I was wondering if it is possible for life to evolve in a world which lacks any transition metals. I am wondering this because, it could give a plausible explanation for a world which is very unlikely to discover or harness electricity.
The setup is:
Ultra-advanced alien civilization comes to world and, due to need for metals/conductors, completely mines it out of all transition metals. They could use self-replicating nanobots (or could even be the results of an AI-explosion gone astray, from Earth or another planet), some chemical vaporization technique, etc.
The entire planet, including iron core, is mined out
The miners are mainly interested in the transition metals. Particularly iron, titanium, platinum, gold, copper, nickel, tantalum, tungsten; i.e. the metals which have the most use for manufacturing more stuff. However it is safe to assume that a lot of other trace materials are used as well.
The original inhabitants are completely wiped out during this (very destructive) mining event.
Whatever entities did the mining move on to other worlds never to be seen again.
As for the hard-science tag, there are two seperate questions.
As millions/billions of years go by:
Can life evolve in such a world without transition metals (without Iron for example)?
Is it even possible for a world to structurally exist without a transition metal core?
There are a host of reasons why the evolution of life on a planet like this will be very, very unlikely.
Planetary Magnetic Fields are produced by hot spinning metals, such fields then help to protect said world from cosmic rays, solar winds and other forms of extra terrestrial radiation such as that emitted by stars. Without a conducting fluid core, may that be iron or other such material, the planet will have no means of projecting a sufficient magnetic series around itself, hence leaving its surface venerable to the harsh conditions of space; this surface will be bombarded by fast moving off-world particles primarily in the form of solar winds, ceasing to have a functional atmosphere, leading to climate cooling (lack of greenhouse effect) and the eventual loss of liquid water on the planet leading to the inability for life as we know it to even exist let alone evolve.
Metals are also dense, adding to the planets overall mass and its structural integrity, removing all said metals off world will lead to a dramatic reduction in planetary mass and therefor reduce the bodies surface gravity- further jeopardising any functioning atmosphere present as well as result in a decreased core temperature (pressure at the planets centre of mass dependant on the amount/mass of material surrounding it). Yes, the decay of nuclear materials plays a part in the constancy of heat at the core/inner mantle, but this energy release alone will not be enough to maintain a fluid planet centre. Saying this though, radioactive material decays continually - by expelling neutrons, electrons or protons - in a bid to produce a stable nucleus (the rate it does this is defined as its half life. If protons are radiated from an atom to gain stability, it forms a new element (such as lead from uranium). This makes it possible therefor for radioactive elements to transmute into various transition metals.
Through the decay of radioactive sources, over the course of many millions of years in the correct conditions, reserves of metals can be increased, yet this will not aid in creating a sustained atmosphere or re-establishing the planets mass, in fact, with such nuclear substances now stable, there will be a further decrease in core temperature that will eventuate, in conjunction with the other listed factors in a dead planet with no way of sustaining life as we know it.
Elements such as iron and copper are vital for life, an organisms cells using these metals to produce red blood cells that carry oxygen around the body. Without enough blood cells, the body cannot effectively carry/provide oxygen around it's systems, resulting in many terminal problems the most serious being death. As mentioned by others, calcium (Ca), phosphorous (P), magnesium (Mg), potassium (K) and all other period 1 and 2 elements are classed as also metals and equally important in maintaining basic biologic functions (the creation of teeth/enamel for instance as well as regulation of nerve/muscle function - and protein synthesis).
From these reasons, it is easy to see how amazing transition metals are in planetary stability and to organic life generally. Without sufficient access to such elements/trace particles the evolution of carbon lifeforms will therefor be almost impossible, stress on almost, for if star trek has taught me anything, its that the universe is a mysterious place where nearly anything can happen given the correct circumstances.
RNA world, maybe possible.
Enzymes, still possible.
The Rules: no d-block elements, same abundance of s and p block elements, and any f-block elements.
The things that is same as earth life: RNA enzymes, or ribozymes; mg-dependent and ca-dependent processes that does not rely on photosynthesis; ionization and uv catalyzed formation of organic molecules. Any proteins that does not require transition metal ligands. Basic life process does not require transition metals for self replication, nor any protocells does for growth/division.
The Things that need to be changed: iron sulfur clusters: pevoskite type lead and sulfur/halogen semiconductors; III-V semiconductors like indium arsenide/antimony sulfides; with lead atoms of 2V oxyreduction potential and thallium with 1V oxyreduction potential substituting fe-s clusters.
Photosynthesis: bacteriorhodopsin pumps protons forming effective photovoltaics, with just carbon/nitrogen/oxygen/hydrogen/sulfur, NADH and ATP comes from electrolysis of the potentialized solution by carbon electrodes. The Calvin cycle, interesting enough, does not require any transition metals. Another Aldol reaction based cycles, which produces pyruvate and formaldehyde/acetate; does not require transition metals.
Respiration: the tricarboxylic acid cycle does not require any transition metals except for cis aconitase, which is easily substituted with a selenium related protein. The citrate cycle can also be reversed, to produce acetyl coa.
the ATP generating process is the reverse of the bacteriorhodopsin electrolysis process, with NADH and O2 reacting in a fuel cell, producing a proton current.
Fatty acids and coenzymes: fatty acid synthesis does not require metals at all, and most aromatic compounds can be synthesized with rare earth elements instead of iron as a catalyst.
Oxyreductases: antimony, bismuth, tin, lead, phosphorus and arsenic will work as 2-electron oxyreductants, cerium/neodymium/samarium/europium/gadolinium/erbium will work as 1-electron oxyreductants.
Oxygen carriers: insect like tracheae will work for Most animals(bugs).
The entire planet, including iron core, is mined out
If they mine the entire core, then is there a void there? So the mantle collapses due to gravity, releasing huge amounts of energy and melting the entire remainder of the planet to a magma ocean? Then in that case, whether transition metals are there or not does not matter, because there is no planet any more to begin with.
You also have to consider the economics of mining. To make mining feasible, it has to be done with a profit. The price of gold, for example, is so high because it is so rare. But that doesn't mean that it doesn't exist. There's gold everywhere. In the dust in the air around you, in the bricks that are used to build your house, in the soil in your kid's playground. To extract it you need to build the machinery and equipment to extract it. And it has to be worthwhile. Presumably, your nanobots will require tantalum and platinum to operate in the harsh environments you expect from them. But if there isn't enough gold to justify what you used, and pay for the salaries of everyone, and get a profit, what's the point? You will not put 2 kg of tantalum in a machine that will eventually only mine 1 kg.
Therefore, blasting an entire planet (a very costly process) just to get some metals is incredibly stupid, and I would expect that an ultra-advanced alien civilisation would know better.
...some chemical vaporization technique,...
Then just go to a nebula instead. A nebula is essentially a vaporised planet (and entire solar system), before it condenses to a planet. The contents are not high enough though..
Consider how mining is done today. Mineral explorers find concentrations of certain elements that were enriched by natural processes, and target those. Tantalum is mined from pegmatites, for example. So you go and find pegmatites. You don't mine a non-pegmatite for tantalum because there isn't any (or enough) there.
If you're looking for iron and platinum in a space setting, you go to an iron asteroid like Psyche, and not to a planet where the mantle has the iron bonded to oxygen and you need to smelt the iron. On Psyche, the iron is already metallic. It's easier and cheaper.
Now that we know that mining is targeted on ore deposit (i.e. natural concentrations of elements), then this does not matter for the transition metal contents of the things that people are living on. Just the fact that there's an iron mine 10 kilometres from you in one direction, doesn't mean that the soil you're growing your food on in the other direction no longer has iron.