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Title: Scaling laws conjecture in superstring theory
Authors: Sun, BoHua 
Keywords: Scaling laws;Point blast;Big bang;String theory;Dimensional analysis
Issue Date: 2017
Publisher: ResearchGate
Source: Cape Peninsula University of Technology, 14 January 2017, 1-3
Abstract: This paper propose a conjuncture on the scaling laws of big bang based on superstring theory. The study reveals that the higher dimensional universe will require more energy than the lower one. If we assume that the universe will develop based on the minimum energy principle, then we will have to ask a big question to all higher dimensional universe model, why the model does not satisfy the minimum energy principle. The study also brings a question on how to define the physics units in the 10-dimensional spacetimes? Does dimensional analysis still works to the superstring theory by using the current seven basic units? PACS numbers: 04.60,04.20 In the history of cosmology, it soon became evident that an expanding universe was once very much smaller so small, in fact, that it was compressed down to a single point (or, at least, a very small area). The theory that the universe started from such a primordial point and has expanded ever since is known as the big bang theory. String theory will hopefully help physicists understand more precisely what happened in those early moments of the universe, so understanding the big bang theory is a key component of string theorys cosmological work. The tremendous explosion of the big bang released a massive energy and makes the universe expanding. The problem we may ask is how much the energy were released from the big bang. To answer this question, we will attack the problem with the help of dimensional analysis and superstring theory. Any physical relationship can be expressed in a dimen-sionless form. The implication of this statement is that all of the fundamental equations of physics, as well as all approximations of these equations and, for that matter , all functional relationships between these variables, must be invariant under a dilation of the dimensions of the variables. This principle is the basis for a powerful method of reduction, which is called dimensional analysis and is useful for the investigation of complicated problems. (Buckingham [1],Bridgman [2]; Sedov [3]; Baren-blatt [4]; Cantwell [5]; Sun [6]). Often, dimensional analysis is conducted without any explicit consideration for the actual equations that may govern a physical phenomenon. From a physics point of view, dimensional analysis is a universal method, which can, of course, be used for the study of big bang. Our belief is that no matter how complex the big bang, as long as we can capture all the primary variables of the problem, then we can formulate it by way of dimensional analysis. G.I. Taylor investigated point blast by using the dimensional analysis [7–9], and Sedov studied the same problem independently [3]. The Taylor-Sedov scaling laws for four dimensional spacetimes is useful in astrophysics. However, the scaling laws for the ten dimensional spacetimes of the superstring theory has not been seen in the literature. We are going to adopt same idea stems from Taylor and Sedov together with the super-string theory to derive the scaling laws of the big bang. According to the big bang theory, our universe is thought to have begun as an infinitesimally small, infinitely hot, infinitely dense, something-a singularity. After its initial appearance, it apparently inflated (the " Big Bang "), expanded and cooled, going from very, very small and very, very hot, to the size and temperature of our current universe. It continues to expand and cool to this day. The singulary point can be viewed as single point, the big bang explosion then can be considered as point blast. Near the blast centre, both temperature and pressure are extremely high, which will drive the wavefront travels away from the centre at a high speed. Let E D be the energy release of the big bang, ρ is undisturbed medius outside of the wave front, R is radius of the spherical wave front, γ is the ratio of heat capacities of the medius. If we denote the dimensions of spacetimes as D, then the dimensions of the big bang is listed table below. TABLE I: Dimensions of point blast R ED γ ρ t L ML 2 T −2 1 ML −D+1 T In the table, notations M, T and L are the dimension of mass, time and length, respectively. From dimensional analysis (Buckingham [1],Bridgman [2]; Sedov [3]; Barenblatt [4]; Cantwell [5]; Sun [6]), we can generate two dimensionless parameters Π, namely Π 1 = RE − 1 D+1 D ρ 1 D+1 t 1 D+1 (1) Π 2 = γ. (2) According to the Buckingham theorem (Buckingham [1],Bridgman [2]), the two Π must have a relation as Π 1 =
URI: 10.13140/RG.2.2.30853.14561
Appears in Collections:Eng - Technical Reports

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