Explaining the Illusion of the Constant Velocity of Light
| Scientific Paper | |
|---|---|
| Title | Explaining the Illusion of the Constant Velocity of Light |
| Read in full | Link to paper |
| Author(s) | Paul Marmet |
| Keywords | light, frames |
| Published | 2000 |
| No. of pages | 10 |
Read the full paper here
Abstract
Considering that photons travel at the velocity of light c in the fundamental frame, we expect logically that these photons travel at velocity c-v (or c+v) with respect to a frame moving at velocity v. We know that the observed velocity is measured as c. However, that logical consequence has never been explained. Using Newton's physics and conventional logic, we explain how the velocity of light APPEARS constant in the two way measurement of the velocity of light, while it is c-v (and c+v) in the Sagnac effect. We answer the question: "With respect to what does light move?" This paper gives a physical explanation how the velocity of light is really (c-v) with respect to the observer, even if the observer's tools always measure a velocity represented by the number c. We explain how this problem is crucial in the Global Positioning System (GPS) and in clocks synchronization. The Lorentz' transformations become quite useless. This apparent constant velocity of light is the most fascinating illusion in science.
Overview
Paul Marmet, a spectroscopist at the National Research Council of Canada and later at the University of Ottawa, wrote this ten-page paper in May 2000 as a condensation of the argument of his 1997 book Einstein's Theory of Relativity versus Classical Mechanics. Its question is deliberately blunt: "With respect to what does light move?" Marmet's answer is that light moves at c with respect to a single absolute frame, that it therefore really does travel at c ± v relative to a moving observer, and that the apparently invariant value every experiment returns is an artefact of the clock synchronization procedure used to obtain it. "This apparent constant velocity of light is the most fascinating illusion in science."
The mechanism Marmet proposes is deliberately un-exotic. He takes only the principle of mass–energy conservation: a clock or a measuring rod set in motion absorbs kinetic energy, that energy materializes as extra mass in its electrons and nuclei, and this alters the de Broglie wavelength, the Bohr radius and hence both the physical length of matter and the rate of atomic clocks. Nothing else is needed. "There exists neither space contraction nor time dilation, just a change of length of physical bodies and a change of clock rate." The Lorentz transformations, on this account, "become quite useless" — a mathematical device with no physics under it, and Marmet is explicit that an equation is never a cause: "A real explanation must answer the question of causality, which is asked by why?"
Two features distinguish his version from an ordinary aether model. First, the length change goes the opposite way from Lorentz contraction: his equation 1 states Lv/Ls = γ, so moving matter gets longer. Second, he insists no medium is needed — "it exists absolutely no observational justification to assume that an aether can possess its own energy that can be borrowed when needed."
The argument
Two sets of units
Marmet's notation separates physical lengths (capital L) from numbers of local units (script ℓ), with a bracketed label showing whose standard is being used. A rod on the moving train is physically γ times longer than at rest, but the train's own standard metre has lengthened in the same proportion, so ℓv[s]/ℓv[v] = γ and the moving observer sees no change. The same doubling applies to time: moving clocks run γ times slower, so ΔCD[v]/ΔCD[s] = 1/γ, and a careful moving observer must correct for both. Because lengths and clock rates change in the same proportion, velocities carry the same number in either frame — a point Marmet uses repeatedly.
Slow clock transport gives a "discordant" synchronization
The core calculation is in section 4. Clocks α and β sit at the ends of the moving train; a third clock μ is carried slowly from α to β at extra velocity ε and used to set β. Since the elapsed station time is ℓv/ε, and α and μ run slow by different factors (μ moves at v + ε, α at v), the displays differ by
- ΔCDα[v] − ΔCDβ[v] = (ℓv/ε)(1/γα − 1/γμ) (9)
Expanding both gamma factors and keeping first order, the ε cancels and
- ΔCDα − ΔCDβ = + ℓv v/c2 (13)
Clock β is permanently behind clock α by ℓvv/c2, and Marmet shows that Einstein's two-way light synchronization produces the identical offset. He calls this "Einstein's discordant synchronization" and sets it out in a table of the four clock displays at successive instants. He notes it "does not seem to have been noticed directly previously" and that it "is the cause of the Sagnac effect".
Why the measurement returns c
Light emitted from the station takes, in station units, ℓv/(c − v) to cross from α to β. Multiplying through by (c + v) gives ℓvγ2/c + ℓvvγ2/c2 (16); converting to the train's slow clock removes one γ (17); converting to the train's long metre removes the other (18):
- ΔCD[v](α to β) = ℓv/c + ℓvv/c2 (18)
Subtracting the synchronization offset (13) leaves exactly ℓv/c, and the same in reverse, so the measured one-way speed is c in both directions (20, 21). "It is an illusion that has been measured by the observer because the real velocity is c ± v."
Marmet stresses the sizes involved. For a frame moving at the Earth's rotation speed, about 10−6c, the synchronization term ℓvv/c2 is a million times larger than the γ correction of order 10−12.
GPS and the Sagnac effect
Sections 8 to 10 are the empirical heart. Citing A. G. Kelly, Marmet writes the GPS correction as 2ωAE/c2, with AE the equator-plane projection of the signal path; substituting ω = v/r this reduces to ℓv/c2 — "perfectly identical to equation 13". For New York to San Francisco the correction is about 14 ns, and Marmet points to the transported-clock experiments of Sadeh and of Saburi as its measurement. He then designs a one-way test: synchronize New York and San Francisco each via the North Pole, where the path crosses no meridians and the projected area is zero, so no correction applies; then exchange signals directly. Over a path of about 4,500 km with an average transit of 15,000 microseconds, light takes 0.014 µs longer eastward and 0.014 µs less westward — "one millionth" of the total, matching the Earth's rotation speed of about 10−6c. "Clearly, the velocity of light... is c + v between N.Y. and S.F. and c − v between S.F. and N.Y."
In section 11 he concedes that the star cluster is itself only another moving frame, and suggests the absolute frame is the one picked out by the 3 K radiation dipole, since light itself "seems to be inadequate" to reveal our absolute velocity.
Assessment
Marmet's algebra is correct, and it is worth saying so plainly, because it is the most instructive thing about the paper. Equations 14 through 21 reproduce, without error, the sequence one-way-anisotropy → longer rods → slower clocks → offset synchronization → measured value c. Equation 13 is right; equation 16's factorization is right; equations 20 and 21 do cancel to ℓv/c. The one slip is at fourth order and harmless: equation 11 expands 1/γα as 1 − v2/2c2 − 3v4/8c4, but the binomial expansion of (1 − v2/c2)1/2 has coefficient 1/8; the 3/8 belongs to γ, not to 1/γ. Only the first-order term is used, so nothing downstream depends on it.
What the correct algebra establishes, however, is the opposite of what the paper claims. Marmet has constructed a Lorentz ether theory — an absolute frame plus length and time changes that conspire to hide it — and then demonstrated in his own equations that it is observationally indistinguishable from special relativity. Every quantity a measurement can return comes out identical. Since his stated aim was to show the Lorentz transformations "become quite useless", it is awkward that his derivation is a proof that they are exactly right about every observable. The disagreement is metaphysical, about what is really happening behind identical predictions, and that is a legitimate thing to argue for — but it is not what the abstract promises.
Two of the specific claims do not hold up.
The GPS Sagnac correction is not evidence against relativity; it is a relativistic result. The Earth-fixed frame rotates and is therefore not inertial, and in a rotating frame the coordinate speed of light is anisotropic. This is standard, derived from general relativity in every technical treatment of GPS timing, and the 2ωAE/c2 term Marmet quotes from Kelly is the textbook Sagnac term. Special relativity claims light speed isotropy in inertial frames only; an observer on the spinning Earth is not in one. Marmet's section 10 experiment — synchronizing through the pole, where the enclosed area vanishes, then measuring east–west — amounts to adopting the non-rotating earth-centred coordinate time and then discovering that a rotating observer sees c ± v. Relativity predicts precisely that. His arithmetic here is also sound: at the latitude of New York and San Francisco the east–west arc is about 4,100 km and the rotation speed about 360 m/s, giving ℓv/c2 ≈ 16 ns against his quoted 14 ns, and 4,500 km/c is indeed 15,000 µs. The numbers are right; the inference is not.
The paper fails its own test. Marmet identifies the absolute frame with the one defined by the 3 K dipole — that is, a velocity of roughly 370 km/s. Put that number into his own equation 13. Over the same 4,100 km New York–San Francisco baseline, ℓU/c2 is about 17 microseconds, a thousand times the 14 ns actually corrected for, and it would swing through a full diurnal cycle as the baseline rotates and an annual cycle as the Earth orbits. Nothing of the kind appears in GPS timing data, which are consistent at the nanosecond level with a correction depending on ω alone. The anisotropy Marmet has correctly identified is entirely accounted for by the Earth's rotation at 10−6c; his absolute frame at 1.2 × 10−3c contributes nothing measurable, which is exactly what an absolute frame should not do.
There is a further internal difficulty with the length rule. Equation 1 makes moving matter γ times longer, and the mechanism — a mass increase changing the Bohr radius — is a scalar, so the change is isotropic. But the Michelson–Morley experiment, which Marmet names in his first sentence and never analyses, requires the direction-dependent shortening of the parallel arm by 1/γ to null the fringe shift. With arms isotropically lengthened to γL0 and light travelling at c in the absolute frame, the transit times are 2γ3L0/c along the motion and 2γ2L0/c across it, leaving a difference of about L0v2/c3 — the same magnitude as the classical prediction that Michelson and Morley failed to find, and that the Kennedy–Thorndike configuration with unequal arms constrains independently. An isotropic expansion cannot cancel an anisotropic delay. Marmet may resolve this in the book, but the paper as it stands invokes the experiment as motivation and never returns to it.
Finally, the "there is only one Real Logic" framing does real damage to an otherwise careful piece of work. The complaint that mathematics "never explains why" is a serious position in the philosophy of science, but here it substitutes for engagement with the measurements — the time dilation of muons in flight, the Ives–Stilwell transverse Doppler shift, the storage-ring tests — that a rival account of clock rates has to reproduce. Marmet's model does reproduce them, since it is empirically equivalent; the paper simply never says so, and the rhetoric of illusion obscures the genuine achievement, which is a clean and correct demonstration of how far a classical picture with an absolute frame can be carried.