First, let me clarify if my understanding of length contraction is correct. Is it accurate to say that relativistic velocities not only affect the measured length of an object in the direction of motion, but also the distance to the object from an observer in the direction of motion? For example, if a 1m wide object (at rest) is 100m away from an observer and travelling away at 0.87c (γ = 2.0), length contraction states that the observer will measure the object as being 0.5m wide. But, does the observer also measure the object to be 50m away, due to the fact that the measured distance gets length contracted?(adsbygoogle = window.adsbygoogle || []).push({});

If so, the following diagram is correct, no?

Anyways, if both the measured length and the measured distance become length contracted, doesn't that mean that the measured velocity becomes length contracted as well? If an object begins at an observer and travels away at 0.9999c with γ = 71, it will have traveled 0.9999 light-seconds in one second (from the observer's perspective). But, due to length contraction, it will appear to have only traveled 0.0141 light-seconds. This means it will appear to have a velocity of 0.0141c, correct? Would an object travelling at 0.9999999999c appear to travel at 0.000014c, and so on?

Taking into account the propagation of light, the observer is said to observe Terrell Rotation. In "Invisibility of the Lorentz Contraction" (1959), Terrell claims that "a Lorentz-contracted moving sphere produces a round photographic image." But, if we agree that the measured velocity of an object is length contracted as well, a ball travelling at a relativistic velocity will be measured to have a velocity far lower than it actually has. Using these assumptions, I have attempted to model the appearance of a relativistic sphere, taking into account length contraction and light propagation, and have found that the sphere appears partially contracted in the direction of motion. How can this be explained?

Finally, is the Doppler Effect affected by an object's actual velocity, or its measured velocity? Would an object travelling very near the speed of light undergo very little Doppler shift due to the fact that an observer would measure a very low velocity?

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# Does Length Contraction affect measured velocity?

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