Exploits in Physics Vocabulary Quiz

Answer: A time at which the Sun appears exactly overhead at a point on the equator

Our planet has seasons because of its tilt. The axis of the Earth, which is the imaginary line through the North and South Poles around which the Earth rotates, is tilted by 23.5 degrees relative to its orbital plane. (That's the flat, 2D space in which the Earth moves as it orbits around the Sun.) In your local summer, you get more hours of daylight because your hemisphere (north or south) is pointed toward the sun by this tilt; in your local winter, you get more hours of darkness because your hemisphere is pointed away from the sun.

There are two equinoxes each year -- in late March and in late September -- and on those days every spot on the planet gets approximately 12 hours of daylight and 12 hours of darkness. (It isn't exact because the Sun takes up space in the sky, and the refraction of sunlight around the horizon also extends the apparent daytime.) You can even calculate a "moment" of equinox, which is when the terminator -- not Arnold Schwarzenegger, but the boundary between day and night -- makes a right angle to the equator.

Tracking the seasons is tremendously important for farmers, hunters, and gatherers, which explains why every culture has carefully watched the sky. Think a moment about how many ancient structures align with the solstice or equinox Sun -- from Stonehenge to El Karnak to Chichen Itza -- and you can tell how hard people have worked to understand the motion of the Earth.

Answer: A planet orbiting a star that is not the Sun

One of the guiding assumptions of modern astrophysics is the Principle of Mediocrity, which says that our planet, star and solar system are not special or unique in the universe. This principle is critical to progress because it allows us to extrapolate from our well-known system to the universe at large.

Astronomers weren't surprised that planets were orbiting other stars, but actually finding them was a tremendous challenge. A planet gives a faint light, reflected from its parent star, but the light of the star will generally wash it out. One very successful method uses the Doppler effect to measure changes in the star's velocity toward Earth, which indicate the gravitational effects of an exoplanet on its star. Another is to monitor the star's apparent brightness over time: if a dimmer planet regularly passes in front, the measured brightness will temporarily drop in a predictable way. Both methods are more likely to detect large planets close in to their parent stars, which give a stronger signal - but advances in telescope technology, combined with dedicated searches like the Kepler space telescope mission, have also allowed the discovery of many Earth-size planets in the habitable zone.

Answer: Entropy

Entropy can be thought of as a measure of how disorganized or unsorted a system is. For example, imagine a dozen gas molecules in a box. We expect them to be spread out more or less evenly -- if they are all sorted into the same corner, we know that that hasn't happened by chance!

Quantitatively, the entropy of some physical state is proportional to the natural logarithm of the number of specific configurations that could possibly make up that state. For example, imagine that I flip 2 coins and end up with one heads and one tails. There are two ways to make that state: the first coin heads and the second tails, or the other way around. By contrast, if I end up with two heads, there's only one configuration that makes it work. The one heads/one tails state has more available configurations, and therefore both higher entropy and higher probability. With a sample of 200 or 2000 coins, we quickly end up with negligible probability for the highly "sorted" cases of all heads or all tails.

Another way to think about entropy is as a measure of the amount of information or detail that you need in order to fully characterize a physical system. If I've got 200 coins and they're all heads, then you instantly know the state of each individual coin. But in the higher-entropy state of 100 heads and 100 tails, you need much more information to know which one is which.

Answer: Leptonic energy

A lepton is a fundamental (i.e. not composite) particle that has spin 1/2 and doesn't participate in the strong force. There's nothing special about the energy of a lepton: part of it could be kinetic (due to its motion), or potential (energy stored in its configuration relative to a external conservative force, like gravity), or could be mass energy (E=mc^2 -- critical to relativity!).

It's often useful to consider additional types of energy -- thermal energy, chemical energy, and so on -- but in the end these are all special cases of these general energy types.

Answer: Elastic collision

Billiard balls or marbles give us great examples of elastic collisions. The kinetic energy of the colliding objects is just their total energy of motion, and when that is left unchanged by the collision, we can readily calculate the resulting speeds.

When is a collision NOT elastic, though? In an inelastic collision, we tend to have deeper changes. For example, imagine a collision between a marble and a wad of chewing gum -- they stick together, and some of that energy of motion is lost in the process. We could also imagine a collision that breaks apart one of the objects, or that induces other internal changes. The initial kinetic energy doesn't disappear, but transmutes into other forms that aren't associated with the final speeds.

Answer: A collection of copies of the original system, each of which could experience a different outcome

The basic idea of an ensemble is to explore the way that all the probabilities can play out. If we run an experiment once, we get one answer. If we run it ten million times, we get a range of answers, and we're able to explore the probabilities of obtaining each one. Once we have that distribution, we can find the average result, as well as a variance that expresses how likely it is for any one system to deviate from that average.

This simple trick can be complicated to put into practice: How exactly do we define a copy? Yet ensembles are a tremendously powerful tool for exploring the behavior of systems.

Answer: Square root of negative one

Euler's formula famously relates the two main trigonometric functions -- sine and cosine -- to complex exponentials, namely e raised to a complex power. The square root of negative 1 -- i to mathematicians and physicists, and j to engineers -- is the prototypical imaginary number: a number that, when squared, yields a negative number. (The square root of a positive number is called a real number, and a complex number is a number that may have some real part, for example 1+i.)

The relationship of sine and cosine to complex exponentials is critically important to wave mechanics and Fourier analysis.

Answer: Spooky action at a distance

In quantum entanglement, two quantum objects are deeply connected to each other, such that the state of one describes the state of the other. For example, maybe we produce two photons such that one of them is horizontally polarized, and the other one is vertically polarized. We don't know which is which before making a measurement, but if we measure the polarization of one, then we immediately know the polarization of the other -- even if it is very far away. When Einstein, Podolsky and Rosen considered this at large distances, they concluded that this result an absurd violation of relativity. The dismissive phrase "spooky action at a distance" was meant to underline the lack of a clear physical mechanism.

Despite its spookiness, however, quantum entanglement is real. Careful experiments have established the quantum behavior of entangled photon pairs at distances beyond 1200 km. Relativity is preserved by noting that such an experiment does not meaningfully transmit *information* faster than the speed of light. Quantum mechanics is weird -- but it is also true.

Answer: Quantum mechanics

In quantum mechanics, we often use bra-ket notation to write states: a state or wave function f could then be written |f>. An operator, let's say the total spin angular momentum S, is applied to the state by multiplying it out front. If and only if |f> is an eigenstate of S, with eigenvalue s, then the following equation holds:

S|f> = s|f>

That is, if you apply the operator to one of its eigenstates, you obtain that eigenstate multiplied by its eigenvalue. For example, an electron wave function is an eigenvector of the spin angular-momentum operator, with eigenvalue s = hbar/2 -- meaning that it has a spin of 1/2, and you can never measure anything else. If we're thinking about a different quantum-mechanical measurement -- say, measuring position or energy -- then different wave functions will be eigenstates of the new measurement, with different associated measurement results or eigenvalues.

When we talk about a wave function being a quantum superposition of states, we're saying that we can express it as the sum of some number of eigenstates, each one weighted in a way that relates to the probability of measuring the corresponding eigenvalue. This vocabulary arises from linear algebra (the study of matrices and vectors) but finds deep physical meaning in quantum mechanics.

Answer: It is made up of a quark and an antiquark.

The electron is a fundamental particle: you can't break it down into any subcomponents. Instead, it's a building block, serving as the part of an atom that's responsible for chemistry. Even its charge -- often denoted e -- is almost fundamental: apart from quarks (which have charges of magnitude e/3 or 2e/3), no other charged particles have less than an electron charge.

In the Standard Model of particle physics, the electron is categorized as a spin-1/2 lepton, which interacts via the weak force, electromagnetism, and gravity, but does not participate in the strong force. The positron is just like an electron, but it's positively charged and it will annihilate any electron it comes near.