My knowledge about school level physics is admittedly not that fleshed out, but we were told that it is possible to convert mass to energy. My google-fu has sadly left me for my question here 🙁
So why can’t we just take e.g. nuclear waste and convert it to energy? After that so is my understanding it wouldn’t simply exist as matter anymore and wouldn’t require to store dangerous trash if you can convert it all to energy.
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It’s more proper to say that mass and energy are the same thing. But that doesn’t mean that it’s easy to convert mass-energy in one form to mass-energy in another form, or that it means anything can be freely converted into anything else.
In particle physics, which is the level we need to be operating on to talk about these things, we say that certain values are *conserved* – they don’t change in any reaction. You might have heard of things like conservation of energy, mass, or momentum (which are all conserved in all common everyday processes), but there’s a long list of conservation laws at the level of particle physics.
Among these conserved values is one called *baryon number*, which is (for ordinary matter) just the number of protons plus the number of neutrons (if you had antineutrons or antiprotons present, they’d contribute -1 to this number). While we have pretty good reason to think this number might not be conserved in *every* possible interaction in the Universe – namely, that our Universe contains matter and not antimatter, so *something* made more of one and not the other – no known actual reaction we can conduct here on Earth changes baryon number. Nuclear reactions can change protons to neutrons or vice-versa via beta decay, but that doesn’t change baryon number (since both protons and neutrons contribute equally to it).
That means we can’t just make materials like atomic nuclei vanish into thin air – they’re made of protons and neutrons, so getting rid of them would change baryon number (which we do not know how to do, and which may be impossible).
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Even if we did know of such a reaction, that doesn’t mean it would be easy to actually conduct.
We already know of reactions that can convert the atomic nuclei in nuclear waste to less harmful forms. So why don’t we do them? Because they’re very hard to do. They require a lot of energy, exotic materials, long processing times, etc, and we have to make those reactions happen to a substantial portion of the billions of billions of billions of atoms in a typical chunk of material.
For example, one major long-lived component of nuclear waste is [technetium-99](https://en.wikipedia.org/wiki/Technetium-99). If we could just stick a neutron onto this nucleus, we’d convert it into technetium-100, which decays very quickly (half life about 15 seconds) into stable ruthenium-100. No physical law prohibits this reaction. But the fact that we don’t do it suggests that it’s probably a hard reaction to actually accomplish in practice – I would guess, though I don’t know, that technetium-99 just doesn’t like to absorb neutrons very much.
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