The Problem:
This one might actually break some laws of physics. The coronal heating problem refers to the unusual phenomenon viewed around our sun. Essentially, the corona of the sun (the area immediately surrounding the surface) is much hotter than the surface itself. Flying in the face of logic and thermodynamic equilibrium, it is energy where energy shouldn't be.
The Physics:
First and foremost thermodynamics. The second law of thermodynamics implies that heat energy should appear as a continuous gradient, and that energy must appear as a function of entropy. Should the heat here be greater than the source that is generating it, then there may be some issues in the way which we are currently viewing the energy. Or perhaps the way that the energy is being generated. The solution to this problem lies in the fields, forces, and processes of the sun's fusion. Perhaps a solution would appear with more careful analysis of the energy production of our sun. Theoretical solutions range from magnetic field incongruities to wave-photosphere interactions.
Why does it matter?
One of a few things might come out of this. One, the discovery of a new physical process by which energy transportation might occur in stellar bodies. Two, a break in what was once viewed as a classically fundamental law by a non-fundamental process: making that law have to change. Three, a discovery of some error in the measurements of the heat of a star: leading to better methods of measurement or improvements in equipment. Basically, we are either wrong about physics, wrong about engineering, or lacking in knowledge of how stars work. The solution to any of these would be greatly beneficial.
Who is going to solve it?
Nasa is sending a solar probe to make measurements on the sun sometime in 2018. They plan to use the data taken from this mission to better understand the corona of the sun, as well as the origin of solar winds and various other processes.
What I think:
The effect might be an illusion in the way that we view the surface of the sun. There might be particles excited by the energy emitted by the sun which react to produce their own energy. Perhaps the corona is composed of molecules held there in a sort of "atmospheric" effect. Or, again: Aliens.
Sources:
4 points.
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