A fundamental prediction of quantum physics is the existence of random fluctuations everywhere in vacuum. This is one of the most remarkable and central ideas in quantum field theory which manifests itself in a variety of situations. Perhaps the most dramatic and well known consequence of this is the existence of an attractive force between two parallel, perfectly conducting plates in vacuum: the Casimir effect. This phenomenon was predicted to occur in 1948 and it took fifty years for the first unambiguous measurement to be carried out. Today the quantum vacuum can be manipulated in MEMS/NEMS (Micro and nano electro-mechanical-systems), and even in the construction of electronic components (transistors, diodes) representing an active area of applied quantum science and engineering. From the point of view of fundamental physics, the idea of a vacuum energy of empty space is tightly linked to many open questions of which dark energy and the Cosmological Constant problem are perhaps the most intriguing basic open problems in physics. In my talk, I will revisit these ideas and discuss some of its history in the context of the developments of quantum field theory as a basis to discuss more recent advancements, new results and open questions in this area.
