Out of Phase

The account of 28 October 1943

The canonical story of matter set out of phase with its surroundings is told about a small warship in a shipyard, and it goes like this.

USS Eldridge, hull number DE-173, was a Cannon-class destroyer escort: 306 feet long, 1,240 tons standard, four diesels driving generators driving two shafts, 21 knots, a crew of 15 officers and 201 enlisted men. In the account, she is at the Philadelphia Naval Shipyard, wrapped in cable and fed by generators, for a test of a field meant to bend light and radar around the hull. On 22 July 1943 the field is switched on and the ship goes nearly invisible, a greenish fog standing where she was, the crew afterwards badly ill. The gear is said to be out of adjustment, and the test is run again on 28 October 1943. This time the ship does not fade: she goes, in a flash of blue light, and is seen at Norfolk in Virginia, more than 200 miles away, about 320 kilometres, before returning to her berth.

The mechanism named in the telling is a military application of Einstein's unified field theory. The cost is paid by the crew.

What the letters actually describe

The oldest written source for the crew's condition is a set of letters signed Carlos Miguel Allende, written by Carl Meredith Allen, born 31 May 1925 at Springdale, Pennsylvania. They went to Morris Ketchum Jessup, an astronomer by training who had published The Case for the UFO in 1955. One letter carries a postmark of 5 January 1956 from Gainesville, Texas, and reached Jessup on 13 January; a second is postmarked 25 May 1956 from DuBois, Pennsylvania. Accounts differ on whether the correspondence and the annotated book that followed began in 1955 or in 1956, and both years are in print.

In the letters, men "Get Stuck" and hold still until another man touches them, or else they "Freeze". A freeze lasting more than a day sends a man, in his capitals, "Stark Raving, Gibbering, Running MAD". Deeply frozen men are described as breathing and looking ordinary while unaware of anything, in what he calls a "Nether World". Two men carrying compasses went into what he calls "The Flame", and he writes: "THEY BURNED FOR 18 DAYS". One man "walked 'throo' His quarters Wall in sight of His Wife & Child" and was not seen again. The field is put at roughly 100 yards out from each beam, an oblate spheroid, meaning a squashed ball, varying with the position of the Moon and with latitude. His summary line is: "The expieriment Was a Complete Success. The Men were Complete Failures."

The image most people carry, of sailors found fused into the deck plating and the bulkheads with steel closed around their bodies, is not in those letters. It belongs to the retellings that follow The Philadelphia Experiment: Project Invisibility by Charles Berlitz and William L. Moore, published by Grosset & Dunlap in 1979, which is also where the two-test structure and the 22 July date were fixed in popular form. That book has been noted for elements it shares with the novel Thin Air by George E. Simpson and Neal R. Burger, published in 1977, two years earlier; Simpson and Burger have said their book came first and was not taken from Berlitz and Moore. The 1943 letters and the 1979 book are two different documents, and the deck-fusing detail is in the second one.

The annotated copy, and how the Navy came to hold it

A paperback of Jessup's The Case for the UFO arrived at the Office of Naval Research in Washington, addressed to Admiral N. Furth, its margins filled with handwriting in three inks: blue, blue-violet and blue-green, reading as three separate voices, conventionally called Mr A, Mr B and "Jemi", discussing craft propulsion, races of beings and the Navy experiment. Captain Sidney Sherby got the book from Major Darrell L. Ritter on reporting aboard. Sherby and Commander George W. Hoover, the Special Projects Officer, had it retyped complete with every annotation and with the Allen letters, and Varo Manufacturing Corporation of Garland, Texas mimeographed it: close to 200 letter-size pages under plastic covers, typed by a high school student, Michael Ann Dunn, engaged by Varo's president Austin Stanton. That is the Varo edition.

How many copies exist is one of the places the record forks, and both figures stay on the table here.

• 25 copiesThe Office of Naval Research's own information sheet says the two officers "personally had the book retyped and arranged for the reprint, in typewritten form, of 25 copies", and that ONR holds no file copy of the annotated book, the officers and their belongings having left the office many years before.
• 127 copiesThe figure repeated through the research literature on the Varo edition and by the people who have handled surviving copies, privately distributed inside the Navy and among interested parties.

Jessup was born on 2 March 1900 near Rockville, Indiana, took a BSc in astronomy at Michigan in 1925 and an MSc in 1926, worked as an observer at the Lamont-Hussey Observatory, and set aside his doctoral dissertation in the spring of 1931 without taking the degree, though he was widely styled Dr Jessup afterwards. He earned his living selling automobile parts and taking photographs, and published four books on unidentified craft between 1955 and 1957. He was found on the evening of 20 April 1959 in a park in Dade County, Florida, in his station wagon with a hose run from the exhaust through a partly opened rear window; carbon monoxide poisoning was given as the cause and the death was ruled a suicide. On the record around it: his wife had separated from him about two years earlier, he had been in a serious car accident and was low about his recovery, and in mid-April 1959 he wrote to the radio host Long John Nebel a letter that has been described as a suicide letter. In the literature that follows the Varo edition, his death is instead tied to the annotated book and to pressure from the material.

What the Navy's own documents say

Two Navy documents answer the question directly, and it is worth reading what they say rather than a summary of them.

That answer is stated as an absence: documents have not been located. The same office also reviewed Eldridge's deck log and war diary from her commissioning on 27 August 1943 at the New York Navy Yard through December 1943, and traced SS Andrew Furuseth, the merchant ship Allende said he watched from, through the Tenth Fleet movement report cards now held at the National Archives at College Park, Maryland.

The two sets of dates

The claimed dates and the recorded dates are both written down. They sit alongside each other here.

The archive adds two further items in the same passage: a letter from Lieutenant Junior Grade William S. Dodge, USNR, master of Andrew Furuseth in 1943, "categorically denying that he or his crew observed any unusual event while in Norfolk", and the sentence "Eldridge and Andrew Furuseth were not even in Norfolk at the same time".

The men who served aboard have spoken for themselves. The Philadelphia Inquirer of 26 March 1999 covered the first Eldridge crew reunion in 53 years, at Atlantic City. Ed Wise, 74, of Salem, Indiana, called the experiment "somebody's pipe dream". Ted Davis, 72, of Grand Island, Nebraska, said "It never happened". Bill Van Allen, 84, of Charlotte, North Carolina, the ship's executive officer and later her captain, said he saw no sign of any experiment and had no idea how the stories began. Ray Perrino of Cranston, Rhode Island, said he had played along with people asking until they worked out he was pulling their legs.

Two threads that run through the story, and where each one lands

Both are checkable, and they land in different places.

Nikola Tesla. He died on 7 January 1943 in Room 3327 of the Hotel New Yorker in Manhattan, aged 86, and was found by a hotel maid on the morning of the 8th; the New York City medical examiner recorded coronary thrombosis. That is nine and a half months before the claimed October date. Within days the Office of Alien Property Custodian took his trunks and notebooks, although he had been a United States citizen since 1891, with his recent public remarks about a directed beam given as the reason. John G. Trump of MIT, a technical aide to the National Defense Research Committee, examined the material and reported nothing in it of significant value to the war effort. His nephew Sava Kosanovic, then Yugoslav ambassador, secured the bulk of the papers and had them shipped to Belgrade in 1952, where the Nikola Tesla Museum opened on 5 December that year. The counts differ: about 80 trunks were taken and about 60 are said to have arrived. The FBI released around 250 pages of Tesla material in 2016.

Albert Einstein. He really was working for the Navy in the window the story covers. Lieutenant Stephen Brunauer, who ran the high explosives research group at the Bureau of Ordnance, approached him in May 1943, and Einstein served as a part-time consultant through 1943 and 1944 on theoretical problems in explosives and explosions, and the problems put to him in that period are on that subject. He declined to travel from Princeton to Washington regularly on account of his age, so the problems were brought to his house. The National Archives holds 23 pages of Einstein's 1943 to 1944 letters to Brunauer in the Bureau of Ordnance records. The Navy's own line alongside that: "There is no indication that Einstein was involved in research relevant to invisibility or to teleportation", and his unified field theory was never completed.

The places the record is still open

These are the loose threads as they stand, each stated as a positive fact about the paperwork rather than a shrug.

• The newspaperAllende said the tavern incident was reported in a Philadelphia paper, and enclosed a clipping about a bar brawl in which waitresses describe sailors who "just sort of vanished into thin air". ONR's sheet records that the identity of the newspaper has never been established.
• The annotated bookONR states plainly that it does not hold a file copy. The physical object that started the Varo edition is not in the office that reprinted it.
• 25 or 127The two copy counts for the Varo edition come from the Navy's sheet and from the researchers who have handled surviving copies. Both figures remain in circulation.
• 1955 or 1956The mailing of the annotated book is dated by postmark accounts to 1955 and by ONR's sheet to 1956. The year is given two ways in the sources.
• 80 trunks or 60The Tesla estate count taken in 1943 and the count that reached Belgrade in 1952 differ by about twenty trunks, and no reconciliation of the two has been published.
• NRS-1978-26The full action report and war diary coverage for Eldridge, including the remarks section of the 1943 deck log, sits on that microfilm reel. It is a readable document, not a sealed one.

What was actually running in 1943

There was a programme in that period for making a ship invisible to something, it involved wrapping the hull in cable and pushing current through it, and it worked. It is called degaussing, and it was cancelling a field rather than a reflection.

A steel hull sitting in the Earth's magnetic field becomes a weak magnet, partly by induction while it sits there and partly permanently, hammered in during building. A magnetic mine on the seabed listens for that. Degaussing puts current through coils fitted around the ship so their field is equal and opposite to the ship's own, and the two add to nothing where the mine is listening. It is a cancellation, and cancellation is a phase problem: same size, opposite sign, same place.

The Navy's own description of the fit, in the same 1998 answer quoted above: "a system of electrical cables are installed around the circumference of ship's hull, running from bow to stern on both sides. A measured electrical current is passed through these cables to cancel out the ship's magnetic field." And on the limit, in the same passage: degaussing done correctly makes a ship "invisible" to the sensors of magnetic mines, and "the ship remains visible to the human eye, radar, and underwater listening devices."

The coils have names and jobs. The M coil, the main one, is a horizontal loop at about the waterline running the length of the ship, and it cancels the vertical part of the field, the part a mine below the keel cares about most. Forecastle and quarterdeck coils, tagged FP-QP and FI-QI, handle the fore-and-aft part. The A coil, athwartships, is a vertical loop running from the keel up to the main deck, dealing with the side-to-side part. Each is fed its own current, set to the ship's own signature, and re-set as she changes latitude, because the Earth's field she is standing in changes with her.

Where a ship carried no coils, the field was beaten out of her instead. Wiping, also called flashing, drags a heavy cable along the outside of the hull carrying a pulse of roughly 2,000 amperes, around two hundred times what a household kettle draws, and leaves the steel magnetically flattened for a few months. Deperming does the same job at a fixed range with the ship wrapped in temporary cable.

Charles Goodeve developed the British version for the Royal Navy from 1939 to 1940, after a German magnetic mine was recovered intact and taken apart. The scale of the fit-out is the part that gets missed: Liberty ships alone, carrying M coils only, accounted for about one per cent of the entire copper consumption of the United States. One per cent of a nation's copper, spent on making ships invisible to one particular kind of eye.

ONR's sheet offers a second and separate source for the stories of levitation and of effects on the crew, and it names a different ship: "experiments with the generating plant of a destroyer, the USS Timmerman. In the 1950's this ship was part of an experiment to test the effects of a small, high-frequency generator providing 1,000 hz instead of the standard 400hz. The higher frequency generator produced corona discharges, and other well known phenomena associated with high frequency generators. None of the crew suffered effects from the experiment."

So the 1943 shipyard held real coils, real currents and a real programme for disappearing from one kind of sensor. What it did not hold, on the paperwork located so far, is a coil set aimed at light. Everything below picks that gap up from the other end, because what phase itself turns out to do is stranger than a cancelled magnet.

Phase, in plain words

Draw a wave. Now draw a second wave of the same size and the same wavelength in the same place, but slid along a little. How much you slid it is the phase difference, measured in degrees, where 360 degrees is a full wavelength and puts you back where you started.

Add the two together and the size of what you get depends on that slide and nothing else. Two equal waves come out at twice the height when the slide is nothing, and at exactly zero when the slide is half a wavelength. In between, the height of the sum is two times the cosine of half the phase difference. That single line of arithmetic runs everything below it, from noise-cancelling headphones to gravitational wave detectors to a molecule going through two slits at once.

The everyday version is in a pair of headphones. A microphone on the outside hears the noise, the electronics turn it upside down and the driver plays it back, and if the upside-down copy reaches your eardrum at the same instant as the original, the two sum to nothing. Paul Lueg patented that idea in 1936, United States patent 2,043,416, and it sat for fifty years while electronics caught up. Lufthansa asked Sennheiser for a pilot's headset in 1984 and the LHM-45 shipped in 1987. Amar Bose worked his version out on a flight in 1978; his aviation headset shipped in 1989 and the consumer one in 2000. What active cancellation buys is about 20 decibels on top of what the ear cup already blocks by being in the way, which is a factor of ten in pressure and a hundred in energy.

The reason it works on aircraft rumble and gives up on speech is a stopwatch problem, and the numbers are worth having. To knock a wave down to a tenth, the copy has to arrive within 5.7 degrees of opposite. Sound travels 343 metres a second in air. At 100 hertz a wavelength is 3.43 metres, so 5.7 degrees is 5.5 centimetres of position or 159 millionths of a second of timing: comfortable. At 1,000 hertz the wavelength is 34 centimetres and the same 5.7 degrees is 5.5 millimetres and 16 millionths of a second. At 5,000 hertz it is about 1 millimetre. Nothing in the headset can place its anti-noise inside a millimetre of your eardrum, so above roughly one to two kilohertz the electronics stop helping and the foam takes over. Cancellation is a precision job, not a power job, and missing the phase does not give you partial cancellation: it gives you reinforcement.

The phase bench

Two wave trains, drawn live, with their sum underneath. Slide the phase and watch the sum vanish and come back. The wavelength control is set out as a sound wave in air so the numbers mean something: the readout gives the tone it corresponds to and how far apart, in centimetres, the two paths would have to be to produce the phase you have dialled in.

Matter is waves too

Here is the leap that makes phase a subject for an atlas of matter rather than a subject for acoustics. Louis de Broglie proposed in his 1924 thesis that every particle has a wavelength, and that you get it by dividing Planck's constant by the particle's momentum, its mass times its speed. Planck's constant is 6.62607015 × 10^-34 joule seconds, fixed exactly by definition since 2019.

Run that on things you can hold and the wave disappears. A 70 kilogram person walking at 1.4 metres a second has a wavelength of 6.8 × 10^-36 metres, which is smaller than a proton by a factor of about a hundred million million million. A 160 gram cricket ball at 40 metres a second comes out at 1.0 × 10^-34 metres. Nothing in a laboratory reads a length like that, which is why nobody notices they are a wave.

Shrink the mass and the wave comes back at sizes instruments can work with. An electron pushed through 100 volts has a wavelength of 0.123 nanometres, about the spacing between atoms in a crystal, which is exactly why Clinton Davisson and Lester Germer saw electrons diffract off a nickel surface in 1927 using 54 electronvolt electrons at 0.167 nanometres. A neutron slowed to 2,200 metres a second by bouncing around a warm moderator comes out at 0.18 nanometres, and neutron diffraction has mapped crystal structures on that number ever since.

The interesting question is how far up in mass this goes, and the answer keeps moving.

The current mark was set on 21 January 2026. Sebastian Pedalino, Bruno Ramirez-Galindo, Richard Ferstl and colleagues with Markus Arndt and Stefan Gerlich at the University of Vienna, working with Klaus Hornberger at the University of Duisburg-Essen, published in Nature, volume 649, pages 866 to 870, an interference pattern from sodium nanoparticles: clusters of 5,000 to 10,000 sodium atoms, the reported ones carrying more than 7,000 atoms and more than 170,000 daltons, about 8 nanometres across. Three diffraction gratings made of ultraviolet laser light, spaced about a ten-thousandth of a millimetre apart, held to about 10 nanometres. That is a lump of metal, wider than the gate of a modern transistor, delocalised across many times its own width. The paper puts its macroscopicity, a single number for how far into everyday scale a quantum experiment has reached, at 15.5, about ten times the 2019 figure of 14.1. The same apparatus works as a force sensor good to about 10^-26 newtons over roughly a hundredth of a second, which is the weight of about two thirds of one proton.

The two-slit bench

Drive the mass and watch the wavelength shrink. Everything on this bench moves at 200 metres a second, a real molecular beam speed, through two slits a tenth of a micrometre apart, which is close to the grating spacing in the 2026 experiment. The second slider shifts the phase of one slit on its own, which slides the whole band pattern sideways without changing anything else.

Two things come out of driving that slider. The first is that the pattern does not go away: at every mass on the slider there is a band spacing, and it is a real number. The second is that it stops being reachable. At the electron end the wavelength is larger than the gap between the slits, so the two stop acting as two slits and the beam just spreads, brightening and dimming as one as you shift the slit phase. At a dust grain the bands sit 3 × 10^-14 metres apart, a fortieth of the width of a single atom, and no screen built has that in it. What changes with mass is not whether the wave is there. It is the size of the ruler you would need.

Phase you can measure but not see

Everything above involves a wave you could point at. The next set does not, and those three measurements are the strongest case going that phase is a physical thing in its own right rather than a bookkeeping device.

A phase from a field the particle never entered

Yakir Aharonov and David Bohm published in Physical Review in 1959, anticipated by Werner Ehrenberg and Raymond Siday in 1949, the result that an electron travelling entirely through field-free space still picks up a phase set by how much magnetic flux is enclosed between its two possible paths. Flux is a plain quantity: how much field is threading through a given loop, area times field strength. No force acts on it at any point. The phase shift is the enclosed flux divided by a fixed quantum of flux, 4.136 × 10^-15 webers, times a full turn.

Robert G. Chambers measured it the following year at the H. H. Wills Physics Laboratory in Bristol, published in Physical Review Letters volume 5 on 1 July 1960. Charles Frank suggested the trick: put an iron whisker, a hair-thin crystal that holds its field inside itself, behind the charged wire that splits an electron beam into two paths. The electrons went past on either side, through space with no field in it, and the band pattern moved. Chambers took the Royal Society's Hughes Medal for it in 1994.

The objection to Chambers was that a whisker might leak a little field where the electrons went. Akira Tonomura's group at Hitachi closed it in 1986, published in Physical Review Letters volume 56 on 24 February. They made a doughnut about 6 micrometres across with a 4 micrometre hole out of permalloy, a nickel-iron alloy that takes up magnetism readily, clad it in superconducting niobium and a copper skin, and held it at 5 kelvin, five degrees above absolute zero. A superconductor expels magnetic field, so there was no field anywhere the electrons could go. Letting the beam that went through the hole interfere with the beam that went round the outside then read the phase between them directly, and it matched the prediction. Better than that: because the superconducting cladding forces the trapped flux into whole units, the measured phase came out at either nothing or exactly half a turn, depending on whether the number of units inside was even or odd. One experiment, two results: a phase from an untouched field, and flux arriving in lumps.

Geometry alone leaves a mark

Michael Berry showed in 1984 that a system taken slowly around a closed loop and brought back to its starting conditions does not always come back unchanged: it can carry an extra phase that depends only on the shape of the loop and not at all on how fast you went round. Akira Tomita and Raymond Chiao measured it two years later at Berkeley, published in Physical Review Letters volume 57 in 1986, by winding a single-mode optical fibre into a helix. The plane of the light's polarisation came out rotated by an angle equal to the solid angle its direction had swept out on a sphere. The telling part is that bending the fibre into a different shape made no difference so long as that solid angle stayed the same. Bitter and Dubbers confirmed the version for neutron spins the following year. The Aharonov-Bohm phase is one case of this larger pattern.

The phase that has to close on itself

In a superconductor, all the electrons pair up and share one wave. That wave has to come back to the same phase when you go all the way round a ring, which forces the magnetic flux through the ring to come in whole units. Bascom Deaver and William Fairbank at Stanford and Robert Doll and Martin Nabauer in Munich measured those units independently in 1961, and both got the same answer: 2.067833848 × 10^-15 webers, exact by definition since 2019. The number came out at Planck's constant divided by twice the electron charge, and that factor of two is the direct fingerprint of electrons travelling in pairs. To put the size of one unit in the mind's eye: send exactly one through a loop one centimetre square and the average field inside it is 21 picotesla, about one two-millionth of the Earth's field.

Turn that ring into an instrument and you get a SQUID: a superconducting loop with one or two weak links in it, whose current is a repeating function of the flux threading it with a period of exactly one unit. It is a two-slit interferometer for the superconducting phase. Brian Josephson predicted the weak-link behaviour in 1962 and took the 1973 Nobel Prize for it; Robert Jaklevic, John Lambe, Arnold Silver and James Mercereau built the first one at the Ford Scientific Laboratory in 1964.

What that buys is the most sensitive magnetometer built. A SQUID with a pick-up coil about a centimetre across reads down to around one femtotesla for each second of averaging, which is one fifty-thousand-millionth of the Earth's own field. That is the sensitivity that lets a machine outside your skull read the magnetic field made by currents inside your head, which runs from 10 femtotesla to a picotesla, and it is how magnetoencephalography works. Published roadmaps aim at a tenth of a femtotesla, which is roughly the magnetic noise floor of a human body itself.

Fields that move and change matter today

The account at the top is about a field doing something drastic to matter. That is worth setting beside what fields are measured doing to matter now, because the list is longer and stranger than most people carry.

A live frog, held up by a magnet

Andre Geim, with Jan Kees Maan, Humberto Carmona and Peter Main, floated a live frog in a 16 tesla magnet at the High Field Magnet Laboratory in Nijmegen in 1997, a field about five times that of a hospital scanner. Michael Berry and Geim wrote the theory up as "Of flying frogs and levitrons" in the European Journal of Physics, volume 18, pages 307 to 313, in 1997.

Living tissue is mostly water and protein, and both are diamagnetic, which means a magnetic field induces a tiny opposing field in them and pushes them away. It is a very weak effect and it acts on every gram of the animal at once, so there is no local strain: the frog is not hanging from anything, every part of it is being pushed equally. The condition for holding it up depends on the field times its own rate of change with height, and it works out to about 1,360 tesla squared per metre for anything with the density of water. Note what is missing from that: the mass. Density decides, not weight, so a frog and a hazelnut float in the same place.

The induced field inside the frog was about 1.5 gauss, roughly three times the Earth's, made by microscopic currents inside atoms rather than any current through the animal, so nothing was shocked. It was held in the energy minimum for up to 30 minutes and came out unharmed. Grasshoppers, water drops, flowers and hazelnuts floated too. A 3 millimetre plastic sphere sat stably between 69 and 86 millimetres above the coil, within a millimetre of where the calculation put it. Geim took the 2000 Ig Nobel Prize for the frog and the 2010 Nobel Prize for graphene.

There is a theorem in the way of this, and the way around it is instructive. Samuel Earnshaw proved in 1842 that no fixed arrangement of charges, magnets or masses can hold an object in stable equilibrium, because the energy has saddle points and no minima. The premise is that the object's own magnetism is fixed. For a diamagnet it is not: the field induces the magnetism, so the energy depends on the square of the field, and the size of a magnetic field in free space is allowed a minimum even though its separate components are not. Name the premise and the exception is right there in it.

A magnet locked in place by holes in a superconductor

Walther Meissner and Robert Ochsenfeld found in 1933 that a superconductor cooled through its transition pushes magnetic field out of itself entirely, which makes it a perfect diamagnet and gives repulsion but no sideways grip. Type II superconductors add the grip: field threads through them as vortices, thin tubes each carrying exactly one flux unit, and those tubes catch on defects in the material. Pin them and the magnet is held in position, not just held up, which is why the levitating-puck demonstration stays where you put it and why superconducting maglev works.

How much field a thumb-sized piece can hold: 17.6 tesla trapped at 26 kelvin, 26 degrees above absolute zero and about minus 247 degrees Celsius, in melt-processed gadolinium barium copper oxide doped with silver and shrink-fitted inside a steel ring, by John Durrell, David Cardwell and colleagues at Cambridge with the National High Magnetic Field Laboratory and Boeing, published in Superconductor Science and Technology on 25 June 2014 and magnetised from a 17.8 tesla field. That is about 3,500 times a fridge magnet, in an object you could close your hand around. On the transport side, JR Central's L0 maglev reached 603 kilometres an hour on the Yamanashi test line on 21 April 2015, and in 2025 a team at China's National University of Defence Technology took a tonne-class maglev vehicle to 700 kilometres an hour in under two seconds along a 400 metre line.

Sound holding things up, and light holding things still

A standing sound wave has still points every half wavelength, and small dense objects sit in them. At the usual 40 kilohertz in air a wavelength is 8.6 millimetres, so the still points are 4.3 millimetres apart, and that spacing is exactly why acoustic levitators hold millimetre-sized things and not larger ones. Asier Marzo, Adrian Barnes and Bruce Drinkwater at Bristol published the reference build, TinyLev, in Review of Scientific Instruments in 2017: two opposed bowls of 36 ordinary 40 kilohertz transducers each, run at about 20 volts and 10 watts total, holding objects up to 4 millimetres across and denser than 2.2 grams per cubic centimetre. Water, fused silica beads, small insects and electronic components all floated. The sound involved is fierce: levitators run above 150 decibels and up to about 166, and 160 decibels is around 2,000 pascals of pressure swing, about two per cent of atmospheric. The whole lifting force is the time-averaged push of that field, and because it is a standing wave it is a phase effect: move one emitter half a wavelength and the trap moves with it.

Light does the same job with a beam instead of a field of sound. Arthur Ashkin at Bell Labs showed in 1970 that laser light could push and trap micrometre-sized particles, and in 1986, with Joseph Dziedzic, John Bjorkholm and Steven Chu, demonstrated the single-beam gradient trap that everyone now calls optical tweezers. He trapped living viruses and bacteria in 1987 and took half the 2018 Nobel Prize in Physics for it, at 96. The force scale falls out of the momentum of the light: 100 milliwatts of infrared in water gives of order 44 piconewtons. Instruments work from a few tens of femtonewtons up to about 100 piconewtons, with trap stiffness reaching about one piconewton per nanometre. That range is not a coincidence: kinesin, the motor protein that walks cargo along a cell's tracks, stalls at about 5 to 7 piconewtons, RNA polymerase at about 25, and double-stranded DNA gives way and stretches at about 65. A beam of light is a mechanical tool at exactly the scale life works at.

The strongest fields made, and what stops them going higher

Three different jobs, three different records.

What sets the ceiling is one line of arithmetic. A magnetic field pushes outwards on whatever is making it, with a pressure equal to the field squared divided by twice the magnetic constant. At 100 tesla that is 4.0 gigapascals, close to 40,000 atmospheres, which is at the limit of the best steels and composites, and that is precisely why 100 tesla is where non-destructive magnets stop. At 1,200 tesla it is 573 gigapascals, about 5.7 million atmospheres, which is around 1.6 times the pressure at the centre of the Earth. Nothing yet built holds that, so the coil is spent on every shot.

What a field of that size does to the matter inside it

Two numbers say when a magnetic field stops nudging matter and starts running it.

The first is the magnetic length: the radius of the smallest circle an electron can be made to travel in. It is 25.7 nanometres divided by the square root of the field in tesla. At 100 tesla that is 2.6 nanometres; at 1,200 tesla it is 0.74 nanometres, which is getting down near the length of a chemical bond. That closing gap is what the Tokyo group means by reaching the quantum limit. The second is the cyclotron energy, how much energy is in one step of that circular motion: at 100 tesla it is 11.6 millielectronvolts for a free electron, which is the same as a temperature of about minus 139 degrees Celsius, or 134 kelvin, so at liquid helium temperatures, about four degrees above absolute zero, the field, not the temperature, decides what the electrons do.

The natural crossover, where the field's own length matches the size of an atom and atoms stop being round and start being needles, is about 235,000 tesla. That is found around neutron stars, at roughly 100 million tesla, some eighty thousand times the strongest field yet made indoors, and around magnetars, up to a hundred thousand million tesla. Set against the crossover itself, the strongest indoor field is about a two-hundredth of it, which is why laboratory fields rearrange the electrons inside solids rather than reshaping the atoms themselves. It is a threshold with a number on it, and the number says which side any given experiment sits on.

Inside that regime the effects are drastic enough. Klaus von Klitzing, with Gerhard Dorda and Michael Pepper, measured the Hall voltage of a silicon transistor at about 1.5 kelvin, a degree and a half above absolute zero, in a field of roughly 15 to 18 tesla on 5 February 1980 and found the resistance locked to fixed steps whose values contain nothing but Planck's constant and the electron charge. A dirty, irregular, impurity-riddled piece of silicon becomes an exact standard when the field is on. Since 20 May 2019 the value is exact by definition: 25,812.807 ohms. It has been the world's resistance standard since 1990 and reproduces to about one part in a thousand million, which is like measuring Sydney to Perth and being out by three millimetres. Its universality was checked head to head: Janssen and colleagues compared graphene against a gallium arsenide device in 2012 and found them agreeing to 8.7 parts in a hundred thousand million, which on the distance to the Moon is about three centimetres.

Push the field further and the material makes new pieces. Daniel Tsui and Horst Stormer, on ultra-pure gallium arsenide grown by Arthur Gossard at Bell Labs, found in 1982 that at high field and low temperature the steps appear at fractions nobody had predicted, starting at a third. Robert Laughlin explained it as an incompressible quantum fluid whose ripples carry a fraction of an electron's charge, and the third-of-a-charge was measured directly through electrical noise in 1997. Laughlin, Stormer and Tsui shared the 1998 Nobel Prize. Apply a magnetic field to a sheet of electrons and what comes out carries a third of the charge that went in.

Field also works as a thermodynamic handle, in the same way pressure and temperature do. Lanthanum cobalt oxide changes the spin arrangement of its cobalt ions at around 60 to 65 tesla and heads towards turning from an insulator into a metal; a 2024 review in the Journal of the Physical Society of Japan maps that phase diagram out to 600 tesla using flux compression and a strain gauge, and reads the smooth curves as two distinct condensates forming. In the other direction, field can create superconductivity instead of killing it: uranium rhodium germanium superconducts again around 12 tesla after having been switched off at lower field, and a europium tin molybdenum chalcogenide superconducts only between about 4 and 22 tesla, where the applied field cancels an internal one.

Making things hard to see

Bending light around an object is the part of the account with the most direct modern work behind it, and the work comes with dimensions.

Two papers in the same issue of Science on 23 June 2006 set out the method. John Pendry at Imperial College with David Schurig and David Smith at Duke, at page 1780, and Ulf Leonhardt at St Andrews, at page 1777. The idea is that Maxwell's equations keep their form if you stretch the coordinates you write them in, so you can distort space on paper, work out what electric and magnetic response a material would need to make light behave as if space really were distorted that way, and then build that material. Squeeze a point out into a sphere and light flows around the hole; anything inside is not lit and casts no shadow. It is a design procedure that tells you the required numbers at every radius, and those numbers are what a metamaterial is built to supply, using patterns of small broken metal loops that answer a radio wave the way an atom answers light.

That last line matters more than it looks. The cloak hid the object from the radar at the cost of being somewhat visible itself, and the authors said so in the paper. The reason is a limit with a proof behind it.

Light sent the long way round a cloak has further to travel than the light it is meant to match, so to arrive with the same phase it has to cover that extra path in the same time, which means going faster than light does in free space. A medium can do that for the phase of a wave, but only over a narrow band of frequencies, because the same physics that lets it do so makes its response change sharply with frequency. David Miller made the argument formally in Optics Express in 2006 and John Pendry made the speed version. Perfect invisibility is a single-frequency result. For any tolerance you set on the leftover scattering, causality puts a hard ceiling on the bandwidth you can have, and that ceiling falls as the object gets bigger: the larger the thing, the narrower the band. Later work gets the same bounds out of the general result for feeding a wave into any load without reflecting part of it back. In practice built cloaks work over a few per cent of their centre frequency.

The everyday version of the same phase trick is the Salisbury screen, patented by Winfield Salisbury and in the open literature since 1952. Put a thin resistive sheet a quarter of a wavelength in front of a metal backing. The sheet is made to about 377 ohms per square, a measure of how much a film resists current that comes out the same whatever size square you cut from it, and 377 ohms is the figure free space itself presents to a passing wave. The reflection off the sheet and the reflection off the backing come back half a wavelength out of step and cancel, exactly like the headphones. Stack several sheets and spacers and you get a Jaumann absorber: a measured six-layer design returns an average 30 decibels of reduction from 7 to 15 gigahertz, with its worst point 27 decibels at 8 gigahertz. Thirty decibels is a factor of a thousand in reflected power. The nearest built thing you can walk into is an anechoic chamber, the spiky blue-foam room where phones, cars and medical devices are tested for what they radiate: the spikes are a graded absorber doing the Salisbury job across a wide band by shape as well as by material.

How much that buys is set by the radar equation, where the range at which something is picked up goes as the fourth root of how much it reflects. Cut the reflection by a factor of four thousand and the range falls by a factor of about eight. The fourth root is why absorbers are hard work: enormous reductions in reflection buy modest reductions in range.

Plasma is the other route, and its physics is ordinary. A gas of free electrons has a natural frequency; radio waves below it are reflected or absorbed rather than passing through. The measured everyday case is a spacecraft coming back through the atmosphere: the hot sheath around it blocks radio and the crew lose contact for some minutes. Proposals to put a plasma sheath deliberately around a vehicle run into the engineering rather than the principle, since the electron density has to be held right across the surface, at the right thickness for whatever frequency is arriving, in fast-moving air, and the plasma glows and radiates on its own account. The Keldysh Research Center in Moscow has stated it built a plasma generator weighing under 100 kilograms. No independently verified reduction figures have been published for any of it, which is the difference worth holding on to: the Duke cloak is a fully specified experiment with published dimensions that works across a 32 millimetre shell at 8.5 gigahertz, and the vehicle-scale version is a statement without numbers attached.

What would be measured

Six things with an instrument attached and a quantity coming back. Each of these moves one of the open questions above rather than settling it by assertion.

Phase costs nothing to change and it changes everything about what two waves do together. That is the whole of the noise-cancelling headset, the whole of the gravitational wave detector reading a shift of about a hundred-millionth of a radian across four kilometres of arm, the whole of the SQUID, and the reason an eight nanometre lump of sodium was seen in two places at once in January 2026. What the bench above holds is a set of measured quantities with instruments beside them. What the account at the top of the page describes sits with the documents named alongside it, and both the claim and the archive are in print for anyone who wants to read them.

Keep exploring

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