...I'm sure my question contains within it at least several misconceptions, but let that just be an illustration of how confused this kind of article leaves laypeople.
...I'm sure my question contains within it at least several misconceptions, but let that just be an illustration of how confused this kind of article leaves laypeople.
To get random breaking in a different way, presumably no amount of mere heating of matter would suffice; you would have to somehow restore the high-energy false vacuum of the Big Bang itself? I don't suppose there's any way to do that in today's universe, even in principle?
You have to understand that there already is a difference between the two things (forces, particles, whatever). It's just in certain temperatures or forces, or size ranges (whatever) that broken symmetry is not visible and the two appear to be identical.
So the search is on to understand why these two things should act so identically in certain ways, and yet not identically in other ways, i.e. what breaks their symmetry.
Finding out what breaks their symmetry tells you a LOT about the particle, it tells you what is identical, and what is different.
For example an up and down quark are identical in all ways - except mass and charge. So in certain experiments they appear identical, in others those things show up - their symmetry is broken.
But noticing that they are identical in certain situations tells you a lot about quarks, and noticing where they differ tells you even more.
You're describing a particle accelerator. When we talk about the LHC accessing "higher energies" than the Tevatron [1] we are saying it is "baking" small parts of the universe to higher and higher temperatures.
[1] http://blogs.discovermagazine.com/cosmicvariance/2009/11/30/...
So there is a search for why.
For example an up and down quark look virtually identical, because they are quite similar. But at a certain point something differs in an experiment, and you realize it's because their masses are not identical, and in a certain situation the symmetry is broken and you can see the different masses.