> To undo this we will essentially need the same amount of energy again that we got out of it when we burned it
Amine based carbon capture at the smokestack captures about 90% of CO2 with a 20% energy penalty. There's a new natural gas turbine design that captures 100% at no energy penalty (Allam cycle).
Both those technologies do not undo the burning process, they just capture the carbon dioxide. Like putting a gigantic balloon on top of the smoke stack to trap the flue gases. The real problem here is what do you do with all your captured carbon dioxide? You are producing it at the same rate as you are consuming fossil fuels, for each tanker, pipeline, or train delivering fossil fuels, you will need an equally sized tanker, pipeline, or train transporting the carbon dioxide to some storage facility. For each well or mine extracting fossil fuels you need a equally sized hole in the ground to dump the carbon dioxide into.
Amine based carbon capture at the smokestack captures about 90% of CO2 with a 20% energy penalty. There's a new natural gas turbine design that captures 100% at no energy penalty (Allam cycle).