The Relativistic Space-Time Perspective

Scientific Paper
Title	The Relativistic Space-Time Perspective
Read in full	Link to paper
Author(s)	David G Taylor
Keywords	Perspective, Physical Values, Relativistic Distortion, distorted Velocity, parallel relativistic equations, Time, Mass, Length, equation confirmation table
Published	2013
No. of pages	12

Read the full paper here

Abstract

This paper formulates additional Relativistic equations. They do not contradict Special Relativity. They examine the deductions of Dr. Einstein from a relativistically distorted perspective. It reasons that the REAL||non-Relativistic velocity value can be distorted just as the Length|Time|Mass values are. The equations examine the both the true/Real (not Special Relativistically Distorted||noSRD) Velocity of an object and use it to determine the distorted (Special Relativistically Distorted||SRD) Velocity for the same object. It also derives opposite equations that calculate the noSRD velocity [Velocity_noSRD] from the SRD velocity [Velocity_SRD].

A Relativistically distorted observation point would not perceive local actions moving more slowly. Rather everything outside moving faster. Fewer seconds for a Relativistic Perspective that has distortion means the perspective equations have a different relation. They calculate the higher Velocity perceived from a distorted viewpoint.

Two example equations show the relation of two points of view. The independent variables have no Relativistic deformation |Velocity_noSRD|; dependent variable would be the value||velocity reasoned to be observed because of the Relativistic deformation |Velocity_SRD|.

Velocity_SRD = Velocity_noSRD/(1 - Velocity_noSRD²/c²)^½

Less Time will go by when there is a relativistic deformation, so Velocity will appear distorted just as Length/Time/Mass are. The inverse relation would be where the independent variable is observed Velocity from the Relativistic or distorted view |Velocity_SRD|. The dependent variable would then be True/non-Relativistic/non-distorted Velocity |Velocity_noSRD|. The parallel equation for that Relativistic Perspective:

Velocity_noSRD= Velocity_SRD /(1 + Velocity_SRD²/c²)^½

This relationship allows the additional development of 8 formula/equations for Velocity, Mass, Time, and Linear deformation. These equations are all of the two Perspectives.

The equations developed in this paper are an absolute advance, but are more “housekeeping” advances than significant ones. Though they do lead to parallel equations in General Relativity that will have considerable Cosmological significance in a later submission.

Overview

David G Taylor's paper is unusual in this collection for what it does not attempt. It is not an attack on Special Relativity; the author states twice that his equations "do not contradict Special Relativity" and describes them as "the same equations from a Relativistic viewpoint". What he proposes is a change of bookkeeping. In the standard treatment, velocity is measured as laboratory distance divided by laboratory time, and the relativistic factor is applied to time, length and mass but not to the velocity itself. Taylor argues that velocity should be distorted too: if the traveller's seconds are fewer, then the same journey divided by the traveller's own shorter tally of seconds yields a larger number, and that number deserves a name and its own set of conversion formulae.

He therefore defines two velocities for a single motion — Velocity_noSRD, referred to an undistorted viewpoint, and Velocity_SRD, referred to the distorted one — and derives eight paired equations relating time, mass and length in the two perspectives. He is candid about their status, calling them "more 'housekeeping' advances than significant ones", and promises a sequel extending the scheme to general relativity with cosmological consequences. The paper also contains a short speculative section on what would physically happen aboard a fast-moving vessel, and that section, unlike the algebra, does contradict special relativity.

The argument

The two velocity perspectives

The starting point is the ordinary dilation relation Time′ = Time/(1 − Velocity_Real²/c²)^½. Taylor introduces "numsec" variables to count seconds rather than measure durations: numsec_SRD = numsec_noSRD(1 − Velocity_noSRD²/c²)^½, "if the distortion factor is two, then as 2 Real seconds pass, 1 Relativistic second will pass". Dividing through by one undistorted metre converts the time relation into a velocity relation and gives

Equation 1: Velocity_SRD = Velocity_noSRD/(1 − Velocity_noSRD²/c²)^½

The inverse is then obtained by straightforward algebra — squaring, clearing the denominator, collecting the cross term — to give

Equation 2: Velocity_noSRD = Velocity_SRD/(1 + Velocity_SRD²/c²)^½

Taylor stresses the resulting symmetry: the ratio Velocity_SRD/Velocity_noSRD equals 1/(1 − Velocity_noSRD²/c²)^½ and also equals (1 + Velocity_SRD²/c²)^½, so "the two expressions can be interchanged by inverting the proportion". That interchange is the engine of everything that follows.

The six derived equations

Because the velocity ratio is the relativistic factor, every standard formula can be rewritten with the ratio substituted in, then flipped to give a "perspective" version:

• Equation 3: Time = Time′/(1 + Velocity_SRD²/c²)^½
• Equation 4: Mass_SRD = Mass_noSRD/(1 − Velocity_noSRD²/c²)^½, with Equation 6: Mass_noSRD = Mass_SRD/(1 + Velocity_SRD²/c²)^½
• Equation 7: Length_SRD = Length_noSRD(1 − Velocity_noSRD²/c²)^½, with Equation 8: Length_noSRD = Length_SRD(1 + Velocity_SRD²/c²)^½

Taylor observes that on this scheme "the Velocity can appear to reach or exceed light speed from the viewpoint of a moving body", since Equation 1 has no upper bound, and he takes the numerical verification seriously: the relations were checked for 37 (elsewhere 39) values of Velocity_noSRD spanning 10⁻⁵⁰⁰ m/s to c − 10⁻⁵⁰⁰ m/s, agreeing to 2000 significant digits with a maximum residual of ±10⁻¹⁹⁹², which he attributes entirely to irrational-number truncation.

Philosophical framing

A recurring theme is that "Real" and "Rest" are not observable categories. Every body in the universe is in motion, so a zero velocity is indeterminate; but indeterminate is not the same as undefinable, and Taylor defends idealisation by analogy with F = ma and F = GMm/r², both of which are useful despite never having all forces accounted for. He accordingly prefers the labels "noSRD" and "SRD" to "Real" and "Relativistic", and suggests using the Einsteinian equations at low speeds and the perspective equations at high ones.

Speculative consequences

The paper closes with claims about what relativistic motion would do to a body. Bosons would slow and lose mass while matter particles gained it, so "any Quantum level interaction would be both dealing with heavier particles and dealing with them with slower (and therefore weaker) Bosonic forces". Gluon binding would weaken toward the infinitesimal, atoms would "dissemble to their component protons, neutrons and electrons", and "any passenger aboard a vessel moving at a relativistic velocity would find themselves both gaining weight and losing muscular force". He further suggests that a large apparent recession velocity might indicate "Relativistic scale distance and Boson decay, not a Universal expansion", so that intergalactic redshift could arise from "EM frequency decay over those distances" — a promissory note toward a tired-light alternative to expansion in a later paper.

Assessment

The algebra in this paper is correct, and it is worth saying so plainly, because that is not always the case in this literature. Equation 2 follows validly from Equation 1, and the chain of substitutions producing Equations 3 to 8 is sound. Taylor is also right about the identity he leans on: writing w for Velocity_SRD and v for Velocity_noSRD, one has 1 + w²/c² = γ²(1 − v²/c² + v²/c²) = γ², so (1 + w²/c²)^½ is exactly the Lorentz factor. His self-assessment — "housekeeping" — is honest and accurate.

It is more accurate than he realises, however, because the quantity he introduces is not new. Velocity_SRD = γv is the proper velocity or celerity, dx/dτ — laboratory displacement per unit of the traveller's own proper time. It is the spatial part of the four-velocity, it appears in standard textbook treatments, and its inverse relation v = w/(1 + w²/c²)^½ is Taylor's Equation 2 verbatim. Its unboundedness is likewise a familiar and unalarming feature: a proper velocity of 10c simply means a traveller crossing ten light years of laboratory distance per year of their own ageing, with the coordinate speed still below c. So the paper's central claim to have "formulated additional Relativistic equations" is a rediscovery rather than an extension, and the eight equations reduce to γ and 1/γ written two ways. The numerical verification, impressive-sounding at 2000 digits, confirms only that an algebraic identity is an identity; no arrangement of digits can test a rearrangement against nature.

Several presentational defects should be flagged for readers. The equations are numbered 1, 2, 3, 4, 6, 7, 8 — there is no Equation 5. The intermediate line "Velocity_noSRD/Velocity_SRD = (1 + Velocity_noSRD²/c²)^½" preceding Equation 3 is inverted and carries the wrong subscript, though the result reached is nonetheless right. And the summary calls Time = Time′/(1 + Velocity_SRD²/c²) "the most crucial equation" while dropping the square root that Equation 3 carries in the body.

The serious problem is the final speculative section, which contradicts both the paper's own opening promise and the experimental record. If a traveller's atoms came apart, their gluon binding weakened and their muscles lost force, that would be a locally detectable consequence of uniform motion — precisely what the principle of relativity forbids, and precisely what the abstract's own better instinct ("would not perceive local actions moving more slowly") denies. The measurements are unambiguous on this point. Cosmic-ray muons reaching sea level do so because their proper lifetime is unchanged while their laboratory lifetime is dilated; protons circulating at γ ≈ 7000 in a modern collider remain protons rather than dissembling into quarks; relativistic heavy ions arrive as intact nuclei; and the Ives-Stilwell transverse Doppler result, repeated to parts in 10⁹ with stored ion beams, measures the dilation without any accompanying change in the ions' internal structure. Nor can bosons "slow down": a photon's speed is c in every frame, which is the postulate the rest of the paper accepts. The suggested redshift mechanism is likewise offered without a mechanism, and is deferred to a paper not present here.

The paper is therefore best characterised as a competent but redundant re-derivation of proper velocity, followed by an appended physical speculation that the derivation does not support and that measurement rules out. Read for the algebra it is unobjectionable; read for the promised consequences it does not deliver them.

See also

• David G Taylor
• Special Relativity
• Time Dilation
• Length Contraction
• Lorentz Transformation
• Speed of Light
• Mass
• Simultaneity
• Tired Light