By Joshua Engel, polymath
You want the simplest possible terms? I'd go with "none." There are no implications to the discovery of the Higgs boson that have any effect outside physics department, nor are they expected to in the foreseeable future. Not even sci-fi guesswork.
That's not to say that nothing will ever happen. The discoverer of positrons had no idea they would lead to Positron Emission Tomography. The discoverers of quantum mechanics had no idea that they would lead to the ability to download Justin Bieber albums over the Internet.
It's unlikely that you'll ever get a Higgs Boson device of any sort. They're too hard to make in isolation and too squirrelly to manipulate. What you'll get will be far more indirect: we now have a firmer place on which to understand the fundamental nature of matter, and that theoretical ground can be the beginning of ... well, nobody knows what. It's unlikely to be any of the fanciful speculation, and far more likely to be something utterly unexpected.
But really, in layman's terms, there are no layman's terms. It's a spectacular confirmation of one of the most important scientific theories of how the universe works. The most important thing that could give to a layman is the inspiration to go out and become more than a layman about physics.
By Jay Wacker, Assistant Professor of Physics at the SLAC National Accelerator Laboratory
Many of the foreseeable uses of the Higgs boson involve understanding the big questions of physics. The Higgs boson really is the lynchpin of the Standard Model and has implications for the early Universe and the ultimate fate of the Universe. For instance, the Higgs boson could indirectly play a critical role in the creation of the matter of the Universe. There are dozens of implications that the Higgs boson has for theoretical physics that physicists from around the world will be working on for the next decade.
Any more technological application requires a lot of speculation. I'd like to note that we're seeing the first multi-GeV accelerators used for technology and the associated physics of pions, kaons, and muons are starting to become relevant for this technology. These particles were discovered in the 1930s and 1940s and even 30 years ago. I don't think many people foresaw the growth of these (formerly) high energy accelerators into technology.
One obvious thing that comes to mind is that you can use the Higgs boson as a very high energy monochromatic photon source, which means that it's good for calibrating signals. It's one of the few standard candles for high energy particles. Probably before the LHC stops running, they will be doing this for the LHC detectors.
Next, we don't know what dark matter is only that it exists, but it could have an intimate tie to the Higgs boson. Many theories of dark matter indicate that the primary force between normal particles and dark matter arises from the Higgs boson. Since 85% of the mass of the Universe is dark matter, if the Higgs boson and dark matter are linked, then we might have some revolutionary ideas in the distant future.
Finally, the Higgs boson might be more easily produced at higher energies. For instance, if it is produced in the decays of other particles that are heavier than what an 8 TeV LHC can produce, then this would dramatically change any applications of the Higgs boson.
However, the only honest answer I can give for what the Higgs boson means for the average Joe of the 21st century that doesn't require wild optimism and speculation is Joshua Engel's answer of "none." Nevertheless, sometimes the implications of speculative research of scientists are far more relevant than they can ever imagine. J.J. Thompson, who discovered the electron, would never have imagined that the electron microscope.
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