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An observer at rest observing an object travelling very close to the speed of light would observe the length of the object in the direction of motion as very near zero. Then, at a speed of 13 400 000 m/s (30 million mph, 0.0447 c ) contracted length is 99.9% of the length at rest; at a speed of 42 300 000 m/s (95 million mph, 0.141 c ), the ...
Fig 4-4 Relativistic length contraction, as depicted in a single Loedel spacetime diagram. Both observers consider objects moving with the other observer as being shorter. Relativistic length contraction refers to the fact that a ruler (indicating its proper length in its rest frame) that moves relative to an observer is observed to contract ...
The diagram is in the rest frame of the garage. The vertical light-blue band shows the garage in spacetime, and the light-red band shows the ladder in spacetime. The x and t axes are the garage space and time axes, respectively, and x ′ and t ′ are the ladder space and time axes, respectively.
Proper distance is also equal to the locally measured distance in the comoving frame for nearby objects. To measure the proper distance between two distant objects, one imagines that one has many comoving observers in a straight line between the two objects, so that all of the observers are close to each other, and form a chain between the two ...
The arclength parameter is called proper time and usually denoted τ. The length of M is called the proper time of the particle. If the worldline M is a line segment, then the particle is said to be in free fall. [1]: 62–63 A world line traces out the path of a single point in spacetime.
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Its initial value is 1 (when v = 0); and as velocity approaches the speed of light (v → c) γ increases without bound (γ → ∞). α (Lorentz factor inverse) as a function of velocity—a circular arc. In the table below, the left-hand column shows speeds as different fractions of the speed of light (i.e. in units of c). The middle column ...