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These revolutionary, precise and well confirmed implications indicate a radical departure from common sense.

  • Linearizing the relativistic wave equation leads to the entirely new notions of intrinsic spin and antimatter in quantum field theory, which already entertains virtual matter.
  • Invariance of probability when the wave function is multiplied by an arbitrary phase factor leads to quantum electrodynamics of electrons and photons and quantum chromodynamics of quarks and gluons as a result of gauge symmetry.
  • An inelegant introduction of a scalar field to break an apparent gauge symmetry associated with weak interactions leads to confirmed predictions of the masses of the associated gauge bosons in the unification of weak and electromagnetic interactions.

These astonishingly precise and well confirmed findings announce a fundamental conceptual departure from familiar ideas of matter and forces.

  • String, which purports to unite all forces including gravity, can be endowed with rigidity through an extrinsic curvature term and tied in stable knots that could conceivably model glueballs.
  • Could a knotted string model like this account for the stability of observed particles like these?  

A trefoil knot might be a good
stringy model of a glueball.

String theory (as opposed to particle theory) has opened up many new areas of thought in mathematical physics.


It makes a lot of sense to suppose that the world is made of tiny indivisible particles, because from that foundation one can imagine the whole familiar physical world being literally built like simple Lego (c.f. Toric Lego!).  This materialistic world view can be traced back to the ancient Greeks with Democritus around the 5th century BC and the ancient Indians with Kanada around the 6th century BC.  Isaac Newton too was clearly sympathetic to an atomic philosophy even though he was a profoundly religious man.

But the 20th century has seen a massive departure from traditional metaphysics - from Boolean logic and common sense ontology and simple cognitive epistemology - even from static empty flat Euclidean 3D geometry and absolute uniform linear time.  21st century mathematical metaphysics, unconstrained by any observational evidence indicating quantitative incorrectness of the standard model of particle physics, has opened the door widely to much imaginative theoretical speculation, the only constraint being consistency with the low energy effective theory. 

The physical world cannot be comprehended in terms of traditional metaphysics.


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