On Spacetime (2010-2019)

"The hypothesis underlying all approaches to the landscape is that there is a cosmological setting in which different regions or epochs of the universe can have different effective laws. This implies the existence of spacetime regions not directly observable […] These regions must either be in the past of our big bang, or far enough away from us to be causally unrelated." (Lee Smolin," A perspective on the landscape problem", 2012)

"One of the most crucial developments in theoretical physics was the move from theories dependent on fixed, non-dynamical background space-time structures to background-independent theories, in which the space-time structures themselves are dynamical entities. [...] Even today, many physicists and philosophers do not fully understand the significance of this development, let alone accept it in practice. One must assume that, in an empty region of space-time, the points have no inherent individuating properties - nor indeed are there any spatio-temporal relations between them - that do not depend on the presence of some metric tensor field. [...] Thus, general relativity became the first fully dynamical, background- independent space-time theory." (John Stachel, "The Hole Argument", 2014)

"The most familiar manifold, however, is the space-time manifold, which has 4 dimensions. It is described by a time coordinate and three spatial coordinates. In addition to being a differentiable manifold, space-time has much more additional structure. It is at the level of this additional structure [...] that the space-time of Newtonian physics differs from the space-time of special relativity and from the space-times of Einstein’s theory of gravity (also called general relativity)." (José G Vargas, "Differential Geometry for Physicists and Mathematicians: Moving frames and differential forms from Euclid past Riemann", 2014)

"For a moving object, time contracts. Not only is there no single time for different places - there is not even a single time for any particular place. A duration can be associated only with the movement of something, with a given trajectory." (Carlo Rovelli, "The Order of Time", 2018)

"Granularity is ubiquitous in nature: light is made of photons, the particles of light. The energy of electrons in atoms can acquire only certain values and not others. The purest air is granular, and so, too, is the densest matter. Once it is understood that Newton’s space and time are physical entities like all others, it is natural to suppose that they are also granular. Theory confirms this idea: loop quantum gravity predicts that elementary temporal leaps are small, but finite." (Carlo Rovelli, "The Order of Time", 2018) 

"Spacetime is a physical object like an electron. It, too, fluctuates. It, too, can be in a 'superposition' of different configurations." (Carlo Rovelli, "The Order of Time", 2018)

"The basic units in terms of which we comprehend the world are not located in some specific point in space. They are - if they are at all - in a where but also in a when. They are spatially but also temporally delimited: they are events." (Carlo Rovelli, "The Order of Time", 2018)

"The computational geometry of space/time is fractal. The entire system is interwoven as a fractal and as each series of iterations occur, there is a dithering of sorts because the difference in possibilities can be matastable in many locations in the computation. Each layer of the system computes in a frequency that is probably following the phi ratio. Measurement is always described as ratio and scale may be, in a sense, an illusion. Light appears to be scale invariant and the cutoff frequency may be another illusion. If this is true, everything is fields and particles are just a smaller version of a field." (Rick Delmonico, "Fractals all the way down", 2018)

"The fractal nesting of the relationship between space and time at different scales causes phase transitions as the influence of one force changes with respect to another. From this we get the astonishing variety of behaviors in the material world." (Rick Delmonico, "Fractals all the way down", 2018)

"There is a fractal nesting of time-like loops in spacetime. Both space and time emerge from a quantum of action in a field. Space and time are united but different. The scale of the dimensions is inversely proportional, as well as the density. The only infinity is one of scale." (Rick Delmonico, "Fractals all the way down", 2018)