Am I wrong to assume that science that is harder to prove will have less impact on human wellbeing? Electricity is easy to run experiments on and prove, meaning humans can manipulate it for our benefits easy. However, the Higgs Boson was extremely difficult to prove and I see no way that it could ever benefit humanity's wellbeing. Now how could humans improve our wellbeing by manipulating dark matter?
You're not "wrong" per se as you're entitled to your views, but a fairly common alternative view goes something like this.
Yes, while we sometimes do pursue scientific inquiry for its practical application to the betterment of humanity, we also recognize the value of scientific inquiry simply for expanding the endowment of human knowledge about the world. That is an "innate good". Moreover, if history is any guide, it's sometimes or even often difficult to predict what practical applications will or won't emerge from any given scientific endeavor. In the case of Dark Matter, it may not be exactly the case that we will ever directly manipulate it in any scientific application. However, it may be the case that by grappling with Dark Matter we will refine and deepen our understanding of the fundamental laws of nature, and that will unlock future practical applications. Then there is the topic of "human capital": training people to be scientists trains cadres of people with strong skills in science, math, engineering, and computer science, which is an investment in that human capital. Often, they're well-equipped to go on to fruitful careers outside of their initial field of inquiry, producing innovations that benefit humanity. Finally, if it's a matter of cost, many people feel that the societal cost (e.g. federal expenditures on science) are puny compared to other things which I need not name here. Consequently, "basic science" which includes fundamental physics and the study of Dark Matter, is always a great investment for society.
Or something like that...that's my understanding of how that argument goes. Make of it what you will.
Sometimes we don't know the improvements until we have done enough experiments to provide a model that aids in discovering improvements. Electricity was hard (even fatal) to experiment with before it was understood (and frontier work in electricity when running at extreme frequencies or energies is still difficult to understand, and if we're counting all EM in there it goes beyond being easy to manipulate and experiment with).
My guess? If we figure out how to detect dark matter we can get closer to figuring out how to interact with it (other than through the very very very weak gravitational force). Or maybe we figure out that it was a spinning universal frame or something that gives us a better Standard Model.
If, however, we figure out how to interact with it and can harness any potential energy from it, then by definition we won't see any interference in the electromagnetic forces. That would be incredible, that would be as good as having readily available superconductors.
To wit, consider the case of Charles Parsons, inventor of the steam turbine engine. He was able to do this because of the lifetime work of Henri Victor Regnault (https://en.wikipedia.org/wiki/Henri_Victor_Regnault) characterizing the behavior of steam under pretty much every possible regime. At the time Regnault's work was largely ignored, and later forgotten, since it was only of minor academic interest.
It was only years after his death that Parsons would use his work to determine the necessary geometry of the rotors and stators in his new and revolutionary engine. Regnault certainly didn't see that coming, the people who overlooked his work didn't either, but that pure science for the sake of science helped to change the world.
So as you say, we often don't realize what we're going to do with the results of pure science until engineering catches up, sometimes decades or centuries later. Still without the pure science we'd never get the engineering.
I hope I am not wrong in imagining you may consider grouping quantum mechanics (QM) with research that has no way to ever benefit "humanity's well-being". (Even if I'd argue like art pure science & maths benefit humanity's well-being for it's own sake). This is relevant since accelerators like which was used for the Higgs Boson discovery are also used in general QM research:
https://www.energy.gov/science/doe-explainsquantum-mechanics
> Quantum mechanics led to the development of things like lasers, light-emitting diodes, transistors, medical imaging, electron microscopes, and a host of other modern devices.
Additionally, it's ironic that you mentioned the Higgs-Boson, while perhaps many years before it's discovery and maybe not research CERN was anticipating in doing it did come up with the first webserver:
https://home.cern/science/computing/birth-web/short-history-...
Everything is hard until it's not. Invisible electromagnetic waves are invisible (hard) and frequently deadly (hard!), but now we have WiFi, cell phones, GPS, xrays, etc.
Superconductivity is absurd magic and took impossibly low temperatures until they weren't impossible, and now it's driving MRIs, massively improving medical research, and the realm of usability is constantly expanding. Absolute zero was known reasonably accurately for over 100 years before liquid helium was achieved, and superconductivity came only three years after.
It's the kind of thing you can frequently only judge accurately in retrospect.
This is a weird thought, but maybe it depends on how far you allow yourself to imagine, and what "acceptable imagining" is? I can imagine a few things that Higgs may end up being useful for, sure, they're "insane" or "wild" or "100% not how things could work you're nuts" - but I can still see ways it could benefit humanity if I was right about my imagination, and I'm not going to bother stopping my imagination.
*well-being