Motion's Observation Through Light's Signals (I)
| Scientific Paper | |
|---|---|
| Title | Motion's Observation Through Light's Signals (I) |
| Read in full | Link to paper |
| Author(s) | Caesar Peter Viazminsky |
| Keywords | contiguity, illusive Lorentz transformations, scaling transformations, universal space, absolute time |
| Published | 2010 |
| No. of pages | 27 |
Read the full paper here
Abstract
A novel view of space, time, and inertial frames that maintains the absolute nature of time is presented. One but arbitrary inertial frame say S, is considered stationary and identified with the absolute space, while all other inertial frames are moving relative to S. The constancy of the light's velocity in free space within each inertial frame is postulated and employed to link time durations measurements to geometric distance. The geometric distance in the chosen stationary frame plays the decisive role in the determination of time and distance in all inertial frames. A unique time prevails in all inertial frames, but distance between a moving object in S and a stationary observer in S is identified by the optical length of a light trip from the object to the observer; this distance functions as the geometric distance in the frame in which the object is at rest when the latter frame is considered stationary. The arbitrariness of the chosen stationary frame guarantees that all inertial frames are equivalent, and according the physical laws are the same in all. The so-called scaling transformations which relate the geometric distances in S and in a moving frame are derived and applied to explain the Doppler's effect and the lifetime of meta-stable particles phenomenon. The quantitative predicted Doppler's effect, which is in a striking agreement with the Ives-Stilwell experimental results, coincides with the relativistic prediction for longitudinal motion, but yet predicts complete absence of a traverse effect. The direction of the light trip is observed from a moving frame to be tilted from its direction in the stationary frame by the aberration angle; a fact which is employed to explain the phenomenon of stellar aberration. The true status of the Lorentz transformations as an equivalent form of the scaling transformation is illuminated. In a forthcoming part of this work, a second type of scaling transformations corresponding to given beginning and end of a light's trip in a stationary frame is derived and employed to explain the Michelson and Morley experiment, the Michelson and Gale experiment, and the Sagnac effect. The translative nature of the latter effect is explored and studied in detail. The pioneer anomaly which can be explained by Euclidation of optical measurements will be discussed separately.
Overview
This is the first part of a two-part statement of the scaling theory developed by C. P. Viazminsky of the University of Aleppo, written with P. K. Vizminiska of the University of Detroit Mercy, and drawing together a series of thirteen earlier notes published in the General Science Journal between 2008 and 2010. Its aim is to keep Newton's absolute time while accepting that the velocity of light is c within every inertial frame — a combination normally taken to be impossible.
The device that makes the combination work is a distinction between two kinds of length. The geometric distance between two points is what a ruler laid down repeatedly gives, and it is frame-dependent. The optical or proper distance of a moving source from an observer is defined as the length of the light trip from source to observer, and it is absolute. One arbitrary inertial frame S is nominated as stationary and identified with what the authors call the universal space; every other frame derives its time from S not by clock synchronisation but by contiguity — a moving observer simply reads whichever S-clock he happens to be adjacent to. Because the choice of S is free, all inertial frames remain equivalent and the laws of physics are the same in all. The Lorentz transformations are then argued to survive only as a disguised, and in the paper's word "illusive," restatement of the scaling relation, with Minkowski space dismissed as "a big unfounded claim." The paper is thus a Lorentzian-style programme, but one that keeps a universal now instead of a preferred aether frame.
The argument
Absolute time from absolute length
Section 3 contains the paper's foundational move, and it runs in the opposite direction from Einstein's. Rather than deriving the relativity of Simultaneity from the invariance of c, Viazminsky derives the absoluteness of time from the absoluteness of length. Take a rod ob of length u·LS at rest in the moving frame s, whose ends are contiguous with points O and B of S at T0 = 0. If the contiguity of o with O occurred before or after the contiguity of b with B, then s would measure OB as shorter or longer than u·LS — "which is a contradiction, since length is absolute." Hence the two contiguities are simultaneous in both frames, and since every S-point has a contiguous s-point at each instant, "all clocks in s must read... the same instant of time t = 0." He states the conclusion plainly: "accepting length as absolute results in time flowing equably in S and s," and therefore "simultaneity is absolute, in the sense that it is frame independent."
Two further definitions follow operationally: the time reading at a point of s is the reading of the contiguous S-clock, and the geometric distance between two s-points is the geometric distance between the S-points they touch. The unit of time is itself defined through spatial displacement — the period in which a lattice point of s moves from one S-lattice point to the next — so that "time and distance have the same dimension."
The scaling transformation of the first type
A source b at rest in s emits a pulse when at B ∈ S; the pulse reaches O ∈ S, and simultaneously reaches the s-observer o who is contiguous to O at that moment. Viazminsky calls O and o conjugate observers and the pair (b at B) a universal point. Because either frame may claim to be stationary, all observers agree that the pulse traced one straight path in the universal space between two universal points — from which follows the striking claim that the direction angles are frame-independent, θ = θ′, φ = φ′, with the relative velocity not appearing.
Applying the Galilean velocity addition law within the stationary frame to compute the trip's proper duration then yields the first-type scaling transformation, anisotropic in direction, with factor
- Γ(β, θ) = γ(β cos θ + √(1 − β2 sin2 θ)), γ = 1/√(1 − β2)
relating optical to geometric lengths, r = Γ(β, θ)R. The units of length in the two frames stand in the ratio Γ(β, θ) : 1. Geometric and optical lengths coincide only when u = 0 or θ = π/2.
Doppler effect and the Ives–Stilwell comparison
Since a trip of n wavelengths in s is the same trip in S, λ = Γ(β, θ)λ0 — the Doppler Effect. Longitudinally the result is identical to the relativistic one: at θ = π, λ = λ0√((1−β)/(1+β)); at θ = 0, λ = λ0√((1+β)/(1−β)). At θ = π/2, however, Γ = 1 exactly, so the scaling theory predicts no transverse Doppler effect at all, where relativity predicts λ = γλ0.
Viazminsky nevertheless argues that the theory matches the Ives–Stilwell experiment. For the mean shift Δλ = ½(λa + λr) − λ0, relativity gives ΔλE ≈ ½β2λ0, while the scaling theory gives Δλ ≈ ½β2cos2θ λ0 = ΔλEcos2θ — a slightly smaller shift. Since Ives and Stilwell set their concave mirror at θ = 7° to the ion beam, the relativistic prediction should be scaled by cos27° ≈ 0.985. The paper tabulates eight rows comparing the relativistic prediction, the observed shift, and the scaling prediction (for example 0.0202 / 0.0185 / 0.0198, and 0.0360 / 0.0345 / 0.0354, in ångström), arguing that in seven of the eight the observed shift falls below the relativistic value and the scaling prediction is closer.
Metastable particles
Rather than dilating the muon's lifetime, the theory shrinks its distance. For a μ-meson created at X = 60 km and approaching the surface, the relevant distance contracts to x = Γ(β, π)X = X√((1−β)/(1+β)). Requiring x < cτ ≈ 0.6 km gives β > 0.9998, "a tangibly probable range in the speed distribution of such particles."
Galileization and the illusive Lorentz transformations
Section 13 asks whether, when the pulse arrives at O, the source can be pictured at b′ at Euclidean distances ut and ct from B and O. Applying the law of cosines to triangle Bb′O gives t = G(β, π−θ)T with the Galilean factor G(β, θ) = Γ(β, π−θ)/(1−β2), which is not the scaling relation — so the answer is negative unless one either contracts cT by γ−1 or expands ut and ct by γ. Crucially, "in both views, only geometric distances are liable either to contraction... or expansion... while the true time t remains intact."
Performing the first of these gives R = γ(r + vti), which "look[s] like one of the Lorentz transformations, but it is radically different in meaning, since r is related to t by r = ct." Supplementing it with its dual and specialising to motion along the line of sight reproduces X = γ(x + vt), T = γ(t + vx/c2). But Viazminsky insists the two relations are one relation in disguise, that R2 − c2T2 = r2 − c2t2 holds only because both sides are identically zero, and that "there is only one time, namely the true time t."
Aberration
From the geometry of a moving telescope of aperture p and ocular o, the ray direction is tilted by sin δ = (v/c) sin θ. Viazminsky emphasises that the source velocity does not enter — only the relative velocity of the observing frame — and presents this as removing an inconsistency he attributes to the relativistic treatment: that the same relative velocity is taken to be large when explaining a star's Redshift but equal to Earth's orbital velocity when explaining Stellar Aberration. For a star at ecliptic latitude Θ, the annual variation follows sin2δ = (v/c)2(1 − cos2Θ sin2φ), with maximum 2δmax ≈ 41.25″. A closing prediction: a satellite in low circular orbit in the ecliptic at v ≈ 7.5 km/s should show an aberration swing of about 10.31″ between observations half a period apart.
Assessment
This is a careful and internally disciplined piece of work, and several things in it are genuinely well done. The distinction between the geometrically measured distance and the optically inferred distance of a moving source is a real and often-blurred one, and making it explicit is clarifying. The contiguity construction is an elegant way to give a moving frame a time without any synchronisation convention, and it sidesteps the circularity that dogs one-way light-speed discussions. The aberration section identifies a point that has troubled other careful readers, including Phipps and Russo, whom the paper cites: aberration depends only on the observer's velocity change, not on the source's velocity, and any relativistic exposition that treats the star–Earth relative velocity as the operative quantity is loosely stated. Viazminsky's derivation delivers the correct 20.5″ constant and the correct annual ellipse. That the scaling factor Γ reduces exactly to the relativistic longitudinal Doppler formula is also not a coincidence to be waved away — the mathematics is competently done, and the paper is explicit about where it agrees with relativity and where it does not.
The decisive difficulty is the one the abstract itself advertises: the theory "predicts complete absence of a traverse effect." Transverse time dilation is not an inference from theory but a directly measured quantity, and it has been measured repeatedly and with increasing precision since the paper's premise was framed. The Rossi–Hall and CERN muon storage-ring measurements give dilated lifetimes agreeing with γ to better than 0.1% at γ ≈ 29.3, in a geometry where the muons circulate and the longitudinal component averages away. The Mössbauer rotor experiments of Hay and of Kündig measured a second-order shift in the strictly transverse configuration. Modern Ives–Stilwell descendants using stored lithium ions at the ESR — Saathoff (2003) and Novotny (2009) — confirm the relativistic time-dilation factor to parts in 107 and 108. A theory predicting Γ(β, π/2) = 1 exactly is excluded by these at overwhelming significance.
The paper's own Ives–Stilwell argument therefore does less than it appears to. The cos2θ correction it invokes with θ = 7° is a 1.5% reduction — smaller than the scatter in the eight tabulated rows, one of which (0.0869 / 0.0900 / 0.0856) has the observation above the relativistic value, in the direction the scaling theory cannot accommodate. Fitting eight points at the percent level cannot distinguish two formulas that differ by 1.5%, and the modern versions of the same experiment, designed precisely to isolate the transverse term, do distinguish them.
There are also steps asserted rather than derived. The claim that a light path's direction angles are identical in both frames, θ = θ′, with "the velocity of the source... [not appearing] in the last relations," is in direct tension with the paper's own section 14, which derives a nonzero aberration angle sin δ = β sin θ between the directions seen from two frames in relative motion. Both cannot hold as stated; the paper distinguishes them by attaching the first to the "universal path" and the second to what is "observed," but never establishes that the two notions of direction can coexist consistently. The foundational rod argument likewise assumes what it sets out to prove: it takes the length of a moving rod to be absolute in order to conclude that time is absolute, and the absoluteness of the moving rod's length is precisely the Newtonian premise that measurement is being asked to adjudicate. Finally, the assertion that the Lorentz invariant is "identically zero" is true only along null paths — light trips — which are the only trips the paper considers; timelike intervals between material events, where the invariant is nonzero and where the interval genuinely does the physical work, are never treated, so the dismissal of Minkowski space is not established.
The muon treatment illustrates the same limitation. Contracting the distance rather than dilating the lifetime reproduces the atmospheric result, as any Lorentzian reading does, because the atmospheric case is a one-way longitudinal geometry where the two accounts agree numerically. The storage-ring case, where the muon's path is closed and its decay rate is measured directly in the laboratory, is where they part, and it is not addressed.
Read as a Lorentzian-style reconstruction, the paper is more thoughtful than most: it accepts the empirical content of the longitudinal results, states its point of divergence honestly, and offers a concrete satellite test. Read as a replacement for special relativity, it is refuted at exactly the point it names as its distinguishing prediction.