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Hi! Have the strong and weak nuclear forces been unified with the electromagnetic force? How could that be theoretically done? Is there some sort of formula or equation for this unification as well?
Answer 1:

The electromagnetic and weak nuclear forces unify with each-other before with the strong, but the strong force unifies with the "electroweak" at higher energies. The way in which this happens is that the particles that mediate the forces approach each-other in energy and in strength at a certain level of energy and temperature. The electromagnetic force is mediated by photons, the strong by gluons, and the weak by W and Z particles (massive as W and Z may be). At energies of 80-90 billion electron volts, the photons, W and Z particles have essentially the same energy and become indistinguishable, performing all functions, indicating that the two forces have merged. The X-boson, which is thought to come in at around 1015 electron volts but which has never been observed, would allow leptons (electrons and neutrinos) to transform into quarks and vice-versa, thereby unifying the strong and electroweak forces. So far, however, we don't have any particle accelerators that can generate even 1012 electron volts, so finding the X-boson and verifying that it indeed exists is well beyond our current capacity.

And then there is gravity. So far we have no good theory of quantum gravitation, or an understanding of how the still-theoretical gravitons would mesh with the X-boson. It's a big mystery.


Answer 2:

The electromagnetic force and the weak force have been unified by theoretical physicists into something called the electroweak force. This theory is called QED, or Quantum Electrodynamics. Looking at the properties of the electromagnetic and weak forces, physicists were able to figure out that at very high energies, the two forces would have identical properties. This doesn't have much bearing on our day-to-day lives - the energies of all the stuff around us is low enough that these two forces look different. However, it does give theoretical physicists some insight into the way the universe works, and particle accelerator experiments have verified these results.

To understand this a bit better, we could relate it to the unification of electricity and magnetism. When these two forces were discovered, it was thought that they were two totally distinct forces. However, James Clerk Maxwell figured out that electricity and magnetism interact with each other in a very interesting way, and that they're not as different as they seem. This gave way to all sorts of great inventions that we use today, like the electromagnetic motor. Albert Einstein later developed his Theory of Special Relativity, and this showed that electricity and magnetism are the same force, just manifested in a slightly different way. However, since we interact with things that move very slowly, they look like two different forces.

The strong force hasn't quite been included into the electroweak force yet. It's hoped that at even higher energies the strong force would look the same as the electroweak force. Physicists call this hopeful theory Grand Unification Theory. Beyond that, it's hoped that some day physicists could unify gravity (the forth and last of the fundamental forces) with all the other forces, thus discovering a Theory of Everying, and hence having a theory that understands the universe at a fundamental level. This has proven to be VERY difficult, but some physicists hope that String Theory could provide the answer.

There is an equation for the electroweak forces. Unfortunately, at this level of physics, theorists use a different notation other than the usual "F=ma" we see in basic physics. This would take a lot to explain, but if you'd like to see some of what these equations look like out of curiosity, you can check out this wikipedia article:
electroweak_f

I didn't try to re-create the equation here, since it's very long. Don't worry about understanding what it means at this point - it's quite complex.



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