Einstein's Three Errors Named Light Constant Velocity

Scientific Paper
Title	Einstein's Three Errors Named Light Constant Velocity
Read in full	Link to paper
Author(s)	Joe Alexander Nahhas
Keywords	Einstein, light velocity
Published	2012
No. of pages	10

Read the full paper here

Abstract

Light velocity is never been measured. Light constant velocity number c = 299792458 meters/second published by NIST (National Institute of Science and Technology) is a measurement error that can be found in Augustine de Coulomb experiment; However light constant velocity can be independently derived and is distance accumulation of three measurements embedded errors that humans made/make all the time when viewing a light source.

Overview

This is a short paper from Joe Nahhas's "real time physics and astronomy" series. Its thesis is that the speed of light is not a property of light at all but an artefact of how terrestrial observers measure: humans measure on the surface of a rotating sphere while using formulas written for a plane, and they keep time by a 24-hour civil clock rather than by the Earth's actual rotation. The residue of those two mismatches, Nahhas claims, is the number 299,792,458 — which he says can be reconstructed from three purely terrestrial quantities and nothing else:

c = [(T_s − T_e)/√(8π)] r_e

with T_s = 86,400 s (the "wrong human made clock"), T_e = 86,164.09724 s (the sidereal day, "right Earth's made spin clock") and r_e = 6,371,000 m (the Earth's mean radius). No property of light enters. The same apparatus is then applied to the Earth–Sun distance and to the perihelion advance of Mercury, both of which are presented as further "visual deceptions" recovered from Earth's rotation.

The departure from the mainstream account could hardly be wider. Nahhas denies that c has ever been measured, denies that the perihelion precession of Mercury requires gravitation, and closes with a general dismissal of "modern and Nobel physical sciences" — the big bang, dark energy, black holes, time travel — as accumulated measurement error. He states that he can reproduce "500 years" of such results "as measurement errors or Earth's Deceptions numbers."

The argument

The "real time" formalism

The derivation begins from an algebraic identity. From A = B + (A − B) and C = D + (C − D), Nahhas obtains ΔD/D = ΔB/B, divides by Δt, takes the limit and defines that limit to be a complex rate (λ + iω). Integrating gives the central object of the whole programme, the "real time distance"

r = r₀ e^(λ+iω)t

from which he differentiates to get "real time velocity" and "real time acceleration", and then builds a catalogue: real-time circumference, area, area velocity, surface area of a sphere, volume, and their first and second time derivatives, twenty numbered equations in all. Two of these are singled out as "the relevant equation": r = r₀e^(λ+iω)t and the surface-area velocity S′ = 8πrv.

Extracting c

From S′ = 8πrv Nahhas takes "√(8π) visual error" and writes a velocity C = (r₀√(8π))ω, with ω = 1/(T_s − T_e) the "visual rotational error" arising because "humans measure on spherical surface and not from the center". He then states: "If a visual error is made then its inverse is measured: (T_s − T_e)/√(8π)", and concludes c = [(T_s − T_e)/√(8π)] r_e = 299,792,458 m/s. Elsewhere he explains the √(8π) as "scientists measure ½ cycle and multiply by 2 or 2√(2π) = √(8π)".

The distance to the Sun

The same machinery is applied to the astronomical unit, motivated by a childhood observation that the Sun does not look 387 times farther than the Moon. Integrating e^iωt gives a "time summation error" sin(ωτ₀)/ω and a reciprocal "frequency summation error" ωτ₀/sin(ωτ₀). With the "distance summation" r_eT_e/(T_s − T_e) and ωτ₀ = (T_s − T_e)/√(8π), he obtains

R = [r_eT_e/(T_s − T_e)] × {[(T_s − T_e)/√(8π)] / sin[(T_s − T_e)/√(8π)]} = 1.495865595 × 10¹¹ m

He also notes that T_e/(T_s − T_e) = 365.2525987, "same as number of days".

Mercury

Finally, as a validity test, the perihelion advance:

Γ_x = (36526 × 24 × 3600 / (360 × 3600)) × {sin[arctan(v/c)] / arctan(v/c)}

with v = 48.1 km/s the orbital speed of Mercury, giving "42.5 arc seconds per century".

Assessment

The three numerical results were recomputed. Two of them reproduce, and the reasons they reproduce are the whole story.

The light-speed formula. The arithmetic is right: (86400 − 86164.09724)/√(8π) = 47.055793, and 47.055793 × 6,371,000 = 299,792,454, against c = 299,792,458 — agreement to eight significant figures. Nahhas has not miscalculated. The problem is that the expression is not a velocity. (T_s − T_e)/√(8π) is a time, 47.06 seconds; multiplied by a length it gives metre-seconds, not metres per second. The consequence is testable and fatal: a dimensionally sound relation cannot depend on the units it is written in, but this one does. Express the same three quantities with the day in minutes rather than seconds and the formula returns 4.996 × 10⁶, while c in metres per minute is 1.799 × 10¹⁰. The agreement exists in SI seconds and metres and in no other system, which is the signature of a numerical coincidence rather than a physical identity. It also rests on one adjustable constant. Solving for the divisor that would make the equation exact gives 5.013250, against √(8π) = 5.013257 — but √(8π) was not derived, it was obtained by taking a square root of the coefficient of an unrelated formula (S′ = 8πrv), an operation with no defined meaning, and then moved from the numerator of C = r₀√(8π)ω to the denominator of the final expression without explanation. With one free constant, any target can be hit to any precision.

Test the claim against itself. If c is fixed by the Earth's radius and rotation, then c would take a different value for an observer on a planet of different size — and it would have been different in the deep past, since tidal friction lengthens the day. It also cannot be reconciled with the historical record: Rømer obtained a finite light speed in 1676 from eclipse timings of Jupiter's moons, using neither the Earth's radius nor its spin; Fizeau and Foucault measured it terrestrially with toothed wheels and rotating mirrors; and in 1972 Evenson and colleagues obtained it as frequency × wavelength of a stabilised laser to about 4 parts in 10⁹. That last measurement is why c was fixed by definition in 1983, so the NIST number is not, as the abstract has it, a published measurement error but a defining constant of the SI metre. The paper's premise that "light velocity is never been measured" is simply not true, and the claimed origin of the error "in Augustine de Coulomb experiment" is never explained anywhere in the ten pages.

The astronomical unit. This one reproduces exactly — 1.4958656 × 10¹¹ m, matching the paper's digits — but only when the sine is evaluated with its argument read as degrees while the same argument is used as a bare number in the numerator. Done consistently in radians, ωτ₀/sin(ωτ₀) = 47.0558/sin(47.0558 rad) = 691.5, and the formula returns 1.61 × 10¹² m, an order of magnitude too large. The result depends entirely on a degree/radian inconsistency worth a factor of 180/π. Beyond that, the expression contains no property of the Sun: not its mass, not the Earth's orbital period. Kepler's third law makes the orbital radius depend on the central mass, so a formula built only from the Earth's radius and spin cannot be a derivation of the Earth–Sun distance, whatever number it produces.

Mercury. Here the check is decisive. Evaluating the brace, arctan(48.14/300000) = 1.6047 × 10⁻⁴ rad, and sinθ/θ = 1 − 4.3 × 10⁻⁹. The brace is unity to nine decimal places; its effect on the answer is 2 × 10⁻⁷ arcseconds. The result is therefore the prefactor alone, and reproducing 42.5 requires dividing 36526 × 24/360 = 2435.07 by a further 180/π = 57.296, which does not appear in the printed formula — 2435.07/57.296 = 42.500, exactly the quoted figure. So the "derivation" of Mercury's perihelion advance is the pure number 36526 × 24/(360 × 57.296). It contains no orbital radius, no eccentricity, no period, and no solar mass; the only Mercury-specific input, v = 48.1 km/s, enters through a factor equal to 1 to within four parts in a billion. The identical calculation would return 42.5 arcseconds per century for Venus, for Mars, for any planet at all, and for a body in no orbit whatever. A formula that returns the same answer for every input is not a prediction. (The observed anomalous advance is about 43.0 arcsec/century, and the general-relativistic value 42.98; 42.5 is close but low, and the 0.5 arcsec shortfall has no source in the paper because the calculation has no free physical content to adjust.)

Two further points of substance. The opening characterisation of light-speed constancy — that two bodies both travelling at c have relative speed c whether they move together or apart — is not what special relativity asserts. The theory forbids massive bodies from reaching c at all, and what it actually states is the composition law u = (u₁ + u₂)/(1 + u₁u₂/c²), which reduces to the everyday sum at ordinary speeds; the car analogy the paper offers against it is therefore an analogy the theory already agrees with. And the observation that T_e/(T_s − T_e) = 365.25, "same as number of days", is not a discovery but a definition: the sidereal day is defined as the solar day scaled by Y/(Y + 1), so recovering the length of the year from it is an identity, not a coincidence in need of explanation.

What can be said in the paper's favour is that it is transparent. Every number is printed, every step is shown, and the author does not hide behind formalism — which is precisely why the calculations can be checked as thoroughly as they have been here. The "real time" exponential r = r₀e^(λ+iω)t is also, taken by itself, an unobjectionable way of writing a damped rotation. But it is introduced by defining a limit to be complex rather than by showing that any measured quantity behaves that way, and nothing in the twenty catalogued equations connects it to the propagation of light. The argument from there to c consists of three unexplained moves — taking a square root of 8π, inverting one factor but not another, and reading a metre-second as a metre per second — and the numerical agreements that follow do not survive a change of units, a change of angular measure, or a change of planet.