In his book “The Elegant Universe”, Briane Greene hypothesises that some superstrings may still be around from the time of the Big Bang, and in fact may have grown to macroscopic or even huge proportions. Is this really plausible? What would such a string look like and behave like? I have trouble believing that the most fundamental “constituent” of matter could have a macroscopic form. Anyone have any ideas?
I haven’t read The Elegant Universe, so I may not be the best person to comment. But one thought is that, in this instance, Greene was refering to cosmic strings rather than superstrings. The former have certainly been hypothesised as possibly forming in the Big Bang and being expanded to cosmic dimensions. Cosmic strings are a bit difficult to explain, but they’re sort of “tangles” in one of the fundamental fields that are currently believed to exist. In the extreme conditions of the Big Bang, things can get knotted up and then blown up to vast proportions. Today a cosmic string would be a very dense thin concentration of energy strung out across the sky.
People have looked for evidence of them, but have come up with nothing convincing. This isn’t necessarily surprising, given that most particle physicists believe that in the aftermath of the Big Bang the universe underwent a series of so-called symmetry breaking transitions. These wipe the slate clean and destroy any cosmic strings. Currently there’s evidence for these transitions, but not for the strings.
Cosmic strings, if they’ve ever existed, would most certainly be an example that a "fundamental “constituent” of matter could have a macroscopic form. " (Technical aside: I’m taking the Higgs field as fundamental for current purposes.) But one of the big developments in quantum field theory in the 1970s and 80s was the realisation that this could be the case. The reasons are deep, but basically it was the realisation that topology was important. I really don’t want to explain topology, but it’s sort of the study of “over all” rather than “just here.” Unfortunately, nobody has ever come up with experimental proof or disproof of these ideas in particular quantum field theory cases, so such issues remain a bit speculative.
Whaaa…??? Topology is a subfield of geometry. It is essentially the study of the relationship of shapes to one another, and concerns itself largely with the classification of shapes and how different shapes within a class can be transformed into one another. In essence, these classifications are based on how many holes a shape has in it, so that a teacup is topologically identical to a doughnut.
I agree - topological notions are, in general, global rather than local ones, the former being preserved under transformations, the latter not.
It’s easy enough to give examples of topological thinking. I’m just not sure there’s an easy way to explain how such ideas tie up to examples of solutions in quantum field theory.