Experiments on synthetic dimensions in photonics The first and introductory section of the dissertation presents the working principle of a one and two dimensional photonic mesh lattice based on the time multiplexing technique. The basis of a random walk interrelated to the corresponding light and quantum walk is comprehensively discussed as well. The second part of the dissertation consists of three experiments on a one dimensional photonic mesh lattice. Firstly the Kapitza based guiding light project models the Kapitza potential as a continuous Pauli Schrödinger like equation and presents an experimental observation of light localization when the transverse modulation is bell shaped but with a vanishing average along the propagation direction. Secondly the optical thermodynamics project experimentally demonstrates for the first time that any given initial modal occupancy reaches thermal equilibrium by following a Rayleigh Jeans distribution when propagates through a multimodal photonic mesh lattice with weak nonlinearity. Remarkably the final modal occupancy possesses a unique temperature and chemical potential that have nothing to do with the actual thermal environment. Finally the quantum interference project discusses an experimental all optical architecture based on a coupled fiber loop for generating and processing time bin entangled single photon pairs. Besides it shows coincidence to accidental ratio and quantum interference measurements relying on the phase modulation of those time bins. The third part of the dissertation comprises two experiments on a two dimensional photonic mesh lattice. The first project discusses the experimental realization of a two dimensional mesh lattice employing short and long range interaction. To some extent the second project presents a nonconservative system based on a two dimensional photonic mesh lattice exploiting parity time (PT) symmetry.