The Physics of Invisible Radiation: What Reaches You

Your Eyes Are Open to One Octave

Stand outside at noon and roughly a kilowatt of solar power lands on every square metre around you. A little under half of it is light you can see. The rest, mostly near-infrared, arrives, warms the pavement and your sleeves, and registers on your eyes as nothing whatsoever.

Human vision runs from about 380 nanometres at the violet end to about 700 at the red end. That is a factor of 1.84 in wavelength: less than one octave, in the sense a musician would mean the word. The electromagnetic spectrum itself runs from extremely low frequency radio waves whose wavelengths are measured in thousands of kilometres down to the gamma rays recorded by observatories such as LHAASO, with wavelengths below 10⁻²¹ m. Lay that out logarithmically, which is the only way it makes sense, and the span is more than twenty-five orders of magnitude, something over eighty octaves. The slice your retina answers to is about one percent of it.

It is worth being precise about why the window sits where it does. Liquid water is nearly transparent between roughly 400 and 700 nanometres and strongly absorbing on either side; the Sun’s output peaks in the same place; and the photon energies there, 1.8 to 3.3 eV, are large enough to flip a molecule of rhodopsin from one shape to another but small enough not to tear it apart. Evolution did not choose that window. Chemistry and the atmosphere chose it, and the eye was built to fit.

Everything else is invisible radiation, which is a category rather than a substance. The electromagnetic spectrum accounts for most of it but not all, because cosmic rays, muons and neutrinos arrive constantly too and none of them are light. What follows is a tour of that category organised around one question: how strongly does each kind couple to matter? That, and not invisibility, is what decides whether we can catch it.

The Invisible Light That Matter Grabs Easily

Start at the long-wavelength end. Radio photons at 100 MHz carry 4.1 × 10⁻⁷ eV each, four hundred nanoelectronvolts. There is no molecular transition that small in your eye or in almost anything else, so radio does not get absorbed one photon at a time; it pushes charges around collectively. That is why it passes through plasterboard, and equally why a thin continuous sheet of metal stops it dead. Seawater, which conducts, has a skin depth of about 2.5 cm at that frequency, which is why submarines are talked to at kilohertz instead.

Microwaves at 2.45 GHz carry about 10 µeV and couple to the rotational modes of the water molecule. Penetration into liquid water is roughly 1.4 cm, which is exactly why a microwave oven heats the outer shell of a potato and then waits for conduction to finish the job. Infrared at 10 µm carries 0.124 eV, enough to excite molecular vibration rather than rotation: water absorbs it within about 12 µm, so thermal infrared never gets past the outermost layer of your skin. You feel it as heat because that is precisely where it stops.

Then comes the window, and then ultraviolet, where photon energies above about 4 eV begin breaking chemical bonds instead of merely shaking them. That is the whole story of sunburn and of ultraviolet damage to DNA. X-rays at 100 keV ionise freely and interact with the inner electrons of heavy atoms: the NIST tables give a mass attenuation coefficient of 0.1707 cm² g⁻¹ in water and 5.549 cm² g⁻¹ in lead, which works out at a mean free path of 5.9 cm of water or 0.16 mm of lead. Gamma rays at 1 MeV fall to 0.0710 cm² g⁻¹ in lead, so about 8.6 cm of lead cuts the beam by a factor of a thousand.

Notice the pattern running through all of that. Every one of those bands is invisible to you, and every one of them is easy to stop and easy to detect. Radio needs a wire. Infrared needs a thermopile. X-rays need a scintillator and a photodiode. We have built whole industries on all of them — broadcasting, radar, thermal imaging, radiology, sterilisation — precisely because they couple to ordinary matter strongly. Invisibility turned out to be no obstacle at all.

When the Coupling Collapses

Now change category. Cosmic rays are not photons: they are mostly protons and heavier nuclei arriving from the Galaxy and beyond, at energies from a gigaelectronvolt up to the absurd 10²⁰ eV of the rarest events. A 1 GeV proton has an inelastic cross-section on an air nucleus of roughly 3 × 10⁻²⁵ cm². It therefore penetrates about 90 g cm⁻² into the atmosphere, twenty kilometres up, before it hits something. Essentially no primary cosmic ray reaches sea level. What reaches you is the debris.

Most of that debris at ground level is muons: heavy cousins of the electron, made in the first collision, living 2.2 µs in their own frame and surviving the trip down only because of time dilation. Roughly one crosses every square centimetre of you every minute. A typical sea-level muon carries about 4 GeV and loses close to 2 MeV for every gram per square centimetre of material it crosses, which buys it some seven metres of rock. Give it a teraelectronvolt and it reaches a kilometre down.

Here is the subtlety that matters for everything after this. A muon is not weakly interacting. Its coupling is ordinary electromagnetism and it ionises atoms continuously along its path, dozens per centimetre of water. It penetrates because each of those interactions costs it only tens of electronvolts, not because interactions are rare. Penetration depth and coupling strength are different quantities, and the muon is the cleanest case where the two come apart.

Neutrinos are the other extreme, and the drop is not a matter of degree. A 1 MeV solar neutrino has a cross-section on a nucleon of order 10⁻⁴⁴ cm², some twenty orders of magnitude below the muon’s effective ionisation coupling and twenty-one below a 1 MeV gamma ray in lead. The mean free path that implies in solid lead is about 1.5 × 10¹⁷ m, roughly sixteen light-years. The Sun is transparent to them, the Earth is transparent to them, and about 65 billion of them cross every square centimetre of you every second without doing anything at all.

So here is the hinge of the subject, worth stating flatly. Invisibility and weak interaction are not the same property. Radio waves are invisible and trivially easy to catch. Neutrinos are invisible and nearly impossible to catch. The difference is not that one is better hidden than the other; it is twenty-one orders of magnitude of interaction cross-section. Nearly every argument that goes wrong about invisible radiation goes wrong at the point where those two ideas get merged.

Select band or particle Visible light

Energy: 2.25 eV (550 nm green)

Wavelength: 550 nm

Cross-section: ≈ 2 × 10⁻²⁶ cm² per water molecule

Penetration (1/e): ≈ 18 m in pure water

Shielding needed: Anything opaque. A sheet of card does it.

Predicting Something Nobody Could See

In December 1930 Wolfgang Pauli wrote to a meeting of radioactivity specialists in Tübingen, addressed them as dear radioactive ladies and gentlemen, and apologised for not coming because of a ball in Zurich. The letter proposed a neutral, nearly massless particle emitted alongside the electron in beta decay, to rescue conservation of energy from the awkward fact that the electron came out with a spread of energies rather than one fixed value. Pauli called it a desperate remedy and admitted he had done the thing a theorist is not supposed to do: invent a particle that could not be observed.

Enrico Fermi gave the idea a working theory in 1934, named it the neutrino, and wrote down a four-fermion interaction that correctly predicted the shape of the beta spectrum. Nature rejected the paper as too speculative. In the same year Hans Bethe and Rudolf Peierls took Fermi’s theory and did the arithmetic nobody wanted: they put the cross-section for a neutrino to interact with matter below 10⁻⁴⁴ cm², and concluded that there was no practically possible way of observing one.

They were right about the number and wrong about the conclusion, and those are separate claims worth keeping separate. The cross-section stands; modern measurements agree with it to within a factor that would not have embarrassed them. What failed was the step from absurdly small to impossible, which quietly assumed the detector volumes and source intensities available in 1934. The full arc from that letter to applied energy research deserves reading in its own right, as does the year-by-year timeline. For this article the point is narrower: the first quantitative thing anyone established about neutrinos was that they were undetectable, and the calculation was correct.

The Line That Kept Moving

Clyde Cowan and Frederick Reines broke the prediction in 1956 by changing one variable. They put a few hundred litres of liquid scintillator and water next to the Savannah River reactor, which delivered of order 10¹³ antineutrinos per square centimetre per second, and watched for a specific double signature: a positron annihilation followed microseconds later by a neutron capture on cadmium. They sent Pauli a telegram. The Bethe-Peierls cross-section had not been overturned. The flux and the target mass had simply grown enough to beat it.

The line kept moving after that. Raymond Davis’s chlorine tank in the Homestake mine found about a third of the solar neutrinos the Sun’s models demanded, a discrepancy that stood for three decades; the resolution, that neutrinos change flavour in flight and must therefore have mass, brought Takaaki Kajita and Arthur McDonald the 2015 Nobel Prize. Then the energy scale went the other way entirely: IceCube turned a cubic kilometre of Antarctic ice into a telescope with 5,160 light sensors, and that work brought Francis Halzen the 2026 Nobel Prize in Physics for the discovery of high-energy neutrinos of astrophysical origin. If you want one number for how much the coupling changes across that range, a 1 PeV neutrino has a cross-section near 10⁻³² cm², twelve orders above the solar value, and at those energies the Earth itself becomes partially opaque.

The last two years have been the steepest part of the curve. In August 2026 the XENONnT collaboration reported the first real-time measurement of low-energy solar neutrinos scattering off electrons, with a threshold near 17 keV. Borexino, which pioneered real-time solar neutrino spectroscopy, worked down to 335 keV. Most of the new signal is pp neutrinos, from the reaction that actually powers the Sun. What that opened up is substantial, with the caveat that it is a preprint still awaiting independent review and should be read as one.

Alongside it, LUX-ZEPLIN reported evidence at 4.5 standard deviations for coherent elastic neutrino-nucleus scattering from solar boron-8 neutrinos in 5.7 tonne-years of xenon exposure, the strongest detection yet of that process from an astrophysical source. Four and a half sigma is evidence rather than the conventional five-sigma discovery, and the collaboration says so. And JUNO, from 59.1 days of data in 20 kilotonnes of liquid scintillator, measured Δm²₂₁ = (7.50 ± 0.12) × 10⁻⁵ eV², a relative precision of 1.55 per cent and a factor of 1.6 better than every previous measurement combined.

The pattern is worth naming. Every generation’s undetectable became the next generation’s measurement, and the generation after that used it as an instrument. That is not a slogan about optimism. It is the documented history of this entire category, band by band.

What We Already Harvest

It is easy to treat invisible radiation as something to be measured. It is more accurate, and more interesting, to notice how much machinery we already run on it.

A silicon photovoltaic cell has a band gap of 1.12 eV, which corresponds to a cut-off wavelength of about 1,100 nm. Everything between 700 and 1,100 nm is near-infrared, invisible, and it is a substantial share of the photons a panel actually converts. The thing on your roof is already an invisible-radiation harvester and nobody finds that remarkable.

A thermoelectric generator works from a temperature difference, which is to say from a flux of heat you cannot see. The Seebeck coefficient converts ΔT directly into volts with no moving parts, and radioisotope thermoelectric generators built on that principle have powered the Voyager probes since 1977. Passive RFID and NFC tags go further and carry no energy store at all: they rectify the reader’s ambient 13.56 MHz field and run their own logic on tens of microwatts of it.

Then there is imaging with particles instead of photons. Muon tomography uses the cosmic-ray muon flux as a free, always-on probe. Because a muon’s energy loss tracks the density of what it crosses, counting muons arriving through an object from many directions reconstructs its interior. The ScanPyramids collaboration used nuclear emulsion films, then scintillator hodoscopes, then gas detectors, to find a previously unknown void at least 30 metres long above the Grand Gallery of Khufu’s pyramid, reported in Nature in 2017 and the first major internal structure identified there since the nineteenth century. The same technique imaged the melted fuel inside the Fukushima Daiichi reactor cores, where no instrument could be sent.

And CEνNS, the process LZ has now seen coming from the Sun, is under development as a reactor-monitoring tool. Because the coherent cross-section scales roughly with the square of the neutron number, the interaction rate is enormously enhanced relative to ordinary neutrino scattering, and a detector of kilogram scale could in principle watch a reactor’s fuel composition from outside the containment building. Invisible radiation is already an engineering input rather than a curiosity. The open question is only how far down the coupling scale that remains true.

The Open Frontier, and a Change of Question

Which brings us to the part of the field that is not settled, and ought to be described that way.

The Neutrino Energy Group, led by Holger Thorsten Schubart, works on what it calls neutrinovoltaic conversion. The specific technical claims are testable, and are being tested. But the contribution worth naming first is not a device at all. It is a change of question.

Every institution in the previous two sections asks: how do we detect this radiation? That question has produced extraordinary physics and several Nobel Prizes. Schubart’s move was to ask a different one: what can this radiation make matter do? Those are not the same question, and the second has been asked far less often. Detection optimises for a clean, rare, unambiguous event inside a very large and very quiet volume. Conversion optimises for a small, continuous, directed effect inside a structured material. A detector physicist and a materials engineer looking at the same flux want almost opposite things from it. That reframing is the original move here, and it is the reason to call Schubart a pioneer of the application side of this subject rather than of its underlying physics.

The engineering follows from the reframing. The twelve-layer neutrinovoltaic converter is a metallic foil carrying twelve to twenty alternating ultra-thin layers of graphene and doped silicon, deliberately asymmetric, because a symmetric structure cannot rectify a symmetric input. That is the same requirement that makes a diode a diode and a ratchet a ratchet. A 200 by 300 mm plate is described as delivering about 1.5 V at 2 A, roughly 3 W. The Neutrino Power Cube packages those plates into a suitcase-sized unit rated at 5 to 6 kW, which is where the engineering difficulty becomes visible: 5,000 watts at 3 watts a plate implies something on the order of two thousand plates inside that volume, which makes packing density and manufacturing yield as decisive as the physics of any single plate.

The theoretical frame is the Schubart Master Formula, published as P(t) = η · ∫ᵥ Φ_eff(r,t) · σ_eff(E) dV, with η a conversion efficiency, Φ_eff an effective flux density summing several channels — neutrino momentum transfer, cosmic muons, ambient electromagnetic fluctuations, thermal gradients — and σ_eff a structural coupling coefficient for the layered material. Its real virtue is that it is falsifiable. Write a claim as an integral over measurable quantities and you have specified in advance exactly which measurements would refute it.

That is how the group frames the matter itself, and it is the strongest framing available to it. The Mathematics Beats Opinion statement proposes stripping the question of belief, authority and headlines and leaving only quantities that can be measured: energy entering the system, interaction channels, material coupling, electrical output, losses, reproducibility. Its companion document sets out a four-gate standard — mathematical consistency, experimental proof, independent reproducibility, technical feasibility — and ends by saying that people remain responsible and reality gets the final vote.

Those four gates are a standard still to be met, not an achievement already banked. Independent reproduction of continuous kilowatt-scale output has not been published, and the group’s own language describes verification as ongoing. Saying so plainly is not a hedge against the work; it is the only thing that makes admiration for it mean anything. A research programme that writes down the conditions under which it would be shown wrong, and then invites people to apply them, is attempting something considerably harder and more honest than a programme that simply announces a result. The gates are the right gates. Whether neutrinovoltaic technology passes them is an empirical question, and the answer is not in yet.

What Becomes Measurable Next

Three thresholds are visibly moving right now.

The cosmic neutrino background is the oldest signal there is: neutrinos that decoupled from the primordial plasma about one second after the Big Bang, some 380,000 years before the photons of the microwave background decoupled. They are still here, at roughly 336 per cubic centimetre, redshifted to a temperature near 1.95 K and energies of order 0.17 meV. Their cross-section at that energy is so small that the PTOLEMY concept, which proposes to capture them on tritium, sits at the edge of the conceivable. The relic neutrino background is this generation’s no-practically-possible-way problem, and the history above suggests which way to bet.

DUNE and Hyper-Kamiokande are the next generation of the ordinary kind, at a scale that is not ordinary at all: 70,000 tonnes of liquid argon 1,300 km from Fermilab, and 260,000 tonnes of water in Japan, built largely to test whether neutrinos and antineutrinos oscillate differently. A difference there would be a leptonic source for the matter-antimatter asymmetry that allows anything at all to exist.

And neutrinoless double beta decay is the experiment that would settle what a neutrino actually is. If that decay happens, the neutrino is its own antiparticle, and the quantity being chased is a half-life beyond 10²⁶ years. It has not been seen. It may not exist. Either answer is worth the effort.

Look back along the whole span and the shape is consistent. The visible window is less than one octave out of more than eighty. Everything outside it was, at some moment, beyond measurement: infrared until Herschel put a thermometer past the red end of a prism’s spectrum in 1800, X-rays until Röntgen’s screen glowed in 1895, cosmic rays until Hess took an electroscope up in a balloon in 1912, neutrinos until a reactor in South Carolina in 1956, astrophysical neutrinos until a hole drilled in Antarctic ice. The history of invisible radiation is not really a history of discoveries. It is a history of thresholds falling, and nothing about the present one suggests it is the last.

Sources and Further Reading

• The Nobel Prize in Physics 2026 (Francis Halzen)
• The Nobel Prize in Physics 2015 (Kajita and McDonald)
• NIST: X-Ray Mass Attenuation Coefficients
• Particle Data Group: Review of Particle Physics
• XENON Collaboration: first measurement of low-energy solar neutrinos scattering off electrons
• LZ Collaboration: searches for light dark matter and evidence for coherent elastic neutrino-nucleus scattering (arXiv:2512.08065)
• JUNO Collaboration: first measurement of reactor neutrino oscillations (arXiv:2511.14593)
• Morishima et al., Discovery of a big void in Khufu’s Pyramid by observation of cosmic-ray muons, Nature 552, 386 (2017)
• Cowan, Reines et al., Detection of the Free Neutrino: a Confirmation, Science 124, 103 (1956)
• Bethe and Peierls, The Neutrino, Nature 133, 532 (1934)
• Neutrino Energy Group: Mathematics Beats Opinion, a statement to the global scientific community
• Neutrino Energy Group: Neutrino Superintelligence Force