Started by Solitary, May 19, 2014, 11:26:08 AM
Quote from: Unbeliever on July 23, 2014, 07:07:14 PMI wonder whether the dualities of string theories have any connection to the geometric dualities of the Platonic solids? Or this merely coincidental?
Quote from: josephpalazzo on July 24, 2014, 09:21:39 AMThere 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 â†' 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, gâ†' 1/g. The types I with Heterotic SO(32), and type IIB with itself are S-duals.
Quote from: josephpalazzo on May 22, 2014, 04:52:45 PM I was very gentile with you...
Quote from: Unbeliever on July 30, 2014, 06:33:27 PMWell, 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.
Quote from: Solitary on August 04, 2014, 12:24:50 PMQuoteWe know that the particle/wave duality is physicalSmOn 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
QuoteWe know that the particle/wave duality is physical
Quote from: Solitary on August 07, 2014, 12:39:29 AMFirst 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.
QuoteThe 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.
QuoteIf 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
Quote from: Solitary on August 07, 2014, 01:58:43 PMYou are correct a single electron does have wave properties, but only when it is moving, which is my point. Solitary