someone wrote this to me, in a discussion about something else:
How can one object be closer to another that the other is to it? That’s like me and Landis standing in a room, and saying that he’s 3 feet away from me, but I’m only 1 foot away from him.
Obviously it’s not possible in everyday earthly physics, but could someone with some knowledge of relativity clue me in as to whether or not it’s possible if one person is travelling near the speed of light?
Peter
If we are moving relative to each other and we want to speak of the distance between us, we have to establish a reference frame. Obviously, since we are moving relative to each other, the distance will vary. So we must decide at what point in time we wish to measure our positions. The problem with this is that events that are simultaneous to me are not necessarily simultaneous to you.
Or you might be talking about the relativistic contraction. If an object is moving relative to me it is contracted in the direction of its motion according to my measurements. If you are moving with the object, you will not observe the object’s contraction. So we will not agree as to the length of the object.
Okay then, DrMatrix, let’s ask a related question that should eliminate the confusion of the measuring point. Imagine that the objects are moving in a trajectory such that there is a closest point of approach. We’ll measure the distance at that point.
I believe that the OP was asking, can the distances measured at that point be different for the two different objects/reference frames?
TheNerd
Interesting. . . Let’s say that I am passing you. We want to measure the distance between our points of closest approach. We will take my reference frame and consider two events: The event of me at my closest approach and the event of your position at that time (relative to me). Since the distance is measured in a direction perpendicular to the direction of our relative motion, there is no contraction in distance between my reference frame and yours and we would agree as to the simultantinaity of the two events. Therefore, I would say that we would agree as to the distance between us at the point of closest approach.