Physics Question #40

David Keirsey, a 49 year old male from the Internet asks on July 26, 1999,

How did neutrinos get to be objects of such low energy? Neutrinos are supposed to have been generated by the "big bang" and form part of background radiation. Supposedly, their energy is so low, nobody has detected them. Why would the neutrinos have such low energy - is it by exchange, hence loss of momentum? And how do scientists decide the distribution of types of neutrinos in this radiation - anti-neutrinos versus neutrinos, electrons, muons, and taus?

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The answer

Doug Hube answered on July 26, 1999

The basic parameters of the 'Big Bang' model of the Universe are relatively well established. That is, we know with reasonably high precision the age of the Universe, its rate of expansion, its temperature (~2.7 degrees above absolute zero), the present energy-density and matter-density, etc. We also are confident that we know the proper mathematical relationships amongst time, space, curvature, etc. To the degree that all of what I claim is true, we can extrapolate backwards from present conditions and determine the state of the Universe as early as a very tiny fraction of a second after the Big Bang. That is, we can calculate as a function of time the temperature, density and characteristic particle energies. That makes it (theoretically) possible to study the various particle creation processes and particle-particle interactions that took place during the first few minutes of cosmological time. It is those processes which generated the neutrinos. For example, every nuclear reaction which involves an electron results in the creation of a neutrino, either an electron neutrino or an electron antineutrino. The relative frequencies of the different reactions determines the relative numbers of the different types of neutrinos. The most abundant particles in the Universe are, almost certainly, the neutrinos created during those first few minutes. (Most of the energy of the Universe is in the form of the cosmic background radiation ... the redshifted photons which were released when the Universe had an age of a hundred thousand years, or so. Prior to that time the Universe was not transparent to photons.) A fundamental discovery of 20th century Physics is wave-particle duality. Every particle has both wave and particle properties, although only one is manifest in a given situation. The cosmic background radiation consists of low energy photons which originally had much higher energies. They have been redshifted; in other words, their characteristic wavelengths have been increased or stretched in direct proportion to the expansion of the Universe. The same is true of neutrinos. We treat neutrinos as particles when they are involved in particle-particle interactions, including the reactions which create them, and the very rare reactions with matter which eliminate them. When in transit through space (and time), neutrinos behave like waves. As is true of light waves, neutrino waves travel through spacetime and are 'stretched' in wavelength in proportion to the cosmological expansion of spacetime. The energy of a particle is inversely proportional to its wavelength. The energies of cosmological/primordial neutrinos are now many orders of magnitude smaller than they were in the beginning, and much too small to be detected with existing technology. There are also many natural sources of neutrinos. They are, for example, generated in the nuclear reactions which power the stars. They are also generated in the Earth's upper atmosphere by cosmic ray particles.

Doug Hube answered on May 2, 2005

Reader James Hope, says:

Dr. Hube said: "the redshifted photons which were released when the Universe had an age of a hundred thousand years, or so. Prior to that time the Universe was not transparent to photons." I thought the universe became transparent to photons after just 3 minutes.

Doug Hube responds:

During the first few hundred thousand years -- best estimate is 300 to 400 thousand years -- following the Big Bang event the Universe was filled with a 'soup' of subatomic particles such as electrons, protons (nuclei of what would be hydrogen atoms), alpha particles (nuclei of what would become helium atoms), deuterons, neutrinos, etc. ... and photons.

During that early period the Universe was so hot and, hence, the particles so energetic that the particles were free ... not bound to one-another. In particular, the electrons were not bound to the protons nor to the alpha particles and, hence, there were no atoms.

When a photon collides (interacts) with a free particle, such as a free electron, the free particle can absorb the energy of the photon regardless of what the photon's energy was ... and the photon disappears. Photons can be created by particle-particle interactions, of course, so there were always photons in the Universe, some disappearing while others were being created. All that means is that photons in the early Universe did not travel very far before being absorbed, and that is another way of saying that the Universe during that eary period was opaque to electromagnetic radiation.

As the Universe aged and cooled the particle energies became lower. Eventually, at a cosmic age of approximately 400,000 years, the energies of the electrons dropped to values near the binding energies of atoms, and they attached themselves to the protons to make hydrogen atoms, and to the alpha particles to make helium atoms.

Electrons that are bound within atoms can carry only limited, discrete values of energy. Hence, a photon that collides with an atom will be absorbed only if it has an energy equal to one of the discrete energy transition values appropriate to that particular atomic species. If the photon has any other energy it will simply continue on its way ... it will not be absorbed.

So, once the Universe became populated with atoms rather than with free electrons and protons, a photon had far far fewer opportunities to interact with particles in ways that would result in absorption of the photon. The 'fog' of the early (first 400 thousand years) Universe that existed because of the abundance of 'free' electrons and low mass nuclei 'lifted' when the electrons and nuclei became bound together as atoms, and the Universe became transparent. The earliest time that we can observe in the history of the Universe is 400,000 years after the Big Bang, the time when photons found themselves free to travel more-or-less unimpeded through space.

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