If you react oxygen and hydrogen you get water plus energy. If you want to get hydrogen from water you have to add energy to the water to split off the hydrogen. This principle is the same for the CO2, all be it a little bit more complicated (hence the water example). The problem becomes, with this reaction, the waste energy in the form of noise, light, heat etc, is lost to the ether.
A simplified version of the laws of thermodynamics says;
You can't win, i.e. you can't get more energy than you started with
You can't break even i.e. there will always be losses in energy
& you can't leave the game i.e. the first two laws apply to everything.
So applying the thermo laws to getting energy from CO2 you can see that there must be a net loss of energy, no matter how efficient the system is. Or to put it more simply you have to put more energy into the system than you will get out of it. This is because the CO2 is a waste product as a result of liberating the original energy.
That is not to say the technology is not worth investigating, I can see applications for it, (carbon sequestration, energy storage for peak usage etc) but as a means of replacing fossil fuels I just don't see it.
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