Toffo wrote:A vehicle loaded with lot of low entropy fuel accelerates itself to speed 0.99 c - No laws of physics violated. Right?
A vehicle loaded with lot of high entropy fuel accelerates itself to speed 0.99 c - Laws of physics are violated, as entropic fuel energy turned into non-entropic kinetic energy. Right?
Sure, if a system is at maximum entropy, it can't convert heat into linear kinetic energy of the center of mass using internal reactions alone, although some external force can still accelerate it.
Toffo wrote:One example of high entropy fuel is black holes. Fusing black holes generates energy. Black holes are so entropic that only 1/2mc2 of energy can be generated from fuel with mass m.
Where does that equation come from? It doesn't ring a bell. And when you say "fuel with mass m" do you mean the black hole has mass m, or the thing you drop into it has mass m? If the latter then you aren't really getting the energy from the black hole itself, but rather to the potential energy of the combined system that includes both the black hole and the thing initially at some distance away from it, and this combined system may not be at maximum entropy even if the black hole's internal entropy is maximized for its mass (see below for more on this point).
Toffo wrote:You see the above is an example of the rule that you can not fuse entropic stuff and extract lot of energy. So as I have been saying there must always be some mechanism that prevents dropping entropic stuff into a black hole and getting too much energy out.
But you can't consider the black hole alone, you have to consider the entropy of the combined system that includes both the black hole and the other system you want to drop into it. This combined system will have lower entropy when the system is at its initial distance than it does after it's been absorbed into the black hole (perhaps emitting some radiation as it is pulled inwards, so you have to include that radiation in the entropy too). And as I said before, the total entropy of the combined system involves a sum
of A) the system's own internal entropy, and B) entropy due to its position relative to the black hole (the number of position and momentum states the system's center of mass can have at different radii and potential energies) along with entropy due to any radiation emitted. The total entropy of the system would also include C), the internal entropy of the black hole, although we can forget about this for now. My point is that when you say "dropping entropic stuff", you seem to be talking purely about A), the "internal" entropy of the stuff being dropped (whether it has internal temperature differences, for example). But since your method of extracting energy using a winch doesn't rely at all on converting any of the system's internal
potential energy into kinetic energy, only in converting gravitational potential, the internal entropy is totally irrelevant, all that matters is B), which increases by exactly the same amount regardless of whether the thing you drop in has high internal entropy or low internal entropy. Do you disagree with this logic? If so, which is the first step in my argument above that you would take issue with?