In physics, the relativity of simultaneity is the concept that distant simultaneity whether two spatially separated events occur at the same time is not absolute, but depends on the observer's reference frame. This possibility was raised by mathematician Henri Poincaré in 1900, and thereafter became a central idea in the special theory of relativity.
According to the special theory of relativity introduced by Albert Einstein, it is impossible to say in an sense that two distinct events occur at the same time if those events are separated in space. If one reference frame assigns precisely the same time to two events that are at different points in space, a reference frame that is moving relative to the first will generally assign different times to the two events (the only exception being when motion is exactly perpendicular to the line connecting the locations of both events).
The relativity of simultaneity is the conceptual foundation from which time dilation and length contraction follow.
History
In 1892 and 1895, Hendrik Lorentz used a mathematical method called "local time" for explaining the negative aether drift experiments. However, Lorentz gave no physical explanation of this effect. This was done by Henri Poincaré who already emphasized in 1898 the conventional nature of simultaneity and who argued that it is convenient to postulate the constancy of the speed of light in all directions. However, this paper did not contain any discussion of Lorentz's theory or the possible difference in defining simultaneity for observers in different states of motion. This was done in 1900, when Poincaré derived local time by assuming that the speed of light is invariant within the aether. Due to the "principle of relative motion", moving observers within the aether also assume that they are at rest and that the speed of light is constant in all directions (only to first order in ). Therefore, if they synchronize their clocks by using light signals, they will only consider the transit time for the signals, but not their motion in respect to the aether. So the moving clocks are not synchronous and do not indicate the "true" time. Poincaré calculated that this synchronization error corresponds to Lorentz's local time.. See also the English translation. In 1904, Poincaré emphasized the connection between the principle of relativity, "local time", and light speed invariance; however, the reasoning in that paper was presented in a qualitative and conjectural manner.
Albert Einstein used a similar method in 1905 to derive the time transformation for all orders in , i.e., the complete Lorentz transformation. Poincaré obtained the full transformation earlier in 1905 but in the papers of that year he did not mention his synchronization procedure. This derivation was completely based on light speed invariance and the relativity principle, so Einstein noted that for the electrodynamics of moving bodies the aether is superfluous. Thus, the separation into "true" and "local" times of Lorentz and Poincaré vanishes all times are equally valid and therefore the relativity of length and time is a natural consequence.. See also: English translation.
In 1908, Hermann Minkowski introduced the concept of a world line of a particleVarious English translations on Wikisource: Space and Time in his model of the cosmos called Minkowski space. In Minkowski's view, the naïve notion of velocity is replaced with rapidity, and the ordinary sense of simultaneity becomes dependent on hyperbolic orthogonality of spatial directions to the worldline associated to the rapidity. Then every inertial frame of reference has a rapidity and a simultaneous hyperplane.
In 1987, Robert Goldblatt published Orthogonality and Spacetime Geometry, directly addressing the structure Minkowski had put in place for simultaneity. In 2006, Max Jammer, through Project MUSE, published Concepts of Simultaneity: from antiquity to Einstein and beyond. The book culminates in chapter 6, "The transition to the relativistic conception of simultaneity". Jammer indicates that Ernst Mach demythologized the absolute time of Newtonian physics.
The mathematical notions preceded physical interpretation. For instance, conjugate diameters of conjugate hyperbolas are related as space and time. The principle of relativity can be expressed as the arbitrariness of which pair are taken to represent space and time in a plane.
Simultaneity, measurement, and the meaning of time
Einstein’s 1905 paper ("On the Electrodynamics of Moving Bodies") did not present relativity of simultaneity via the familiar train/embankment thought experiment. Instead, he derived it operationally from a close examination of how time is measured and how distant clocks are defined and synchronized within a given inertial frame.
What it means to assign a time to a distant event Newton believed in absolute time as a sort of flow progressing uniformly throughout the universe. Newton admitted, though, that absolute time was intrinsically imperceptible. In contrast, Einstein pointed out that time is something that we assign to events following agreed-upon procedures within a reference frame using artifacts that we term "clocks".
"Local time" must be distinguished from "coordinate time". An isolated clock can only apply timestamps to events that it directly encounters. Local time refers to these local timestamps. Coordinate time refers to labels applied to events occurring elsewhere. To assign a time to a distant event, an observer must always apply some sort of convention that relates distant events to the local clock readings.S A Klioner (1992), "The problem of clock synchronization - A relativistic approach", Celestial Mechanics and Dynamical Astronomy, vol.53 (1992), pp. 81-109.
Clock synchronization and invariant signal propagation Any procedure for assigning time to distant events must rely on the exchange of signals between the distant event and a local clock.
In practice, light, or more generally, electromagnetic radiation, is used for the establishment of timing relations because light has the fastest observed speed of propagation. This propagation speed is empirically observed to be invariant across inertial frames.
Synchronization of clocks is an operational task. In 1905, Einstein proposed a concrete set of steps for performing synchronization: At time , clock 1 sends a signal to clock 2 which is immediately reflected back. Its arrival time back at clock 1 is . The time which the signal reached clock 2, designated , is defined to be
Why synchronization is not a purely local operation Even if clocks are perfect locally, synchronization depends on assumptions about distant physics which cannot be verified by local measurements alone. In particular, the validity of Einstein synchronisation depends on. isotropy of space, homogeneity of time, finite and invariant signal speed.
Synchronization of clocks is therefore a matter of "convention", a procedure with unproven elements adopted because of its agreement with human intuitions about the physical world.
Relativity of simultaneity – qualitative demonstration
Einstein demonstrated relativity of simultaneity algebraically after first deriving the Lorentz transformation using his two postulates. We will not do this here. Instead, we illustrate relativity of simultaneity using spacetime diagrams, which provide a graphical representation of the Lorentz transformation.
Einstein's procedure for synchronizing separated clocks immediately leads to the observation that simultaneity cannot be absolute. In Fig. 4a, A and B are two observers at rest in reference frame S, while X is a light source located midway between the two observers along the x-axis. The diagram illustrates a coordinate system where ct constitutes the vertical axis, where c, the speed of light, is a scaling factor so that distances in time have the same scale as distances in space. The three vertical lines, termed "world lines", illustrate the positions of A, X and B as a function of time. The world lines are vertical since A, X and B are stationary in this reference frame. Suppose that X emits a signal at ct = 0. It travels at speed c forwards and backwards along the x-axis. The signal is represented by two dashed lines of slope ±45° with respect to the x-axis. The arrival of the signal at the positions of A and B is simultaneous, since the intersections of the signal with observers A and B share the same value of ct.
But now suppose that A, X, and B are all moving with respect to S at a constant speed v in the x-direction. Their world lines are tilted as shown in Fig. 4b, reflecting their uniform motion in this frame. Since the speed of light is invariant, the signal emitted by X continues to be represented by dashed lines of slope ±45°. The intersections of the signal with A and B are clearly no longer simultaneous as measured in frame S. In particular, the signal reaches A before it reaches B, because A is moving toward the incoming light pulse while B is moving away from it. However, observers comoving with A, X, and B do not agree with this conclusion. In their own rest frame, they have synchronized their clocks using Einstein’s procedure, so that the signals from X are required to reach A and B simultaneously. In Fig. 4b, the set of all events that are simultaneous in this moving frame must therefore include the two reception events at A and B. The straight line joining these events (line AB) represents “equal time” for the moving observers.
Thought experiments
Relativity of simultaneity can be understood without spacetime diagrams using Einstein’s train thought experiment.
Einstein's train
Einstein's version of the experiment, Chapter IX presumed that one observer was sitting midway inside a speeding traincar and another was standing on a platform as the train moved past. As measured by the standing observer, the train is struck by two bolts of lightning simultaneously, but at different positions along the axis of train movement (back and front of the train car). In the inertial frame of the standing observer, there are three events which are spatially dislocated, but simultaneous: standing observer facing the moving observer (i.e., the center of the train), lightning striking the front of the train car, and lightning striking the back of the car.
Since the events are placed along the axis of train movement, their time coordinates become projected to different time coordinates in the moving train's inertial frame. Events which occurred at space coordinates in the direction of train movement happen than events at coordinates opposite to the direction of train movement. In the moving train's inertial frame, this means that lightning will strike the front of the train car the two observers align (face each other).
The train-and-platform
A popular picture for understanding this idea is provided by a thought experiment similar to those suggested by Daniel Frost Comstock in 1910.The thought experiment by Comstock described two platforms in relative motion. See: . It also consists of one observer midway inside a speeding traincar and another observer standing on a platform as the train moves past.
A flash of light is given off at the center of the traincar just as the two observers pass each other. For the observer on board the train, the front and back of the traincar are at fixed distances from the light source and as such, according to this observer, the light will reach the front and back of the traincar at the same time.