# When does light travel in a straight line?

Category: Physics

Published: November 22, 2023

Light never travels exactly in a straight line. There are several effects that can prevent light from traveling along a straight line. However, most of these effects can be avoided. There are two effects that can never be avoided and therefore will always prevent light from traveling exactly in a straight line. These two effects are diffraction and spacetime curvature.

Diffraction involves the natural tendency of light to spread out as it travels. As a beam of light travels, the different parts of the beam naturally bend away from the exactly-forward direction, as shown in the figure on the right. The parts of the light beam that are to the left of the beam's center bend leftward as they travel. The parts of the light beam that are to the right of the beam's center bend rightward as they travel. This causes the overall beam to spread out.

You could make an argument that the one part of the light beam at the exact center of the beam travels in a straight line (assuming that the beam is symmetric). Therefore, you could say that at least *some* of the light is traveling along a straight line. However, this statement is not as meaningful as it sounds. Light is a quantized wave and therefore must be extended across many points in space while traveling. If you refer solely to the exact center of the beam, you are not really talking about light anymore. All light waves that are physically real experience diffraction.
Even a pencil-thin laser beam spreads out as it travels (which you can confirm yourself if you look close enough).

Diffraction is a complicated wave effect that causes more than just beam spreading. It also causes diffraction patterns and edge effects. The fact that light does not exactly travel along a straight line is what gives rise to diffraction artifacts in high-quality photographs and in human vision. For instance, a high-quality photograph of stars will show spikes attached to the stars.

Look at the photo on the right that was captured by the James Webb Space Telescope. Every spike of light attached to a star in this photo is a direct result of light not traveling in a straight line. Interestingly, this photo also demonstrates the fact that spacetime curvature forces light to travel along a curved path, which is what caused many of the galaxies in this image to be smeared along arcs. Diffraction can also lead to other imaging artifacts such as Airy disks and rings, as well as diffraction bokeh.

Light can experience a lot of beam spreading or a little bit, depending on the situation. In general, the wider the beam, the less it will spread out as it travels (and therefore the more closely it will be to traveling along a straight line). For instance, a beam of light that is formed by sending light through a large hole will diffract less than a beam of light of the same frequency that is formed by sending light through a small hole. Also, the higher the frequency of the light, the less it diffracts. To have exactly zero diffraction, you would have to have a beam that is infinitely wide. However, it is fundamentally impossible to fit an infinitely-wide beam into a finite observable universe. The closer that a light beam is to being an infinitely-wide plane wave, the less it will diffract.

Almost every physics course and textbook that teaches about light starts with plane waves. A plane wave is a light wave where the wavefronts are a series of a parallel, infinitely-wide, flat planes that have constant amplitude and phase along them. Interestingly, true plane waves indeed experience zero diffraction. This means that every part of a plane wave travels forward in a straight line. But there's a catch. Plane waves do not actually exist in the real world. A true plane with zero diffraction would require infinitely-wide wavefronts. This is not possible in a finite observable universe.

So why does almost every course and textbook that teaches about light start with plane waves? There are two reasons. First, a plane wave has the simplest mathematical expression out of all the different shapes that light can have. This makes it an ideal place to start so that students can begin learning the physics of light without being overwhelmed by the math. Secondly, many of the light beams that we encounter in everyday life can be approximated to be plane waves without losing too much accuracy. In addition to plane waves, light in the shape of a Bessel beam experiences zero diffraction. However, like plane waves, true Bessel beams are infinitely wide and cannot exist in the real world.

The other effect that always prevents light from traveling exactly in a straight line is spacetime curvature. Space and time form one unified physical entity called spacetime. Interestingly, spacetime is not a background, fixed, absolute, flat framework. Rather, spacetime itself is a physical object that can be warped. This fact has been part of mainstream science for over a hundred years and has been verified experimentally countless times. All gravitational effects are ultimately caused by spacetime curvature. When objects move through warped spacetime, their trajectories curve as if they were experiencing a gravitational force.

For light that is traveling along an approximate straight line relative to its local spacetime, the warping of spacetime causes this straight line to become a curve. In other words, light traveling through warped spacetime travels along curved paths. This effect is called gravitational lensing. Interestingly, spacetime is *always* curved, *everywhere* in the universe. Spacetime curvature on the global scale is what holds people and objects on earth's surface. Spacetime curvature on the scale of the solar system is what holds the planets in orbit around the sun. Spacetime curvature on the galactic scale is what holds the various solar systems in orbit around the center of the galaxy. Spacetime curvature on scales above the galactic scale is what holds galaxies together to form galaxy groups, clusters, superclusters, and cosmic filaments.

You may have heard that on the cosmic scale, spacetime is flat. However, this is simply referring to the *average* spacetime curvature, where the average is done over all scales below the cosmic scale. Although the universe's spacetime is flat on average, spacetime at any particular point in the universe is curved. Therefore, light is bent away from straight-line motion by spacetime curvature everywhere in the universe. On human scales and smaller, the bending of light's path by spacetime curvature is extremely weak and undetectable. Therefore, on human scales and smaller, we can get away with pretending that spacetime curvature does not bend light.

As you see, diffraction and spacetime curvature always prevent light from traveling exactly in a straight line. In addition to these two effects, there are other effects that *sometimes* bend the path of light. For instance, in certain cases light will attach to a physical surface and ride along the curved surface. Also, any time that light travels through a spatially non-uniform medium, the non-uniformities will bend the path of the light. For instance, a layer of cold air above a layer of warm air bends light to form mirages. Also, any time that light travels from one medium into another medium, its path bends. For instance, a glass lens surrounded by air will bend the path of the light, such as used in eyeglasses. The bending of light by a spatially non-uniform medium or by the interface between two different media is called refraction. Refraction also includes birefringence effects, which arise from anisotropic material properties. Additionally, when light is trapped in a waveguide such as a fiber optic cable, the light is forced to travel along the curved path of the waveguide. Lastly, if you give a light beam a complicated shape so that it becomes self-accelerating structured light, the entire beam will bend to one side. Note that the term "self-accelerating" used here is referring to the type of acceleration associated with light traveling on a curved path, and not the type of acceleration associated with speeding up or slowing down. When traveling through vacuum, light cannot locally speed up or slow down. In summary, the following effects can prevent light from traveling in a straight line:

**Effects that Prevent Light From Traveling in a Straight Line**

- Diffraction (which is always present)
- Spacetime curvature (which is always present)
- Surface propagation
- Refraction by spatial non-uniformities
- Refraction at the interface between two different materials
- Waveguide propagation
- Self-accelerating structuring of light

Even though light never actually travels exactly in a straight line, in some situations light will travel along a path that is extremely close to being a straight line. To get light to travel along a path that is as close as possible to being a straight line, you would try as much as possible to remove the above effects. This means that you would make sure to: use light with a high frequency, use light with a large beam width, use light that is close to being a plane wave, send the light over small distances so that the effect of spacetime curvature is negligible, not let the light attach to a surface or cross the interface between materials, send the light through a uniform, isotropic medium, not send the light through a waveguide, and not give the light self-accelerating structure. If you do all of this, then the path that the light travels along with be extremely close to being a straight line. As restrictive as this all sounds, light traveling through air in everyday life is very close to meeting all of these criteria. Therefore, to a reasonable approximation, light traveling through air in everyday life travels along a straight line. Since much of the light that we encounter in everyday life is traveling short distances through uniform air, it can be very useful in everyday life to pretend that light travels along straight lines.