The Sun Isn’t Hot Enough to Shine

Nuclear fusion requires 100 million degrees Kelvin, yet the Sun’s core can only reach 15 million. How then does it create light? A quantum phenomena known as quantum tunneling is the answer.

The Happy Neuron
Dec 17, 2020 · 5 min read
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Students are taught that a star has enough gravity from its immense size to create high enough pressure and temperature to overcome the natural repulsion of protons in hydrogen atoms and fuse them into helium. The helium weighs slightly less than the original hydrogen atoms, and the missing mass is released as an enormous amount of energy, as dictated by Einstein’s E=mc^2. According to this equation, even a tiny amount of mass (m) becomes a lot of energy (E) when multiplied by the speed of light squared (c^2), which is roughly 9 x 10 16m^2/s^2.

While this sounds like a solid explanation, there’s a massive problem: the Sun’s core doesn’t get anywhere near hot enough for nuclear fusion to occur. Here on Earth, our fusion reactors, which may actually power the grid soon, need much higher temperatures.

The mind-bending world of quantum mechanics, though, provides a solution.

Quantum mechanics is the science of the very small, where the rules of reality are very different from what we expect. The laws that govern our everyday world don’t make sense at this scale, as particles can appear on the other side of insurmountable obstacles, don’t exist in a specific location until observed, can interact instantaneously with other particles over long distances, among many other counter-intuitive principles. Despite being so weird, quantum mechanics has been a gem for modern science, as it provides incredibly precise solutions to many problems in the classical world of physics.

The crux of quantum mechanics is wave-particle duality, as explained by Schrödinger’s equation. This explains that particles exist as a wave of probability until they are detected, at which point they choose a location. Yes, it sounds insane, but it’s been proven again and again.

This was first shown in Young’s famous double slit experiment. In this experiment, photons were fired at a barrier with two slits in it. Behind this barrier was a wall that could detect where the particles hit. If they behaved as solid particles, then they would pass through the two rectangular slits and produce two corresponding rectangles on the back wall. However, if they behaved as a wave, then they would pass through the slits, begin to propagate again on the other side, and interfere with each other, producing an interference pattern of dark and light bands.

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When the crests and troughs of each wave meet, they add. When the crests meet the troughs, though, they cancel. (Creative Commons License)

During the experiment, when the only detector was the back wall, the photons produced a wave pattern. But, when the particles were detected as they were going through the slits, they produced a particle pattern. The pattern produced on the back wall depended entirely on the particles being observed as they went through the slits. This forced them to stop existing as a wave of probability and to choose a specific location.

So what does this have to do with solar fusion? Thinking of hydrogen atoms — more specifically the single protons in their nuclei — as a particle means they don’t have enough energy to get close enough to each other for the strong nuclear force to take over. This force only operates within 10 −15meters. Thinking of them as a probability wave, though, means they can tunnel through this energy barrier via a strange phenomenon of wave mechanics known as evanescent waves.

When a wave traveling through one medium hits another medium it will do two things: reflect and refract. Imagine pointing a laser at a pool of water. Some of the light will bounce off and some will go through. How much reflects and how much refracts depends on the angle of the light and the properties of the two mediums. When it comes to air and water, the common explanation is that the angle at which 100% of the light is reflected is 48.5 degrees. This is known as total internal reflection.

However, it’s more complex than that. Looking at Maxwell’s equations, which explain all of classical electromagnetism, at the point where the wave hits the new medium, a tiny, fleeting wave is produced. It usually only lasts a few wavelengths, but this evanescent wave can continue much further under the right conditions.

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The infrared beam is displaying total internal reflection, in which the beam is supposed to stay contained with in the crystal, reflecting off of the boundaries between it and surrounding media. Even at the perfect angle for total internal reflection to occur at the intersection of these particular media, the beam emits an evanescent wave. (Creative Commons License)

So far, we have quantum particles existing as a probability wave and the fact that when a wave should be 100% reflected it’s not due to evanescent waves. Based on this, if quantum particles are, for example, contained in a box, they will have certain probabilities of being found in different areas of the box and a non-zero possibility of being found outside the box. They have a small chance of appearing outside of where they are supposed to be, on the other side of barriers that should be insurmountable.

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The red line is a probability wave, with quantum particles being more likely to be found at the peaks. Like all waves, this probability wave can extend through a barrier due to evanescent waves. Therefore, there is a small probability of quantum particles being found, quite surprisingly, on the other side of an impenetrable barrier. (Creative Commons License)

Applying this to solar fusion, the quantum particles in question are the protons of hydrogen atoms and the insurmountable barrier is the large energy spike needed to fuse them. Because they behave as a probability wave and have a non-zero chance of getting through it, some will inevitably get to the other side, allowing the strong nuclear force to take over and solar fusion to happen. Think of it a different way: protons have a tiny chance of being places they shouldn’t be, including right next to each other without the necessary energy to do so.

It’s sounds crazy, but the math works. The Sun’s core has about 10^56 hydrogen atoms, and the chances that two of these protons will fuse because of quantum tunneling is about 1 in 10^28. For the Sun to output the energy that it needs, roughly 3.7 x 10^38 fusion reactions per second need to occur. Even though quantum tunneling is exceedingly rare, the Sun has enough protons within such a tightly packed core that the tiny odds of quantum tunneling can easily be overcome.

Originally published at http://thehappyneuron.com on December 17, 2020.

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