Frame of reference
A frame of reference is the essence of the physicist’s laboratory, if you will. The procedure given in the following paragraphs for constructing a frame of reference, is rather general and may be modified rather extensively. However, it should help to understand the essential concepts of the frame of reference.
Obtain one device (or more) to measure and record the distance to, and one timepiece (or more) to mark and record the time, of an event. Also obtain four (or more) accelerometers. An accelerometer indicates or registers absolute acceleration. If you have been in an elevator, you may already understand what absolute acceleration is. The pressure that your feet feel from the elevator floor is caused by your absolute acceleration. As the elevator moves up, your feet may feel more pressure especially when the elevator begins to move up. That means your absolute acceleration has increased. However, as the elevator nears your floor, it goes less fast. The pressure on your feet decreases; your absolute acceleration decreases accordingly.
One may wonder here, "Acceleration relative to what?" After all, one standing on Earth feels pressure on the feet, yet is not moving relative to Earth. This fact is what can make absolute acceleration so hard to understand correctly. Another fact can also; it is that a person in free fall towards the center of the earth feels no pressure on his body, if the air can be ignored. (This condition is called weightlessness, or, misleadingly, "zero gravity"). The person is accelerating to Earth, yet is not being accelerated absolutely. The answer to the question that was asked earlier is, "Relative to a nearby person in free fall, if you want a simple answer." If you are standing on the ground, or sitting in a chair which stands on the floor, all ultimately on the surface of Earth, your absolute acceleration is about 9.8 meters per second per second upward. Another way to view the situation is that the surface of Earth is accelerating you from "free fall" at the rate of 9.8 m/s/s. A simple accelerometer is a weight attached to a spring. The end of the spring that is not attached to the weight is attached to the frame of reference at some point. If the point is undergoing acceleration, the elongation of the spring indicates the acceleration’s direction and magnitude.
The frame of reference always has a point called the origin. (One may wonder, "The origin of what?" Another name may be "the base point." Another candidate is "the cornerstone point." However, "origin" is the established name.) Where the origin is to be placed does not depend on anything but the need to obtain experimental data as expeditiously or economically as possible (hence, one's belly button is not always acceptable as the origin). To the origin the physicist attaches one of his four accelerometers. At some distance from the origin, he places the second accelerometer. Again, the location does not depend on anything other than expediency or economy. The third accelerometer is placed at some distance from the origin and another distance from the second accelerometer. The fourth accelerometer must be placed so that it is not in the plane that contains the origin, the second point and the third one, and should be roughly equidistant from the other accelerometers. Notice that these four points form three planes that intersect each other in three lines. One line may be labeled the X axis; another, the Y axis; and the other one, the Z axis (diagram to be given later).
An interesting event occurs in the frame of reference and the physicist wants to record where and when it occurs. The "where" and "when" can be given by four numbers. One number is, of course, the time of the event. (The physicist uses UTC, sets his clocks to be zero at the start of the experiment, or uses a different initial time; that is a matter of individual choice.) Another number is the perpendicular distance to the XY plane (called the "z" coordinate); the third number is the perpendicular distance to the XZ plane ("y") ; and the last one YZ ("x"). Hence, (x, y, z, t) = (2 meters, 1 meter, -5 meters, 3 seconds) may mean that the event occurred 3 seconds since the start of the experiment, 2 meters in the positive direction from the YZ plane ("to the North"), 1 meter in the positive direction from the XZ plane ("to the West"), and 5 meters in the negative direction from the XY plane ("below").
A particular kind of reference frame is the inertial reference frame. It is the one in which the mathematical description of the trajectory of an object that "feels" zero absolute acceleration is simplest. If the effects of gravitation, such as that of Earth, can be ignored, the object either travels relative to the inertial frame of reference in a simple straight line at constant velocity or remains at a point in the frame (not moving). Also, all points in the inertial frame experience zero acceleration. It can be approximated by any non-rotating space station in orbit about the Sun or Earth.
If, on the other hand, the space station is rotating but is in free fall, then a frame of reference attached to the station is a rotating frame of reference. The accelerometer at the origin may or may not show acceleration, depending on where the origin is; but the other accelerometers will. An object that is moving in a straight line at constant velocity relative to a nearby inertial frame of reference will appear to have a crooked trajectory as seen from the rotating frame of reference. A frame of reference attached to Earth whose origin is located at the center of the Earth is a rotating frame of reference. The accelerometer at the origin shows zero acceleration.
A frame of reference attached to the surface of Earth is both rotating and accelerated, but in many experiments it may be taken to be a good approximation of an inertial reference frame. This is especially true in particle physics (smashing gold atoms into lead, for example).