What Conservation Laws Tell Us: Newton's Cradle, Reactionless Drives and the Neutrino

What the conservation laws forbid

Conservation laws do not just help you solve problems. They also tell you what cannot happen, and when nature seems to break them, they point to something new. This lesson looks at what the conservation laws rule out for mechanical systems (perpetual motion, reactionless drives) and how they pick the outcome for Newton's cradle, then tells one of the great detective stories of physics: how these two laws predicted a new particle, the neutrino, more than 25 years before anyone detected it. Part of that story was finished in a nickel mine near Sudbury, Ontario.

Two laws, two kinds of "impossible"

Remember from Work, Energy and Simple Harmonic Motion (the lesson Damped Harmonic Motion, Shock Absorbers and Perpetual Motion): conservation of energy rules out a perpetual motion machine, because no machine can put out more energy than it takes in, and real machines always lose some energy as thermal energy. Shock absorbers use that same loss on purpose: they turn the energy of a car's bouncing into thermal energy in oil.

Conservation of momentum rules out a different dream: a "reactionless drive", a sealed box that could push itself through space just by moving things around inside it. Every force inside the box comes with an equal and opposite third-law partner, also inside the box, so internal forces can never change the box's total momentum. A weight swung back and forth inside a sealed spacecraft can make the craft wobble, but its centre of mass cannot start moving. To move, a spacecraft must throw something out (see Rockets and Propulsion: Momentum in Action) or be pushed by something outside it.

Often the two laws work together: each one alone allows many outcomes, but only a few outcomes obey both. Newton's cradle is the classic example.

A crisis in beta decay

Remember from Grade 11: in the SPH3U unit Thermal and Nuclear Energy you met alpha and beta decay. In beta-minus decay, a neutron in a nucleus changes into a proton, and an electron (the beta particle) shoots out.

Think about what conservation laws predict for a nucleus at rest that splits into two pieces (like an explosion from rest, earlier in this unit):

• The two pieces must fly apart in exactly opposite directions with momenta of equal size.
• The energy released is shared in a fixed way: the lighter piece gets the fraction m_heavy ÷ (m₁ + m₂) of it.
• So every decay of the same kind should give the emitted particle the same kinetic energy.

That is exactly what happens in alpha decay: alpha particles from a given isotope come out with one sharp energy (or a few). But in 1914, James Chadwick showed that beta-decay electrons come out with a continuous range of energies, from almost zero up to a maximum. Most electrons were missing some energy. Later experiments also showed that the electron and the recoiling nucleus were not always moving in opposite directions: momentum seemed to be missing too.

Some leading physicists, including Niels Bohr, seriously considered that energy might not be conserved in individual nuclear events.

Pauli's "desperate remedy"

In December 1930, Wolfgang Pauli wrote a famous letter to a physics meeting, addressed "Dear Radioactive Ladies and Gentlemen". Rather than give up conservation of energy, he proposed what he called a desperate remedy: beta decay produces a third particle, which:

• has no electric charge (charge is also conserved, and the proton and electron already balance it),
• has very little mass (because the most energetic electrons carry almost all the available energy),
• interacts so weakly with matter that it escapes every detector, carrying away the missing energy and momentum.

In 1933 to 1934, Enrico Fermi built a theory of beta decay that included Pauli's particle and named it the neutrino, Italian for "little neutral one". With three bodies sharing the energy, the electron can get any amount from almost zero to the maximum, exactly as observed. (Today we write the beta-minus product as an antineutrino, its antiparticle.)

Here the conservation laws were used as predictive tools: the properties of the neutrino (charge, approximate mass, the energy and momentum it carries) were worked out from what had to be conserved, years before it was found. In 1956, Clyde Cowan and Frederick Reines finally detected neutrinos produced in huge numbers by a nuclear reactor.

A Canadian chapter: the Sudbury Neutrino Observatory

Neutrinos are so hard to stop that most pass straight through the whole Earth. To catch a few, physicists build huge detectors deep underground, where rock blocks other particles. The Sudbury Neutrino Observatory (SNO) was built about 2 km underground in the Creighton nickel mine near Sudbury, Ontario. Its heart was a large acrylic sphere holding 1000 tonnes of heavy water, on loan from Canada's nuclear program, watched by thousands of light sensors.

In 2001 and 2002, SNO showed that neutrinos from the Sun change type on the way to Earth, which is only possible if neutrinos have mass. This solved a decades-old puzzle about "missing" solar neutrinos. For this work, Arthur B. McDonald of Queen's University in Kingston shared the 2015 Nobel Prize in Physics with Takaaki Kajita of Japan. The lab has since grown into SNOLAB, which continues to study neutrinos and search for dark matter.

Particle physics, astrophysics and the engineering of detectors like SNO are careers that start with exactly the physics in this course.