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If a splitting atoms / fusing isotopes (fission bomb, fusion bomb) yields more energy than chemical changes (TNT, et al) yields more energy than physical change (hydrogen bonds forming during water condensation), then why doesn't the trend continue BELOW the atomic level, or do physicists have no clue about that stuff yet? I know we cannot examine things smaller than atoms, but are there any models or theories yet?

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Einstein's famous $E = mc^2$ equation sets the upper bound for the amount of energy contained in a particular amount of mass - in a nuclear reaction, mass is "converted" to energy. The highest possible energy yielding reaction for a particular amount of mass would be annihilation of equal amounts of matter and antimatter - this would "convert" all mass in the system into energy. So the energy contained in a system of finite mass is limited due to special relativity - independent of the type of change that is occuring. –  user758556 Aug 17 '12 at 15:19
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Your "knowledge" about not being able to examine things smaller than atoms is incorrect. Particle accelerators do so every day. –  AdamRedwine Aug 17 '12 at 15:23
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@orokusaki - What makes you think that observing "their effects" is different from "examining things"? When you look at something, you do not see the thing itself, you see the effect the thing has on the photons that are incident on it. Or, rather, you see the photons and your brain infers the effect the object has. Etc., etc., etc. –  AdamRedwine Aug 17 '12 at 18:37
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@dmckee - Ha, if you'd read it, you'd have know that OPERA was the name of the experiment, by CERN, not some other agency - public.web.cern.ch/public/en/spotlight/SpotlightCNGS-en.html –  orokusaki Aug 19 '12 at 21:02
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A few words about how particle physics is organized and works. There are labs (which is what CERN is) and there are experimental collaborations (such as OPERA). Both are funded mostly by national funding agencies. Labs provide infrastructure. Experiments do physics. Lab scientists are heavily involved with experiments which is acknowledged by making them part of the experimental collaboration. The paper was issued by OPERA. Had it been real the credit would have gone to OPERA. (Labs do--quite properly--take some of the credit for every thing that experiments do with their infrastructure.) –  dmckee Aug 19 '12 at 21:48
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Let me first express my agreement that in terms of pure energy I am in concurrence with the points made in the comments. That is, the energy availability from any amount of matter is $E=mc^2$ and thus, complete annihilation is the best you can do. We have no near-term energy sources that could get this limit, although energy extraction from black holes could. Energy from BH Hawking radiation would be 100% efficient conversion of matter into energy and would still probably be called nuclear power. To end the conversation at this point, however, would be showing a major lack of creativity, and I think wouldn't do justice to the true strangeness of the universe. That said, the rest of my answer will necessarily have subjectivity, because the argument in terms of energy availability alone is finished.

One could argue that energy reuse offers "more energy" in a certain sense. This is a complicated and sometimes confused argument. For a conceptual tool, let me turn your attention to the concept of concentric Dyson Spheres. It has been argued (really just in science fiction) that each sphere would be able to use the waste radiation from the last sphere. Ergo, the power output from the star, $\dot{Q}$ is used in full by each shell. So if there are $N$ shells, one may naively argue that the total energy used is $N \dot{Q}$. The problem is, the more shells you have, the lower quality of energy each shell gets! Even if such a society uses space-age solar photovoltaic panels, they can not violate the fundamental Carnot efficiency limit. Formally, let me claim that the useful energy is less than the thermal energy, which can be directly related to Einstein's matter-energy equivalence.

$$\dot{Q}_{useful} < \left( 1- T_C/T_H \right) \dot{Q} $$ $$ \dot{Q} = mc^2$$ $$\dot{Q}_{useful} < \left( 1- T_C/T_H \right) m c^2 $$

This implies $\dot{Q}_{useful} < m c^2$. So even though we have changed the nature of the problem we're looking at, we're still not going to do better than the theoretical nuclear limit. In other words we haven't "beat" nuclear power. That doesn't mean there's nothing to the concept of "negawatts", but we have to change the problem yet again. If we venture into the softer sciences, our energy use is only to some particular useful ends. Discussions about the evolution of technology often focus on computation for instance. So let's say we're interested in floating operations per second. We can get so many computations per unit energy.

$$FLOPS = \alpha \dot{Q}_{useful} $$

As an alternative to unlocking more energy, or using more energy efficiently, we can improve the efficiency of the thing we're doing. A good subsequent question is then if there is a theoretical maximum to the value of $\alpha$, and I believe the answer is "yes". The Heisenberg uncertainty principle will require a minimum amount of energy for any deterministic calculation, else the calculation becomes probabilistic. This is the concept of quantum computers. If we could build quantum computers, they would be fundamentally limited by the energy available.

There is another argument as to why this $\alpha$ must have a maximum. Hopefully I can find this link later and add it later, but there have been actual demonstrations that showed computer memory can be used to store information and make decisions about a quantum system, causing this system to "violate" the second law of thermodynamics. The specifics are not terribly important for this answer, but the argument goes that if you could store information with infinite efficiency and could do computation with infinite efficiency, you could then, one way or another, become a Maxwell's demon. I find this to be a fairly convincing argument.

This brings me to another potential "answer", which is that any Maxwell's demon could eventually be configured to reuse energy indefinitely. This would violate the limits I've discussed so far, and violating those limits would functionally unlock infinite energy. Infinite energy is greater than any nuclear energy resource, QED. Obviously, the problem is that Maxwell's demon doesn't exist. Still not satisfied? Maybe you're still interested in finding a loophole. You wouldn't be alone.

Frank Tipler is a real scientist, although I'm not sure if what he writes as popular literature could be called science. I'll quote Wikipedia, because I'll be honest that even I don't understand this:

The Omega Point is a term Tipler uses to describe a cosmological state in the distant proper-time future of the universe that he maintains is required by the known physical laws. According to this cosmology, it is required for the known laws of physics to be mutually consistent that intelligent life take over all matter in the universe and eventually force its collapse. During that collapse, the computational capacity of the universe diverges to infinity and environments emulated with that computational capacity last for an infinite duration as the universe attains a solitary-point cosmological singularity – with life eventually using elementary particles to directly compute on,[clarification needed] due to the temperature's diverging to infinity[clarification needed]. This singularity is Tipler's Omega Point.

Ah ha! As per my arguments, computational capacity diverging to infinite would necessarily imply an energy source or "method of use" that surpasses nuclear power.

In short, the 2nd law of thermodynamics will ultimately prevent anything from surpassing a perfect nuclear source of energy, but maybe if threw the end of the universe, or the multiverse, or something else like that into the mix, there could be a loophole that would open up an even greater resource, but I'm pretty sure it would require redefining spacetime itself somehow.

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