> For instance, SU(5) groups quarks and antiquarks together with leptons and antileptons into “fiveplets,” which are like the indistinguishable sides of a regular pentagon.
The idea is to put the 5 particles in 5 places that are undistinguishable.
For that you need to use the vertex corners of an hyper-tetraedrum ( https://en.wikipedia.org/wiki/5-cell ). Don't get confused by the bad drawings, if you have one of them in 4 dimensions, you can put each point at the same distance of all the other points.
If you use a regular pentagon, then you must select an order for each of the particles/vertex. If you select one, some are more close than the others.
(An alternative is to use a pentagon, but consider not only the rotations and flip, but also the operations that mix the vertex/particles in any order. But then the nice identification with the symmetry of the geometric figure is gone. You can use a square with the central point.)
In some sense, no. The SU(5) group includes all the symmetries of the hyper-dodecahedron, were you can rotate it in the 4-dimmensional space to exchange one of the vertex/particles with another. But it also includes more strange things, like half mixing two particles.
a -> (a+b) / srqt(2)
b -> (a-b) / sqrt(2)
The use of geometric shapes like the hyper-dodecahedron is more a nice visualization technique. It's easier to explain than the details of the SU(5) group and it provides a good intuition, even after studding the theory with more details. So I prefer to ignore this technical detail, specially for a popular science article.
begin your search for letter c."
Throw it away, what's left to need
When you’ve got infinity
So much out there left to find
We'll do that some other time
Are they ? As far as I know, neurons last more or less from before birth to death. There is neurogenesis in the hippocampus but it doesn't replace existing neurons, and the new cells themselves last until death.
Why assume we are blind?
Complex numbers are an underlying structure that has unified wide ranging physical phenomena
And yet complex numbers are merely a shadow of much deeper unifying structures
The thing I like the most is that don't play the "analogy game" too much and instead generally teach a small concept and then build up on it.
While other popular media outlets like Wired or Verge simply dumb it down too much or are factually incorrect.
I do like WIRED's Science Blogs though even though they are a little bit inactive.
"Japan is considering building a $1 billion detector called Hyper-Kamiokande, which would be between eight and 17 times bigger than Super-K and would be sensitive to proton lifetimes of 10^35 years after two decades."
All this to possibly detect a single proton decay in 20 years. Now that's some serious commitment!
"In the meantime, a Nobel Prize has been won for a different discovery in the cathedral-esque water tank pertaining to particles called neutrinos."
Hyper-K is a dual-purpose detector, a neutrino detector as well as a proton decay detector. Substantial part of Hyper-K funding should be interpreted as investment to a neutrino detector.
So it'd be a quark-antiquark pair popping up.
The proton is the lightest Baryon (3 quark particle), there is no lighter Baryon it could decay into. The decay products have to be lighter than the original proton, by at least the mass of the virtual quark pair, to repay the energy 'borrowed' from the vacuum to create the virtual quark pair (because energy is always conserved). So the proton remains unaffected by the virtual particles popping in and out of existence around it. The virtual particles have no choice but to effectively to annihilate with one another and disappear, to pay back the energy debt.
Heavier Baryons (Sigmas, Lambdas) are indeed destabilized by virtual quark pairs, that is the mechanism by which they decay, almost instantaneously, on their own.
You could have an up-anti up quark pair that pops up close to the up quark of the proton, the up quarks could 'swap places', and then the up of the proton annihilates with the anti up of the virtual quark pair, but the the result is still a proton.
It's required that quantum interactions obey conservation laws, and any non-conserving "virtual configuration" must be short-lived, only existing to the extent it might affect interactions with "real", physically allowed configurations. There's no quantum interaction that lets a proton turn into something else while obeying conservation laws. In particular, normal interactions can't change the number of quarks in a given configuration, and the proton is the lowest energy configuration of 3 quarks. So it can't "tunnel" via a virtual configuration into some other real configuration.
Grand unified theories usually introduce additional mechanisms that can turn quarks into leptons, so proton decay is a test of those theories.
...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  we are saying it is "baking" small parts of the universe to higher and higher temperatures.
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.
Well, "extra ... variables that can make ..." is often a sign of EOL desperation for theories. What I got from Kuhn, anyway.
Why do we assume the theories are unifiable?
From the article:
> If the forces were indeed one during the “grand unification epoch” of the universe’s first trillionth of a trillionth of a trillionth of a second, then particles that now have distinct responses to the three forces would then have been symmetric and interchangeable, like facets of a crystal. As the universe cooled, these symmetries would have broken, like a crystal shattering, introducing distinct particles and the complexity seen in the universe today.
What if the universe we experience is the product of interactions between distinct universes, which circumscribed by different physical laws, and the only universe we can sufficiently experience and observe is that which is governed by the Strong Nuclear Force?
One problem with simply combing the current General Relativity and Standard Model theories is local vs non-local determination. That is moderately complex to explain... perhaps someone has a better source than Wikipedia:
I think it's a great question. Maybe the universe itself is the attempt to unify these theories. Greg Egan style.