The Sun illustrates several themes of 264L

Our huge Sun, whose diameter is about 110 times the diameter of the Earth, illustrates several topics that we will discuss in Physics 264L:

• The energy of the Sun comes from nuclear fusion reactions in a small hot dense core, where four protons collide in several steps to eventually produce a helium nucleus (alpha particle), several other particles (positrons, neutrinos, and photons), and energy. The total mass after the fusion of four protons is slightly less than the initial total mass of the four protons, and the difference Δm produces energy via Einstein's famous relation from his theory of special relativity E=(Δm)c². This relation says that mass is a kind of potential energy, with a small amount of mass corresponding to a huge amount of energy. Each second, about 600,000,000 metric tons of protons fuse to produce about 596,000,000 metric tons of alpha particles, so about 4,000,000 metric tons of matter disappear completely each second, being converted into the energy of massless photons and kinetic energy of product particles. Despite this large rate of mass loss, the Sun has been producing energy for five billion years and will do so for another five billion years.

• The nuclear reactions in the core of the Sun can only be understood in terms of quantum mechanics, they cannot be understood in terms of classical physics, in terms of Newton's laws of motion and of Maxwell's equations of electricity and magnetism. In particular, the appearance of new particles like neutrinos and positrons via the nuclear reactions is a fundamentally quantum phenomena, it can not be explained as the releasing of pre-existing particles that were somehow inside the nuclei that collided. (It is not like two pre-existing balls attached by a spring such that, if spring breaks because of a collision, the two balls then appear as free particles.)

• The Coulombic repulsion of two positively charged protons is so great that, even with the high core temperature of about 15,000,000 K, which implies that the protons on average move with a speed of about two percent of the speed of light (0.02c), nuclear fusion reactions would not occur at a sufficient rate to support life on Earth if not assisted by quantum tunneling, which enables protons to get close enough (about the diameter of a proton) to fuse via the short-ranged weak interaction . This semester, you will use the Schrodinger equation to study quantum tunneling mathematically and then apply that knowledge to several problems, including understanding how radioactive nuclei have lifetimes that vary from 10^-23 seconds to 10³⁰ seconds, an astounding range of time scales.

• Despite the intricate structure of the Sun's surface (arising from highly conducting plasma that is convecting in the presence of a strong magnetic field), the light emitted from the Sun's surface is accurately described as ideal blackbody radiation that is emitted from a sphere whose uniform surface temperature is about 6,000 K. As you will learn in 264L, any hot opaque material in thermal equilibrium emits light with a universal spectrum that depends only on the temperature of the surface, and not on the details of what the surface is made of. Studies of blackbody radiation in the late 19th century led to serious contradictions with classical physics and these contradictions stimulated the invention of quantum mechanics. That the Sun is a blackbody emitter with its particular surface temperature also explains why plants and animals have evolved to respond especially to light in the visual range of wavelengths (400-750 nm), since this range of wavelenths lies near the peak of the Sun's light intensity curve. If the Sun were cooler or hotter, life presumably would have evolved to be most sensitive to wavelengths near the peak of the blackbody spectrum, a prediction that can be tested if life is ever discovered in some remote planetary system whose star has a different surface temperature than the Sun's.

  By the way, the photons emitted from the surface of the Sun arose as high-energy photons (gamma rays) from the fusion reactions in the Sun's core. Although the radius of the Sun is only 2.3 light-seconds, photons collide so often in the Sun that it takes from 10,000 to 100,000 years for the photons to random walk to the Sun's surface, where it then takes about 8 minutes to travel to the Earth's surface.

• The mass of the Sun slightly warps the surrounding space-time so that starlight, consisting of massless photons, passing near the Sun is deflected by a tiny amount that was first predicted by Einstein through his theory of general relativity, and confirmed by a dramatic experiment of Arthur Eddington in 1919, during a solar eclipse of the Sun. The Hubble telescope later discovered more spectacular examples of this so-called gravitational lensing, such as this Einstein ring. Such rings aid scientists in understanding the mysterious dark matter, which is some unknown stuff that makes up 27% of the universe's mass (compared to normal what-we-are-made-of matter, that makes up about 5% of the universe's mass).

  Some stars that are about 10-20 times the mass of the Sun collapse at the end of their lifetimes into black holes whose Schwarzschild radius is about 10 km (very tiny compared to size of the original star), and these black holes represent a major challenge and frontier of physics and science. General relativity predicts that, inside the black hole and in a finite amount of time, all matter must accumulate at a geometric point but such a point mass is not compatible with the uncertainty principle of quantum mechanics. Starting with Einstein, many theorists have tried to unify gravity with quantum mechanics, which has led to new fields of physics like string theory with its intriguing predictions of more than three spatial dimensions, but so far this effort has not been successful.