Ten true things in physics that sound wrong

Negative temperatures are hotter than infinity

On the usual definition of temperature, a system can have a negative absolute temperature, and heat flows out of it into anything at any positive temperature, however high.

Temperature is defined by how a system’s entropy S changes when energy E is added: 1/T = ∂S/∂E. Entropy counts the ways the energy can be shared out. Usually more energy opens up more ways, so entropy rises and the temperature is positive. A system whose energy has a ceiling behaves differently. Once most of its parts sit in high-energy states, more energy leaves fewer ways, entropy falls, and the temperature is negative.

Negative here does not mean colder than absolute zero. Put such a system beside anything at a positive temperature and heat flows out of it, which is the test of being hotter. On the scale of heat flow, temperature climbs from +0 K through every positive value to infinity, wraps round to negative infinity, and ends at −0 K, the hottest state of all.

Nuclear spins at negative temperature were made in 1951. In 2013 a team from the Max Planck Institute of Quantum Optics in Garching and Ludwig-Maximilians University in Munich managed it for atoms that move, using potassium atoms held in a lattice of laser light.

Not every physicist accepts the definition. In 2014 Jörn Dunkel and Stefan Hilbert argued that Gibbs’s entropy, which never falls as energy rises, is the consistent one, and that temperature then stays positive. In 2015 Daan Frenkel and Patrick Warren replied that Gibbs’s version fails to give two bodies in equilibrium the same temperature, so negative temperatures are unavoidable when energy has a ceiling. The argument is about which entropy defines temperature, not about what the atoms did.

Braun et al., Science 339, 52 (2013); Purcell and Pound, Phys. Rev. 81, 279 (1951); Ramsey, Phys. Rev. 103, 20 (1956); the dispute: Dunkel and Hilbert, Nature Physics 10, 67 (2014), and Frenkel and Warren, Am. J. Phys. 83, 163 (2015).

Your head ticks faster than your feet

Clocks run faster the higher they sit, and an optical clock can see the difference across 33 centimetres.

In 2010 a team at NIST compared two aluminium-ion optical clocks and raised one by 33 centimetres. The raised clock ran fast by (4.1 ± 1.6) parts in 10¹⁷, which is what general relativity predicts and corresponds to a height difference of 37 ± 15 centimetres.

The familiar explanation, that gravity is weaker higher up, is wrong. What sets a clock’s rate is the gravitational potential: the energy it takes to lift each kilogram from the floor to the clock’s height. Near the ground that energy is g·h, and a clock at height h runs fast by the fraction g·h/c². The calculator below does exactly this. It uses the same g at every height, so the pull never weakens, and the whole effect still appears.

The centre of the Earth makes the point sharper. Gravity there is zero, yet the potential is lowest, so a clock at the centre runs slowest. Over the age of the Earth it would fall about 2.5 years behind a clock on the surface. A published transcription of a talk by Richard Feynman gives a difference of one or two days rather than years, a slip that has since been repeated in a few places.

Over an 80-year life the gain at 33 centimetres is about 90 billionths of a second. Slide the height to your own and see what a lifetime at that height gains over a lifetime at floor level.

Chou, Hume, Rosenband and Wineland, “Optical clocks and relativity”, Science 329, 1630 (2010); the 90-nanosecond lifetime figure is from Physics World; potential rather than field strength: Gravitational time dilation; the Earth’s centre: Uggerhøj, Mikkelsen and Faye, “The young centre of the Earth”, Eur. J. Phys. 37, 035602 (2016).

A warmed rubber band pulls tighter

Heat a stretched rubber band and it shrinks. Almost everything else expands.

A rubber band is a tangle of long molecules. Stretching straightens them into line, and a lined-up chain can be arranged in far fewer ways than a tangled one. In the simple model of rubber, the internal energy does not change with stretch, so the band’s pull is entirely this loss of ways to arrange the chains. Heat makes the molecules jostle harder, which favours the many tangled arrangements, so a warm band under load shortens and lifts a hanging weight.

The same argument works in reverse. A band stretched quickly warms up, and a stretched band released suddenly cools below room temperature. The shortening on heating needs a decent stretch: the standard demonstration hangs a weight that lengthens the band by at least half, then warms it with a lamp. At small stretches ordinary thermal expansion wins.

John Gough noticed the effect in the early 1800s and James Joule measured it in the 1850s. It now has both their names.

Brzinski and Daniels, “Stretching Rubber, Stretching Minds” (the heating, the cooling and the entropy model); Gough–Joule effect (dates, and the 50% demonstration quoted from Nagdi, Rubber as an Engineering Material); small-stretch behaviour: Caborgan, Muracciole, Wattrisse and Chrysochoos, EPJ Web of Conferences 6, 25008 (2010).

A cart can drive straight downwind faster than the wind

On 2 July 2010 a wind-powered cart travelled directly downwind at nearly 2.8 times the speed of the wind.

The cart, Blackbird, had no engine and no sail. A large propeller sat on top, geared to its wheels. On El Mirage Dry Lake in California it reached 27.7 miles per hour (44.6 km/h) in a sustained 10 mph (16 km/h) wind, driven by Rick Cavallaro and certified by the North American Land Sailing Association.

It sounds like a machine pulling itself up by its own bootlaces, but the wind is not the only thing the cart works against. The ground and the air move at different speeds, and the cart takes energy from that difference. Once the cart is faster than the wind, the ground is the fastest-moving thing relative to the cart, so the wheels draw power from the ground and drive the propeller, which pushes against the air. In 2012 the same cart went directly upwind at about twice the wind speed.

The result has been doubted in public. In 2021 the UCLA physicist Alexander Kusenko questioned the run, citing possible gusts. After model experiments and a re-examination of the original data he conceded a bet on a technicality, but said he still saw no evidence that the cart beat the wind within the terms of the experiment.

NALSA record page (archived 2010); Blackbird (wind-powered vehicle) for the mechanism, the 2012 upwind record and the 2021 dispute.

Light bounces off light

Two photons can scatter off each other. The LHC has now seen it.

Classical electromagnetism says light waves pass through one another without a trace. Quantum electrodynamics disagrees: a photon can briefly turn into an electron and a positron, and those can scatter another photon. The calculation goes back to Euler and Köckel in 1935 and Heisenberg and Euler in 1936.

Lead nuclei carry intense electromagnetic fields, so when two of them pass close without touching, their fields act as beams of photons. ATLAS reported strong evidence for the scattering in 2017, at 4.4 standard deviations, and CMS followed in 2018 with 4.1. In 2019 ATLAS published the observation: 59 candidate events against about 12 expected from background, a significance of 8.2 standard deviations.

The measured rate came out at 78 nanobarns, between 1.5 and 1.7 times the predicted 45 to 51, a difference of under two standard deviations. In everyday conditions the effect is far too weak to notice, so two torch beams still cross cleanly.

ATLAS Collaboration, “Observation of light-by-light scattering in ultraperipheral Pb+Pb collisions with the ATLAS detector”, Phys. Rev. Lett. 123, 052001 (2019), which also cites the 1935 and 1936 papers and the 2017 evidence.

Nearly all the mass of a proton is not in its quarks’ masses

The three quarks inside a proton supply about 1% of its mass. Even counting the quark-mass term in full, it is about 9%. The rest is energy.

A proton holds two up quarks and one down quark. Add up their own masses, a few million electronvolts each, and you reach about 1% of the proton’s 938 million. The Higgs field is the origin of those quark masses.

The remainder is the energy of the strong force at work inside the proton. A lattice calculation of quantum chromodynamics splits the proton’s mass into four parts: the quark-mass term (9%, counting the up, down and strange quarks that flicker in and out of the vacuum), the energy of the quarks’ motion (33%), the energy of the gluon field (37%) and a quantum correction called the trace anomaly (23%). Mass and energy are the same currency, so that energy weighs.

Other lattice work reproduces the proton’s mass from first principles and agrees with experiment. Most of the mass of every atom, and so of you, is this energy of the strong force.

Yang et al., “Proton mass decomposition from the QCD energy momentum tensor”, Phys. Rev. Lett. 121, 212001 (2018); Dürr et al., “Ab initio determination of light hadron masses”, Science 322, 1224 (2008); summary in Proton.

Stirred tea leaves gather in the middle, and the reason shapes rivers

Spinning water should fling tea leaves outwards. They end up in the centre of the cup.

Stir a cup and the water spins, piling slightly higher at the rim. That slope creates a pressure that pushes inwards, and in the bulk of the water it exactly balances the spin. Near the bottom, friction slows the water, so it needs less inward push to stay on its circle, but the pressure from the raised surface is unchanged. The unbalanced pressure drives a flow along the bottom towards the middle, carrying the leaves with it. The water returns along the surface and down the walls.

In 1926 Einstein used the same idea to explain why rivers meander. In a bend the water surface stands slightly higher on the outer side, and friction with the bed sets up the same circulation: the bed flow carries eroded material from the outer bank to the inner one. The outer side deepens, the inner side silts up, the bend sharpens, and because the water has inertia the effect peaks beyond the tightest point, so bends drift downstream.

Einstein was not the first. James Thomson had shown the teacup flow in 1857 and linked it to river sinuosity in 1876, and a 1911 physics textbook explains it clearly. Real meandering is far more complicated than this one mechanism, and Einstein’s paper is rarely cited in the river literature.

Einstein, “Die Ursache der Mäanderbildung der Flußläufe und des sogenannten Baerschen Gesetzes”, Die Naturwissenschaften 14, 223 (1926), as set out, with Thomson and Edser, in Silagadze, “Einstein, tea leaves, meandering rivers…” (arXiv:2503.23847); Tandon and Marshall, “Einstein’s tea leaves and pressure systems in the atmosphere”, The Physics Teacher 48, 292 (2010); Alpher and Herman, “Tea leaves, Baer’s law, and Albert Einstein”, Am. J. Phys. 28, 748 (1960).

The Sun’s core makes less heat per cubic metre than you do

A resting adult releases more than three times as much heat per cubic metre as the very centre of the Sun.

The Sun gives out 3.828 × 10²⁶ watts across a volume of about 1.41 × 10²⁷ cubic metres, an average of 0.27 watts per cubic metre. A standard model of the Sun puts the peak, at the exact centre, near 280 watts per cubic metre. That falls to about 100 at a tenth of the way to the surface and below 1 at a quarter of the way, where 99% of the Sun’s power has already been made. An adult at rest burns roughly 80 watts in about 0.075 cubic metres, around 1,000 watts per cubic metre. The science broadcaster Karl Kruszelnicki likened the core to a compost heap.

The Sun is hot because it is enormous and its heat escapes slowly, not because fusion is intense. Fusion in the core is a gentle simmer spread over a huge volume.

Core profile from the Lawrence Livermore National Laboratory model, “Layers of the Sun” (archived 2002), via Solar core; the compost comparison: Kruszelnicki, ABC Science (2012); luminosity and volume from Sun; the human figure is an estimate of resting metabolism (about 80 W) over an assumed 75 kg body at the density of water.

The Sun’s atmosphere is hundreds of times hotter than its surface

The visible surface is about 5,500 °C. The corona above it is typically 1 to 2 million °C, and NASA gives up to 2 million. Nobody can yet fully explain the heating.

Moving away from a fire should feel cooler. Above the Sun’s surface the temperature instead leaps by a factor of up to roughly 350 (346 in kelvin). The ratio of the two Celsius numbers, 364, would flatter the jump. NASA calls what heats the corona “a major unsolved puzzle in the study of the Sun”. Two families of explanation are in play: waves rising from the surface, and magnetic energy released by reconnection in flares and the many small events called nanoflares. At least some of the heat is known to come from reconnection.

This breaks no law of heat, because the energy does not flow up from the cooler surface as heat, which the second law forbids. It is carried up as magnetic and wave energy and turned into heat in the corona. The corona’s thinness explains something else: with only 10¹⁵ to 10¹⁶ particles per cubic metre, it holds and radiates very little energy in total even at that temperature.

NASA, Sun facts; the density, and the wave and reconnection explanations, from Sun, which cites Erdélyi and Ballai (2007) and Russell (2001).

A star that loses energy can get hotter

A ball of ordinary gas held together by its own gravity has negative heat capacity: take energy away and its temperature goes up.

For a classical, nonrelativistic, ideal gas the virial theorem ties the ball’s thermal energy to its gravitational energy: the thermal energy is minus half the gravitational energy. When the ball radiates, it shrinks, and gravity pulls the gas inwards. About half the energy released goes out as light and the other half heats the interior.

So a star of this kind that loses energy with nothing to replace it contracts and gets hotter, not cooler. While fusion makes up what the star radiates, the effect keeps it steady: a core that heats up burns faster and pushes back. The condition matters. A white dwarf is held up by degenerate electrons, not by hot gas, and it has no fusion. It does what a hot body normally does: it radiates and cools, its interior falling from about 100 million kelvin soon after formation to under a million for the coolest known.

The same behaviour makes some systems of stars unstable. V. A. Antonov showed in 1962 that a self-gravitating cluster of point masses has no state of maximum entropy. Donald Lynden-Bell and Roger Wood explained it in 1968 through negative heat capacity and named the runaway the gravothermal catastrophe.

Princeton University Press, chapter 3, “Stellar Physics”; White dwarf; Glass, “Gravothermal catastrophe, an example” (arXiv:1008.0448), for Antonov, and Lynden-Bell and Wood, MNRAS 138, 495 (1968).

Where each claim comes from

Every fact above ends with its references. What was opened, as of October 2026:

• Read in full: Braun et al.; Chou et al.; the ATLAS paper; Yang et al.; Uggerhøj et al.; Silagadze; Brzinski and Daniels; the Princeton chapter on stellar physics; Glass; the archived NALSA record page, the archived Livermore model table and Kruszelnicki’s column.
• Read as an abstract or record only: Dürr et al.; Dunkel and Hilbert; Frenkel and Warren; Tandon and Marshall; Lynden-Bell and Wood; Purcell and Pound and Ramsey (their result is as reported in Braun et al.); Caborgan et al. (full-text transcription read, figures not inspected).
• Not opened: Einstein’s 1926 paper itself (its content is as set out in Silagadze), and the Euler–Köckel and Heisenberg–Euler papers (cited as ATLAS cites them).
• Reference pages: Wikipedia pages for the Gough–Joule effect, Blackbird, gravitational time dilation, the proton, the Sun, the solar core and white dwarfs; NASA, Sun facts; Physics World.

What is estimated or still open

• Negative temperature. The 2013 experiment covers atoms in a lattice. That such a state is hotter than every positive temperature follows from the usual (Boltzmann) entropy and the direction of heat flow. Physicists who prefer Gibbs’s entropy deny negative temperatures exist.
• Clock at 33 cm. The measured shift, (4.1 ± 1.6) × 10⁻¹⁷, is about two and a half times its uncertainty. It agrees with the prediction; it is not a precision test at that height.
• Blackbird. The 2.8 ratio is from NALSA’s certified run; the 2021 dispute above is recorded in Wikipedia’s article.
• Light by light. The measured rate is 1.5 to 1.7 times the predictions, under two standard deviations above them.
• Proton mass. The four-way split comes from one lattice calculation and one renormalisation scheme. The shares depend on the energy scale and scheme chosen, so other ways of organising the calculation give other splits.
• Tea and rivers. The cup mechanism is established. Einstein’s river argument is one account of meanders among several.
• Sun’s centre. About 280 W/m³ comes from a standard model of the Sun’s interior, not from direct measurement.
• Resting adult. The 1,000 W/m³ figure is a rough estimate: 80 W of resting metabolism and an assumed body volume.
• Corona heating. The temperatures are measured. What supplies the energy is not settled.
• Negative heat capacity. The result holds for classical ideal gas; it fails for degenerate matter.