## Introduction: Grasping Gravitational Waves: Augmented Reality Robots Teach Physics Fundamentals to Children and Adults Alike

Make invisible gravitational waves, radio waves, sound waves, etc., graspable and more comprehensible with AR (Augmented Reality) robotics using a simple device I invented at the age of 12, in 1974. This device is so simple that a child can build it, yet by combining it with robotics, it can provide a true 3D augmented reality display that does not require any special eyeglasses to see.

In this Instructable we'll take this simple device, which is simply linear array of light sources that displays a physical quantity (a previous Instructable showed how to make one), and animate it using robotics. Some very simple robotics you can make from found objects, will move the device in a controlled fashion. It is this control that allows for repeatability, and repeatability is what makes waves and other periodic patterns visible through Persistence of Exposure (to the human retina or to photographic recording media).

Rationale:

Gravitational waves are invisible, intangible, and difficult to understand, but I wanted a way to teach my children about this important contribution to physics. To make the waves visually comprehensible I decided to add to them their Hilbert Transform times the square root of negative one, so that the energy in the signal, rather than rapidly disappear and reappear, slowly varies with time, making more visible the underlying energy envelope.

I worked with my children and my graduate students, as well as undergraduate students at the University of Toronto to assemble a team, and we reached out to the LIGO group at my alma mater (MIT), and also obtained data from the LIGO sites, to work with.

Teaching and teambuilding:

This has been a great team-building project, and projects like this represent a really good teaching opportunity, with exemplary teambuilding as follows:

I proposed the spinning SWIM idea to students in my ECE516 class, and Anshuman (a student in the class) wrote a 3D visualizer to visualize what the spinning SWIM would look like. Marc and I also built some ARbotics systems, and Max came up with some 3D printed designs. Pictured above are Ken, Max, myself, Anshuman, Sarang, Nitin, Adnan, and Pete, also working on the project; Pete and Sarang are doing ongoing work on SWIM, and the two Alexanders also worked on the SWIM. Stephen and Helton (not pictured above) helped in some of the earlier photographic capture of this project. Sarang, Adnan, and Nitin, are working on using the Chirplet Transform to represent gravitational waves; you can clearly see that the signal here takes the form of a chirplet. In the same way that a wavelet is a piece of a wave, a chirplet is a piece of a chirp, i.e. a localized (windowed) chirp.

Together we built a simple robot that moves a SWIM (Sequential Wave Imprinting Machine) in a simple controlled pattern, allowing it to imprint the gravitational waves onto the human retina or onto photographic film using PoE (Persistence of Exposure). See my earlier Instructables on SWIM and on Phenomenal Augmented Reality using a simple light bulb or LED.

This Instructable will introduce Augmented Reality robotics ("ARbotics"): robotics combined with the phenomenological persistence of exposure principle, to make waves tangible and thus more teachable to children as well as adults alike.

## Step 1: It Started With the Railway: Phenomenal Augmented Reality With SWIM on the Train Tracks

(Rails as a form of visual art: here's 3 photos I took near the railway tracks in the town of Dundas, Ontario, in the 1980s, one of which was used as a full page ad in Impulse Magazine: visualization of circularly polarized radio waves with Sequential Wave Imprinting Machine.)

I've always had a childhood fascination with railway tracks, as a way of guiding my arrays of light sources through a straight or gently curved spacetime continuum. Walking along the tracks with the SWIM during a long exposure photograph, I could plot out or map out a physical reality along a smooth trajectory. I also grew up with model railway and toy racecar (slotcar) sets, which I also used as a basis for creating phenomenological augmented reality systems.

I used to sometimes build small railcars and other objects for use on real train tracks, e.g. to push along one of the tracks, or sometimes something a little bigger that would straddle both tracks. In 1984 my parents moved to a new house that was located directly beside a beautiful set of railway tracks that defined the border between the towns of Ancaster and Dundas, so I immediately intensified this work through a series of phenomenological augmented reality photographs.

But you don't need railway tracks to make phenomenal augmented reality SWIMbots, you just need a small model railroad or toy racecar or toy slotcar, and even if you don't have any of those, a simple straight or gently curved piece of wood or metal will do. You can even use the edge of a desk, and you can make a simple "railcar" out of an L-shaped wooden block that slides along the edge of the desk!

## Step 2: Model Railway, Toy Racetracks, ARbotics, and SWIMbot

Let's build on my previous Instructable, and assume that you have a SWIM (Sequential Wave Imprinting Machine). I gave my 9-year old daughter a SWIM and she was able to use it to visualize radio waves from a microwave motion sensing burglar alarm.

We're surrounded by surveillance cameras and computer vision cameras watching us, e.g. Internet of Things (IoT), yet we ordinarily never get to see how these things see us. With SWIM you can make visible the otherwise invisible "rays" of sight as if emanating from these smart "things" that surround us.

The system we use for teaching these principles is the SWIM that was outlined in a previous Instructable.

You will need the following:

• a mechanism capable of rapidly moving a light source through space. This can your hands, as guided by a rail, or it can be made from an old X-Y plotter, or using more modern drive mechanisms such as stepper motors or the like;
• a light source such as a light bulb or LED, or an array of light sources such as a linear array of computer-addressable lights (SWIM);
• a phenomenon amplifier as described in a previous Instructable.

It also helps to have a dark environment, e.g. a room with subdued lighting, so you can see (or photograph) the phenomenological augmented reality more readily.

## Step 3: Build Your Railway

Find or construct some kind of guideway, rail, track, or the like.

A toy racecar set, for example, can make a great guideway.

You can also use a piece of straight or gently curved wood, or even the edge of a desk.

If you want to curve the spacetime continuum, try "wiggleboard" or a piece of thin wood that can be gently bent.

Make splines out of metal or plastic, if you like.

## Step 4: Find or Build Your Car and Attach One or More Light Sources to It: Exploring Space and Time

You need at least one car to ride on the guideway. If you're using a slotcar track, you can attach something to the slotcar.

In the pictures above, a small piece of plastic is attached to the slotcar, and the linear array of lights you built from a previous Instructable can then be attached to the plastic piece.

You can begin testing by attaching a single light to the car, to move along in a long exposure photograph.

If you get this far, please click "I made it" and post some pictures and I'll give you some feedback and constructive criticism.

You can learn quite a bit from simply moving light sources along known trajectories. The patterns you generate will help you understand the nature of space and time in the context of Persistence of Exposure.

Then you will be ready to try with the SWIM (Sequential Wave Imprinting Machine) that you built from the previous Instructable.

## Step 5: Connect the Light Source to a Physical Quantity Being Sensed

Now you're ready for some phenomenal augmented reality.

Connect the light source to a quantity to be sensed.

This allows us to visualize the data on the moving light source(s).

## Step 6: Visualizing Complex Quantities

What we have here is a true volumetric augmented reality display, and things get interesting when we have 3D functions to visualize.

Take for example a wave, which is formed from a cosine plus the square root of minus one times a sine wave, thus a complex-valued wave, as shown above. Here we can see that the energy is constant, i.e. the radius from the central time axis is constant.

To visualize 3D content, we simply spin the SWIM while moving it along the rail, as I did in my 1985 picture shown in Step 1 (e.g. to show circularly polarized radio waves).

You can have one motor spin the SWIM and another move it along the track, or you can have just a motor to spin the SWIM and push it along the track manually, while reading out its position, and have the position as an index to drive the motor that spins.

Pick any simple example to start with: to visualize the "WAVE", simply have a light source move in a helical pattern, along the rail.

To visualize a WAVELET (a "piece" of a wave, i.e. localized, windowed wave), we have the radius slowly increase as the SWIM spins around as it moves along the rail.

To visualize a CHIRP, the SWIM needs to begin spinning slowly, and then spin faster as it moves along, if visualizing an upchirp (or begin fast and slow down as it moves if visualizing a downchirp).

Finally, to visualize a CHIRPLET (a "piece" of a chirp, i.e. localized, windowed chirp), we have also now the amplitude grow and then decay so that there is a concentration of energy about a particular point in time or space.

Once you can visualize a WAVE, WAVELET, CHIRP, and CHIRPLET, you're ready to download some of the LIGO data and visualize that!

In Octave, load in the data, say, x(t), and then compute z=hilbert(x);

Now you have an analytic signal, ready to be visualized on the spinning SWIM.

## Step 7: If You're Having Trouble Doing This Instructable, Start With Something Very Simple

If you're having trouble putting together the different parts of this Instructable, consider as a minimum "I made it", to simply show any light source moving trough space, along a rail of some kind, in a long exposure photograph, like the "EXIT" sign that was being thrown in the garbage when the electricians upgraded to the new "green" LED exit signs.

Pick some interesting light source and simply side it along a rail.