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Someone is able to use compression and expansion to matter and space-time.

Law of preservation is still in effect so no matter how small the matter is, it will still weigh the same as if it was uncompressed, same with expansion.

I know that I can possibly create heavy nuclear elements or atomic heavy ones with compression of matter and make matter soft probably comfy enough if used with expansion

The question how useful this kind of magic/ability could be if I use it for industrial purpose or economic(Trading).

The scenario is Middle ages with magic instead of technology being prevalent.

The catch is now you're not a criminal, but instead, you're an artificer or blacksmith.

You must make sure that by any means that no fingers will be pointed in your direction that will make them think that your magic can be used for war, BY ANY MEANS NECESSARY.

NOTE: Since I can compress and expand space-time I have in theory an alcubierre drive. means I can travel FTL.

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  • $\begingroup$ That about the alcubierre drive is purely speculative, you don't need to use that idea (it's nothing more than an idea - a mathematically self consistent idea, but quite possibly not real). $\endgroup$
    – Nobody
    Commented Nov 19, 2016 at 23:31

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Short answer: you have a cheap source of energy. You can add air to a container and expand or shrink it to power machinery and other things that can be used at a blacksmith. This is similar to how combustion and steam engines work. So you essentially have the beginnings of a magic powered industrial revolution.

One thing that it can also be used for is transportation of goods. Many things are limited by size rather than weight in how well they can be moved. Things like grains and fresh produce and other not so dense objects.

You also have access to the biggest headache in fictional writing with time manipulation. Be careful of how you do this. Make an analysis of how you want it to work and be consistent in that. Having a story that is inconsistent in how time works leads to plot holes and confused readers. It can work in some cases, usually in less serious works with a focus on comedy, like discworld and futurama where that kind of thing is lampshaded or ignored.

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Depending on what sort of setting you're trying to create and how comfortable you are with handwaving things, you might want to think about another venue of applying such magic before thinking about anything else - weaponization. Depending on the exact modalities of your setting's magic, you might easily end up with just about anything from hyper-sharp swords capable of slicing through anything (just build an oversized sword, then shrink it down - and there you go, you've got yourself an ultra-thin edge that's still as sturdy as a claymore), sniper rifles (real-life ballistic vests work by distributing the kinetic energy of a projectile across a large surface - your magic may be used to do the reverse), and (again, specifics matter) possibly even magical hyper-nukes.

I know you've asked for industrial applications first and foremost, but realistically, possibilities such as those I've outlined above (and many, many more - you can get far more creative than that) would have very strong (and, if that's the sort of story you'd like to tell, very interesting!) implications to the use, regulation, and cultural perception of magic.

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