Matter to Energy to Matter Conversion

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Einstein's equation E = mc2 says that mass can be converted to energy and vice versa. If you extrapolate the expansion rate and temperature of the universe back to much closer to the Big Bang than when the cosmic microwave background was produced, you find that within the first few seconds, the energy of the photons was great enough to create particles like electrons and protons. But along with the ordinary particles, the photons also created the antimatter counterparts to the particles, e.g., anti-electrons (called positrons) and anti-protons. Antimatter is briefly discussed in the context of nuclear fusion and the neutrino sections of another chapter.

The antimatter counterpart of an ordinary particle has the same mass and opposite charge of the ordinary particle (if it is not neutral). When an ordinary particle and its antimatter counterpart collide, they completely annihilate each other to create photons. The process can be reversed if the photons have enough energy (i.e., are high-energy gamma ray photons). Within the first microsecond (10-6 second), the universe was hot enough for the photon radiation to undergo this matter-antimatter particle transformation using massive particles like protons and neutrons. When the temperature dropped to about 1013 K at one microsecond after the Big Bang, this process stopped for the protons but it continued for the less massive particles like the electrons. Neutrons were not created in the energy-matter conversion process but some were created when protons and electrons fused together.

energy to matter to energy transformation

When the universe had expanded for another few seconds, it cooled to a temperature of "only" 6 × 109 K and the electron-positron production and annihilation process ceased. This is also the time when the number of neutrons stopped increasing from the proton-electron fusion process. The number of neutrons was fixed at a ratio of 1 neutron for every 5 protons. For reasons not completely understood, there was a very slight excess of ordinary matter over antimatter (by about 1 part in 109). This is why there was still some ordinary matter left over when all the antimatter had been annihilated. (This must be the case, otherwise you wouldn't be here!) All of the protons, neutrons, and electrons in matter today were created in the first few seconds after the Big Bang.

The extreme conditions described above have been reproduced in high-energy particle accelerators on Earth and the experiments have confirmed this description. For times much closer to the moment of the Big Bang we need to extend the theory beyond direct experimental bounds to much higher energies and temperatures. At a time of 10-38 to 10-36 second after the Big Bang, most early universe models say there was an ultra-fast expansion called "inflation".

Cosmic Abundance of Helium and Hydrogen

The Big Bang theory provides a natural way to explain the present abundance of the elements. At about 2 to 3 minutes after the Big Bang, the expanding universe had cooled to below about 109 K so that protons and neutrons could fuse to make stable deuterium nuclei (a hydrogen isotope with one proton and one neutron) that would not be torn apart by energetic photons. Recall that deuterium is one part of the fusion chain process used by nature to fuse hydrogen nuclei to make a helium nucleus. The fusion chain process in the early universe was slightly different than what occurs in stars because of the abundant free neutrons in the early universe. However, the general process is the same: protons react to produce deuterium, deuterium nuclei react to make Helium-3 nuclei, and Helium-3 nuclei react to make the stable Helium-4 nucleus.

The deuterium nucleus is the weak link of the chain process, so the fusion chain reactions could not take place until the universe had cooled enough. The exact temperature depends sensitively on the density of the protons and neutrons at that time. Extremely small amounts of Lithium-7 were also produced during the early universe nucleosynthesis process. After about 15 minutes from the Big Bang, the universe had expanded and cooled so much that fusion was no longer possible. The composition of the universe was 10% helium and 90% hydrogen (or if you use the proportions by mass, then the proportions are 25% helium and 75% hydrogen).

Except for the extremely small amounts of the Lithium-7 produced in the early universe, the elements heavier than helium were produced in the cores of stars. Stars do produce some of the helium visible today, but not most of it. If all the helium present today was from stars, then the nuclear reaction rates would have to be extremely high and the galaxies should be much brighter than they are.

The deuterium nucleus is a nucleus of special importance because of the sensitivity of its production to the density of the protons and neutrons and temperature in the early universe. The number of deuterium nuclei that do not later undergo fusion reaction to make Helium-3 nuclei also depends sensitively on the temperature and density of the protons and neutrons. A denser universe would have had more deuterium fused to form helium. A less dense universe would have had more deuterium remaining. The amount of the final Helium-4 product is not as sensitive to the ordinary matter density of the early universe, so the amount of the remaining deuterium seen today is used as a probe of the early density. Therefore, measurement of the primordial deuterium can show if there is enough ordinary matter to make the universe positively-curved and eventually stop the expansion. Current measurements of the primordial deuterium show that the density of ordinary matter is about only 5% of the critical density—the boundary between having too little to stop the expansion and enough to eventually stop the expansion.

Measuring the abundances of the primordial material and comparing it with what is predicted in the Big Bang theory provides a crucial test of the theory. Astronomers have measured the abundances of primordial material in unprocessed gas in parts of the universe where there are no stars around to contaminate the gas when the stars die. The observed abundances match the predicted abundances very well.

The Big Bang nucleosynthesis also turns out to place great constraints on the variation of G, the gravitational constant, because a different value of G in those first few minutes than what we see today would have significantly changed the expansion rate of the universe and that would have significantly (measurably) altered the relative abundances of the primordial elements. The gravitational constant G appears to truly be constant. The Big Bang nucleosynthesis also provides constraints in the number of types of neutrinos in the universe. It shows that there cannot be more than the three types of neutrinos already given by the Standard Model of Particle Physics. More than three families of particles would also have significantly changed the expansion rate of the early universe to produce abundances of the primordial elements much different than what we observe. This result also constrains the possibilities for the nature of dark matter. Measuring the masses of galaxies and galaxy clusters through several independent methods shows us that the overall density of matter in the universe is about 30% of the critical density but Big Bang nucleosynthesis shows us that the density of ordinary matter is just 5% of the critical density. The dark matter must be made of particles that are not the usual protons, neutrons, electrons, etc. of ordinary matter. In fact, the dark matter must be made of particles not within the three families of particles in the Standard Model.

A nice interactive to get a handle on the stages of the Universe's history and its future (in preparation for the next major section of this chapter) is History of the Universe interactive from NOVA's Origins series that was broadcast on PBS (selecting the link will bring it up in a new window either in front of or behind this window).

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last updated: April 27, 2013

Is this page a copy of Strobel's Astronomy Notes?

Author of original content: Nick Strobel