Length Contraction (Dilation?)

1. Jun 14, 2010

skycastlefish

Do fast moving objects in relative motion always observe length contraction regardless of their direction of travel? In every example I find the train or the rod appears to be “moving toward you.” I can’t find any thought experiments describing what happens after you pass the train and it appears to be moving away from you. It seems to me that the length might appear to dilate? But then, wouldn’t the light from the rear of the train reach the relative observer first and the light from the front delayed making it still measure contracted? I don’t know… help?

2. Jun 14, 2010

starthaus

No,you'd observe the same exact length contraction

3. Jun 15, 2010

yuiop

In SR, when we talk about an observer in a given inertial reference frame measuring a moving as length contracted, we are in fact really talking about the measurements made by a network of observers (possibly infinite) that are all at rest with respect to each other and all with clocks synchronised according to the Einstein convention. With respect to this infinite set of observers there is no real notion of heading towards the observer or heading away from the observer. Visual effects due to light travel times are neglected and for an object travelling with constant velocity relative to the given inertial reference frame the measured length contraction is constant. The measurement is carried out by two inertial observers that are at rest with respect to each other, that happen to be at the front of the train and at the rear of the train, simultaneously in their reference frame.

If you work out what an a given observer actually sees when taking visual effects due to light travel times into account you will find that when the train is coming towards the observer it appears longer and after it passes the observer and heads away, it appears shorter. There is also a slight visual rotation of the object. This visual rotation can, in the case of a sphere, cancel out the length contraction and make a moving sphere appear normal (as long as there are no distinctive identifying patterns on the sphere). This is known as Penrose-Terrell rotation. This started a popular myth that it not possible for an observer to actually see length contraction even in principle. This is not true, because for non-spherical objects like a train, an observer can actually see the length contraction visually (for example in a photograph).