Only three dimensions exist in the Universe, as most humans have long suspected, with the exception of mathematicians and physicists. Albert Einstein at one point approached this realization but geometry prevented his making the logical connections necessary to understand this basic principle. Today mathematicians and physicists fantasize about eleven, fifty – six and two hundred and fifty – si...

An important conclusion of both string theory and loop quantum gravity theory is that space and time are ultimately discrete. A consequence of discrete space is that there is empty space between the basic elements of space. Analogously, there are empty times between the times where time exists. When time does not exist, it is meaningless to consider the existence of the universe. In this note w...

Second-order time correlations of polaritons have been measured across the condensation threshold in a CdTe microcavity. The onset of Bose-Einstein condensation is marked by the disappearance of photon bunching, demonstrating the transition from a thermal-like state to a coherent state. Coherence is, however, degraded with increasing polariton density, most probably as a result of self-interact...

A method of solving the Einstein equations with a scalar field is presented. It is applied to find higher dimensional vacuum metrics invariant under the group SO(n + 1) acting on n-dimensional spheres. PACS number: 04.50.-h

By Jules C Beal MD (Dr. Beal of Albert Einstein College of Medicine has no relevant financial relationships to disclose.) Koshi A Cherian MD (Dr. Cherian of Albert Einstein College of Medicine has no relevant financial relationships to disclose.) Solomon L Moshe MD (Dr. Moshe of Albert Einstein College of Medicine received honorariums from UCB as a member of a data and safety monitoring board.)...

Jane Oba, Ana Maria Escobar, Benita G. S. Schvartsman, José Luiz Gherpelli I Hospital Israelita Albert Einstein, São Paulo, São Paulo, Brazil. Instituto do Coração of Hospital das Clı́nicas, Faculdade de Medicina da Universidade de São Paulo, São Paulo, São Paulo, Brazil. II Hospital Israelita Albert Einstein, São Paulo, SP, Brazil. Instituto da Criança ‘‘Prof. Pedro de Alcântara’’ of Hospital d...

Jane Oba, Ana Maria Escobar, Benita G. S. Schvartsman, José Luiz Gherpelli I Hospital Israelita Albert Einstein, São Paulo, São Paulo, Brazil. Instituto do Coração of Hospital das Clı́nicas, Faculdade de Medicina da Universidade de São Paulo, São Paulo, São Paulo, Brazil. II Hospital Israelita Albert Einstein, São Paulo, SP, Brazil. Instituto da Criança ‘‘Prof. Pedro de Alcântara’’ of Hospital d...

We produce some explicit examples of conformally compact Einstein manifolds, whose conformal compactifications are foliated by Riemannian products of a closed Einstein manifold with the total space of a principal circle bundle over products of Kähler-Einstein manifolds. We compute the associated conformal invariants, i.e., the renormalized volume in even dimensions and the conformal anomaly in ...

We show that #9(S 2 S 3) admits an 8-dimensional complex family of inequivalent non-regular Sasakian-Einstein structures. These are the rst known Einstein metrics on this 5-manifold. In particular, the bound b 2 (M)8 which holds for any regular Sasakian-Einstein M does not apply to the non-regular case. We also discuss the failure of the Hitchin-Thorpe inequality in the case of 4-orbifolds and ...