If an object or event is in one position so that it can be measured at leisure, then time is not an explicit factor in its measurement. However, length units are defined in terms of time: “The meter is the length of the path travelled by light in vacuum during a time interval of 1/299 […]
“You can have time without moving but you can’t move without any time.” Actually, no, that is not correct. I introduced this topic here but let me go into more detail in this post. The previous post on measurement sets the background: we need to be very careful what it is we’re measuring and how.
Measurement is the act of comparing something, X – an object, an event, a phenomenon, anything that can be compared – with an independent standard unit and its multiples, and then assigning the corresponding quantity of units to X as the measure of that aspect (characteristic, property) of X. I want to focus on the
A number of word problems involve vehicle or aircraft speeds over two distances or two time periods and ask what the average speed is. The student is expected to understand the difference between the space-mean speed and the time-mean speed (though these terms are not typically used). What about the “average velocity”? Since velocity is
Aristotle described the four “causes” (really “becauses” or explanatory factors) that are required for a full explanation. These are called the material cause, the efficient cause (or mechanism), the formal cause (or design), and the final cause (or purpose). It seems as though trying to cover all four causes at once is either too much
There are a number of references for maps with multiple dimensions of time or a symmetry of space and time. Nothing refers to both. Maps with multiple dimensions of time I have argued that isochron(e) maps show time in two dimensions. Such maps have been made for over a century. The Wikipedia article on isochrone
Total energy is conserved because time is homogeneous (time translation invariance). Total linear momentum is conserved because space is homogeneous (space translation invariance). Total angular momentum is conserved because space is isotropic (rotational invariance). These are examples of how symmetries determine the laws of physics. Another way of looking at it is that linear and
Evolution is the ultimate theory of modern science because it’s all about utility. Early modern scientists and philosophers of science dismissed formal and final causes in favor of material and efficient (i.e., mechanistic) causes. Galileo Galilei rejected final causes and endeavored to answer how things happened, not why. Francis Bacon spurned formal and final causes
There are many kinds of space. The most common space is that of positions, that is, distances and directions. There is also velocity-space. There is force-space. There is duration-space, too. Particles travel on trajectories, points move on curves, vehicles travel on streets or routes, etc. Trajectories have distances traveled, travel times (durations), velocities, accelerations, etc.
Rindler’s Essential Relativity is a well-written monograph that we can use to explore time and relativity. He describes the coordinate lattice of a single inertial frame of reference (section 2.5). Let us consider it with an eye toward the corresponding temporal coordinate lattice. Start with the observer at the origin of an inertial frame, with
