# Intro - Galileo's Mechanical Relativity Imagine two bowling balls, speeding towards each other. Now, though this might mean that your excursion to the bowling alley has, in some ways, gone terribly, let's look at the physical interpretation of it instead. Let's say that each bowling ball moves at the same speed, but in opposite directions. This begs the question: **from one bowling ball's perspective, how fast will the other be moving?** ![[bowlingballsrelativity.png]] The answer seems obvious - the other ball will look like it's moving at a speed of 2v - and you'd be correct. Strictly speaking, this is one of the **Galilean Transformations** - ways to 'transform' the physical properties of objects from one **frame** relative to another. In other words, we use these transformations to look at a system from another object's point of view. Neat, huh? # Reference Frames Before we start, let's talk a bit about **reference frames**. Strictly speaking, a 'frame' is simply a means of specifying which object we take the zero-coordinate of each physical quantity involved in the system at. In each system, we typically have an **inertial frame of reference**, which serves as the baseline coordinate to each system. In Galilean Relativity, the frame used is the **non-inertial** frame, one which does not experience acceleration. These 'frames' are better explained using [[Reading Spacetime Diagrams|spacetime diagrams]], of which basic examples are given below: ![[bowlingballspacetimediag.png]] The 'relative' speed of the bowling ball is better visualised using these diagrams; as for each unit of 'time' elapsed the bowling ball moves a greater distance along the x axis. Note that the gradient in the frame (x', t') is shown to be exactly half of that in the frame (x,t). This brings us to one of the **postulates** - statements seen and considered as true - of Galilean Relativity, that being that **time is absolute.** That means that there's no change in the scale of the time coordinate between frames. # Galilean Transformations This brings us to the regular galilean transformations: $x' = x - vt \tag{1}$ $t' = t \tag{2}$ $y' = y \tag{3}$ $z' = z \tag{4}$ The postulate of absolute time is shown in equation (2). Equations (3) and (4) are only applicable if stated that the objects move exclusively in one direction, though this is usually the case as the coordinate system is typically defined from one of the objects in the system. # What's Next? If you're doing IB relativity, feel free to move on to the next part, [[Special Relativity - Foundations]]