Quantum Mechanics 101 · Unit 6: Quantum Technology & Frontiers

Quantum Academy · Chapter 25: Frontiers: Quantum Fields, the Standard Model & Quantum Gravity

Where the map ends — and where tomorrow's headlines begin

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Instructions. Work through these questions with the lesson closed first, then check yourself against it. Show every step in the calculations. Useful values: c = 2.998×10⁸ m/s, ħ = 1.0546×10⁻³⁴ J·s, G = 6.674×10⁻¹¹ in SI units, 1 eV = 1.602×10⁻¹⁹ J, one kiloton of TNT = 4.184×10¹² J, proton mass 938.27 MeV, up-quark mass 2.16 MeV, down-quark mass 4.70 MeV. For two photons from one decay, mc² = √(2E₁E₂(1 − cos θ)). One point for each vocabulary match and each question; the challenge is a bonus.

Part A Vocabulary matching

Write the letter of the matching definition in the blank beside each term.

1.Quantum field
2.Antiparticle
3.Annihilation
4.Quantum electrodynamics
5.Feynman diagram
6.Virtual particle
7.Renormalization
8.Quark
9.Lepton
10.Gauge boson
11.Higgs field
12.Hawking radiation

A.A particle with the same mass and spin as its partner but opposite charge and other opposite quantum numbers; the positron is the electron's antiparticle.
B.A spin-1 force-carrying particle arising from a gauge symmetry: the photon, the eight gluons, and the W and Z bosons.
C.The procedure that expresses a quantum field theory's predictions in terms of measured masses and charges, removing the infinities of naive calculations.
D.A physical quantity defined at every point of space and time whose excitations come in discrete quanta; in quantum field theory, every particle is a quantum of some field.
E.The quantum field theory of charged particles interacting through the electromagnetic field, developed by Tomonaga, Schwinger, Feynman and Dyson; its predictions match experiment to about a part in a trillion.
F.A spin-½ matter particle that does not feel the strong force: the electron, muon and tau, each with charge −1, and their three neutral neutrinos.
G.Thermal radiation that quantum field theory predicts a black hole emits, at a temperature inversely proportional to its mass; predicted by Stephen Hawking in 1974 and not yet observed from a real black hole.
H.A picture standing for one term in the calculation of a quantum amplitude, with lines for particles and vertices for interactions.
I.A field filling space whose nonzero lowest-energy value gives mass to the W and Z bosons, quarks and charged leptons; its quantum is the spin-0 Higgs boson, found in 2012.
J.A spin-½ matter particle that feels the strong force and carries charge +2/3 or −1/3; quarks are confined inside composite particles such as protons and neutrons.
K.The conversion of a particle and its antiparticle into other particles, such as two gamma-ray photons, carrying away their total energy and momentum.
L.An internal line of a Feynman diagram: a term in a perturbative calculation rather than a detectable particle, not obeying the usual energy-momentum relation.

Part B Questions

1.
According to quantum field theory, what is an electron?Circle one
1. AA tiny hard sphere orbiting inside a field
2. BA point where several fields cross
3. COne quantum of excitation of the electron field, which fills all of space
4. DA small region where the electromagnetic field happens to be strong
2.
Antimatter was predicted by theory before it was observed in an experiment.Circle one
TrueFalse
3.
Each extra pair of vertices in a QED Feynman diagram multiplies its contribution by roughly the fine-structure constant, α ≈ 1/ .Fill in the blank
4.
One gram of antimatter annihilates completely with one gram of ordinary matter. How much energy is released, in joules and in kilotons of TNT?Show your working
Working
Answer:
5.
Which particle carries electric charge −1/3 and is found inside every proton and every neutron?Circle one
1. AThe up quark
2. BThe down quark
3. CThe electron
4. DThe gluon
6.
A detector records two photons from one decay with energies E₁ = 75 GeV and E₂ = 55 GeV, where the cosine of the angle between them is −0.90. What is the mass of the parent particle, in GeV?Show your working
Working
Answer:
7.
A proton is made of two up quarks and one down quark. Using the quark masses in the instructions, what fraction of the proton's 938.27 MeV mass do the quarks' own rest masses supply?Show your working
Working
Answer:
8.
Virtual particles drawn in Feynman diagrams are routinely detected in particle colliders.Circle one
TrueFalse
9.
Name the five major things the Standard Model does not explain, and give one piece of evidence for any two of them.Short answer
10.
Calculate the Planck energy E_P = √(ħc⁵/G) in joules and in GeV, and compare it with the 13.6 TeV collision energy of the Large Hadron Collider.Show your working
Working
Answer:
11.
If a black hole's mass is doubled, what happens to its Hawking temperature?Circle one
1. AIt doubles
2. BIt quadruples
3. CIt stays the same, because the temperature depends only on the constants of nature
4. DIt halves
12.
What is the difference between an arXiv preprint and a peer-reviewed paper, and why does neither by itself settle a scientific claim?Short answer
13.
Particle physicists require a significance of five before announcing a discovery.Fill in the blank
14.
What do neutrino oscillations, observed by Super-Kamiokande and the Sudbury Neutrino Observatory, prove?Circle one
1. AThat neutrinos have nonzero masses, which the original Standard Model did not include
2. BThat neutrinos travel faster than light, as the OPERA experiment first reported
3. CThat neutrinos are made of quarks, which rearrange themselves in flight
4. DThat neutrinos feel the strong force, which twists one type into another

Part C Mad scientist challenge bonus

Build a black hole that is exactly as warm as the universe. (a) What mass must a black hole have for its Hawking temperature to equal the 2.725 K of the cosmic microwave background? (b) Compare that mass with the Moon's, 7.342×10²² kg, and find the black hole's size using the Schwarzschild radius r = 2GM/c². (c) Using the photon-only estimate t ≈ 5120πG²M³/(ħc⁴), how long would a black hole of one solar mass, 1.989×10³⁰ kg, take to evaporate, and how does that compare with the age of the universe, 1.38×10¹⁰ years? (d) Give two reasons the real lifetime of a solar-mass black hole would differ from your estimate.

Working

Memory aid

Mnemonic Remember the zoo as 'Six, six, four and one: seventeen in all, and the model is done.' Six quarks come in pairs, recalled by 'Unusually Daring Cats Steal Tasty Bacon': Up and Down, Charm and Strange, Top and Bottom, where the first word of each pair carries charge +2/3 and the second −1/3. Six leptons are the Electron, Muon and Tau, each shadowed by a ghostly neutrino. Four force carriers are the photon, gluon, W and Z, and one Higgs completes the set. Then, for the frontier, recite the five gaps as 'Go Dig Deeper, Not Away': Gravity, Dark matter, Dark energy, Neutrino masses, Antimatter asymmetry. Use it in the Particle Zoo lab: chant the cats line as you fill the quark rows left to right, and say 'Go Dig Deeper' whenever a headline claims physics is finished.

In one line Particles are quantized ripples in fields; the Standard Model lists seventeen, misses gravity and the dark universe, and tomorrow's headlines live in that gap.