## Quantum Terminology 101

Many people on the web and especially twitter use Quantum Mechanics (QM) terms without understanding their meanings and as a result sound to me like angry clueless tourists. So in the interests of making twitter a better place and me less baffled by conversations what follows is a super short synopsis of some QM terms/ideals. I have avoided all maths as QM equations can look a bit intense and this scares away many people. However it is impossible to simplify QM terms in words alone without being vague, a bit imprecise or just wrong. Hence corrections are welcome. I also linked the paragraph titles to the appropriate wikipedia articles so you can read more if you like.

**Why anyone cares about "Quantum stuff":**

On very small scales in transpires that our reality, somewhat surprisingly, appears to not allow just any amounts of certain measurable quantities but to instead only allow discrete amounts. If this applied on much larger scales it would lead to almost unimaginably odd situations. Can you imagine a world where all items **must** have a weight that divides evenly by 10 kg, were 6 kg objects are utterly physically impossible to construct? In reality the discrete steps are so small that they are normally invisible at all but the very smallest scales. Hence due to it's strongly associated scale "Quantum" can often be simply read as concerning the very small.

**Quantum:**

A minimal piece or bit.

**Quantized:**

Composed of bits or discrete levels. A digital signal is quantized being either 0n (1) or Off (0). Similarly so is the height of a configuration^{1} of stackable toy cylinders (1 cylinder high, 2 cylinder high etc)

**Quantum Mechanics/Physics:**

Literally: bit physics. The field of physics that covers the mechanics/dynamics of systems on a sufficiently small size that any model of them will only accurately depict reality if it predicts quantized outcomes.

**Classical Physics:**

This is context dependent but is often meant in QM discussions as non quantized continuum physics (which is pretty much all of physics bar QM). However it can very occasionally refer to older atomic models (eg Bohr's model) rendered defunct by later improved QM models.

**Classical limit/Convergence:**

A QM description must tend to the classical description as the described system itself tends to the size at which a classical description applies. If it did not there would be some size of system for which there would be a discontinuity in our descriptions. (Physicists do look for these but haven't found any so far.)

**Wavefunction/Waveform:**

The mathematical entity used by QM models that describes every aspect of a system or particle. By applying mathematical operations on a wavefunction we can get other functions that can describe the likelihood of various outcomes if they were to be measured on the system.

**Collapsing the wavefunction/waveform:**

The result of the mathematical operation on a wavefunction can predict the likelihood of a certain outcome but only once the measurement is made can the actual result be known. In other words the measurement "collapses" the probability distribution to one actually measured result. For example on a perfect die all values are equally likely (ie there are probabilities of 1/6,1/6,1/6,1/6,1/6,1/6 for the values 1-6) but when you roll you get a result of one number (ie for a 4 the probablities are 0,0,0,1,0,0). In other words the collapsing of the wavefunction is the moment when probablities stop and the outcome is revealed.

**Schrödinger's cat:**

This is a famous thought experiment that can demonstrate certain aspects of QM. In it a cat is placed in a perfectly sealed box in which a vial of poison gas is set to be broken at the moment a radioactive atom decays. Due to quantum indeterminacy (see below) once the box is sealed we cannot know at any moment whether the cat is alive or dead. As a consequence the QM description (wavefunction) of this system describes a mixed state ie the cat as described as both alive and dead simultaneously. Once the box is opened the wavefunction collapses as we know for certain whether the cat is alive or dead.

**Philosophical implications of QM: **

The massive success of QM has lead to various guesses as to how much reality might "really" be as it appears to be according to the QM description and how such descriptions might "arise". Alas as is typically of much of philosophy often these ideals are not falsifiable and thus are not really scientific views. So whilst they make for truly excellent pub talk^{2} arguing about them is precisely as pointless as debates about how many angels fit on a pinhead and other nonsense. Oh and it is worth pointing out that the vast majority of stuff written on the web on QM interpretations is just plain wrong (even on quite respectable sites). Thus be warned that bringing these notions up without at least knowing the experimental QM work from which they arose makes you sound like the worst kind of time waster (to me anyway).

**Entanglement:**

This is tricky and best explained by an example. Consider a perfectly sealed machine that places either a red or brown ball into a sealed box. (Again it does this on the basis on whether or not a radioactive atom has decayed.) It then blasts the sealed box to the moon and retains the remaining ball in its own sealed box. The wavefunction of the moon box and the machine's box system describes a mixed states (see Schrödinger’s cat) and so both boxes are described as both red and brown simultaneously. They are also fundamentally linked (which is known as entangled) as if the moon's box has a red ball the machine's must be brown and vice versa. An issue arises as if someone opens the moon box they instantly (faster than light) collapse the wavefunction on earth ie If you stand on the moon and open the box when you see a red ball you know instantly the earth box contains a brown ball. **Important Note:** The existence of a mixed state before the measurement/waveform-collapse can result in different behaviour from merely unknown states as elegantly demonstrated by the double slit experiment (see below).

**A radioactive atom:**

An atom with an unstable centre (nucleus). This means that it has the possibility to undergo a nuclear process that will emit one or more particles in turn letting the nucleus of the atom relax into a stable state or at least a state one step closer to stable. There is no current physics model that tells you exactly when this is going to happen for a single atom. You can however very accurately predict the rate at which it occurs for groups of atoms.

**An excited atom:**

An atom which has one or more of it's electrons in more energetic orbits than it would have in the lowest energy configuration (also called ground state) for this particular atom. The atom has the possibility to "relax" into a less energetic or possibly ground state by emitting electrons/photons or exciting nearby particles. Again like the radioactive atom you cannot know the precise moment this will happen with a single atom thou you can very very accurately know the rate.

**Uncertainty principle:**

This states that the accuracy of the knowledge of the values of two variables is coupled and limited to a certain minimum value. Thus as you improve the accuracy with which you know the value of one variable the accuracy of the other becomes worse and worse. It applies to many pairs of physical properties the most famous pairing being position and momentum.

**Quantum indeterminacy:**

This refers to the incompleteness of QM descriptions. Consider an isolated excited hydrogen atom. We can write the wavefunction precisely and even accurately calculate the likelihood/rate of relaxation. But we cannot calculate the exact moment when the atom will actually relax. QM simply doesn't cover this hence we call it incomplete. The same applies as to when a single radioactive atom will decay. In fact their is no known physics that can state the exact moment relaxation/decay will occur. The exact moment is currently viewed as one of the true sources of entropy (chaos) in the universe. Even if (ignoring the uncertainty principle) we precisely knew the entire state of the universe at any instance QI means we could not predict the exact future.**Half-Life/Lifetime:**

Half-Life is the time a radioactive sample takes for half of it's atoms to decay. Lifetime is the average time for an excited state to relax. While we cannot predict when an isolated excited atom will relax or when a isolated radioactive atom will decay we can precisely predict the rates for both. Consider a lump of plutonium, from the moment you start measuring some atoms will be decaying and yet if we waited 10 half lives we would still have ~0.1% of the original atoms undecayed. But atoms are indistinguishable and thus when viewed at the start the long lived ones cannot be identified from the ones that would decay in the next 5 seconds. Thus if you had selected one atom from the plutonium lump at the start there is simply no way of knowing whether it is a long life atom or not so basically you cannot say anything about when it will decay. Conversely if you took 2 billion atoms you could easily predict when you would have 1 billion left in their original state. (about 24,200 years later for Pu-238).

**Double Slit experiment:**

The double slit experiment is in my mind (and the minds of many other physicists) the most beautiful experiment in all of physics. Enjoy it. It goes like this: take a narrow ray of light and pass it through a narrow slit. Light passing a narrow slit diffracts into a wider beam which is then passed through two more narrow slits. The diffracted light passing the two narrow slits forms an distinctive interference pattern which can be visible on a screen or recorded onto a detector. So far so good. This is all standard optics that high school physics kids might know. Now the trouble starts. What if I reduce the light intensity to the point that only one light particle (called a photon) goes through at a time. As one photon seemingly can only take one path it shouldn't be able to form an interference pattern. After all what would it be interfering with, itself? However if you run one photon over and over and add up the results you find that actually the result does indeed form an interference pattern. Worse it does so if, and only if, you do not attempt to measure which path it takes. Does that sound crazy? Good, it is and it gets worse. We can even measure one path and if a particular photon didn't take that path include it otherwise exclude it from the results. You would think given you are not affecting the photons you include the resultant interference pattern should be unchanged. However the fact that you know the photons' path (in other words have collapsed their waveforms) seems to prevent the interference pattern forming. This experiment has also been done with electrons, atoms and even large molecules. To my mind this amazing experiment is the closest thing to outright demonstration of magic that science has yet discovered.

## FootNotes

- assuming you don't do anything "clever" like placing the cylinders at funny angles.
- You could guess this by their often funky titles Copenhagen interpretation, Non Local Hidden Variables, Many Worlds, Quantum mysticism, Consistent Histories, Temporal Symmetry, Participatory anthropic creation etc etc