Massic activity is a sample's radioactive activity divided by its mass:Its SI unit is the becquerel per kilogram, $\mathrm{Bq}\mathrm{k}{\mathrm{g}}^{-1}$. State both the material included in the denominator and the time to which the activity refers. For a solution, the mass of the complete sample is different from the mass of its radioactive constituent.^[ref]

For an own bookkeeping example, suppose a sample has total activity $A=60\mathrm{Bq}$ and total mass $m=0.020\mathrm{kg}$ at a specified instant. ThenImagine adding nonradioactive material so that the total mass becomes $0.040\mathrm{kg}$, with no loss of activity and no relevant elapsed decay time. The total activity remains $60\mathrm{Bq}$, butA lower massic activity therefore does not by itself demonstrate radioactive decay or loss of radioactive atoms: the denominator can change.

Time introduces a separate effect. For a fixed sample mass and a single decaying constituent with radioactive decay constant $\lambda$, use the usual mean exponential law:After one half-life, the massic activity halves under those assumptions. Comparing standards requires either a common reference time or the appropriate decay correction. Additional radioactive constituents, production of daughter activity or changing sample mass require a correspondingly different model.

The quantity also supports experimental cross-checks. In a 2000 study, L. L. Lucas compared massic-activity ratios of available NBS/NIST water standards containing tritium, issued between 1954 and 1999. Liquid scintillation counting supplied measured ratios; where the records allowed it, gravimetric dilution supplied independently calculated ratios. The paper reports agreement within the stated measurement uncertainties.^[ref]

This compares two kinds of evidence: radioactive counting with its detector response, and mass-based preparation records. A measured count rate still needs a detection efficiency and measurement model before it becomes an activity estimate. Dividing a detector's raw counts by sample mass alone is not the definition of massic activity. Also distinguish radioactive activity concentration, which uses volume rather than mass in the denominator.

Radio direction finding estimates the direction from which a radio wave arrives at a receiving station. It uses directional information in an antenna response, such as changes in amplitude or relative phase across several antennas. A direction is a bearing from one station; it is not, by itself, the distance to the transmitter. Combining bearings from separated stations can constrain position.

A two-element interferometer illustrates the measurement. For a plane radio wave arriving at angle $\theta$ from the perpendicular to an antenna baseline of length $d$, the path difference is $d\sin \theta$. Thus the relative phase iswhere $\lambda$ is the wavelength. With $d=\lambda /2$ and measured $\Delta \varphi =\pi /2$, the ideal model gives $\sin \theta =1/2$, hence $\theta =30^{\circ }$ within a chosen arrival sector. One baseline does not resolve every directional ambiguity, and phase wrapping can introduce additional candidates. More antennas and other directional information can help distinguish them.

A useful field test places a transmitter at a known location, compares measured and geometric bearings, and repeats the comparison across directions and frequencies. The International Telecommunication Union's originating test recommendation includes controlled transmitters and known broadcast stations, emphasizing that a final installation can behave differently from an ideal test range. Reflections, obstructions and signal properties can bias the direction estimate; an error measured at one site cannot simply be transferred to another installation.^[ref]

URLSearchParams is an API for representing and manipulating an ordered list of name/value pairs, commonly obtained from a URL's query string. Repeated names are permitted. It uses form URL encoding, rather than imposing its interpretation on every conceivable query syntax.^[ref]

For new URLSearchParams('tag=a&tag=b&q=a+b'), getAll('tag') returns both a and b, while get('q') returns a b. Calling set('tag','c') replaces the repeated entries with one: toString() then returns tag=c&q=a+b. An associative array holding just one value for each name would discard the original repeated-field information.

A literal plus needs a different spelling. Appending the pair q and a+b to a URL's searchParams produces query ?q=a%2Bb. The plus in the data is represented by percent-encoding, whereas the plus in q=a+b represents a space under this parser. These examples distinguish a character in a value from a character used by the encoding convention.^[ref]

A URL's searchParams object is connected to that URL; changes update its query. Constructing a separate URLSearchParams from a query string instead gives an independent object, useful when the original spelling must remain available for comparison.^[ref]

Form URL encoding is the application/x-www-form-urlencoded format for serializing an ordered list of name/value pairs. It is used by URLSearchParams and common form-processing conventions. Repeated names are allowed; the data model need not be a dictionary with one value per name.^[ref]

For example, the three pairs ("q", "a b+c"), ("tag", "x") and ("tag", "y") serialize as q=a+b%2Bc&tag=x&tag=y.
Here the space becomes +, while the literal plus in the value becomes %2B. Parsing the result recovers a b+c and both tag values. Replacing every plus with a space before deciding which encoding convention applies would misread data from other URL contexts.

Structural separators must also be distinguished from value data. The encoded pair q=a%26b has one value, a&b, rather than two pairs. The form parser first recognizes pair boundaries and then decodes their component data. Percent-encoding inside a component is consequently not an instruction to reinterpret the resulting characters as new separators.^[ref]

For modern serialization, text is encoded as UTF-8 bytes before the relevant bytes are percent-encoded. The name/value pair ("word", "café") therefore produces word=caf%C3%A9. This connects a text character with its byte representation rather than assigning one arbitrary percent code to the whole character.^[ref]

A query string can use this format, but generic URL syntax does not require every query to be interpreted this way. State the parser and encoding when comparing an original spelling with its recovered list of values.

An open quantum system interacts with degrees of freedom treated as an environment. If system and environment jointly have density matrix ${\rho }_{SE}$, the system state is the partial trace ${\rho }_S={\mathrm{Tr}}_E{\rho }_{SE}$. Even unitary joint evolution can change the system's purity because correlations with the environment are discarded.

For example, an interaction mapping $|0⟩|e⟩$ to $|0⟩|e_0⟩$ and $|1⟩|e⟩$ to $|1⟩|e_1⟩$ multiplies the system coherence by $⟨e_1|e_0⟩$. Distinguishable environment states suppress that coherence. A time-local memoryless master equation is an additional approximation, not part of the definition of an open system.

Quantum dynamics describes the time evolution of a quantum state and its observable predictions. For an isolated system with Hamiltonian operator $H$, the Schrödinger equation is $i\hslash {\partial }_t|\psi ⟩=H|\psi ⟩$. Equivalently, a density matrix satisfies $i\hslash \dot{\rho }=[H,\rho ]$.

For time-independent $H$, the evolution operator is $U(t)=e^{-iHt/\hslash }$. An energy eigenstate changes only by a global phase, whereas a superposition develops relative phases and can display oscillating observables. Interaction with an unobserved environment generally requires open quantum system dynamics rather than a unitary evolution for the subsystem alone.

G. Lindblad characterized generators of completely positive quantum dynamical semigroups. In finite-dimensional trace-preserving dynamics, the corresponding Lindblad equation can be written, with $\hslash =1$,where $H$ is a Quantum Hamiltonian, $\rho$ a density matrix and $L_a$ the Lindblad operators.^[ref]

Complete positivity preserves positivity even when the system is considered together with an untouched auxiliary quantum system. The semigroup and continuity assumptions are substantive: the displayed time-independent Markovian form does not describe every possible reduced evolution with memory.

A. Yu. Kitaev proposed fault-tolerant quantum computation using anyons in a two-dimensional quantum system. In the model, moving excitations around one another performs unitary transformations, while fusing excitations provides a measurement outcome.^[ref]

Information is encoded in collective degrees of freedom rather than simply in an isolated local two-state object. This can protect it against specified local perturbations. Fault tolerance depends on the physical model and error processes; it does not imply immunity to every disturbance or that every possible anyon species supplies universal computation by braiding alone.

Simon Braun and collaborators prepared a state with negative temperature for motional degrees of freedom in an ultracold atomic system. They tailored a lattice model so the occupied high-energy states were compatible with the relevant upper-energy bound.^[ref]

In this regime $\beta =\partial (S/k_B)/\partial E<0$: increasing energy reduces the entropy of the constrained system. The state is not colder than absolute zero. Its population favours high-energy states, and its thermodynamic ordering differs from the positive-temperature branch. The experimental energy bounds and stability conditions are essential.

Freddy Cachazo co-developed the scattering equations with Song He and Ellis Ye Yuan. Their work connected kinematic invariants with punctures on a sphere and provided an inductive solution method, together with a proof of KLT orthogonality.^[ref]

The resulting auxiliary geometry organizes calculations of massless-particle scattering without treating that sphere as physical spacetime.

Song He, with Freddy Cachazo and Ellis Ye Yuan, established KLT orthogonality for objects built from solutions of the scattering equations. The orthogonality uses a specified bilinear form, not an arbitrary Euclidean inner product.^[ref]

This relates alternative organizations of particle-scattering data while keeping the momentum constraints explicit.

Ellis Ye Yuan co-developed the scattering equations with Freddy Cachazo and Song He, connecting massless-particle kinematics with marked points on a sphere.^[ref] In a common convention,with conserved massless momenta $k_a$ and puncture coordinates ${\sigma }_a$. The equations provide algebraic structure for scattering calculations rather than trajectories of particles moving on that auxiliary sphere.

Riccardo Rattazzi developed a path-integral account of quantum mechanics that connects interference, operator evolution and statistical methods. His notes derive the path integral from quantum time evolution, work out the free-particle propagator and treat Gaussian fluctuations.^[ref]

The weight $e^{iS/\hslash }$, with $S$ the action functional, is an amplitude with a phase, not a classical probability assigned to each path. Combining amplitudes before taking probabilities produces interference. Analytic continuation to Euclidean time then connects suitable quantum calculations with statistical-mechanical formulations, under the required convergence and boundary assumptions.

Sergey Bravyi developed rigorous treatments of the Schrieffer-Wolff transformation with David DiVincenzo and Daniel Loss. Their 2011 work derives low-energy effective quantum dynamics through a unitary transformation that decouples low- and high-energy subspaces.^[ref]

For a Quantum Hamiltonian $H$, an anti-Hermitian generator $S$ gives $H_{\mathrm{eff}}=P{e}^{S}H{e}^{-S}P$ with $P$ the orthogonal projection onto the chosen low-energy subspace, when the transformation is constructed appropriately. Bounding the approximation matters: formally discarding high-energy states without controlling their virtual coupling can miss low-energy corrections.

Sougato Bose and collaborators proposed a spin-based witness for gravitationally induced quantum entanglement. Their 2017 design places two small masses in neighbouring matter-wave interferometers, with an embedded spin in each mass providing a correlation readout.^[ref]

Different branch separations acquire different gravitational phases, potentially entangling the two systems. Competing electromagnetic forces and decoherence must be controlled before attributing a witness signal to gravity. The contribution is a proposed experimental strategy, rather than a claim that the experiment had already measured quantum gravity.

Chiara Marletto and Vlatko Vedral developed a quantum-information route to testing gravity without detecting an individual graviton. Their proposal uses quantum entanglement between two initially independent masses to witness nonclassical properties of the interaction mediating it.^[ref]

The experimental question is stronger than measuring a gravitational phase shift alone. It requires establishing the appropriate quantum entanglement and controlling alternative couplings. The inference concerns the mediator under the stated assumptions, rather than uniquely selecting a complete microscopic theory of gravity.

Vlatko Vedral, with Chiara Marletto, proposed using gravitationally generated quantum entanglement as an indirect witness of quantum features of gravity. Their 2017 argument considers two masses in spatial quantum superpositions and asks whether their gravitational interaction can entangle them.^[ref]

Under the assumed local mediation and initial-independence conditions, a mediator restricted to classical commuting information cannot generate the required quantum entanglement. The conclusion is conditional on that model of mediation and exclusion of other entangling interactions. The paper proposes a test; it does not report an observed laboratory detection of quantum gravity.

Quantum metrology studies estimation of physical parameters using quantum states, evolution and measurements. A parameter changes the probe state; the measurement outcome distribution carries information about that change.

For $N$ independent comparable probes, uncertainty often scales as $N^{-1/2}$. Entangled states can improve scaling under suitable ideal resource assumptions, but losses, decoherence and the allowed preparation and measurement operations matter. Quoting an enhanced sensitivity requires identifying what counts as a resource and which noise model is being compared. Quantum Fisher information bounds the attainable local precision under specified estimation assumptions.