# How much does my shadow weigh?

In the world of the ephemeral, there are few elements that accompany us wherever we go, every day of our lives, in almost any circumstance. Something we barely notice is our shadow.

The shadow is nothing more than the absence of a light that was expected, but that does not reach its destination because it was blocked by an object. Explaining what light is is not so easy.

In a simplified way we can say that it is made up of photons, elementary particles without mass but with energy and "momentum". This "momentum" is the ability of physical objects to push each other. When the photons that make up a ray of light shine on an object, they push it away, exerting a slight pressure on it that we call "radiation pressure." When we put our body in the sun feel this pressure, while the area that we shadow, which the photons do not reach, does not feel it.

When the photons that make up a ray of light shine on an object, they push it, exerting a slight pressure on it that we call 'radiation pressure'

We can quantify this pressure difference with weight, which is the force we exert on the ground, or on a scale. When we are illuminated we exert a greater force than when we are in the dark, since the moment transferred by the photons that collide with us must be added to the force of our body.

Thus, we can say that an object weighs more when it is illuminated than when it is not.

In the same way, the region where our shadow lies feels less radiation pressure than it would if we weren't there, blocking out the light. In other words, the excess weight we feel when illuminated corresponds to a defect in the weight of our shadow.

In the case of an adult person of average height, located under the sun at the latitude of Madrid, and assuming that the dimensions of his shadow are the same as those of his body, this weight defect in the shadow will be equivalent to that which would be exerted by a mass of about 0.00000004 kilograms.

### Beyond white light and mirrors

This is not all: photons of light of different colors have different moments, so their energy and the pressure they exert will be different. This means that if we illuminate ourselves with red light we will weigh less than if we do it with the same number of photons of blue light.

On the other hand, just because we don't see something doesn't mean it doesn't exist. When it comes to light, most of it is invisible to human eyes. This is the case of ultraviolet photons, such as those from the Sun, which, in addition to tanning us, are more energetic than visible ones and, therefore, subject our bodies to a greater push.

In this way, the difference in weight with respect to the illuminated object is greater for the shadow that we do not see than for the one that we do. Curious, right?

Do all objects respond the same to radiation pressure, regardless of their properties? Of course not.

An object's ability to absorb, transmit, or reflect photons will also affect its shadow: if it's perfectly transparent, then it will let photons through and therefore won't feel too heavy.

Instead, a reflective object, a mirror, it will feel twice as much thrust as an object that totally absorbs radiation (black body), by reflecting the photons that reach it.

### From the scale to the Nobel (and into space)

Our calculations about the weight of shadow and light are fun, but are they of any use? The difference in weight between an illuminated object and one that is not illuminated is tiny: one hundredth of the weight of a single grain of sugar. As a miracle diet it seems poor.

However, these considerations were the reason for the Nobel Prize in Physics 2018 that went to Arthur Ashkin, Gérard Moureau and Donna Strickland, for the development of "optical tweezers", a method of catching and manipulating tiny objects using the radiation pressure of a laser.

A laser light source, in which photons move coherently, as if coordinated, can be used to move objects with great precision.

The first experiments were done in the 1960s by Ashkin's team at Bell Labs. The researchers shone tiny, partially transparent spheres with a laser to move and levitate them, counteracting their weight with radiation pressure.

In addition, by focusing the beam with a lens at one point, they were able to trap particles, thus creating the first optical tweezers. Over the following decades they were perfected and made it possible to observe, rotate, cut and push the investigated objects without touching or modifying them. Therefore, they are ideal for studying biological processes.

Isn't that enough? There is another field in which radiation pressure is also used, but on a large scale: space exploration.

As the push of the photons depends on the size of the surface they hit, it can become relevant when we consider a sufficiently large region.

This is how "solar sails" were designed: a revolutionary way of propelling aircraft in space, consisting only of a large surface that reflects sunlight.

Like the sails of a ship when the wind blows, these solar sails take advantage of the radiation pressure of the photons that collide with them to make the aircraft move.

One of the great advantages of this propulsion system is the high speeds that the ships that use it can reach. In addition, since they do not have to store fuel to move, they are lighter and can travel for longer periods of time. Therefore, they are one of the few technologies that could be used for interstellar travel.

Although these ideas may sound like science fiction, the first aircraft to use sunlight to change its orbit around the Earth It was launched in June 2019 as part of an aerospace project called LightSail..

NASA also plans to experiment with these new propulsion technologies in space with the 2022 launch of ACS3, a spacecraft the size of a toaster that will use these sails for orbit changes.

Whether for futuristic applications or fundamental issues, what is clear is that if Peter Pan had been aware of his relevance, he would have been much more careful before losing his shadow. Fortunately, we still can't get rid of it.