## Tt

Aberration of starlight. (a) Assume that the telescope is moving to the right as the beam of light enters, with the telescope tube lined up with the beam of light. Since the speed of light c is finite, the telescope moves as light passes through, and the light strikes the side. (b) To observe the light, we must tilt the telescope slightly.Thus, as the telescope moves over, the beam is always centered in the tube. We must tip the telescope in the direction in which it is moving.

originally done by A. A. Michelson in 1881, and in an improved fashion by Michelson and Morley in 1887, was designed to measure the motion of the Earth through the ether by measuring the speed of light in two directions perpendicular to each other. No change was found. This meant that the Earth could not be moving through the ether. If the ether existed, it must be dragged along with the Earth. However, there is another observation which rules out the dragging of the ether by the Earth. It is illustrated in Fig. 7.2, and is called aber ration of starlight. (This has nothing to do with aberrations in optical systems.) It is a slight change in the angle at which light from stars appears to be arriving due to the motion of the observer, in this case the motion of the Earth about the Sun. (It is analogous to the change in the apparent angle at which rain is falling when you start to move.) The shift is always in the direction of the motion of the Earth, so it changes throughout the year. The positions of some stars are shifted by as much as 20 arc seconds from their true positions. (This effect has been used in the past to measure the speed of light.) In the ether theory there is no way for aberration to be observed if the Earth is dragging the ether.

The fact that the speed of light is independent of the velocity of the observer contradicts our everyday experience, in which relative velocities are additive. Einstein began to look at the underlying cause for the speed appearing to be constant. In measuring a speed, we measure a distance and a time interval. Einstein suspected that the problem lay in our traditional concepts of space and time. Physicists such as Newton simply assumed that space and time were given. Einstein suggested that they might not be absolute but might depend on the motion of the observer. Einstein examined the idea of an absolute time and looked at whether time might actually be a quantity that depends on the motion of the observer.

### 7.1.2 Problems with simultaneity

Einstein realized that an absolute time was tied to the concept of absolute simultaneity. By absolute simultaneity we mean that if two events appear simultaneous to one observer, they appear simultaneous to all other observers. This is important because telling time is actually noting the simultaneity of two events. For example, if we say the train left the station at 7:00, we are saying that two events are simultaneous. The first event is the train leaving the station, and the second event is the clock showing 7:00. If those events are simultaneous for one observer, but not for all observers, then the concept of absolute time has no meaning.

An experiment depicted in Fig. 7.3 shows that two events can be simultaneous for one observer, but not another. The two observers are at the centers of identical railroad cars. One car is at rest with respect to the station. The other is moving past at some speed. When the two observers are opposite each other, two flashes go off at the ends of one car. The flashes are judged to be simultaneous by the observer at rest. How are they seen by the other observer? The figure shows that the flashes that the observer is moving toward is seen first. The flashes are not simultaneous for the moving observer. Simultaneity is not absolute. Therefore, time is not absolute.

Flashes in railroad cars and simultaneity.The top car is moving past the bottom car. (a) When the observers at the centers of each car are closest to each other, flashes go off at opposite ends of the lower car. (b) The motion of the top car means that the observer in that car sees the right flash first. (c) The observer in the bottom car sees both flashes at the same time.

With this as a starting point, we now go on to investigate how different types of situations appear to observers with different velocities. In special relativity, we deal only with reference frames that are not accelerating with respect to each other or in which there are no external gravitational forces. Such a reference frame is called an inertial reference frame. An inertial frame might be provided by a space station far from any mass and with the engines off so there is no acceleration. Einstein's postulate about the laws of physics being the same in different reference frames only applies to inertial frames. (We know that accelerating frames must be different, because they have pseudoforces, such as centrifugal force.) Another way of stating Einstein's postulate is that There is no experiment we can perform to tell us which inertial frame is moving and which is at rest. There is no 'preferred' inertial frame. All we can talk about is the relative motion of two inertial frames.