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The first diagram used a branch of the unit hyperbola = to show the locus of a unit of proper time depending on velocity, thus illustrating time dilation. The second diagram showed the conjugate hyperbola to calibrate space, where a similar stretching leaves the impression of FitzGerald contraction. In 1914 Ludwik Silberstein [9] included a ...
Figure 3-3. Spacetime diagrams illustrating time dilation and length contraction. It is straightforward to obtain quantitative expressions for time dilation and length contraction. Fig. 3-3 is a composite image containing individual frames taken from two previous animations, simplified and relabeled for the purposes of this section.
Since the velocity of the object is the derivative of the position graph, the area under the line in the velocity vs. time graph is the displacement of the object. (Velocity is on the y-axis and time on the x-axis. Multiplying the velocity by the time, the time cancels out, and only displacement remains.)
Given a timelike vector v, there is a worldline of constant velocity associated with it, represented by a straight line in a Minkowski diagram. Once a direction of time is chosen, [nb 4] timelike and null vectors can be further decomposed into various classes. For timelike vectors, one has
Time dilation is the difference in elapsed time as measured by two clocks, either because of a relative velocity between them (special relativity), or a difference in gravitational potential between their locations (general relativity). When unspecified, "time dilation" usually refers to the effect due to velocity.
The velocity is the time derivative of the displacement: () ... This diagram shows the normal force (n) pointing in other directions rather than opposite to the ...
The vertical direction indicates time, while the horizontal indicates distance, the dashed line is the spacetime of the observer. The small dots are specific events in spacetime. Note how the momentarily co-moving inertial frame changes when the observer accelerates. time-like curves, with a speed less than the speed of light. These curves must ...
A plot of position and momentum variables as a function of time is sometimes called a phase plot or a phase diagram. However the latter expression, " phase diagram ", is more usually reserved in the physical sciences for a diagram showing the various regions of stability of the thermodynamic phases of a chemical system, which consists of ...