can preach their beliefs to a smaller, and less informed audience).
You know...there is a technical loophole here- just as gravitational acceleration allows the accleration of particles (and objects) past lightspeed (i.e falling inwards to a black hole) in GR and QM, the fact is that gravity (except in certain readings of hte ZPF) isn't really energy- when objects path's are moved by gravity, they havn't actually "moved," per se- they appear to have moved to people not following the same gravitational path, but they havn't actually moved with respect to the space they're on ...
This post is somewhat interesting, because it seems to suggest that the author thinks that physical laws are like manmade legal laws, in which "loopholes" can be found. There are no "loopholes" in fundamental physical laws- they are not enforced, and there are no lawyers who can argue your case for you or have the rules bent or changed. In addition, there are numerous factual errors in the post:
Objects do not exceed the speed of light as they fall into a black hole. In fact, the light-speed limitation dicated by General Relativity is the foundation for the Chandrasekhar limit for the minimum size of a star which will collapse to form a black hole. The author repeats a very common misconception here, based on the fact that light cannot escape from within the event horizon of a black hole. However, gravity is not a linear "pulling force". Gravity is a distortion in the fabric of space-time, and the extreme small-radius curvature of space-time inside a black hole's event horizon means that all straight lines lead back into the black hole. Light, and objects, do not get "pulled" back into the black hole ... if you are a hypothetical particle inside a black hole, no matter which way you turn, you are looking straight into the centre of the hole! It would be like a nightmare, except that of course, if you were inside the black hole, you would be dead and unable to dream.
The author's latter statement is poorly worded and meaningless. He claims that gravity is not "really energy", but of course gravity is not energy- it is a curvature in space-time which we perceive as force. But gravitational potential energy is energy. As for an object being moved by gravity, it moves through space-time, and the lines of space-time curve toward large masses. So as it moves through time, it naturally moves toward a large mass such as a planet, star, or black hole. We perceive this movement as "gravitational pull", but it is simply a side-effect of curved space-time. As for his strangely worded statements about objects not having moved "with respect to the space they're on", that is simply meaningless. Objects move through space-time continuously, unless time is frozen.
It is exceedingly strange that someone would choose to believe that gravitational potential energy is not real. I can only surmise that this misconception is due to the word "potential", which some laypeople have trouble understanding. If it's just "potential" energy, then it's not real because it doesn't exist until it is used, right? Well, that isn't really the way potential energy should be conceptualized.
For example, let us examine the formation of a star: take a cloud of diffuse gases, of approximately one solar mass. Its gravitational potential energy state is near-zero in this state. However, given enough time, it will eventually collapse to form a star much like the Earth's sun. When this happens, the gravitational potential energy of the cloud goes from near-zero to a value which is somewhere on the order of -2E41 joules. Conservation of Energy dictates that if 2E41 joules of gravitational potential energy are removed from the cloud, then 2E41 joules of some other form of energy must appear to "balance the scales", if gravitational potential energy is "real".
Does this happen? Yes! The missing 2E41 joules of gravitational potential energy is converted to another form: thermal energy. This thermal energy manifests itself as the tremendous heat and pressure inside a stellar core, and it causes the phenomenon which gives life to the universe: the ignition of a star's fusion reaction. The birth of a star.
As an aside, it is possible to see this entire process from a mechanistic perspective rather than a thermodynamic perspective (in other words, from the perspective of forces and processes rather than energy balances). Some people envision it as gravitational forces which pull the star together, and once it is assembled, those same gravitational forces "squeeze" the stellar core so much that it heats up and ignites. This is true- that is exactly what happens. However, what many people do not realize is that the "energy explanation" and the "force explanation" are not contradictory! Energy is force multiplied by distance, so the "energy explanation" actually incorporates the "force explanation", but it is conceptualized in a manner which allows us to easily generate lower-limit energy estimates. The "force explanation" helps people to visualize the process but it is useless for generating energy estimates.
Therefore, since we know that gravitational potential energy is converted into some other form of energy when a celestial body collapses, the reverse must also be true: if it is blown apart, then some other form of energy must be converted back into gravitational potential energy. The scales must balance, otherwise Conservation of Energy is violated. Gravitational potential energy is just as "real" as any other form of energy, and it is certainly not an exemption from Conservation of Energy! There is nothing in the entire universe that is exempt from Conservation of Energy.
Let us take a somewhat more small-scale example: if we take a 10kg mass and raise it to a height of 100 metres off the ground, its gravitational potential energy will increase by approximately 9.8 kJ, and therefore at least 9.8 kJ will have to be expended, in order to achieve this altitude (thanks to Conservation of Energy). If it is dropped from this height, it will gain approximately 9.8 kJ of kinetic energy before it strikes the ground. If it were possible to raise it to 100m without having to do 9.8 kJ of work, we would have an instant violation of Conservation of Energy, and we would have the first infinite source of free energy! This is because we can generate 9.8 kJ of work by dropping a 10kg mass from 100m altitude, so if we can raise it to that height without expending at least 9.8 kJ of energy, then we can generate infinite energy by simply raising it cheaply, and then dropping it and harvesting the "free" gravitational potential energy increase. This is obviously ludicrous, and a complete violation of Conservation of Energy.