physics

Distance without time

“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. …

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Measurement

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 …

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Velocity puzzle

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 …

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Symmetries and relativities

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 …

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Distance, duration and dimension

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. …

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Coordinate lattices

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 …

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Independent and dependent time

We are so accustomed to having time as the independent variable that it takes effort to think of it as the dependent variable. This reflects the Newtonian absolute time. But either time or space can be an independent variable. The Einsteinian the use of simultaneity is another reflection of the independence of time. If time …

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Claims about time

It’s time to list the claims about time made in this series of blog posts. Time is 3-dimensional. This is the over-arching claim which is explained and expanded by the other claims. Time is duration with direction. That is, time is a vector variable similar to a position vector in space. Time as ordinarily conceived …

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Reality and relativity

As a realist I respect what is often called “common sense.” This means that our faculties of discerning reality in everyday life are basically correct. Yes, we make some mistakes, we can get fooled by a illusionist, but we almost always agree what it is that happens when things happen to us or in front …

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