String Theory

[josephpalazzo]

I wonder whether the dualities of string theories have any connection to the geometric dualities of the Platonic solids? Or this merely coincidental?

There are lots of dualities: the wave/particle duality; in the Hilbert space, there is a duality between the bra  and the ket vectors, and so on. The word "duality" simply means "two". Wherever there are two kinds of things that are somewhat related, there is a duality. In String Theory, the dualities are related to some transformations: in one case, called T-duality, the two string theories are related by the transformation of the distances: R → 1/R. The types IIa with IIB, and Heterotic E8xE8 with Heterotic SO(32) are T-duals. While the S-duality is related by the couplig transformation, g→ 1/g. The types I with Heterotic SO(32), and  type IIB with itself are S-duals.

[Solitary]

Light and dark, up and down, in and out, big and small, mind and body, human and animal, smart and dumb, reality and fantasy, gravity and energy, etc. So what?  Solitary

[Unbeliever]

There are lots of dualities: the wave/particle duality; in the Hilbert space, there is a duality between the bra  and the ket vectors, and so on. The word "duality" simply means "two". Wherever there are two kinds of things that are somewhat related, there is a duality. In String Theory, the dualities are related to some transformations: in one case, called T-duality, the two string theories are related by the transformation of the distances: R → 1/R. The types IIa with IIB, and Heterotic E8xE8 with Heterotic SO(32) are T-duals. While the S-duality is related by the couplig transformation, g→ 1/g. The types I with Heterotic SO(32), and  type IIB with itself are S-duals.

Well, yes, I understand that part, but I noticed a possibly interesting link, specifically between the Platonic solids and the dualities of the coupling constants in string theory.

I was reading a book about symmetry (appropriately titled "Symmetry") by Marcus du Sautoy, in which he discusses these Platonic dualities (pg. 57-58). The cube is dual to the octahedron, the dodecahedron is dual to the icosahedron, and the tetrahedron is dual to itself. This reminded me of reading about the coupling strength dualities of the various string theories in Brian Greene's book "The Elegant Universe" (pg. 313) in which he says that the coupling strength of Type-I is dual to the coupling strength of Heterotic-SO(32), the coupling strength of Heterotic-E8xE8 is dual to the coupling strength of type-IIA, with type IIB being dual to itself.

It just seemed to me to be of a similar pattern, and I thought there could be some subtle connection. But I'm neither scientist nor mathematician enough to be able to tell if there is any significance to this.

[Solitary]

I was very gentile with you...

And wrong! Ha! Ha! Solitary

[josephpalazzo]

Well, yes, I understand that part, but I noticed a possibly interesting link, specifically between the Platonic solids and the dualities of the coupling constants in string theory.

I was reading a book about symmetry (appropriately titled "Symmetry") by Marcus du Sautoy, in which he discusses these Platonic dualities (pg. 57-58). The cube is dual to the octahedron, the dodecahedron is dual to the icosahedron, and the tetrahedron is dual to itself. This reminded me of reading about the coupling strength dualities of the various string theories in Brian Greene's book "The Elegant Universe" (pg. 313) in which he says that the coupling strength of Type-I is dual to the coupling strength of Heterotic-SO(32), the coupling strength of Heterotic-E8xE8 is dual to the coupling strength of type-IIA, with type IIB being dual to itself.

It just seemed to me to be of a similar pattern, and I thought there could be some subtle connection. But I'm neither scientist nor mathematician enough to be able to tell if there is any significance to this.

I guess it all depends on the nature of the duality. For instance, if you take an equation in type IIA that contains R, the radial distance, and substitute 1/R, you get the equivalent equation in type IIB. Does that mean anything? Witten proposed that it was symptomatic of a theory in higher dimension - String Theory in 10-D to a hypothetical M-Theory in 11-D - but no one has figured out that M-Theory so far. Note that these dualities in ST are mathematical in nature. We don't really know if it corresponds to anything physical, and if it does, what is that physical reality. We know that the particle/wave duality is physical, and we were able to transform that into a mathematical language, which we call Quantum Mechanics. In ST, we have the reverse, a mathematical duality, but we are still uncleared as to what physical reality that would correspond to.

EDIT: See https://en.wikipedia.org/wiki/M-theory

[Unbeliever]

OK, thanks Joe!

[Desdinova]

[josephpalazzo]

We know that the particle/wave duality is physical

SmOn Who is this we?

when physicist talk about the wavelength of a photon, they are not referring to a property of an individual photon but to a characteristic of the mathematical function that that describes a statistical ensemble of identical photons. The same can be done with electrons or any other particle. The electron, photon, and all other submicroscopic objects are localized particles and their wavelike effects refer to their only to the statistical behavior of a large group of them.

It does not matter whether you are trying to measure  a particle property or a wave property. YOU ALWAYS MEASURE PARTICLES. Quantum mechanics is just a statistical theory like statistical mechanics, reducible to particle behavior. Keep the cards and letters coming.  Solitary

Not really. A single electron can exhibit wave properties. And yet no one thinks that the single electron is made up of a statistical ensemble of identical particles.

[josephpalazzo]

First of all, you cannot observe the "wave like distribution," or interference, with only one electron. The interference pattern emerges statistically, after many electrons have been detected at the screen.

Yes it happens with a single photon. Google: Mach–Zehnder interferometer.

The electron must be moving to acquire mo and a wave property. We are thus dealing with a momentum-wave duality rather than a particle-wave duality. When an electron is not accelerated, it could be bound as a particle with mass but it has no mo and no wave properties.

Speculation.

If the energy given to the particle stays with the particle then that means there is such a thing as absolute rest. With absolute rest Newton is in and Einstein is but a pretender he always was. Solitary

You're out of luck. GR has been verified over and over again over the last 99 years. (Hint: next year will mark GR's 100 years,  )

[josephpalazzo]

You are correct a single electron does have wave properties, but only when it is moving, which is my point. Solitary

The Heisenberg Uncertainty Principle forbids any particle to be at rest. Without this principle, quantum fluctuations can't exist... oh wait, QM can't exist.