Large radio telescopes are not solid dishes, but rather an open mesh. This is largely done to save on weight, since the dish doesn’t need to be solid to reflect radio waves. You see a similar thing on a microwave, where the door is covered with an open mesh so you can watch what’s cooking. The mesh blocks microwaves from reaching you, but not visible light. But how is that possible? Aren’t photons supposed to be point particles? Radio, microwaves are light, so how does a mesh prevent their photons from passing through it?

The short answer is it’s complicated. Although photons are often referred to as particles, they aren’t particles in the traditional sense. They are light quanta, which have both particle and wave properties. Depending on the situation, sometimes the particle aspect is useful, and sometimes the wave aspect is. While photons don’t have a physical diameter, and can be treated as point particles, their quantum behavior gives them a probabilistic size. As a photon gets closer to another object, the chance of it interacting becomes greater. This is often represented as a cross section given in terms of area.

Different cross sections vs energy for light with lead. Credit: J. H. Hubbell

You could say the cross sectional area represents the “size” of a photon, but the problem with this is that a photon’s cross section varies depending on what it is interacting with. Photons interact pretty strongly with electrons, and have a relatively large cross section, but with neutrons the interaction is smaller. Under this definition there is no absolute “size” to a photon. The cross section also depends upon the energy of the photon and things like its polarization. There are also different cross sections for absorption vs scattering.

Despite all this complexity, there is a basic way to talk about the effective “size” of a photon, and that is through it’s wavelength. Very roughly, the interaction range of a photon scales with its wavelength, so light of longer wavelength is more likely to interact with a conductive material than light of a shorter wavelength. In this way you could say the “size” of photon is basically the width of its wavelength. The  wavelength of green light is about 500 nanometers, or two thousandths of a millimeter. The typical wavelength of a microwave oven is about 12 centimeters, which is larger than a baseball.

It’s a bit odd to think of a microwave photon as being larger than a baseball, but it is a simple way to explain how mesh reflectors work. The “size” of microwave and radio wave photons is simply too large to fit through the mesh, and so are reflected. Visible light is much smaller, so it easily passes through the mesh. It’s important not to take this model too literally, but it’s good enough for rough estimates.

And that’s about the size of it.

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There’s buzz in the press recently claiming that scientists have shown the speed of light in a vacuum isn’t constant. It all starts with a new paper in Science that looks at spatially structured photons that travel in free space slower than the speed of light. Like most stories of this type, the work is interesting, but not in the way that is being hyped.

To begin with, no one (not even the authors of this paper) is claiming that the speed of light isn’t an absolute physical constant. In electromagnetism there are two parameters known as permittivity (which governs electric fields) and permeability (which governs magnetic fields). Combining these two parameters gives you the value of what is commonly called the speed of light. That’s because the speed of a wave is governed by these parameters, giving the usual speed we observe. All experiments we’ve done show that these parameters and the speed of light are constant, and there’s nothing in this new work that says otherwise.

So what’s with the claim? Well it turns out that “speed of light” as the term is usually used actually means “the group velocity of plane waves in a vacuum.” There are actually other velocities that can be used to describe velocity, such as phase velocity, that aren’t governed by the absolute limit. To give you an example of the difference, suppose we had a long row of people standing in a row. You could send a signal along the row of people by agreeing to tap the shoulder of the person next to you when your shoulder is tapped. So someone taps you, you tap the next person, and so on down the line. This would be a group velocity, where one tap triggers the next, and it has a speed limit. If, for example, it takes a second for a person to react to a tap and tap the next person, and everyone is standing a meter apart, then the speed of a tap through the line would be one meter per second. Suppose, however, that everyone in the line agreed to tap the person next to them at a particular time. The first person would tap at exactly 9:00 am, the second person would tap half a second after 9, the third a second, and so on. Everyone has previously agreed to tap at half-second intervals, so when 9:00 am rolls around it looks like the wave of taps has happened twice as fast. But this is a phase velocity. It occurs because of the pre-arranged timing rather than being triggered.

The same thing can happen with light. The propagation of light through space occurs at a fixed speed, but you can pre-arrange things to get a different velocity that is faster or slower than “the speed of light.” This has been known for a very long time, and is nothing new. What makes this new work interesting is that the modified vacuum speed worked for photons. This means the quantum effect of light can be manipulated in the way standard classical waves can. We’ve thought that this was possible, but this team has shown that it works.

So the upshot of this work is that we’ve learned something new and interesting about quantum optics. But this doesn’t really change anything in astrophysics. This new discovery doesn’t change our understanding of the big bang, or dark matter, or dark energy, or any other unsolved mystery of cosmology.

Paper: Daniel Giovannini, et al. Spatially structured photons that travel in free space slower than the speed of light. Science DOI: 10.1126/science.aaa3035

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Imagine you were standing in the center of a circle 100 meters in radius. How long do you think it would take to leave the circle? Usain Bolt could do it in 10 seconds, but most people could leave the circle in under a minute. After all, it’s just a casual 100 meter stroll and you are out of the circle. But suppose we added a rule that you couldn’t simply walk in a straight line. Suppose after each step you were required to change to a new random direction. Take a step, random direction. Another step, another random direction. You can’t control your direction, all you can do is take a step. Random turn, step, random turn, step, etc. Now how long would it take you to leave the circle? A minute? Ten?

This idea of taking each step in a random direction is called a random walk. While it might seem like a pointless game, random walks show up in the real world quite a bit. One of the most common examples is known as brownian motion, where a larger object is hit by lots of smaller particles, such as a pollen grain in water being bounced about by the water molecules. Brownian motion was the first strong evidence that things were made of atoms. Random walks also occur in astrophysics, particularly by photons in the heart of a star.

The heat of a star is generated primarily in its core. In the Sun, for example, hydrogen ions are fused together into helium ions, photons and neutrinos. Neutrinos don’t react strongly with the ions in the Sun’s core. The chance of a neutrino colliding with an ion is extremely small. So the neutrinos leave the core at just under the speed of light, and reach the surface of the Sun a couple seconds after they’re born.

Credit: ATNF

But photons interact quite strongly with the ions. Even though they travel at the speed of light, the core is so thick with ions that they almost immediately collide with one. On average, a photon in the Sun’s core will travel less than a centimeter before colliding with an ion. It is then scattered in an almost random direction. Imagine a photon trying to leave the Sun, but getting bounced in a random direction every centimeter. You can begin to see that it will take the photon a bit longer than a couple seconds to leave the Sun.

On average it actually takes tens of thousands of years. Most estimates put the average between about 20,000 to 150,000 years. For a purely random walk the answer just depends on the length of each step. But in the Sun’s core a photon’s path is not quite a random walk. For one thing, the density decreases as you move from the Sun’s core to its outer layers. This means the path length increases as the photon moves away from the core. It also means there is a slight bias, where the photon is a bit more likely to be scattered away from the core than toward it.

When a photon makes it about two thirds of the way to the Sun’s surface, it enters what is known as the convection zone. In this region, the solar material cycles up to the surface and back again, which means that the photons can move with the ions to reach the surface. Of course then it takes 8 minutes to travel from the surface of the Sun to the surface of Earth.

So the next time you are outside on a sunny day, remember that the warmth you feel on your face was generated by fusion in the Sun’s core. And it has made a very long journey to make your day a bit brighter.

Some things in life are so random.

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