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Determining the column density of a cloud of chemical atoms from the attenuation of a probe beam of light; the measured image integrates through the cloud along the viewing direction.

Producing a perceived color by superposing light with different spectra.

The Airy disk is the central bright region, up to the first dark ring, in the scalar diffraction pattern of a uniformly illuminated, unobscured circular aperture. The whole pattern includes the weaker surrounding rings; its radius is distinct from its full width at half maximum.

For a circular optical pupil of diameter $D$ under normal, uniform monochromatic plane wave illumination, Fraunhofer diffraction givesHere $I_0$ is the on-axis light intensity, $\theta$ is the angle from the optical axis, $\lambda$ is the wavelength in the propagation medium, and $J_1$ is the order-one Bessel function of the first kind. The paraxial approximation replaces $\sin \theta$ by $\theta$, measured in radians. The first positive zero $j_{1,1}=3.831705970\dots$ givesThis is the angular radius of the Airy disk; the angular diameter is twice as large. The Airy disk derivation explains the origin of the Bessel function of the first kind and of the numerical coefficient.^[ref]

The image and both radial curves show the same calculated light intensity, divided by its peak. The image's logarithmic scale makes the weak rings visible; its colour is a display choice. The linear curve shows how small the ring peaks are compared with the centre. A dark ring marks a zero of wave amplitude, produced by cancellation across the optical pupil; it is not the edge of all transmitted light. The first Airy disk contains about $83.78\%$ of the total radiant flux, as calculated in Airy disk normalization and encircled energy.

For an original design example, take an ideal optical lens in air with focal length $f=100\mathrm{mm}$, circular optical pupil diameter $D=5.00\mathrm{mm}$ and wavelength $\lambda =550\mathrm{nm}$. In the focal plane, the radial coordinate $r\simeq f\theta$ givesThe first-zero diameter is $26.8327\mu \mathrm{m}$. Solving $P(u_{1/2})=1/2$ gives $u_{1/2}=1.616339948\dots$, so the diameter measured by full width at half maximum is onlyThus a quoted “spot diameter” is incomplete without its definition. Doubling $D$ halves both widths at fixed wavelength and focal length; increasing magnification alone changes the image scale without improving object-space discrimination.

The Airy disk supplies a calculable reference for a point spread function, allowing diffraction to be distinguished from defocus and optical aberrations. Its beauty is that one circular boundary determines an entire sequence of bright and dark rings through a Fourier transform. The ideal formula assumes an unobscured pupil, uniform illumination, ideal optical focus, a single wavelength, and a scalar description with small output angles. A blocked centre, nonuniform pupil transmission or a significant pupil wave phase error changes the response. High numerical aperture may require polarization of an electromagnetic wave and a vector field description. The circular-aperture diffraction laboratory experiment tests the far-field pattern directly; the Rayleigh criterion uses its first zero to define a two-source convention.

A physicist whose work connects special relativity, general relativity, Brownian motion and the photoelectric effect. He worked at the Institute for Advanced Study from 1933 until his death in 1955.^[ref]

In 1905, Albert Einstein used the photoelectric effect to explore quantized light, related Brownian motion to molecular agitation, formulated special relativity, and connected changes in mass and energy. These problems link visible measurements to otherwise inaccessible structure: emitted electron energies, suspended-particle displacements and comparisons of clocks.^[ref]

The Millikan photoelectric experiment follows one of those predictions into the laboratory. Its stopping-voltage measurements test a quantitative relation; the experiment's apparatus, surface preparation and electrical corrections matter to that inference. The Einstein field equations and general relativity lead to a different set of tests involving gravity and spacetime.

The Nobel Prize in Physics in 1921 recognized his theoretical work, particularly the law of the photoelectric effect; the award was presented in 1922.^[ref]

Luis Walter Alvarez's program extended the Glaser bubble-chamber experiment into large hydrogen bubble chambers and systematic analysis. His lecture credits John G. Wood, an accelerator technician, with early hydrogen tracks, and emphasizes technicians' responsibility for chamber development.^[ref]

Alvarez's 1956 report describes a ten-inch hydrogen bubble chamber in a steady magnetic field, exposed to a $700\mathrm{MeV}$ negative-pion beam for proton scattering. Liquid hydrogen was the target. Horizontal windows admitted illumination and stereo viewing; a shielded light source let bubble-scattered light reach the lenses. A temperature gradient initially restricted sensitivity near the top. Tilting and fast recompression improved uniformity.^[ref]

The same report compares tracks without a magnetic field against straightness expectations, testing spurious curvature. Multiple Coulomb scattering remained a limitation. This separates an instrumental check from the physical momentum inferred with the field on.^[ref]

The scientific opportunity is to turn a visible geometry into a test of an invisible intermediate state. The bubble-chamber pressure cycle prepares the sensitive target; bubble-chamber track readout supplies geometric measurements. Neither step alone identifies a particle resonance.

An analogue-to-digital unit is a unit of a digitized photodetector output after electronic conversion. Its relation to collected electrons is set by the detector conversion gain; an additive electronic offset must be removed before interpreting a count as a light signal.

Anderson localization is the confinement of electron wave functions, or other wave modes, by interference between repeated wave scattering paths in static disorder. A localized eigenstate occupies a limited region even in a much larger sample. Disorder can therefore suppress diffusion without absorbing the wave. In 1958, Philip Warren Anderson studied random site energies and intersite coupling, finding a regime without transport. His paper develops a theoretical model; it does not report an Anderson laboratory measurement.^[ref]

The distinction from ordinary multiple scattering is the retention of wave phases: alternative paths contribute probability amplitudes before their squared modulus is taken. Adding path probabilities alone loses the cross terms responsible for interference. This makes Anderson localization useful as a warning about transport models: repeated deflections need not produce unlimited diffusion. It also connects electron transport with wave propagation in a random medium, although the detailed equations and experimental diagnostics differ between electrons, light and acoustic waves.

Philip Warren Anderson's 1977 lecture distinguishes localized magnetic moments from disorder-localized states. It credits Nevill Francis Mott with recognizing the significance of the mobility edge. A Mott insulator instead requires electron interactions and can exist without disorder.^[ref]

John Hasbrouck Van Vleck developed quantum mechanics explanations of magnetic susceptibility, including its temperature dependence; this is a distinct contribution from Anderson localization.^[ref]

Anoxygenic photosynthesis captures light without producing molecular oxygen. It occurs in some bacteria and uses electron sources other than water. Whether carbon fixation accompanies this light capture depends on the organism and conditions; photosynthesis does not imply one universal carbon-assimilation pathway. See Alberts et al.: chloroplasts and photosynthetic bacteria.

An aperture is an opening that admits light into or through an optical instrument. Its shape and size select the transmitted light rays; an aperture alone does not bend them as an optical lens does. The aperture stop is the opening that most restricts the bundle from an on-axis object point. The entrance pupil is the image of that aperture stop formed by the preceding optical lens elements, viewed from the object side. Consequently the effective collecting diameter $D$ is the entrance pupil diameter, which can differ from the physical hole's diameter. For example, preceding optical lens elements that enlarge a $10\mathrm{mm}$ aperture stop by a factor of two give $D=20\mathrm{mm}$; measuring the physical hole alone would misidentify the focal ratio. ^[ref].

For an unobscured circular entrance pupil under a uniform beam normal to its plane, the collecting area and admitted radiant flux arewhere $E_{\mathrm{pupil}}$ is incident irradiance. Doubling $D$ quadruples admitted radiant flux. Obstructions, nonuniform illumination and losses after the entrance pupil require the actual illuminated area and transmission to be included. The same $D$ also sets an angular diffraction-limited resolution scale $\lambda /D$ at wavelength $\lambda$. Collection and diffraction therefore answer different questions from field of view: an aperture selects the bundle from each object point, while the receiving plane's extent helps select which object directions appear in the image.

NASA/JPL's published pinhole demonstration uses two white cards, foil taped over a window in one card, and a small hole pierced in the foil. Sunlight passes through the hole onto the second card; the projected image is viewed on that card. The activity describes a larger image when the card separation increases, improved visibility when the receiving card is shaded, and a separate image from each of several holes. These are qualitative observations of image formation, rather than calibrated measurements of radiant flux or diffraction. ^[ref].

A proposed quantitative extension replaces sunlight by a steadily illuminated asymmetric target and puts the foil and a translucent receiving screen in a dark box. Record target distance $u$, hole-to-screen distance $b$, hole diameter $d$, image height, orientation and edge blur. Measure screen brightness with a fixed photodetector, or record the screen with an optical camera whose integration time and gain stay fixed. Exchange centred foils of measured $d$ at fixed $u,b$; then vary $b$ with the same foil. Geometrical optics predicts an inverted image with transverse magnification $m=-b/u$ and a point's geometric blur diameter $d(1+b/u)$. Thus a larger hole admits more radiant flux without changing the central image scale, whereas increasing $b$ enlarges the image. These are predictions to test, not reported data. Keep target illumination and detector position fixed, subtract a hole-covered dark reading, repeat the original foil to check drift, and avoid clipping the detector response. Foil thickness and ragged edges can block oblique light rays; at sufficiently small $d$, diffraction invalidates the claim that ever smaller holes always sharpen the image. A lensless optical camera has no optical lens focal length: $b$ is a propagation distance, not that focal length.

Astrometry measures the positions and motions of celestial objects. Repeated position measurements can distinguish stellar parallax, caused by the observer's motion, from proper motion of the source across the sky.

An astrometry measurement needs a date and a reference frame, as well as an angle. In an equatorial coordinate system, right ascension and declination label two viewing directions. A catalogue's reference date states when its quoted position applies; comparing entries at different dates without accounting for proper motion can make the same star appear misplaced. The observational problem is to infer a consistent history from successive incoming light directions, while accounting for the observer's changing position and measurement error.

To see the separation clearly, consider just one angular coordinate $\theta$, with $t$ the numerical elapsed time in years. Assume a simplified circular orbit of the Earth, a fixed source Euclidean distance, constant proper motion in this coordinate and no other accelerations. Choose the direction and the starting date so that the annual stellar parallax projection is the cosine termHere ${\theta }_0$ is the coordinate without the annual stellar parallax offset at the reference date; the observed $\theta (0)$ is ${\theta }_0+p$. The proper motion coefficient $\mu$ is quoted in arcseconds per year, and $p$ is the annual stellar parallax in arcseconds. This is an illustrative choice of a full-amplitude projection. General sky directions have different projected amplitudes and phases in their two coordinates; their apparent paths need not be circles. Real astrometry uses the observer's calculated position rather than imposing this single cosine. ^[ref].

Set ${\theta }_0=0$, $\mu =100\mathrm{mas}\mathrm{y}{\mathrm{r}}^{-1}$ and $p=50\mathrm{mas}$, where $1\mathrm{mas}$ is one thousandth of an arcsecond. The model gives $\theta (0)=50$, $\theta (0.5)=0$ and $\theta (1)=150\mathrm{mas}$. Same-season observations one year apart differ by $100\mathrm{mas}$ because the annual stellar parallax contribution repeats. Subtracting that fitted straight trend leaves an annual signal between $-50$ and $+50\mathrm{mas}$. The existing stellar parallax distance relation then gives $20$ parsecs.

Observing only at the same annual phase would recover the proper motion trend but leave $p$ indistinguishable from a constant offset. Sampling several seasons as well as several years separates the repeating signal from the accumulating displacement. The two signatures answer different questions using the same measurements.

The astronomical horizon is the great circle where the horizontal plane through the observer intersects the celestial sphere. It is perpendicular to the local vertical, so every direction on the astronomical horizon has altitude $0^{\circ }$ and zenith distance $90^{\circ }$. In the local horizontal coordinate system, it consists of the unit vectors satisfying $\mathbf{n}\cdot {\mathbf{e}}_U=0$. This geometric reference remains defined when buildings or mountains hide it; a visible skyline is not a calibration of zero altitude.

Three boundaries must be distinguished. The astronomical horizon fixes the angular reference. Terrain supplies a site-dependent boundary with apparent altitude $t(\eta )$ that changes with azimuth. Atmospheric refraction changes the apparent direction of incoming light, and can also change the apparent distant boundary. A point source clears an opaque terrain boundary only if ${\gamma }_{\mathrm{app}}>t(\eta )$ when both are expressed in the same apparent horizontal coordinate system; this clearance condition does not guarantee visibility through clouds or bright sky. In the synthetic diagram, a source with geometric altitude $3^{\circ }$ and an imposed illustrative upward correction $R=0.2^{\circ }$ remains behind a $4^{\circ }$ boundary. The chosen $R$ is an algebraic illustration, not a fitted atmospheric prediction.

Even an unobstructed sea boundary need not coincide with the astronomical horizon. On a spherical Earth of radius $r$, an observer at height $q$ sees the unrefracted tangent to the surface at a downward angle $D$ satisfying $\cos D=r/(r+q)$. The right-angle tangent triangle supplies this relation; the visible boundary then has altitude $-D$. With illustrative $r=6371\mathrm{km}$ and $q=10\mathrm{m}$, $D\simeq 0.1015^{\circ }$, before atmospheric refraction. Raising the eye therefore changes the visible boundary without redefining the horizontal plane.

The US Naval Observatory's rise/set definitions explicitly distinguish the geometric reference from apparent contact with a visible disk: the standard Sun calculation puts its centre $50^{\prime }$ below the horizontal plane, combining an average $16^{\prime }$ radius with $34^{\prime }$ of atmospheric refraction. An angular minute is $1^{\prime }=1/60^{\circ }$ in the minute and second of arc convention. This is an operational average under stated conditions, rather than a universal zero of altitude. The same source identifies weather, local topography and observer height as limits on predicted rise/set time. An observation log should therefore retain the level reference, site and eye height, terrain profile, observation time, and whether each reported altitude is geometric or apparent. ^[ref].

Astronomy studies celestial objects and phenomena, including stars, planets and galaxies. Astrometry measures their positions and motion; astrophysics uses physics to explain their properties and behaviour.

Much of astronomy begins with incoming light. An image tells us which direction the light arrived from, rather than directly providing the source's three-dimensional position. Two stars close together on the sky may be very far apart in space. The celestial sphere organizes these viewing directions; locating an object on it is a different task from measuring how far away that object is. Repeated observations turn this limitation into an opportunity: the changing direction of light contains evidence about both Euclidean distance and motion.

The particularly satisfying combination is stellar parallax with proper motion. The first supplies a geometric Euclidean distance, while the second measures how rapidly the viewing direction changes after accounting for the observer's annual motion. Together they give a transverse speed, connecting tiny angles on an image to kilometres travelled each second. This bridge from a flat sky map to moving stars is one reason astrometry matters to the study of the Milky Way.

Astrophysics uses physics to explain stars, planets, galaxies, and their electromagnetic radiation; cosmology extends the questions to the universe as a whole. Much of its evidence arrives as light. The challenge is to infer the source's physical properties from what reaches an observer: a bright star might be nearby, unusually luminous, or both. Stellar parallax and observed radiative flux make this distinction quantitative.

This is an inverse problem. A forward problem predicts observations from a source model and the intervening radiative transfer; the inverse problem works backwards from observations to possible models. A spectral line can constrain chemical elements, temperature, and motion through the Doppler effect, but its strength also depends on the stellar atmosphere. Combining different measurements is therefore more informative than interpreting brightness alone. The attraction is that a tiny change in the direction of light can supply a distance, turning received radiative flux into intrinsic luminosity. ^[ref].

In the constant-parameter battery internal resistance model, the source's available electrical power splits between the electrical load and internal dissipation:The stipulated $3\mathrm{V}$, $1\Omega$, $4\Omega$ calculation gives $P_L=1.44\mathrm{W}$, $P_{\mathrm{int}}=0.36\mathrm{W}$, and $\mathcal{E}I=1.80\mathrm{W}$. A resistive electrical load converts its share to Joule heating; another electrical load might convert some of it to mechanical work or light. The source term is available electrical work per time, not a complete cell heat budget: reaction entropy can also matter.

Define the delivery efficiency relative to the source's available electrical work, rather than to all chemical energy or to a complete charging cycle:Here $\eta =0.80$. The largest load power occurs at $R=r$: since $(R+r{)}^2\ge 4Rr$,Thus maximum load power and maximum delivery efficiency ask different questions. As $R\to \infty$, $V_L\to \mathcal{E}$ and $\eta \to 1$, but $I\to 0$ and $P_L\to 0$: a high nearly unloaded voltage supplies almost no power. As $R\to 0$, the model gives $V_L\to 0$, $P_L\to 0$ and internal power tending to ${\mathcal{E}}^2/r$. Real high-current operation can invalidate constant $r$ and $\mathcal{E}$; the mathematical maximum does not establish a permissible operating point for an actual battery.

A beam splitter is an optical instrument that routes an incident beam of light into transmitted and reflected beams. It also combines incident complex amplitudes: two inputs can contribute to the same output. A common geometry has four optical ports, with two chosen as inputs and two as outputs. A beam splitter changes the field; a photodetector supplies a measurement.^[ref]

For one illuminated input of a passive beam splitter, at specified wavelength, angle of incidence and electromagnetic polarization, define power transmittance $T=P_{\mathrm{transmitted}}/P_{\mathrm{in}}$, reflectance $R=P_{\mathrm{reflected}}/P_{\mathrm{in}}$ and radiometric absorptance $A=P_{\mathrm{absorbed}}/P_{\mathrm{in}}$. In steady operation, with no gain or other source, no net stored energy change, and all escaping light included in the transmitted or reflected collection,This is conservation of energy divided by incident power. If $T$ and $R$ count only the intended output beams, include a separate scattered or otherwise uncollected fraction $L$: then $T+R+A+L=1$. Missing output power need not be wave absorption. For an original specified example, $P_{\mathrm{in}}=10\mathrm{mW}$, $T=0.45$, $R=0.50$ and $A=0.05$ give $4.5\mathrm{mW}$ transmitted, $5.0\mathrm{mW}$ reflected and $0.5\mathrm{mW}$ absorbed; these are assumed values, not measurements.

A 50:50 beam splitter specifies equal output powers for one input, not equal complex amplitudes without a relative wave phase. Recombination needs the beam splitter scattering matrix, including its wave phases. A nonpolarizing beam splitter approximately divides both orthogonal linear polarizations in the same power ratio over its specified operating range; a polarizing beam splitter deliberately routes the two differently.

The useful surprise is that the same component divides power with one input and steers power by wave interference with two inputs. In a Michelson interferometer or Mach-Zehnder interferometer, mirror motion changes relative wave phase, turning a small change in optical path length into a measurable change in output power.

An actual teaching experiment prepares a Kool-Aid stock by weighing powder, transferring it quantitatively into a volumetric flask, and filling to the mark with water. A Genesys 30 spectrophotometer, blanked with water in a cuvette, scans for the peak absorbance wavelength. A Genesys 10 then measures absorbance at that wavelength, with a water reference blank. Each serial dilution transfers $50\mathrm{mL}$ of the preceding chemical solution to a $100\mathrm{mL}$ volumetric flask and fills to the mark; the protocol records the blank and sample readouts and repeats the halving sequence. These are prescribed experimental steps, not a published numerical data set.^[ref]

The experiment tests whether absorbance tracks the prepared concentration. Its concentration is powder mass per final volume, so the calibration does not by itself supply a single dye's molar absorption coefficient. The manual identifies loss of discrimination for very concentrated, very dilute, or very similar samples.^[ref]

To interpret such a calibration, hold cuvette orientation fixed with its clear faces in the light path, keep fingerprints and bubbles out of that path, and keep the geometric length unchanged. Mix each dilution completely. Re-read the reference blank during the sequence and re-read one standard to test drift. A separate preparation of a standard checks errors propagated through serial dilution; repeating only its instrumental reading does not test the transferred volumes. These controls follow from keeping $P_0$, $l$, and $c$ comparable between readings.

Three mechanisms explain why a straight line can fail. First, scattering of light can divert radiant power away from the photodetector, so cloudiness can raise apparent absorbance without the intended absorbing solute. A reference blank removes only losses shared with the sample. Second, stray light reaching the photodetector can make a strongly absorbing sample appear too transmissive. In an original model with extra detected radiant power $s{P}_0$ in both readings,As the ideal transmittance approaches zero, the reported absorbance approaches ${\log }_{10}((1+s)/s)$ for $s>0$. This finite ceiling is a model prediction, not measured instrument performance.

Third, chemical equilibrium can redistribute the absorbing chemical species when dilution, pH, or temperature changes. Even if each chemical species separately follows the Beer-Lambert law, their combined absorbance is $A=l{\sum }_i{\epsilon }_i{c}_i$, where $c_i$ is each species' molar concentration; changing those fractions need not preserve one effective molar absorption coefficient. Thus an unknown should be compared with standards under matching chemical solution conditions, within the tested concentration range. A good linear regression alone does not establish chemical selectivity.

Perceived amount or intensity of light from a stimulus. It is distinct from physical luminance and from lightness as a judgment related to surface reflectance.

An optical power meter makes the definition operational: collect a specified beam on a calibrated photodiode, measure its electric current, and infer incident radiant flux using spectral responsivity. In the manufacturer-authored Model 1830-R Series Optical Power Meters User's Manual by Newport Corporation, §5.5.1 specifies a concrete sequence: connect the detector and its calibration module, select watt mode and the source wavelength, block the beam and press ZERO, then unblock it and read the display. The stored background includes dark current and ambient light present during zeroing. For narrowband radiation,The electric current difference divided by spectral responsivity has units $\mathrm{A}/(\mathrm{A}{\mathrm{W}}^{-1})=\mathrm{W}$. For a stipulated $R=0.40\mathrm{A}{\mathrm{W}}^{-1}$ and difference $0.20\mathrm{mA}$, the inferred radiant flux is $0.50\mathrm{mW}$; these numbers illustrate the inference and are not reported measurements. The entire beam must hit the active area, and §5.6 calls for correct wavelength, background subtraction, and operation below detector saturation. If an optical attenuator is fitted, §5.4 requires the calibrated detector–attenuator pair and the matching meter setting.

The calibration itself must connect electric current to independently known incident power. NIST's Spectroradiometric Detector Measurements: Ultraviolet, Visible, and Near-Infrared Detectors for Spectral Power by Thomas C. Larason and others describes this chain. A cryogenic radiometer, an electrical substitution radiometer, compares temperature changes from absorbed light with those from known Joule heating (§5.2). Transfer and working detectors carry that watt scale to a spectral comparator (§5.1). A source, monochromator, focusing optics, shutter, beam splitter, and monitor photodiode illuminate a standard and test detector in turn; calibrated current-to-voltage electronics and voltmeters provide the readout (§§3.2.2–3.2.4, 4.3.1). At each wavelength, subtract blocked-beam signals and normalize each detector signal by the simultaneously sampled monitor signal. Comparison with the standard yields the test detector's spectral responsivity. NIST uses two working standards and alignment normal to the beam (§6.1.1).

Controls distinguish a smaller collected radiant flux from a faulty conversion: block and unblock the beam to check the baseline; check that its footprint fits the active area; verify the calibrated optical attenuator configuration; and test proportional response within the specified operating range. Source drift faster than monitor sampling is not removed. NIST discusses finite spectral bandwidth, stray light, temperature, and spatial response variations (§§3.1.1, 6.2, 7.2). A broadband optical spectrum requires the weighted integral in spectral radiant flux, rather than dividing by an arbitrary single spectral responsivity. These limitations explain why the meter's displayed watts need a stated collection boundary, spectral assumptions, and calibration conditions.

The Calvin cycle couples carbon fixation to use of ATP and NADPH. In a chloroplast it takes place in the chloroplast stroma. Its chemical reactions incorporate carbon dioxide, use NADPH-supplied electrons, and regenerate the molecules that accept further carbon dioxide.

In the standard Calvin cycle bookkeeping, three carbon dioxide molecules require nine ATP and six NADPH for one net three-carbon triose phosphate. A six-carbon sugar equivalent therefore corresponds to six carbon dioxide, eighteen ATP and twelve NADPH; subsequent sugar synthesis is separate. These are pathway requirements, not a universal measured photosynthesis yield. See OpenStax Biology 2e, 8.3: Calvin cycle bookkeeping.

Calling the Calvin cycle light-independent means its individual chemical reactions do not directly capture light; it does not mean the Calvin cycle runs only at night or independently of the supplies from light-dependent reactions.

A capillary wave is a wave along a fluid interface whose restoring stress is predominantly supplied by surface tension. A curved free surface requires a pressure jump by the Young–Laplace equation; increasing its corrugation also costs surface energy. In the ideal limit, inertia carries the interface through its flat position and the resulting oscillation propagates. When gravity also contributes appreciably, use the combined gravity-capillary wave model. Within the capillary wave regime, shortening a ripple makes it travel faster. ^[ref]

The laser-diffraction measurement of capillary waves below turns this mechanism into a test: set the frequency, measure the wavelength independently with light, and ask whether the dispersion relation follows. The theory is useful both for predicting how ripple wave packets separate and for inferring surface tension from their motion.