Which of the following statements about special relativity is false?
a).The proper length of an object is always larger than the length of the object in a frame where it is moving.
b).The proper length of an object depends on the relative speed between the object and an observer in a different reference frame.
c).The proper length is the measured distance between two points as measured by an observer at rest with respect to the two points.
d).Dimensions of an object that are perpendicular to the direction of motion are never contracted.
e).Dimensions of an object that are parallel to the direction of motion are always contracted.
To determine which of the statements about special relativity is false, let's examine each statement individually:
a). The proper length of an object is always larger than the length of the object in a frame where it is moving.
This statement is true. According to special relativity, as an object moves faster relative to an observer, its length in the direction of motion appears to contract. The proper length, which is the length of the object as measured by an observer in its own rest frame, is always larger than the contracted length observed by an observer in a different frame.
b). The proper length of an object depends on the relative speed between the object and an observer in a different reference frame.
This statement is true. The proper length of an object does depend on the relative speed between the object and the observer in a different frame. As the relative speed increases, the length of the object appears to contract. However, the proper length remains constant in the object's own rest frame.
c). The proper length is the measured distance between two points as measured by an observer at rest with respect to the two points.
This statement is true. The proper length is defined as the distance between two points in the object's rest frame. It represents the intrinsic length of the object, independent of any relative motion.
d). Dimensions of an object that are perpendicular to the direction of motion are never contracted.
This statement is true. According to special relativity, only the dimensions of an object parallel to the direction of motion appear to contract. The dimensions that are perpendicular to the motion remain unchanged.
e). Dimensions of an object that are parallel to the direction of motion are always contracted.
This statement is false. Although the dimensions of an object parallel to the direction of motion do appear to contract as observed from a different frame, they are not always contracted. The degree of contraction depends on the relative velocity between the object and the observer. At lower speeds, the contraction is negligible, but it becomes more significant as the relative velocity increases.
Therefore, the false statement is: e). Dimensions of an object that are parallel to the direction of motion are always contracted.