Question: What replace notions of absolute time and space with spacetime?
About the article "Physics", section "Difference between classical and modern physics".

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Relative locality is a proposed physical phenomenon that different observers would disagree on whether two space-time events are coincident.
This is in contrast to special relativity and general relativity in which different observers may disagree on whether two distant events occur at the same time but if an observer infers that two events are at the same spacetime position then all observers will agree.
When a light signal exchange procedure is used to infer spacetime coordinates of distant events from the travel time of photons, information about the photon's energy is discarded with the assumption that the frequency of light doesn't matter.
It is also usually assumed that distant observers construct the same spacetime.
This assumption of absolute locality implies that momentum space is flat.
However research into quantum gravity has indicated that momentum space might be curved which would imply relative locality.
To regain an absolute arena for invariance one would combine spacetime and momentum space into a phase space. 
In some of his later papers (especially in 1920 and 1924), Einstein gave a new definition of the aether by identifying it with "properties of space".
Einstein also said that in general relativity the "aether" is not absolute anymore, as the gravitational field and therefore the structure of spacetime depends on the presence of matter.
(It also must be said that Einstein's terminology ("i.e."
aether = properties of space) was not accepted by the scientific community.)
While physics aims to discover universal laws, its theories lie in explicit domains of applicability.
Loosely speaking, the laws of classical physics accurately describe systems whose important length scales are greater than the atomic scale and whose motions are much slower than the speed of light.
Outside of this domain, observations do not match their predictions.
Albert Einstein contributed the framework of special relativity, which replaced notions of absolute time and space with spacetime and allowed an accurate description of systems whose components have speeds approaching the speed of light.
Max Planck, Erwin Schrödinger, and others introduced quantum mechanics, a probabilistic notion of particles and interactions that allowed an accurate description of atomic and subatomic scales.
Later, quantum field theory unified quantum mechanics and special relativity.
General relativity allowed for a dynamical, curved spacetime, with which highly massive systems and the large-scale structure of the universe can be well-described.
General relativity has not yet been unified with the other fundamental descriptions; several candidate theories of quantum gravity are being developed.
Markopoulou received her Ph.D. from Imperial College London in 1998 and held postdoctoral positions at the Albert Einstein Institute, Imperial College, and Penn State University.
She shared First Prize in the Young Researchers competition at the Ultimate Reality Symposium in Princeton, New Jersey.
She has been influenced by researchers such as Christopher Isham who call attention to the unstated assumption in most modern physics that physical properties are most naturally calibrated by a real-number continuum.
She, and others, attempt to make explicit some of the implicit mathematical assumptions underpinning modern theoretical physics and cosmology.
In her interdisciplinary paper "The Internal Description of a Causal Set: What the Universe Looks Like from the Inside", Markopoulou instantiates some abstract terms from mathematical category theory to develop straightforward models of space-time.
It proposes simple quantum models of space-time based on category-theoretic notions of a topos and its subobject classifier (which has a Heyting algebra structure, but not necessarily a Boolean algebra structure).
For example, hard-to-picture category-theoretic "presheaves" from topos theory become easy-to-picture "evolving (or varying) sets" in her discussions of quantum spacetime.
The diagrams in Markopoulou's papers (including hand-drawn diagrams in one of the earlier versions of "The Internal Description of a Causal Set") are straightforward presentations of possible models of space-time.
They are intended as meaningful and provocative, not just for specialists but also for newcomers.
In May 2006, Markopoulou published a paper with Lee Smolin that further popularized this Causal Dynamical Triangulation (CDT) Theory by explaining time slicing of the Ambjorn–Loll CDT model as result of gauge fixing.
Their approach relaxed the definition of the Ambjorn–Loll CDT model in 1 + 1 dimensions to allow for a varying lapse.
In 2008, Markopoulou, Tomasz Konopka and Simone Severini initiated the study of a new background independent model of evolutionary space called quantum graphity.
In the quantum gravity model, points in spacetime are represented by nodes on a graph connected by links that can be on or off.
This indicates whether or not the two points are directly connected as if they are next to each other in spacetime.
When they are on the links have additional state variables which are used to define the random dynamics of the graph under the influence of quantum fluctuations and temperature.
At high temperature the graph is in Phase I where all the points are randomly connected to each other and no concept of spacetime as we know it exists.
As the temperature drops and the graph cools, it is conjectured to undergo a phase transition to a Phase II where spacetime forms.
It will then look like a spacetime manifold on large scales with only near-neighbour points being connected in the graph.
The hypothesis of quantum graphity is that this geometrogenesis models the condensation of spacetime in the big bang.
A second model, related to ideas around quantum graphity, has been published. 
Spacetime is a mathematical model in mathematics and physics.
Spacetime, space-time, space time or Space and time may also refer to the following.