Search results
Results from the WOW.Com Content Network
From our previous analysis, given that v = 0.25 and c = 1, the equation of the dashed line of simultaneity is t − 0.25x = 0 and with v = 0, the equation of the dotted line of simultaneity is t = 0. In general the second observer traces out a worldline in the spacetime of the first observer described by t = x / v , and the set of simultaneous ...
The origins of frames S and S′ coincide at time t = 0 in frame S and also at t′ = 0 in frame S′. [2]: 107 Frame S′ moves in the x-direction of frame S with velocity v as measured in frame S. This spatial setting is displayed in the Fig 1-2, in which the temporal coordinates are separately annotated as quantities t and t'.
Figs. 2-6 and 2-11 illustrate the concept of lines (planes) of simultaneity: Lines parallel to the observer's x-axis (xy-plane) represent sets of events that are simultaneous in the observer frame. In Fig. 2-11, the blue lines connect events on Terence's world line which, from Stella's point of view , are simultaneous with events on her world line.
Observers moving at different relative velocities have different planes of simultaneity, and hence different sets of events that are present. Each observer considers their set of present events to be a three-dimensional universe, but even the slightest movement of the head or offset in distance between observers can cause the three-dimensional ...
Interlacing blue and grey stripes show change of t (stripes of simultaneity). Orange curves (/ \) are light-like curves (null geodesics) with fixed r. In relativistic physics, the Born coordinate chart is a coordinate chart for (part of) Minkowski spacetime, the flat spacetime of special relativity.
When reflected in the x-axis, a line y = mx becomes y = −mx. In this case the lines are hyperbolic orthogonal if their slopes are additive inverses. x 2 − y 2 = 1 with y = x as asymptote. For lines y = mx with −1 < m < 1, when x = 1/m, then y = 1. The point (1/m, 1) on the line is reflected across y = x to (1, 1/m).
Time is a scalar which is the same in all space E 3 and is denoted as t. The ordered set { t} is called a time axis. Motion (also path or trajectory) is a function r : Δ → R 3 that maps a point in the interval Δ from the time axis to a position (radius vector) in R 3.
A fuller explanation of the concept of coordinate time arises from its relations with proper time and with clock synchronization. Synchronization, along with the related concept of simultaneity, has to receive careful definition in the framework of general relativity theory, because many of the assumptions inherent in classical mechanics and classical accounts of space and time had to be removed.