Fall semester   Leave a comment

Classes start next week, and with it the annual Physics I and II series. Physics I is all about motion- Newtonian kinematics and dynamics, variational principles, classical field theory…

One common thread in all physical studies of motion (with one notable exception!) is the difference between ‘time’ and ‘space’. Even in our everyday experience, we conceptually distinguish between changes in time and changes in position.

That said, if we disregard our personal experiences and instead seek a more abstract understanding and treat time and space as equals, it’s possible to gain a (to some people) more interesting point of view.

One does not have to be mathematical- using imaging techniques it’s possible to convert temporal changes into spatial changes.

A simple example is so-called ‘star trails’. In this imaging method, the shutter is open for long periods of time- hours, days, even a year. Stars, being imaged as points (more accurately the point-spread function), trace out a curve as the Earth rotates. Thus, the temporal changes in position are collapsed onto a single static image.

In this image, the shutter was left open for 4 hours. The North star, Polaris, is in the lower corner. Note that Polaris does in fact move- it’s not located *exactly* on the axis of rotation.

If you click on the image to pull up the full-size one, you can find a meteor streak near an Iridium flare. There’s a lot that can be said of this image- the changes in path from circles to conic sections to lines, for example- that can be said very simply with mathematics, but we’ll pass over that. Instead, here’s an image showing (mathematically) equivalent curves, but in a completely different context:

One does not have to leave the shutter open the whole time- one can create a variety of composite images to demonstrate motion, like this. The point is, there are many ways to depict a dynamic process on a single image aside from graphs.

Here’s another:

This is an image of stalagmites located in the Luray Caverns. These formed during the past 65 million years, and are still growing at the rate of 1 cubic inch per 120 years. This is perhaps a qualitative rather than quantitative way of depicting time, but in any case the sizes of the speleothems are correlated with their ages.

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Posted August 22, 2012 by resnicklab in Pedagogy, Physics, pic of the moment, Science

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