A Conceptual Derivation of Einstein's Postulates of Special Relativity
Thomas E. Bearden · US Army Missile Command, Redstone Arsenal
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Sixteen pages, fifty-two numbered statements, and one question: can the two postulates of special relativity be argued for from something more elementary than themselves? The report's route is to treat every observer — a person, an instrument, a single particle — as a physical detector that can register only changes to its own mass, and then to ask what such a detector must produce. Length and time come out as two kinds of separation the detector creates rather than reads off a pre-existing stage; the constancy of the speed of light comes out as the statement that every detector of this kind shares one operating limit; and the relativity of the laws of physics between uniformly moving frames comes out as the ordinary fact that differentiating a function and differentiating that function plus a constant give the same answer. It is a short, unusually disciplined document: numbered steps, each depending only on the ones above it, and an explicit statement of what it has not done.
Dlaczego ma tu znaczenieChapter 2 argues that empty space is not empty and not a passive backdrop; this report is the same author's attempt to make that structural, by deriving the relativistic properties of space and time from the act of measurement rather than assuming them. Chapter 3 gets the closing note, which is where the applicability sits: the model's author states that it yields a single generating mechanism for force, and therefore makes inertial and gravitational mass identical by construction — which is a claim about the equivalence principle, the quantity every inertia-and-gravity programme on this site is trying to get a handle on.
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01The report's starting chain is about what a detector can do, and it is stated as a ladder of numbered steps rather than asserted. Every observer and every instrument has mass and is therefore a physical detecting system; a physical detecting system registers only changes to some part of itself; shrink it until the whole of it must change for any detection to occur and you have the limiting case the report names a perceptron. From that it follows, on the report's reading, that detection is a differentiating operation — it responds to change and not to state — so a constant input yields no output, and zero output does not mean zero input.Section 2, Perception of Change, numbered statements 1 to 11
What to watch02Space and time enter as two kinds of separation that the detector produces rather than inhabits. The report argues that relation, separation and operation imply one another, so a Cartesian space — one in which every point has a definite length to every other — is a space whose lengths have all already been defined by an operation, and defined in a linear way, the same operation identically repeated. A curved or accelerated frame is then the same construction with the repetition varied. The report reaches simultaneity by the same route and credits Einstein's 1905 paper with having shown it to be operational.Section 3, Space and Time, numbered statements 21 to 27 and 38 to 43
What to watch03Einstein's second postulate is reached as a statement about a shared limit. Physical phenomena are finite, so the detecting process must have a finite maximum rate; because the report has already identified detection with change itself, that maximum rate of operation is the maximum rate of observed change, which is the speed of light in vacuum. Every detector of this kind therefore has the same ceiling, and the speed of light is the same for every observer. The postulate itself is settled physics and the report treats it as the target to be recovered, not as something to be revised.Section 3, numbered statements 29 to 37
What to watch04The first postulate is reached through a dimensional argument with a neat closing step. Taking matter and energy as interconvertible — the report's warrant is photon emission and absorption, which is measured physics — and writing the energy molecule as mass times velocity squared, the mass divides out and velocity is left dimensionless in the absolute sense. A dimensionless velocity cannot change the detector's relative outputs, which the report identifies with the elementary fact that the derivative of a function and the derivative of that function plus a constant are equal. So the laws of physics are the same for observers in uniform relative motion. The same line yields, as the report puts it, a bonus: length and time are dimensionally interchangeable up to constants of proportionality.Section 4, Derivation of Einstein's First Postulate, equations 44 to 52
What to watch05The two postulates the report is aiming at are settled physics and the report states them accurately, citing Einstein's 1905 paper on the electrodynamics of moving bodies for both. Nothing in the document proposes that either postulate is wrong or that any relativistic prediction should change; the proposal is entirely about where they might be argued from.Notes 12, 13 and 15
Settled physics06The applicability the report names for itself is stated in its closing section and in its final note, and it is a claim about force and mass rather than about relativity. The author writes that the same approach yields a generating mechanism for force of any type, that the resistance to force — mass — therefore comes out the same in every case, and that inertial and gravitational mass are consequently identical; and that the equivalence principle needed by general relativity and a new definition of mass both follow, though neither is carried out in this report. The definition of mass as a rate, and the derivations of Newton's laws of motion and gravitation, are referred to the author's 1973 report, which this site also holds. The step that would settle any of it is the one the report itself asks for: a physicist taking the construction seriously enough to push it to a prediction that differs from the standard one.Section 5, Closing Remarks, and note 17
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Droga do źródła
https://eric.ed.gov/?id=ED141089WHAT THIS PAGE IS WRITTEN FROM, AND THE SAME RIGHTS CHECK RUN AGAIN. Technical Report SAM-D 76-4, US Army Missile Command, Redstone Arsenal, Alabama, dated 8 October 1975, sixteen pages. The report carries the distribution statement approved for public release, distribution unlimited — and that statement governs circulation, not copyright. Block 11 of its report documentation page, supplementary notes, reads copyright 1975 Thomas E. Bearden, printed by permission, and the same notice is printed again under the title on the cover. It is therefore an author-copyrighted work carried by the Army with permission, not a public-domain US government record, exactly as its companion ED141090 turned out to be; this page is summary-only and reproduces none of its text, and the verbatim treatment this site gives to patents and to genuine government records does not apply. The check was run on this report separately rather than inherited: the 1973 report from the same author and the same arsenal, AD 763 210, has that block blank and IS carried as a public-domain record, so the notice is a per-document fact and has to be read per document. Read in full for this sheet on 2026-09-11 — all sixteen pages, including the five numbered sections and the seventeen notes and references — from the free ERIC copy ED141089, sha256 92257ef80252d932c5c82e184696ed4adbfbbd0d2faf4925f84a0e4ad1d2fb78. The scan is a 1975 typescript with occasional broken characters, so locators name the report's numbered statements and sections rather than lines. Also indexed as DTIC ADA020799; apps.dtic.mil was serving a scheduled-maintenance page on 2026-09-11 and could not be reached.
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Thomas E. Bearden, US Army Missile Command, Redstone Arsenal (1975) A Conceptual Derivation of Einstein's Postulates of Special Relativity. https://eric.ed.gov/?id=ED141089
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