Abstract
Measurable relics of the Big Bang include the observed background radiation at 2.7 Kelvin, the inhomogeneities in the energy distribution, the relative abundance of the chemical elements in our universe, and more. The Big Bang theory provides a quantitative explanation of what we see today, by relying on our theoretical understanding of the rest of the universe. The great success is that the prediction matches the experimental observation in quantitative detail. This is what gives us the confidence that the Big Bang and inflation theories are more or less correct.
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Notes
- 1.
A little mathematical background on Sp(2, R) as a symmetry group: The mathematical language of symmetries in physics is group theory. In the 19th century, the French mathematician Elie Cartan classified all the so-called Lie groups, and the corresponding Lie algebras, into seven “simple” classes that he called A, B, C, D, E, F, G. There are an infinite number of Lie groups in the following classes A n , B n , C n , D n , each labeled by an integer n that takes values n = 1, 2, 3, …, ∞. The E, F, G classes are called “exceptional” and there are only a few of them labeled as E 6, E 7, E 8, F 4, G 2. In terms of Cartan’s classification, the Sp(2, R) Lie group relevant for 2T-physics is identified as C 1. But in this classification A 1 = B 1 = C 1 are all the same as long as they are all taken in their real forms (i.e., only real numbers are involved in all transformations). Hence another name for Sp(2, R) = C 1 is SL(2, R) = A 1, and both of them are the same as Spin(1, 2) = B 1. In any case, in Cartan’s classification, Sp(2, R) is the smallest possible “simple Lie group.” The acronym Sp(2, R) is developed from the large characters in the following description of a specific group of transformations: “ymlectic transformations in dimensions as applied on eal numbers.” In the present application of Sp(2, R) in 2T-physics, the “2” does not stand for two dimensions, but rather for the 2 symbols X and P which are the covariant position X M and contravariant momentum P M, in every direction of space–time labeled by M, including the extra dimensions. Symplectic transformations have the property of leaving invariant the Poisson brackets in classical mechanics or the quantum commutators in quantum mechanics. This is the main reason for why symplectic transformations applied in phase space X M, P M is relevant in 2T-physics.
- 2.
Students of philosophy may find some similarities between the shadows analogy used to explain 2T-physics and Plato’s allegory of the cave (see, e.g., http://en.wikipedia.org/wiki/Allegory_of_the_cave). Indeed some familiarity with Plato’s ideas may be helpful in understanding one aspect of the shadows, namely the question of how observation is related to reality? But there are actually important differences between 2T-physics and Plato’s ideas. In particular, in Plato’s allegory, there is a one-to-one correspondence between a real “form” and the corresponding shadow. But in 2T-physics there are many shadows of the same 4+2 events or history that are interpreted as different from each other by observers in 3+1 dimensions. The crucial point in 2T-physics is that it predicts hidden relations between apparently distinct 3+1 systems, thus making testable predictions that correctly fit nature. 2T-physics unifies quantitatively, not just descriptively, distinct 1T-physics systems into one 4+2-dimensional system.
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Bars, I., Terning, J. (2010). Why Higher Space or Time Dimensions?. In: Nekoogar, F. (eds) Extra Dimensions in Space and Time. Multiversal Journeys. Springer, New York, NY. https://doi.org/10.1007/978-0-387-77638-5_5
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