Analogies for Symmetry Breaking and the Higgs Particle

[lpetrich]

Any good ones?

I like this one:

For full symmetry, imagine a marble and a bowl with rotational symmetry. Drop the marble into the bowl. It will oscillate back and forth and settle down in the center. The bowl+marble system still has rotational symmetry. If you push the marble out of the center, it will oscillate back and forth with the same frequency no matter what direction.

For broken symmetry, imagine a bowl with a hump in the middle, but still with rotational symmetry. A bowl like a juice squeezer. Drop a marble into that bowl. It will come to rest in the trough around the hump. The bowl+marble system has lost its rotational symmetry. Furthermore, if you push the marble, it will oscillate radially, but keep going without oscillating tangentially.

It seems to me that the tangential motion, with the marble following the trough, is a Goldstone mode of the marble's motion. It has zero "mass" (oscillation frequency). Would that be a good way of explaining Goldstone modes?

One can even illustrate symmetry restoration with high-enough temperature in this analogy, by making the marble move faster and faster. If fast enough, then it is not much affected by the central hump.

I may have seen this analogy somewhere, but if I didn't, I was inspired by the shape of the Higgs particle's potential.


I've also thought of using crystallization as an analogy for symmetry breaking, but unlike a marble in a bowl, it does not have dynamics.


I've seen various analogies for the Higgs particle. Any favorites?

 

[AndyW]

I find this analogy to be quite interesting and thought-provoking. It effectively illustrates the concept of symmetry breaking and the emergence of Goldstone modes. The comparison to the Higgs particle's potential adds another layer of understanding to the analogy.

I have also come across other analogies for the Higgs particle, such as the idea of a field of snow on a mountain, with the snow representing the Higgs field and the skiers representing particles gaining mass as they interact with the field. Another analogy I have seen is comparing the Higgs field to a crowded room, where particles moving through the room interact with the "people" (Higgs bosons) and gain mass as a result.

Overall, I think analogies like these can be helpful in explaining complex concepts in a more relatable and visual way. It's always interesting to see different perspectives and ways of understanding scientific concepts.