Light Needs a Medium
One formula fits every wave. Applied to light, it uses two measured properties of empty space.
Apply it to light and it does not fail. Empty space has a measured permittivity and a measured permeability, and the speed of light is what you get by putting them into that same formula: permittivity in the place of density, the reciprocal of permeability in the place of stiffness. In 1856 two men obtained the speed of light by measuring a capacitor and a coil, with no light in the experiment at all. Maxwell saw what it meant in 1862.
Empty space also has an impedance of 376.73 ohms, the same unit as a resistor, which every antenna is matched to. It slows light by a measurable amount in matter. It absorbs nothing over nine billion light years. Its properties have been measured for a hundred and seventy years, and are called properties of the vacuum in every textbook.
None of this compels a substance, and the memo does not claim otherwise: modern physics holds the field is fundamental, predicts the same numbers, and no experiment has ever separated the two views. Every other wave in physics is given a medium as a matter of course, and light alone is treated as an exception — but that exception was made for good reasons, and section 10 gives them. Two results stand against this memo rather than for it, and the stronger of the two is not answered anywhere in this series.
Proven in this memo
- The formula that gives the speed of light is the same formula that gives every other wave speed — permittivity occupies the density slot, the reciprocal of permeability the stiffness slot. This is Maxwell's own energy decomposition, not an analogy.
- Empty space has an impedance, and it governs reflection at a boundary by the identical formula that governs sound at a water surface.
Neither establishes that a substance exists. The first shows a correspondence of algebraic form, not that permittivity is a density — nobody has weighed the vacuum. A field account predicts every number here correctly. What the memo asks is why light is the one wave treated as needing no medium, and section 10 gives the serious answer to that. Section 9 names two results that stand against this memo, and the stronger is unanswered.
Draft. A working draft, published for scrutiny rather than as a settled result. The ledger at the foot records what is derived, what is measured, what is assumed and what remains unanswered.
This memo makes the case for a medium. It does not prove one exists, and section 10 sets out the standard answer fairly. The detailed work on the experiments is in memos E.7 to E.12.
1. Every Wave We Know, And What It Waves In
Start with what is not in dispute. Here is every familiar kind of wave, with the thing that does the waving.
| Wave | Travels in | Speed | What actually moves |
|---|---|---|---|
| Sound | air | 343 m/s | the air, back and forth |
| Sound | water | 1,483 m/s | the water |
| Sound | steel | 5,100 m/s | the steel |
| An ocean wave | water | ~10 m/s | the water, in circles |
| A wave on a rope | the rope | ~20 m/s | the rope, sideways |
| An earthquake | rock | 4,500 m/s | the rock, shearing |
| A drumbeat | the drumskin | ~200 m/s | the skin |
| Light | ? | 299,792,458 m/s | ? |
Seven entries with a substance named, and one without. That is the whole question.
2. One Formula Fits Them All
The speed of a wave is not a property of the wave. It is a property of what it travels through, and it is settled by two things: how stiff the material is, and how heavy.
| Material | Stiffness (Pa) | Density | Predicted | Measured | Error |
|---|---|---|---|---|---|
| Air | 1.4 × 105 | 1.2 | 340 | 343 | −1% |
| Water | 2.2 × 109 | 1,000 | 1,483 | 1,483 | 0% |
| Steel | 2.0 × 1011 | 7,850 | 5,048 | 5,100 | −1% |
| Diamond | 1.05 × 1012 | 3,510 | 17,296 | 18,000 | −4% |
Why this matters more than it looks
A gas, a liquid and two solids. Speeds spanning a factor of fifty. One formula, four per cent at worst, and nothing adjusted between them.
Nobody regards that as a coincidence. It is what a wave is — a disturbance travelling through something, at a speed the something decides. Every wave in the table above obeys it.
3. The Same Formula Gives The Speed Of Light
Empty space has two measured electrical constants. Its permittivity describes how much electric field it will hold; its permeability, how readily it carries magnetism. The speed of light follows from those two alone:
ProofEquation (2) has the form of equation (1)
Rearranged, equation (2) reads c = √((1/permeability) ÷ permittivity). That is the same algebraic form as equation (1), with one constant in the stiffness position and the other in the density position.
The correspondence is not arbitrary. In Maxwell’s theory the energy stored in an electric field is ½ε0E², which enters the equations where ½ρv² enters a mechanical one; the magnetic energy ½B²/μ0 enters where ½kx² does. The two constants occupy the positions that density and stiffness occupy.
What this proves is a correspondence of form, and no more. It does not show that ε0 is a mass density — nobody has weighed the vacuum, and modern electromagnetism treats both constants as coefficients in the field equations with no mechanical reading at all. The identification is Maxwell’s model, not a measurement.
Chain: wave speed = √(stiffness/density) → the electric energy term enters where the kinetic term does → the magnetic term where the potential term does → the same algebraic form follows. Premise not established: that occupying a position in an equation means being the quantity that usually occupies it.
4. Two Men Measured It Without Using Any Light
In 1856 Wilhelm Weber and Rudolf Kohlrausch measured the same quantity of electric charge in two different ways — once by the force between charges at rest, once by the force between currents — and took the ratio. A capacitor and a coil on a laboratory bench. There was no light anywhere in the experiment.
The number they got was 3.107 × 108 metres per second.
Seven years earlier Fizeau had measured the speed of light with a toothed wheel and got 3.13 × 108.
Neither of them was looking for it
Weber and Kohlrausch were settling a question about units. Fizeau was measuring light. The two results had no reason to agree, and they agreed to within one per cent.
Maxwell noticed in 1862 and drew the conclusion that founded the whole electromagnetic theory of light: if the electrical properties of space give you the speed of light, then light must be an electrical disturbance in whatever those properties belong to.
That is the argument of this memo, and Maxwell made it first. What has changed since is only that the medium those properties belonged to was later removed, and the properties kept.
5. Empty Space Has An Electrical Resistance
The two constants can be combined a second way, and the result is the vacuum’s impedance: 376.73 ohms. The same unit as a resistor.
Impedance is what decides how much of a wave bounces back at a boundary. One formula covers every kind of wave there is:
| Boundary | Reflected |
|---|---|
| Sound, air into water | 99.9% |
| Sound, air into steel | 100.0% |
| Light, space into glass | 4.3% |
| Light, space into diamond | 17.2% |
| Radio, space into seawater | 99.5% |
This one is not a formality
The four per cent you see reflected in a window is an impedance mismatch. So is the near-total reflection of sound at a water surface. Same formula, same table, and free space sits in it as one medium among others with a number beside its name.
And engineers use it. Every antenna ever built is matched to 377 ohms. Get it wrong and the power reflects back down the feed instead of radiating, which radio operators measure with a standing-wave meter. It is not a piece of mathematics — it is a thing that goes wrong.
6. Light Slows Down In Matter
Light does not always travel at 299,792,458 metres per second. It slows in matter, by amounts that have been measured for thousands of substances.
| Light travelling through | Speed (m/s) | Fraction of full speed |
|---|---|---|
| Deep space | 299,792,458 | 100% |
| Air | 299,704,645 | 99.97% |
| Water | 224,900,569 | 75% |
| Glass | 197,231,880 | 66% |
| Diamond | 124,034,943 | 41% |
| Silicon | 86,147,258 | 29% |
What is being read
Light in diamond runs at 41 per cent of its full speed. On this account that is because the Aether inside diamond is in a different state from the Aether outside it — and the refractive index has been measured for thousands of materials since the 1800s, so the readings already exist in every optics handbook.
What the readings mean is less settled than it looks. Memo 4.6 shows that the density cannot simply be read off the refractive index, because the stiffness changes too and one measurement cannot separate two quantities. That the slowing and the state of the medium are connected is not in doubt. The exact relation is.
So the question of section 1 sharpens. Sound travels at 343 metres per second relative to the air. An earthquake at 4,500 relative to the rock. Light travels at 299,792,458 relative to what?
7. It Never Loses Anything
Voyager 1 transmits with about 22 watts, the power of a fridge bulb, from twenty-five billion kilometres away. What arrives at Earth is 0.46 attowatts — one part in 5 × 1019 of what left. It is still decoded, every day, by a seventy-metre dish.
Weak is not the same as absorbed
The signal is faint because it spread out over a sphere, not because anything ate it. Every watt that left is still out there, thinned across a surface now larger than the orbit of Saturn. Gather it all back and you would have 22 watts again.
Spreading is geometry. Absorption is loss. The two are different and the whole question turns on keeping them apart.
So how much is actually absorbed? We see quasars nine billion light years away, arriving at close to the brightness expected. That puts the absorption below one part in 1026 per metre. The medium is transparent across the entire observable universe. The best optical fibre ever made loses half its light in seventy kilometres.
And that is very strange indeed
Light is said to sustain itself: a changing electric field makes a magnetic field, a changing magnetic field makes an electric field, and the two take turns forever.
That is exactly a tuned circuit — energy sloshing between a capacitor and a coil. Every tuned circuit ever built rings down and stops, because the wire has resistance. Free space has a capacitance, an inductance and an impedance of 377 ohms. What it does not have is a resistance.
The reason it has none is that its two constants are written as plain numbers. A material that absorbs has a second, hidden part to those constants, and that hidden part is the absorption. The vacuum is given none.
Neither account derives this. Standard physics writes the vanishing absorption into the vacuum's constants; this account requires a medium so nearly frictionless that nothing has come within twenty-four orders of it. Both postulate it. Neither explains it.
8. So Have We Just Not Seen It?
The honest answer is that its properties have been measured for a hundred and seventy years, and are called properties of the vacuum in every textbook. What is disputed is not whether they exist but what having them amounts to.
| What has been measured | What has not |
|---|---|
| Permittivity, since 1837 | Any density |
| Permeability | Any drag on a moving body |
| Impedance, 376.73 ohms | Any state of rest |
| Reflection at every boundary | Any particle of it |
| The speed a wave crosses it | Any weight |
One argument that must not be made. It is tempting to say that a pump removes atoms but cannot remove the medium, so every measurement was made inside it. That is circular. If the medium is defined as unremovable then of course no measurement escapes it, and nothing has been shown. The point is only worth making as a statement of what the word “vacuum” means — atoms removed, not nothing present — and it is examined properly in memo E.12.
Both accounts say space is full of something
This is the part most often missed. Modern physics does not hold that space is empty. It holds that every field has a lowest energy that is not zero, that pairs of particles appear and vanish in it continuously, and that this has measurable consequences — two uncharged plates attract each other, and the hydrogen spectrum is shifted by it.
So the dispute is not whether something is there. It is what sort of something. One account calls it a substance with a density and a stiffness. The other calls it the ground state of a set of fields. The arguing is about the description.
9. The Experiments That Settled It
Five results are usually cited as having removed the need for a medium. They are not equal in force and this memo does not treat them as such. Each has its own memo.
| Experiment | What it is said to show | Standing |
|---|---|---|
| Michelson–Morley, 1887 | There is no medium | Shows no motion relative to one was found. A different claim — E.7 |
| The photoelectric effect, 1905 | Light is particles | Reproduced in 1969 without photons, by a quantised atom and a classical field — E.9 |
| Stellar aberration, 1729 | Cited against a medium | Requires the medium not to be dragged along. Argues for one at rest — E.11 |
| The rotating resonators | No preferred direction exists | Severe. Bounds Earth’s motion at 0.95 m/s against an orbital speed of 29,780 — E.8 |
| Antibunching, 1977 | Light arrives one piece at a time | The hardest result for this memo. A wave would sometimes deliver two — E.10 |
The first three are misread. The last two are not.
How bad the resonator result is
A medium has a state of rest, and the Earth moves. Rotating optical cavities compare the speed of light in different directions to one part in 1017 and find no difference, bounding any such motion at under a metre per second.
The Earth travels round the Sun at thirty kilometres per second, and the solar system through the galaxy at two hundred and thirty. The bound is thirty-one thousand times below the smallest speed the Earth is known to have.
That is the principal reason a mechanical medium was abandoned, and this series does not answer it. It is faced in memo E.8, and it is the strongest argument against everything in this memo.
10. The Answer From Modern Physics
The standard reply is not that space is empty. It is that the field is fundamental.
On that view an electromagnetic field is not a disturbance in anything. It is a thing in its own right, as basic as matter, and asking what it is made of is a question that does not apply — like asking what a number is made of. Permittivity and permeability are then simply constants in the equations, not properties of a substance.
This is a serious position, not a dodge
It accounts for everything in this memo. It predicts every number in section 5’s reflection table, the speed in section 3, the impedance in section 5, and the slowing in section 6. There is no measurement in this memo that it gets wrong.
It also has an advantage this account does not: it requires no state of rest, and so is untroubled by the resonator result in section 9.
No experiment has ever separated the two views. They are not two theories making different predictions; they are two descriptions of the same equations.
And the mechanical aether was not dropped by preference. It was dropped because relativity, and later quantum field theory, accounted for more observations while carrying fewer leftover structures — no preferred frame to hide, no substance whose properties had to be stipulated. That is the ordinary reason a theory is replaced, and it is a good one.
What this memo can fairly say is narrower. Every other wave in physics is given a medium without argument, and the properties set out here are the properties a material has. To hold the field view is to accept all of them and decline the conclusion they usually carry. That may well be right. But it is a position taken, not a result obtained, and this memo asks that it be recognised as one.
11. What Would Prove This Wrong
- Finding the medium’s state of rest would settle it; never finding it is the standing problem. Every improvement in precision without a detection makes this position harder to hold, and the current bound is 0.95 m/s.
- A demonstration that empty space has no structure. The measurements run the other way: two uncharged plates attract, and the hydrogen spectrum is shifted, both measured.
- A wave found travelling with no medium at all, in a case where the absence could be established rather than assumed. No such case exists, and it is not obvious what one would look like.
- Antibunching already stands against the pure-wave account, and this memo does not resolve it.
12. The Numbers
In summary, the figures behind the argument:
- Familiar waves with a named medium: every one.
- Error in the medium formula across a gas, a liquid and two solids: 4% at worst.
- Speed of light from the electrical constants of space, with no light used: 299,792,458 m/s.
- Impedance of empty space: 376.73 ohms — the same unit as a resistor.
- Light in diamond: 41% of its full speed.
- Absorption over nine billion light years: none measurable.
- Experiments performed outside the medium: none.
Terms Used Here
| Word | What it means |
|---|---|
| Aether | The proposed substance filling all space: one kind of particle which light would travel through and which matter would be built from. Not an established entity — the memos set out what would have to be true for it to exist. |
| Deep space | The Aether far from any matter, at its natural density of about 0.9 kg per cubic metre. |
| Shear stiffness | How hard a material resists being pushed sideways, one layer sliding over another. Fluids have none. |
| Sideways wave | A wave where the material moves across the direction of travel, like a shaken rope. Light is one. |
| Squeeze wave | A wave where the material moves the same way the wave goes, like sound in air. |
| Polarisation | The orientation of a sideways wave. Polarised sunglasses block one and pass the other. |
| Refractive index | How much slower light travels in a material than in empty space. Water is 1.33, diamond 2.42. |
| Dispersion | When waves of different wavelengths travel at different speeds. A prism splitting white light is dispersion. |
| “Empty space” | A misleading but unavoidable phrase. The space between the stars is not empty. What is genuinely empty is the void — the room the Aether occupies, which has no properties at all. |
| Antibunching | Light from a single atom arrives one piece at a time, never two together. A wave would split at a mirror and sometimes register on both sides. Measured 1977. |
| Impedance | What a material presents to a wave, and what decides how much bounces back at a boundary. Measured in ohms. Empty space has one: 376.73. |
Every term used across the series is on the terms page.
13. Sources
Reference codes read source.work.passage and resolve on the Master Source Register, which carries every source used across this series.
- Bureau International des Poids et Mesures. The International System of Units (SI), 9th edition (2019). The speed of light and the electrical constants. 72
- J. C. Maxwell. On Physical Lines of Force, Philosophical Magazine (1861–62). The calculation in section 4 and the conclusion drawn from it. 79
- W. Weber & R. Kohlrausch (1856). The ratio of electrostatic to electromagnetic units. Carried as reported from secondary sources; the original has not been consulted.
- H. J. Kimble, M. Dagenais & L. Mandel. Photon Antibunching in Resonance Fluorescence, Physical Review Letters 39 (1977) 691. The result named in section 9 as the hardest here. Carried as reported; not verified.
- W. E. Lamb & M. O. Scully. The photoelectric effect without photons (1969). Carried as reported; not verified.
- S. G. Lamoreaux. Demonstration of the Casimir Force in the 0.6 to 6 µm Range, Physical Review Letters 78 (1997) 5. Carried as reported; not verified.
- Handbook values for the densities, stiffnesses and refractive indices in sections 2, 5 and 6. Standard reference data; individual sources not listed.
Verification register: references 3 to 6 are carried as reported from secondary sources and have not been checked against the originals. Reference 3, the Weber–Kohlrausch value, is load-bearing for section 4 and should be read before publication. The wave speeds in section 2 and the reflection coefficients in section 5 are computed from handbook constants rather than cited.
Ledger — memo T.3
- Derived
- That the formula giving the speed of light is the same formula that gives every other wave speed, with permittivity in the density position and the reciprocal of permeability in the stiffness position
- The wave speeds in section 2 from handbook stiffnesses and densities, to within 4%
- The reflection coefficients in section 5 from the impedance mismatch
- Measured
- Permittivity, permeability and the resulting impedance of free space
- Weber and Kohlrausch's 1856 ratio, obtained without light
- Refractive indices for every material in section 6
- Voyager's received signal strength, and the transparency bound from distant quasars
- Antibunching (1977) and the resonator bounds — both against this account
- Assumed
- That a wave requires a medium. This is the thing being argued for, and it cannot also be used as a premise. Section 10 states the position that denies it, and no measurement in this memo distinguishes the two.
- That the mechanical analogy holds at all scales. Every wave in section 1 is a disturbance in matter made of atoms. Whether the same reasoning applies to a medium below the atomic scale is an extrapolation.
- Open
- The state of rest. Any real medium has one. It has not been found, to 0.95 m/s against an orbital speed of 29,780 — a factor of 31,000. The central unanswered objection, and memo E.8 is where it is faced
- Antibunching. A single atom emits light one piece at a time and a wave would sometimes deliver two. Not resolved here or anywhere in this series — memo E.10
- Why nothing is ever absorbed. Neither account derives it. Standard physics writes it into a definition; this account writes it into a requirement — memo D.6
- The exact relation between the slowing of light and the state of the medium, which memo 4.6 shows is not the simple one previously assumed
- Prior art
- Weber & Kohlrausch (1856) — the speed of light from electrical measurements alone
- Maxwell (1861–62) — the identification of light as an electromagnetic disturbance, and the argument of this memo in its original form. Section 4 adds nothing to what he wrote
- Lorentz — the medium retained after 1905, with the same predictions
- What is new here is only the collection: the same case assembled from measurements made since, by people not making it