It sounds like a contradiction. Light has no mass — a photon weighs nothing at all — and yet sunlight warms your skin, charges a solar panel, fades a curtain, and can even push a spacecraft across the solar system. If energy comes from mass, as E = mc² seems to promise, how can something with zero mass carry any energy at all?
The short answer: mass is only one of two ways to store energy, and E = mc² is only half of the real equation. A photon simply uses the other half. Its energy comes from its momentum and its frequency, not from any mass — and once you see the full equation, the paradox dissolves completely. This guide walks through exactly how that works, why light must be massless, and the surprising twist where trapped light gains weight after all.
The Equation Everyone Half-Remembers
Almost everyone knows E = mc². Almost no one knows it is incomplete. Einstein's 1905 result, from his paper "Does the Inertia of a Body Depend Upon Its Energy Content?", describes the energy of an object sitting still. It is really the rest energy — the energy an object has purely by existing.
The complete relationship, the one physicists actually use, adds a second term:
E² = (pc)² + (mc²)²
Here E is total energy, m is mass, c is the speed of light, and p is momentum — a measure of "quantity of motion." Read it as a simple statement: an object's total energy comes from two sources added together — its motion (the pc term) and its mass (the mc² term).
Now watch what happens in the two extreme cases:
- An object at rest. Its momentum p is zero, so the first term vanishes and the equation collapses to the famous E = mc². This is the version everyone quotes.
- A photon. Its mass m is zero, so the second term vanishes and the equation collapses to E = pc. The photon's energy is all momentum, and there is nothing contradictory about it.
Setting mass to zero doesn't break the equation. It just moves all the energy into the other term. Light was never disobeying E = mc² — we were only ever taught the half that didn't apply to it.
Where a Photon's Energy Actually Comes From
If a photon's energy isn't stored in mass, what sets it? Frequency — which you perceive as colour. This is the second pillar of the story, from quantum mechanics rather than relativity, and it's captured in the Planck–Einstein relation:
E = hf
E is the photon's energy, f is its frequency, and h is Planck's constant, a tiny fixed number that stitches the quantum world together. The message is simple: higher-frequency light carries more energy per photon. A red photon carries less energy than a blue one; an ultraviolet photon carries more than either, which is why UV can damage skin and DNA while visible light cannot.
This is exactly the effect Einstein used to explain the photoelectric effect in 1905 — light knocking electrons out of a metal — the work that won him the Nobel Prize. Dim blue light could eject electrons while intense red light could not, which only makes sense if each photon's energy depends on frequency, not brightness. (For the fuller story of the particle itself, see our guide to what a photon actually is.)
So a photon carries a very definite amount of energy — hf — with no mass involved anywhere. Concentrate enough of that massless energy into one place and it becomes ferociously powerful: 192 laser beams, pure photons, delivered enough energy to ignite nuclear fusion at the National Ignition Facility. Energy without mass is not a weak or ghostly thing.
Massless but Not Motionless: Momentum Without Mass
Here is the mental hurdle. In everyday physics you learn momentum as p = mv — mass times velocity. If mass is zero, that formula gives zero. So how can a massless photon have any momentum?
Because p = mv is itself a low-speed approximation, not the full truth. Rearrange the complete equation for a massless particle and you get:
p = E / c
A photon's momentum is its energy divided by the speed of light. Since its energy hf is not zero, its momentum is not zero either. Light carries a genuine, physical "push" — it is simply very small, because you divide by the enormous number c.
This isn't abstract bookkeeping. Photon momentum shows up in hard experimental facts:
- The Compton effect (1923): X-ray photons bouncing off electrons transfer momentum and recoil to a longer wavelength, exactly as billiard-ball collisions would predict. It was decisive proof that light carries momentum.
- Radiation pressure: James Clerk Maxwell predicted in 1862 that light exerts pressure. Russian physicist Pyotr Lebedev measured it in 1900, and Ernest Nichols and Gordon Hull confirmed it in 1901. Light really does push on what it hits.
The Proof You Can Launch: Solar Sails
The most spectacular demonstration of massless momentum is a spacecraft that flies on nothing but light.
A solar sail is a large, ultra-thin, mirror-like sheet. Photons from the Sun strike it, reflect, and hand over their momentum — and by Newton's third law the sail recoils forward. There is no fuel and no exhaust. There is only light, pushing.
This is real, flown hardware, not theory:
| Mission | Agency | Year | Milestone |
|---|---|---|---|
| IKAROS | JAXA (Japan) | 2010 | First craft to cross space propelled by a solar sail |
| LightSail 2 | The Planetary Society | 2019 | Raised its orbit using sunlight alone |
| ACS3 | NASA | 2024 | Deployed a ~9-metre composite-boom sail to test scalable designs |
NASA's Advanced Composite Solar Sail System (ACS3) launched in April 2024 and unfurled its roughly 30-foot sail in orbit that August. Every metre of thrust it produces comes from massless photons handing over momentum. If light carried no energy or momentum, none of these missions could move.
The Twist: Trapped Light Does Have Mass
Now for the part that surprises even physics students. A single photon is massless. But a box of photons is not.
Mass, in relativity, is really the energy a system has when its total momentum is zero — its invariant mass. Imagine a perfectly mirrored box with light bouncing around inside. The photons fly in all directions, so their momenta cancel out: the box as a whole isn't going anywhere. But the energy is still in there. With the momentum term cancelled, that trapped energy shows up as extra mass of the box, following E = mc² in reverse.
The numbers are real, if tiny. A hot object weighs infinitesimally more than a cold one because the extra thermal energy — including trapped radiation — adds to its mass. Most strikingly, the vast majority of the mass of everyday matter isn't the mass of its particles at all; it's the energy of the massless force-carriers and motion binding them together. Individual photons are massless. Bottled-up light has weight. Both statements come from the same single equation.
Does Light Have Exactly Zero Mass?
In the Standard Model of particle physics, the photon's mass is exactly zero, and everything above assumes that. But is it measured to be zero? Physicists never get to prove an exact zero; they can only tighten the limits.
Experiments have squeezed any possible photon mass down to an almost absurdly small ceiling. The Particle Data Group, the standard reference for particle properties, lists an upper limit on the order of 10⁻¹⁸ electron-volts — around a thousand trillion trillion times lighter than an electron — with some methods pushing even lower. For every practical and theoretical purpose, that is zero.
It matters because a truly massless photon is why light always travels at exactly c, and why the electromagnetic force reaches across infinite distances. If the photon had even a minuscule mass, light would slow slightly at different frequencies and the reach of electromagnetism would fade with distance. We see neither. So far, light is massless to the limit of what we can measure.
Energy, Gravity, and Bending Light
One last piece ties it together. If light has no mass, why does gravity bend it? Sunlight skims past the Sun and curves; a black hole traps light entirely.
The answer completes the whole picture: in Einstein's general relativity, gravity responds to energy, not just mass. Because a photon carries energy, gravity acts on it. Light follows the curves that mass and energy carve into spacetime. This was confirmed in 1919, when Arthur Eddington measured starlight bending around the Sun during a solar eclipse — one of the first great tests of general relativity.
The same logic explains gravitational redshift: a photon climbing out of a strong gravitational field loses energy, and since its energy is hf, losing energy means its frequency drops and its colour shifts toward red. The photon never slows down — it always moves at c — but it can gain or lose energy. That interplay of light, energy, and gravity is exactly what makes extreme objects so strange, as we explore in what would happen if you fell into a black hole.
Quick Glossary
These are the load-bearing terms behind the whole idea; for more on the underlying particle and the physics it drives, see our physics topic hub.
- Rest mass (invariant mass): the energy a system has when it isn't moving. A photon's rest mass is zero.
- Momentum (p): quantity of motion. For light, p = E/c — real, even without mass.
- Rest energy (mc²): energy locked in mass. Zero for a photon.
- Frequency (f): how fast the light wave oscillates; sets a photon's energy through E = hf.
The Bottom Line
Light has no mass, yet carries energy, because mass is just one form of energy, not the only one. The complete equation, E² = (pc)² + (mc²)², gives every object two ways to hold energy — through its mass and through its motion. Ordinary objects lean on the mass term; a photon uses the momentum term alone, its energy set by frequency through E = hf. That massless energy is not a loophole — it warms planets, drives solar sails, bends around stars, and even adds weight to a box of trapped light. The real surprise isn't that light carries energy without mass. It's that we spent a century quoting only half of the equation that explains it.
Frequently Asked Questions
Does light have any mass at all?
No — in the Standard Model the photon's mass is exactly zero, and experiments have constrained any possible mass to less than about 10⁻¹⁸ electron-volts, effectively zero. Light still carries energy and momentum, but it has no rest mass, which is precisely why it always travels at the speed of light.
If light has no mass, how does it have energy?
Because energy doesn't require mass. A photon's energy is set by its frequency through the equation E = hf: higher-frequency (bluer) light carries more energy per photon. Mass (via E = mc²) is only one way to store energy; motion and momentum are another, and light uses that one.
How can a massless photon have momentum?
The everyday formula momentum = mass × velocity is only a low-speed approximation. The full physics gives a photon momentum p = E/c — its energy divided by the speed of light. Since its energy isn't zero, its momentum isn't either, which is why light can physically push on objects.
Can light really push objects?
Yes. It's called radiation pressure, predicted by Maxwell in 1862 and measured by Lebedev in 1900. The push is tiny but real, and solar-sail spacecraft such as NASA's ACS3 (2024) and LightSail 2 (2019) actually fly on it — accelerating with no fuel, driven only by reflected sunlight.
Why does gravity bend light if light has no mass?
Because gravity responds to energy, not just mass. In general relativity, mass and energy curve spacetime, and light — which carries energy — follows those curves. Eddington confirmed this in 1919 by measuring starlight bending around the Sun during an eclipse.
Does a photon experience the passage of energy differently than mass does?
A photon's energy can change — it redshifts when climbing out of gravity or stretches as the universe expands — but it never slows down; it always moves at c. A massive object, by contrast, can sit still and store energy as rest mass. That difference is the whole point: light holds energy in motion, matter can hold it in mass.
