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Lets say you have a geothermal or nuclear power plant and nearby you have system which converts that energy into nutrient porridge. This nutrient porridge must have everything the human needs to survive long term.

Is this physically possible?

Could it be more efficient than traditional geoponics?

Can it be done underground?

Can the system function independently of hydrocarbons?

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    $\begingroup$ You cannot create food from energy alone. You also need carbon, hydrogen, oxygen, nitrogen etc.. It should be conceivable to create such an apparatus that recycles waste and air, though, but i imagine this would be very complex. You could use the energy to bring light to hydroponics, though. $\endgroup$ – Burki Dec 15 '16 at 12:25
  • $\begingroup$ Is there no process for converting electrons into the chemicals you need? $\endgroup$ – Ama Dec 15 '16 at 12:42
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    $\begingroup$ Converting? No. But one could conceivably build the atoms from available electrons, protons, and neutrons. The process of creating larger atoms occurs naturally in stars. $\endgroup$ – Frostfyre Dec 15 '16 at 13:21
  • $\begingroup$ Possibly related: worldbuilding.stackexchange.com/q/56560/809 $\endgroup$ – Mołot Dec 15 '16 at 18:01
  • $\begingroup$ Also worldbuilding.stackexchange.com/questions/36046/… $\endgroup$ – user25818 Dec 16 '16 at 2:50
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In theory? Yes. In practice? Heck no...

Mass and energy are equivalent. This is the essence of Einstein's famous equation $E=mc^2$. So in theory you can create any mass $(m)$ from energy $(E)$, and any energy from mass.

And when you look at for instance nuclear plants this is exactly what happens. The used nuclear fuel is lighter when it is taken out after having had its energy extracted from it. Some of its mass has been converted to energy. There is nothing to suggest we cannot do the opposite. So in theory we can create any element from energy, and from any element we can create any molecule, and from these molecules we can make nutrients.

However...

That c squared... $c^2$. That is the speed of light (in vacuum), which is a lot. $299,792,458 m/s$ to be exact. And if you square that, then that is a lot, squared. So you can see that it only takes a very tiny amount of matter to become a whole lot of energy. And this conversely means it takes huge amounts of energy to make matter. To make 1 kg of matter, you need the entire energy output of a decently sized nuclear reactor running for about a year.

Also we have not really learned how to make energy into matter on any large scale. We are quite good at doing the opposite, but not at creating something material out of the figurative thin air.

So the answer to your question:

No, we cannot do it. It is not practically possible to make food out of energy alone.

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  • $\begingroup$ Ok. Is there any process which would be sufficiently similar, such as growing the relevant plant tissue in large amounts? $\endgroup$ – Ama Dec 15 '16 at 12:48
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    $\begingroup$ Any process to create something out of nothing? What would that be, apart from the Big Bang? You need to provide context here: what is your setting? And how is it that you have lots of energy available but no matter to make food out of? $\endgroup$ – MichaelK Dec 15 '16 at 12:50
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    $\begingroup$ No. I mean a process for creating food indoors without the traditional method of growing plants or animals. The setting is a post-collapse world where traditional farming is no longer viable and living on the surface is no longer healthy, but we still have nuclear reactors and geothermal energy with which we can use to create some form of complex society. $\endgroup$ – Ama Dec 15 '16 at 12:52
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    $\begingroup$ @Ama Well what is the starting-material? Bare elements like carbon, nitrogen, hydrogen and phosphorous, or something a little more advanced? Again we run into the problem of theory vs practicality. In theory we can create any molecule. In practice, it takes quite a large facility to do that. The problem you have is that you need a lot of different molecules to sustain yourself. Making simple sugars for instance will get you the all the calories you need, but then there is the problem of proteins, minerals, vitamins and trace elements. You essentially need one whole factory for each. $\endgroup$ – MichaelK Dec 15 '16 at 12:59
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    $\begingroup$ @Ama Well what I do not understand is why you are so keen on avoiding growing stuff. As AlexP just said: let biochemistry do what it does best: grow and convert basic elements to yummy nutrients. Plant life is one of the best converters of clean and free energy to nutrients there is. Some bacteria are quite good at it too. Why do you try to avoid that? In any case your main problem is the diversity of nutrients you need. We are talking about dozens of different substances: caloric intake, all the essential amino acids, the vitamins, the minerals, the trace elements. $\endgroup$ – MichaelK Dec 15 '16 at 13:30
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Depends whether you want to use purely chemical and electrical means, or whether some genetic engineering is allowed.

If it's the former then almost certainly not. Whilst we can realistically make chemicals out of simpler ones such as the constituents of air and water, to actually make all of the various chemicals that humans need to survive would probably be prohibitively expensive to synthesise.

But if the question is "could you create a life-form that survives purely on photosynthesis (or perhaps heat or even directly from electrical energy), air and a solution of water and some salts then the answer might well be yes.

If you get it all right, then there's a good chance you'll have a highly efficient process that could work underground.

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