FRAMES OF REFERENCE Colloquially, a frame of reference refers to one’s view of the world. The term “worldview” is a calque from the German “Weltanschauung”. In physics, a frame of reference (or reference frame) is a SYSTEM OF COORDINATES FOR SPACE AND TIME in order to describe the natural world. You need a reference frame before you can discuss physics, even if you are not explicitly aware of this! Different observers can have different reference frames. Gallilean Transformations Newton’s laws of motion relate forces to acceleration. These laws are thus valid for any observer who is moving with constant velocity relative to distant “fixed” stars, since there is NO ACCELERATION INTRODUCED by the choice of reference frame. We call such reference frames “inertial” frames of reference, and these inertial frames are related to any other inertial frame by the ADDITION OF A CONSTANT VELOCITY VECTOR to all the velocities measured in the other frame. (For simplicity, we are ignoring more trivial ways in which reference frames can differ, e.g. in the relative orientation of the direction for “up” or “right”, the choice of units for measuring distance and time.) This addition of a constant velocity is what we term a Gallilean transformation, since Gallileo first described this principle of the invariance of mechanical laws in 1632 using the example of a ship travelling on a smooth sea . We also describe such switches between reference frames as “boosts” from one frame to another. Suppose the inertial frame S′ is moving with velocity $$ relative to the inertial frame S, and the origin of both frames coincide at time t = 0 = t′. Mathematically, the GALLILEAN TRANSFORMATION for position is: $$ = - t$$ where t = t′ is the time measured by the common synchronised clock in both frames. There is a NEGATIVE SIGN in this equation because the frame S′ is moving with velocity $$ as seen by S. (Note that Einstein realised that such a concept of “absolute time” is not tenable, and developed relativity theory, but we won’t go into that here.) The velocity comes from the time derivative of position, $$ = }{dt'} = }{dt} - $$ and if we differentiate once more with respect to time to get acceleration, we find no difference between the accelerations measured in either frame.