Quantum Diaries

Update: I accidentally miscalculated the decay rate of K40 in a banana. There are 12 decays, per second, per banana, not 18.

Wimps, they are everywhere! They pervade the Universe to its furthest reaches; they help make this little galaxy of ours spin right round like a record (we think); and they can even be found with all the fruit in your local grocery store.

Figure 1: ( L) Two colliding galaxies galaxy clusters (Image: NASA’s Chandra X-Ray Observatory). (R) Bananas, what else? (Image: Google)

WIMPs: Weakly-Interactive Massive Particles, is an all-encompassing term used to describe any particle that has (1) mass, and (2) is unlikely to interactive with other particles. This term is amazing; it describes particles we know exist and is a generic, blanket-term that adequately describes many hypothetical particles.

Neutrinos: The Prototypical WIMP

Back in 1930, there was a bit of a crisis in the freshly established field of particle physics. The primary mechanism that mediates most nuclear reactions, known as β-decay (beta-decay), violated (at the time) one of the great pillars of experimental physics: The Law of Conservation of Energy. This law says that energy can NEVER be created or destroyed, ever. Period. Sure, energy can be converted from one type, like vibrational energy, to another type, like heat, but it can never just magically (dis)appear.

Figure 2: In β-decay, before 1930, neutrons were (erroneously) believed to decay into a high speed electron (β^–) and a proton (p⁺).

Before 1930, physicists thought that when an atom’s nucleus decayed via β-decay a very energetic electron (at the time called a β particle) would be emitted from the nucleus. From the Conservation of Energy, the energy of an electron is exactly predicted. The experimental result was pretty much as far off from the prediction as possible and implied the terrifying notion that perhaps energy was not conserved for Quantum Mechanics. Then, in 1930, the Nobel Prize-Winning physicist Wolfgang Pauli noticed that the experimental measurements of β-decay looked a bit like what one would expect if instead of one particle being emitted by a radioactive nucleus, two particles were emitted.

Prof. Pauli thought the idea of a radioactive nucleus emitting two particles, one visible (the electron) and one invisible, was horrible, silly, and unprofessional. Consequentially, he decided to pen a letter to the physics community suggesting there existed such a particle. 🙂 Using this idea and what could only be described as a level of intuition beyond that of genius, Nobel Laureate Enrico Fermi suggested that perhaps nuclear decay was actually the manifestation of a new, weak force and aptly named it the Weak Nuclear Force (note the capitalization).

To recap: 1 hypothetical particle mediated by 1 hypothetical force.

Figure 3: Prof. Pauli proposed that β-decay actually included an electrically neutral particle with little mass (χ⁰), in addition to the final-state electron (β^–) & proton (p⁺). This once-hypothetical particle is now known as the anti-neutrino (ν).

30 years later, in 1962, Prof. Pauli’s invisible particles (by then called neutrinos) were discovered; 20 years after that, the Weak Force was definitively confirmed; and after another 20 years, neutrinos were found to have mass.

Since 1930, hundreds of theories have invoked the existence of new particles that (1) have mass, and (2) interact weakly (note lack of capitalization) with other particles, which may/may not involve the Weak Nuclear Force (note capitalization, again). At some point in the 1980s, it was finally decided to coin a generic term that described these particles from other large classes of particles that are, say, massless or readily interact with other particles, e.g., with photons or gluons.

Dark Matter: The Elephant in the Galaxy

Kepler’s Laws of Motion & General Relativity are phenomenal at predicting the orbits of planets and solar systems around immense sources of gravity, like stars & black holes. However, there are two known astronomical observations where our predictions do not readily match the experimental results.

The first has to do with how our galaxy spins like a top. Theoretically, the more distant you are from a galaxy’s center, the slower you orbit around the center; vice versa, the closer you are to the center of the galaxy’s center, the faster you orbit around it. Experimentally, astronomers have found that after a certain distance from the galaxy’s center an object’s speed becomes roughly constant. In other words, if Earth were half as close to the galactic center as it is now, its speed will not have appreciably changed. See figure 4 (below) for nice little graph that compares what is observed (solid line) and what is predicted (dotted line). Furthermore, this is not just our galaxy; this is common to all galaxies. Weird, right?

Figure 4: (A) The theoretical prediction of how fast an object travels (velocity) around the galactic center, as a function of (radial) distance from the center. (B) The experimental observation. (Image: Penn State)

The second disagreement between theory and experiment comes from watching galaxies collide with one another. Yes, I literally mean watching galaxies collide into one another (and you thought the LHC was wicked). This is how it looks:

Figure 5: Chandra X-Ray Image of two galaxies galaxy clusters colliding. The pink regions represent the visible portions of the galaxies; the blue regions represent the invisible (dark matter) portions, as calculated from gravitational lensing. (Image: NASA)

Astronomers & astrophysicists can usually determine how massive galaxies & stars are by how bright they are; however, the mass can also be determined by a phenomenon called gravitational lensing (a triumph of General Relativity). When NASA’s Chandra X-Ray telescope took this little snapshot of two galaxies (pink) passing right through each other it was discovered, rather surprisingly, that the mass deduced from the brightness of the galaxies was only a fraction of the mass deduced from gravitational lensings (blue). You can think of this as physically feeling more matter than what can visibly be seen.

What is fascinating is that these problems (of cosmic proportion) wonderfully disappear if there exists in the universe a very stable (read: does not decay), massive, weakly-interacting particle. Sounds familiar? It better because this type of WIMP is commonly known as Dark Matter! Normally, if a theory does not work, then it is just thrown out. What makes General Relativity different is that we know it works; it has made a whole slew of correct predictions that are pretty unique. Predicting the precession of the perihelion of the planet Mercury is not as easy as it sounds. I am probably a bit biased but personally I think it is a very simple solution to two “non-trivial” problems.

Bananas: A Daily Source of K-40

Since I bought a bunch of bananas this morning, I thought I would add a WIMP-related fact about bananas. Like I mentioned earlier, β-decay occurs when a proton neutron decays into a neutron proton by emitting an electron and an anti-neutrino. From a particle physics perspective, this occurs when a down-type quark emits a W^– boson (via the Weak Force) and becomes an up-type quark. The W^– boson, which by our definition is a WIMP itself, then decays into an electron (e^–) and an anti-neutrino (ν – a WIMP). This is how a neutron, which has two down-type & one up-type quark, becomes a proton, which has one-down type & two up-type quarks.

Figure 6: The fully understood mechanism of β-decay in which a neutron (n⁰) can decay into a proton (p⁺) when a d-type quark (d) in a neutron emits a W^– boson (W^–) and becomes an u-type quark (u). The W^– boson consequentially decays into an electron (e^–) and an anti-neutrino (ν_e).

This type of nuclear transmutation often occurs when a light atom, like potassium (K), has too many neutrons. Potassium-40, which has 19 protons & 21 neutrons, makes up about 0.01% of all naturally forming potassium. Bananas are an exceptionally great source of this vital element, about 450 mg worth, and consequentially have about 45 μg (or ~6.8·10¹⁷ atoms) of the radioactive K-40 isotope. This translates to roughly 18 12 nuclear decays (or 18 12 neutrinos), per second, per banana. Considering humans and bananas have coexisted for quite a while in peaceful harmony, minus the whole humans-eat-banans thing, it is my professional opinion that bananas are perfectly safe. 🙂

Dark Matter Detection: CRESST

Okay, I have to be honest: I have a secret agenda in writing about WIMPs. The Cryogenic Rare Event Search with Superconducting Thermometers (CRESST) Experiment Collaboration will be announcing some, uh… interesting results at a press conference tomorrow, as a part of the Topics in Astroparticle & Underground Physics Conference (TAUP 2011). I have no idea what will be said or shown aside from this press release that states the “latest results from the CRESST Experiment provide an indication of dark matter.”

With that, I bid you adieu & Happy Colliding.

– richard (@bravelittlemuon)