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Picked this one up in preparation for an event with Brian Greene. Written over 15 years ago, it is missing the latest developments and consensus, which seems to be that the original vision for String Theory (ST) as a TOE didn’t pan out, yet it is still the only TOE we got. It's a bitch we can’t test it, and a shame we can’t find the shape of the Calabi-Yau manifold that corresponds to reality that we live in, but otherwise ST is quite beautiful indeed.
On the plus side - ideas from ST are now firmly embedded into quantum field theories, condensed matter physics, and cosmology. Also, in select areas, but in an unprecedented fashion, ST forged away ahead of mathematics by providing the intuitions that weren’t available to the latter.
Anyway, back to the book - regardless of where we are today, Greene gives a nice intro into the historiography and basic tenets of ST, and provides a nice expose on the challenges that any TOE would have to grapple with sooner or later. Rest are notes to self.
Starts off with Einstein’s resolution to Maxwell-Newton incompatibility (via special relativity), and then Newton’s gravity as force-at-distance paradox (general relativity); frames ST as an attempt to resolve GTR and QM.
Brief, fairly conventional overview of SR/GTR and QM. Nice stories of how SR logically falls out of fully appreciating the absoluteness of c, and similarly how QM falls out of fully accepting implications of h (Planck’s constant) . Feynman sum-over-history interpretation is rarely covered, so that was cool.
Unification attempts. Must explain all 4 fundamental forces at quantum level. Quantum Field Theory(s) do it for 3. Issues with G: Schrodinger’s equation blows up at sub-Planck level, Heisenberg’s “borrowing of energy” resulting in “constant creation and destruction” is a real nuisance, and zero-gravity flat space is no longer flat due to quantum foam.
Enter ST. Standard Model’s zero-dimension point particles blow up math with zero distances and infinite energies at the limit. But Strings are 1-dimensional, and end up quantizing size with a minimum non-zero value, and so quantum foam is masked. Now zero-g space is actually flat, ‘cause smallest building block (1D string) is too coarse. QM and GTR play nicely together.
Crap, infinities are avoided, but you still get probabilities going negative in Schrodinger’s equation… Not to worry – add 6 curved dimensions to spacetime and you are home free! But where is “home” in the 10D Calabi-Yau landscape of possibilities??
Btw, “String Theory”’s full name is Superstring Theory with “super” for supersymmetry. Quite nifty with particles, antiparticles and spin symmetries.
But it gets even better with symmetry, you see – with ST when you collapse something you don’t shrink to zero (minimum size constraint), but you go through the minimum and blow it out on the other side. And so you got “mirror symmetry” Calabi-Yau manifolds – geometrically different, yet physics-wise equivalent.
And boy, ST gets a lot of mileage out of minimum size and mirror symmetry – seems like whenever there is an issue, just transform it into a different geometric space where it is easier to solve. And if math blows up, dig up that minimum size constraint and avoid that pesky singularity.
For example, in the 90s there were 5 legitimate and different formulations of ST (“Type I”, “Heterotic” etc.), a tad hard to maintain a straight face when you are shooting for an ultimate TOE… But in ’95 Edward Witten himself unifies them all into M-theory, by throwing in another (11th!) dimension and demonstrating the equivalence of the 5 ST theories. Not to be complacent he even throws in a bonus 6th one - 11D supergravity!
Now let's launch ST into outer space and see what sticks. Black Hole as elementary particle? No problem, ST got you covered via Calabi-Yau equivalence. Hawking radiation and black hole entropy? ST jumps in with black hole thermodynamics. And now, for the encore - what happens when black hole swallows Schrodinger’s wave function!? Is information lost? Not sure about ST, but I distinctly hear Claude Shannon’s muffled moan coming from his grave… Curtain falls.
On the plus side - ideas from ST are now firmly embedded into quantum field theories, condensed matter physics, and cosmology. Also, in select areas, but in an unprecedented fashion, ST forged away ahead of mathematics by providing the intuitions that weren’t available to the latter.
Anyway, back to the book - regardless of where we are today, Greene gives a nice intro into the historiography and basic tenets of ST, and provides a nice expose on the challenges that any TOE would have to grapple with sooner or later. Rest are notes to self.
Starts off with Einstein’s resolution to Maxwell-Newton incompatibility (via special relativity), and then Newton’s gravity as force-at-distance paradox (general relativity); frames ST as an attempt to resolve GTR and QM.
Brief, fairly conventional overview of SR/GTR and QM. Nice stories of how SR logically falls out of fully appreciating the absoluteness of c, and similarly how QM falls out of fully accepting implications of h (Planck’s constant) . Feynman sum-over-history interpretation is rarely covered, so that was cool.
Unification attempts. Must explain all 4 fundamental forces at quantum level. Quantum Field Theory(s) do it for 3. Issues with G: Schrodinger’s equation blows up at sub-Planck level, Heisenberg’s “borrowing of energy” resulting in “constant creation and destruction” is a real nuisance, and zero-gravity flat space is no longer flat due to quantum foam.
Enter ST. Standard Model’s zero-dimension point particles blow up math with zero distances and infinite energies at the limit. But Strings are 1-dimensional, and end up quantizing size with a minimum non-zero value, and so quantum foam is masked. Now zero-g space is actually flat, ‘cause smallest building block (1D string) is too coarse. QM and GTR play nicely together.
Crap, infinities are avoided, but you still get probabilities going negative in Schrodinger’s equation… Not to worry – add 6 curved dimensions to spacetime and you are home free! But where is “home” in the 10D Calabi-Yau landscape of possibilities??
Btw, “String Theory”’s full name is Superstring Theory with “super” for supersymmetry. Quite nifty with particles, antiparticles and spin symmetries.
But it gets even better with symmetry, you see – with ST when you collapse something you don’t shrink to zero (minimum size constraint), but you go through the minimum and blow it out on the other side. And so you got “mirror symmetry” Calabi-Yau manifolds – geometrically different, yet physics-wise equivalent.
And boy, ST gets a lot of mileage out of minimum size and mirror symmetry – seems like whenever there is an issue, just transform it into a different geometric space where it is easier to solve. And if math blows up, dig up that minimum size constraint and avoid that pesky singularity.
For example, in the 90s there were 5 legitimate and different formulations of ST (“Type I”, “Heterotic” etc.), a tad hard to maintain a straight face when you are shooting for an ultimate TOE… But in ’95 Edward Witten himself unifies them all into M-theory, by throwing in another (11th!) dimension and demonstrating the equivalence of the 5 ST theories. Not to be complacent he even throws in a bonus 6th one - 11D supergravity!
Now let's launch ST into outer space and see what sticks. Black Hole as elementary particle? No problem, ST got you covered via Calabi-Yau equivalence. Hawking radiation and black hole entropy? ST jumps in with black hole thermodynamics. And now, for the encore - what happens when black hole swallows Schrodinger’s wave function!? Is information lost? Not sure about ST, but I distinctly hear Claude Shannon’s muffled moan coming from his grave… Curtain falls.