Simultaneity
Simultaneity is the relation between two events that happen "at the same time". In special relativity it is not absolute: two spatially separated events judged simultaneous in one inertial frame are judged non-simultaneous in another moving relative to it. This relativity of simultaneity is the hinge on which length contraction and time dilation turn, and it is the single most disputed element of relativity among the researchers catalogued on this wiki.
The standard account
For events separated by distance Δx along the direction of relative motion, the Lorentz transformation gives Δt' = γ(Δt − vΔx/c²). If Δt = 0 in one frame it is not zero in the other unless Δx = 0 or v = 0.
Einstein reached this in 1905 by first asking what "simultaneous" could operationally mean for distant clocks. His answer was a definition: clocks at A and B are synchronised if a light signal leaving A at t₁, reflecting at B and returning at t₂ arrives at B at t₁ + (t₂ − t₁)/2 — that is, if one stipulates that light takes equal time each way. He illustrated the consequence with the train-and-embankment thought experiment: lightning striking both ends of a moving train simultaneously for the embankment observer strikes at different times for the observer on the train.
Two things about this are uncontroversial even in the mainstream. First, the one-way speed of light has never been measured without assuming a synchronisation convention — only the two-way average speed is directly measurable. Second, Einstein's synchronisation is one choice among conventionally equivalent alternatives (Reichenbach's ε-synchronisation makes this explicit), and theories such as Lorentz aether theory that use absolute synchronisation are empirically equivalent to special relativity for all experiments performed to date. What is contested here is not that but the further claim that no fact of the matter about distant simultaneity exists.
On this wiki
The critiques divide into logical, definitional and operational arguments.
Logical. John E Chappell's Simultaneity Cannot Possibly be Relative to Motion (1999), a reworking of Melbourne Evans's 1962 critique, argues that Einstein reached relative simultaneity in the train thought experiment only by contradicting himself within a single chain of reasoning, and that avoiding the contradiction leads inevitably to absolute simultaneity whatever velocity is attributed to light. The paper adds that the alternative mathematical route — proving relative simultaneity from the Lorentz transformations — rests on an invalid shift in which symbols first designating lengths are quietly reassigned to designate points. Chappell developed the theme in Simultaneity and Time (1995) and Crucial Flaws in Special Relativity: Logic and Simultaneity (1996). Neil E Munch pressed the same class of objection in Precision; Simultaneity and Consequences of Relativity's Failure To Control Assumptions.
Definitional. Andrew R Dring's The Definition of Simultaneity (Galilean Electrodynamics, 1996) argues that Einstein's definition is logically circular — it uses light propagation to define the simultaneity that the propagation law presupposes — and offers a manifestly frame-independent replacement, from which he derives that the two relativity postulates are inconsistent. Thomas E Phipps takes a constructive line in Absolute Simultaneity With and Without Light Signals (Galilean Electrodynamics, 1996): if relative clock rates are set by relative states of motion rather than by position, absolute synchronisation of permanently-at-rest clocks is attainable with no clock transport and no light signals at all — and can also be had using light signals if electromagnetism is neo-Hertzian rather than Maxwellian. In The Relativity of Simultaneity is a Mistake (2013) he argues that abandoning frame time for a single invariant time parameter, as the GPS effectively does, restores distant simultaneity along with much else of pre-relativistic physics.
Operational. Curtis E Renshaw's A Test of Relativistic Simultaneity (2016) is the most concrete item here: he designs an experiment using GHz carrier signals from satellites 20,000 km out and phase-locked laboratory oscillators, arguing that phase comparison removes any dependence on clock synchronisation between frames and so permits a genuine direct test — which, he notes, has never been attempted. Stephan J G Gift argues from GPS operation that Einstein synchronisation is not what the system actually uses (Implications of Relativity Without Einstein Synchronization in the GPS), and Tom Van Flandern made the same point about the GPS common time frame. Franco Selleri reached absolute simultaneity from a different direction, arguing that the rotating-platform and Sagnac cases force a preferred synchronisation in the limit of vanishing rotation.
See Category:Relativity for the full set.