Does the poincare conjecture disprove the shape of strings in string theory

In summary, it seems that the smallest particles in nature are supposed to be strings, which are donut and line shapes. The Poincare conjecture says the simplest shape in nature is a sphere, so if particles combine to form other shapes, it's from some other property of nature. String theory, as any fundamental theory, has to start from somewhere, and it's not clear whether the fundamental entities of string theory are a product of a fundamental wave dynamic that might be connected to, say, the Poincare conjecture and the Huygens-Fresnel principle.
  • #1
clearwater304
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Considering that the smallest particles in nature are supposed to be strings, which are donut and line shapes. And the poincare conjecture says the simplest shape in nature is a sphere. wouldn't it make sense that the true fundamental particles are sphere shaped and that if they combine to form other shapes, it is from some other property of nature.
 
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  • #2
clearwater304 said:
Considering that the smallest particles in nature are supposed to be strings, which are donut and line shapes. And the poincare conjecture says the simplest shape in nature is a sphere. wouldn't it make sense that the true fundamental particles are sphere shaped and that if they combine to form other shapes, it is from some other property of nature.
Not some other property of nature, per se, necessarily, but that there had been a considerable amount of activity by the time the doughnut or line shape entities emerged. String theory, as any fundamental theory, has to start from somewhere. Are the fundamental entities of string theory a product of a fundamental wave dynamic that might be connected to, say, the Poincare conjecture and the Huygens-Fresnel principle?
 
  • #3
How could the poincaré conjecture possibly disprove string theory?
To start off with, there's no way any theorem from pure mathematics could ever prove or disprove the applicability of any theory based on correct mathematics to the real world.
Secondly, it doesn't say that the simplest shape in nature is a sphere. It says that any simply connected 3-manifold is homeomorphic to the 3-sphere.
Thirdly, strings aren't 3-dimensional objects, and their two-dimensional worldsheets aren't simply connected at anything other than the first order in perturbation theory, so it seems to me to be a fairly unlikely candidate to have anything to do with some more fundamental physics.
Fourthly, and we're now onto topics that I don't claim to understand at all, but I'm aware that there's a connection between the mathematical techniques Perelman used to prove the conjecture and certain features of RG running and the dilaton in string theory. I don't understand this point at all, although David Tong seems to- see section 7 of his lecture notes.

If there's a productive conversation to be had here, it might also be more likely to be had in the 'beyond the standard model' forum rather than this one.
 

1. What is the Poincare Conjecture?

The Poincare Conjecture is a famous mathematical problem, proposed by French mathematician Henri Poincare in 1904, that states that any closed 3-dimensional manifold (a type of geometric shape) is topologically equivalent to a 3-dimensional sphere.

2. What is string theory?

String theory is a theoretical framework that attempts to reconcile the currently known laws of physics, including gravity and quantum mechanics, by modeling particles as tiny strings rather than point-like objects.

3. How does the Poincare Conjecture relate to string theory?

The Poincare Conjecture is a purely mathematical problem and does not directly relate to string theory. However, some scientists have suggested that if the Poincare Conjecture were true, it could have implications for the shape and structure of strings in string theory.

4. Does the Poincare Conjecture disprove the shape of strings in string theory?

No, the Poincare Conjecture has not been proven or disproven yet. Even if it were proven, it would not necessarily disprove string theory. String theory is a complex and ongoing area of research, and the shape of strings is just one aspect of the theory.

5. Could the Poincare Conjecture have an impact on our understanding of the universe?

Possibly. If the Poincare Conjecture were proven, it could provide valuable insights into the structure of 3-dimensional space. However, it is unlikely to have a direct impact on our understanding of the universe or on the validity of string theory.

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