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REVIEW 4 major objections 6 minor 122 references

Defining of three-dimensional acceleration and inertial mass leading to the simple form F=MA of relativistic motion equation

T0 review · 4 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A force-aligned velocity subtraction makes the relativistic equation of motion take the simple form $F=MA$ with a single inertial mass $M=m\gamma$ in every direction.

desk verdict The F=MA claim is a definitional identity; the vector variable-mass equation is a real contribution. read the letter →

arxiv 1909.09084 v3 pith:AYPFASAJ submitted 2019-08-30 physics.hist-ph gr-qcphysics.class-ph

Grzegorz M. Koczan This is my paper · ORCID
classification physics.hist-phgr-qcphysics.class-ph PACS 03.30.+p01.65.+g02.00.0045.05.+x01.55.+b
keywords relativisticaccelerationmassvelocitysubtractionspecialrelativitylongitudinaltransversevariablemass-energyequivalence
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that the familiar split of relativistic inertial mass into longitudinal and transverse components comes from using the wrong velocity difference inside the definition of acceleration. It defines a three-dimensional relativistic acceleration $A$ through the differential $(dv)_{\rm rel}=\gamma^2 dv_\parallel+dv_\perp$, produced by a subtraction rule that changes only the component of velocity parallel to the force. With that definition the relativistic equation of motion takes the simple vector form $F=M A$, where the inertial mass $M=m\gamma$ is the same for every direction of the force. The same differential also yields a general variable-mass equation and collapses ten historical formulas for velocity-dependent mass into the single expression $M=m\gamma$. If the definitions hold, the longitudinal/transverse mass debate dissolves and the strong form of mass-energy equivalence $E=Mc^2$ becomes the natural reading of the theory.

What carries the argument

The load-bearing object is the relativistic velocity differential $(dv)_{\rm rel}$ (Eq. 54), generated by the subtraction operation $\ominus_\parallel$ (Eq. 52), which leaves the velocity component perpendicular to the chosen direction unchanged while applying the one-dimensional relativistic subtraction rule to the parallel component. Dividing by $dt$ defines the three-dimensional relativistic acceleration $A$ (Eq. 55); because this $A$ is constructed along the direction of the force, the vector equation $F=M A$ holds with scalar $M=m\gamma$ for any force direction. The paper also proves that the alternative operations $\ominus_\perp$, $\ominus_\wedge$, $\ominus_\vee$, and several related antisymmetric operations are differentially equivalent to $\ominus_\parallel$, whereas the standard vector rule $\ominus_0$ is not, and it uses $\ominus_\perp$ to write the thrust term in the variable-mass equation.

What would settle it

A relativistic rocket experiment with exhaust ejected at an angle to the rocket's velocity would test the machinery: Eq. (92) predicts a thrust term $\gamma\,(dm/dt)\,u\ominus_\perp v$, whereas a rate-form treatment that ignores the new subtraction predicts a different recoil. Measuring the rocket's transverse acceleration under such conditions would select between the two descriptions.

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Extended reading notes

Core claim

The central claim is that the correct three-dimensional "relativistic differential of velocity" is $(dv)_{\rm rel}=\gamma^2 dv_\parallel+dv_\perp$ (Eq. 54), obtained by the operation $\ominus_\parallel$ (Eq. 52) rather than by the standard vector velocity-subtraction rule. Dividing this differential by coordinate time defines acceleration $A$ (Eq. 55), and the equation of motion becomes $F=m\gamma\,(dv)_{\rm rel}/dt=M A$ (Eq. 70). Consequently the inertial mass is $M=m\gamma$ in all directions, so the historical longitudinal and transverse masses are unified. The paper extends the same construction to variable rest mass, obtaining $M A=F_{\rm ext}+(\partial M/\partial t)\,u\ominus_\perp v$ (Eq. 93), and argues that ten independent-looking definitions of mass—force-to-acceleration, momentum-to-velocity, energy differentials, thrust—all reduce to $M=m\gamma$ once this differential is used.

Load-bearing premise

The entire result turns on choosing $\ominus_\parallel$—a subtraction rule that modifies only the velocity component parallel to the direction of interest—for the velocity differential in acceleration, a choice the paper motivates by requiring $F$ parallel to $A$ but supports with no independent physical principle or experiment; using the standard vector subtraction $\ominus_0$ instead brings back the longitudinal and transverse mass split.

Editorial extensions

If this is right

  • The inertial mass of a moving body can be written as $M=m\gamma$ independent of force direction, so the longitudinal and transverse mass distinction becomes unnecessary.
  • The simple form $F=MA$ is valid in every orthonormal Cartesian frame, matching the power of the rate form $F=dp/dt$ for constant rest mass.
  • The variable-mass equation $MA=F_{\rm ext}+(\partial M/\partial t)\,u\ominus_\perp v$ generalizes the one-dimensional relativistic rocket equation to arbitrary jet directions and external forces.
  • Ten historical definitions of velocity-dependent mass—ratios of force to acceleration, momentum to velocity, energy differentials, and thrust—collapse to the same $M=m\gamma$.
  • The rank-2 correspondence between four-acceleration and three-acceleration places $A$ on the same footing as other spacetime-space quantities, supporting the general mass-energy relation $E=Mc^2$.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • As an editorial extension: if the definition is adopted as convention, special-relativistic dynamics could be taught with a single scalar inertial mass and the vector equation $F=MA$, at the cost of redefining acceleration along the force direction rather than along the velocity.
  • Because the alternative subtraction operations are only differentially equivalent, the distinction between them can matter at finite velocity differences; this makes the variable-mass thrust term in Eq. (93) the most experimentally accessible place to test the convention.
  • The same rank-based correspondence could be extended to higher derivatives of position, yielding a hierarchy of relativistic kinematic quantities with rank equal to the order of the time derivative.
  • The paper leaves the gravitational status of $M$ open; if $M$ is taken as the source of gravity, the strong version of mass-energy equivalence $E=Mc^2$ would connect to composite-system gravitational mass measurements.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper argues that the relativistic three-dimensional acceleration should be defined through the nonstandard velocity-subtraction operation ⊖∥, Eq. (52), yielding the velocity differential (dv)_rel = γ² dv∥ + dv⊥, Eq. (54), and the acceleration A = (dv)_rel/dt, Eq. (55). With this definition, the standard momentum-change equation F = dp/dt is rewritten as F = mγ A = M A, Eq. (70), so that the inertial mass M = mγ is the same for all force directions and the longitudinal/transverse mass distinction disappears. The paper also derives a relativistic variable-mass equation from a four-force balance, Eqs. (72)–(93), identifies the jet-velocity subtraction ⊖⊥ with Oziewicz's binary relative velocity, and surveys the historical literature on relativistic mass from Lorentz, Kaufmann, Einstein, Planck, and later authors.

Significance. The paper has real strengths: the historical material is extensive, and the algebraic relations among the several velocity-subtraction operations are worked out carefully enough to verify. The variable-mass derivation, if the mass-conservation assumptions are supplied, connects a covariant four-force form to a three-dimensional Meshchersky-type equation and introduces a clean jet-velocity operation. However, the central result, Eq. (70), is not a physical prediction. It is an algebraic identity obtained by choosing the definition of the velocity differential, and the paper supplies no independent kinematic or experimental criterion that fixes this choice. With the standard Einstein subtraction ⊖0, Eqs. (17), (58), and (59), the same force law reproduces the familiar directional masses γ³m and γm, as the paper itself notes. The advertised unification of inertial mass is therefore a convention-dependent restatement of F = dp/dt rather than a resolution of the historical controversy. The variable-mass section is the only part with substantial independent content, and it does not rescue the title claim.

major comments (4)
  1. [Section X, Eq. (70), with Eq. (54)] The central equation is an algebraic identity. Starting from F = d(mγv)/dt = mγ³a∥ + mγa⊥ and the proposed A = γ²a∥ + a⊥, one obtains F = mγ A by construction. Thus the claim that the inertial mass is mγ in every direction is not a determination from dynamics but a consequence of the definition of A. The stated justification for choosing ⊖∥, namely that it makes A parallel to F, is the desired conclusion itself; no independent physical principle or experimental test is offered. This is a load-bearing circularity for the paper's central claim.
  2. [Section IX, Eqs. (52), (17), (58), (59)] The choice of ⊖∥ over the standard Einstein subtraction ⊖0 is unconstrained. With ⊖0, the differential (dv)0 = γ²dv∥ + γdv⊥ leads to the rest acceleration a0 = γ³a∥ + γ²a⊥ and hence to exactly the longitudinal/transverse mass split that the paper aims to eliminate. The paper acknowledges this and explicitly states that A is not the spatial part of the four-acceleration, Eq. (56). Since no experimental or operational test is derived that distinguishes the two subtractions, the claimed unification is a matter of convention rather than a result with independent predictive content.
  3. [Section XI, Eqs. (72)–(75)] The variable-mass derivation is presented as independent confirmation of the earlier definitions, but the meaning of δm needs clarification. The orthogonality condition f_ext·ẋ = 0 together with Eq. (74) gives δṁ = −ṁc²/(υ·ν), which differs from the rest-mass conservation δṁ = −ṁ expected for a closed body-plus-ejecta system unless the four-velocities coincide. Without an explicit constitutive assumption about how rest mass is transferred between the body and the small additional mass, the step from Eq. (73) to Eq. (75) is not a standard momentum balance, and Eq. (77) cannot serve as an unambiguous check of the earlier definitions.
  4. [Section XII, Eqs. (97)–(110)] The list of ten 'equivalent' definitions of inertial mass does not provide independent support for the central claim. Five of the definitions, Eqs. (101)–(103) and (110), are constructed using the same relativistic differential (dv)_rel, so their reduction to M = mγ is guaranteed by construction. The list therefore demonstrates internal consistency of the proposed convention, not a derivation of the physical content of the mass concept.
minor comments (6)
  1. [Section IX, Eqs. (47)–(48)] The notation for a∥ and a⊥ is ambiguous: the same symbols are used for ordinary acceleration components and for components of the spatial part of the four-acceleration, which makes equations such as Eq. (47) appear to assert γ²a∥ = a∥/γ². Please disambiguate the two usages.
  2. [Section III, Table I and Fig. 2] The reanalysis of Kaufmann's 1901 data is not parameter-free: the conclusion that the raw data favor Lorentz over Abraham depends on the assumed fringe-field height h′, set to h′ ≈ 1.06h in the text. The sensitivity of the five points to this parameter should be quantified, and the statement that the h version can be considered correct 'post factum' is circular if used as evidence.
  3. [Introduction, first two paragraphs] The digression on quantum mechanics, the absence of a time operator, and the Wheeler–DeWitt equation is not needed for the argument and claims more support for the three-dimensional formalism than the cited references provide. It should be shortened or removed.
  4. [Section III, Eq. (14)] Equation (14) is labeled '(incorrect)' even though the surrounding text says the inequalities are correct relative to Abraham's equalities; the label is confusing and should be explained explicitly.
  5. [Section XIII, Table II] The rank −1 assigned to mass is unusual and appears chosen to make the table symmetric; the operational meaning of a negative rank should be stated.
  6. [General] There are numerous typographical and grammatical errors, including 'corespondence' in the Section XIII title, 'proove' in Section XI, 'fource' in Eq. (72), and 'oryginal' in Section III. A careful language edit is needed before publication.

Circularity Check

3 steps flagged · score 8.0 of 10

The central F=MA unification is built into the chosen velocity-differential definition rather than derived from independent physics.

  1. self definitional [Sec. IX-X, Eqs. (54), (55), (70)]
    "in the linear part (by differential definition) takes the following form: (dv)rel =dv +γ2 v(vdv)/c2 =γ2dv‖ +dv⊥. (54) ... thanks to (53) in every direction and in every orthonormal Cartesian coordinate system the motion equation is true in the following vector form: F =mγ (dv)rel/dt =M A. (70)"

    From the standard rate form F=dp/dt=mγ³a∥+mγa⊥=mγ(γ²a∥+a⊥) (Eq. 29), and from the chosen differential (dv)_rel=γ²dv∥+dv⊥ (Eq. 54), the bracket is exactly (dv)_rel/dt. Hence (70) is F=mγA by substitution; it adds no relation beyond the definition of A. With the standard rest differential (Eq. 58) one gets a0=γ³a∥+γ²a⊥ and the longitudinal/transverse masses γ³m, γm, so the claimed 'same mass in every direction' is contingent on the nonstandard choice (54), not derived.

  2. renaming known result [Sec. IX, Eqs. (52)-(56); Sec. X, Eq. (70)]
    "The operation ⊖‖ (52) in velocity differential (53) can be equivalently replaced by ⊖ (16) or ⊖1 in Frenet base, but not by ⊖0 (17). ... In the direction of force, however, the Lorentz transformation is performed at a velocity projected on the direction of force."

    The operation ⊖∥ is defined so that the perpendicular velocity component is unchanged, which is exactly the condition producing γ²dv∥+dv⊥ rather than γ²dv∥+γdv⊥. The paper justifies the choice by saying the Lorentz transformation should be performed in the direction of force; but the force direction enters only because the target equation F=mγA requires it. No independent kinematic or experimental criterion selects ⊖∥ over ⊖0; the paper itself notes ⊖0 gives the rest acceleration and Einstein's directional masses. Thus the mass unification is a renaming of the standard decomposition under an operation chosen to make it true.

1 more flagged steps
  1. self definitional [Sec. XII, Eq. (97)]
    "1. Force and relativistic acceleration ratio (for A ≠ 0): M := F/A = F/((dvF)rel/dt). (97) All the definitions lead to the same formula M =mγ."

    This 'definition' of inertial mass is just F divided by A, with A already defined as (dv)_rel/dt; substituting (54) makes M=mγ an algebraic identity. Presenting it among ten equivalent definitions and concluding 'all the definitions lead to the same formula M=mγ' gives the appearance of a derived unification, but for this item the equality is true by definition. The other momentum/energy definitions are standard and do provide independent support for M=mγ, so this step alone would not be decisive.

full rationale

The central claim reduces by construction: Eq. (70) is algebraically identical to F=dp/dt after substituting the definition of A from Eq. (54). The paper is transparent that A is defined, and the variable-mass derivation (75)-(93) and the historical Kaufmann reanalysis are independent, so the paper is not globally circular. However, the title claim—that inertial mass is the same in every direction and longitudinal/transverse mass are unified—is the content of the chosen velocity-subtraction operation, not a consequence of it. With the standard Einstein subtraction the directional mass split reappears. The score is therefore 8: the central result is forced by definition, while ancillary derivations retain independent content. There is no load-bearing self-citation; citations to Oziewicz, Ungar, and Dragan are used as mathematical structures, not as justification for the chosen differential.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

The central derivation introduces no new physical entities. The main load-bearing assumption is the choice of velocity subtraction operation ⊖∥, which is an ad hoc convention that makes the simple F = M A identity hold. The historical reanalysis uses one hand-set parameter h'/h for the fringe field. No new particles, forces, or dimensions are introduced.

free parameters (1)
  • h'/h = 1.06 (h' = 1.873 cm)
    In the reanalysis of Kaufmann's 1901 data (Section III), the electric field fringe extension h' is set to 1.06h, which makes the results favor Lorentz's theory over Abraham's. The paper itself notes that this choice is post factum.
assumptions (3)
  • domain assumption The force on a particle is given by the rate form F = dp/dt (Eq. 28).
    Standard special relativity, adopted without dispute; the paper treats this as the unambiguous starting point.
  • ad hoc to paper The relativistic velocity differential for acceleration should be calculated with operation ⊖∥ (Eq. 52) rather than the Einstein subtraction ⊖0 (Eq. 17).
    This is the load-bearing choice that makes A parallel to F and produces F = M A. It is not derived from experiment and is one of several differential-equivalent operations; it is selected because it yields the desired simple form.
  • domain assumption The external four-force is orthogonal to four-velocity, f_ext^ν ˙x_ν = 0, in the variable-mass derivation.
    Standard property of the four-force in SR, used in Section XI to derive the mass-rate relation (74).

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Pith. "Pith review of Defining of three-dimensional acceleration and inertial mass leading to the simple form F=MA of relativistic motion equation." pith.science (2026). https://pith.science/paper/AYPFASAJ

@misc{pith2026190909084,
  author       = {Pith},
  title        = {Pith review of: Defining of three-dimensional acceleration and inertial mass leading to the simple form F=MA of relativistic motion equation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AYPFASAJ}},
  note         = {Machine review of arXiv:1909.09084}
}
read the original abstract

Newton second law of dynamics is a law of motion but also a useful definition of force (F=MA) or inertial mass (M=F/A), assuming a definition of acceleration and parallelism of force and acceleration. In the special theory of relativity, out of these three only the description of force (F=dp/dt) does not raise doubts. The greatest problems are posed by mass, which may be invariant rest mass or relativistic mass or even directional mass like longitudinal mass. This results from breaking the assumption of parallelism of force and standard acceleration. It turns out that these issues disappear if the relativistic acceleration A is defined as a relativistic velocity subtraction formula. This basic fact is obscured by some subtlety related to the calculation of the relativistic differential of velocity. It is based on the direction of force rather than on transformation to a resting system. The reference to a non-resting system generates a (seemingly) different velocity subtraction formula. Thus, the relativistic three-dimensional acceleration is neither rest acceleration, nor four-acceleration, nor standard acceleration. As a consequence, inertial mass in any direction of the force has the same value as relativistic mass. In other words, the concepts of transverse mass and longitudinal mass, which depend on velocity, have been unified. In this work a full relativistic equation is derived for the motion of a body with variable mass whose form confirmed the previously introduced definitions. In addition, these definitions are in line with the general version of the principle of mass and energy equivalence. The work presents a detailed review and discussion of different approaches to the subject in relation to original historical and contemporary texts. On this basis, a proposal is made for consistent definition of relativistic quantities associated with velocity change.

Figures

Figures reproduced from arXiv: 1909.09084 by the authors.

Figure 1
Figure 1. FIG. 1: A print from Kaufmann’s work from 1901 [ [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: The dependence of ratio of dynamic mass (trans [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Diagram showing the relations of the main ac [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗

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Reference graph

Works this paper leans on

122 extracted references · 78 canonical work pages

  1. [1]

    (97) The direction of the force is absolutely free, and the velocity subtraction rule for differential of velocity does not go beyond (16)

    Force and relativistic acceleration ratio (for A⁄= 0): M := F A = F (dvF)rel dt . (97) The direction of the force is absolutely free, and the velocity subtraction rule for differential of velocity does not go beyond (16)

  2. [2]

    This definition of mass does not refer directly to the velocity of light c and it is correct also in the Galilean spacetime

    Time component of mass-momentum four-vector: M :=pt , ˆp =mγ ∂ ∂t +mγv ∂ ∂r, (98) where ˆp is expressed here in the language of mod- ern differential geometry (classical, not quantum). This definition of mass does not refer directly to the velocity of light c and it is correct also in the Galilean spacetime

  3. [3]

    Mass energy equivalent in general form: M := E c2 = pt c2 , ˇp =mγc2dt +mγvdr. (99) This definition is not the same as (98) because energy-momentum four-covector ˇp does not exist in Galilean spacetime, which makes the correspon- dence with a non-relativistic theory difficult. Ein- stein used the formula E0 = mc2 or E = mγc2, but he eventually did not decide...

  4. [4]

    (100) This is the simplest definition of the notion of mass, but it may not be convincing in the light of the redefinition of the formula for momentum with the factor γ

    Momentum and velocity ratio (for v ⁄= 0): M := p v. (100) This is the simplest definition of the notion of mass, but it may not be convincing in the light of the redefinition of the formula for momentum with the factor γ. This definition was used, among others, by Abraham, Lewis and Tolman and Feynman

  5. [5]

    (101) The original formula (12) without the relativis- tic differential of velocity determined longitudinal mass

    Generalization of Abraham’s first formula: M := dp (dv)rel . (101) The original formula (12) without the relativis- tic differential of velocity determined longitudinal mass

  6. [6]

    (102) This definition used without the velocity substra- tion formula (11) determined the longitudinal mass

    Generalization of the Kaufmann formula: M := 1 v dE (dv)rel . (102) This definition used without the velocity substra- tion formula (11) determined the longitudinal mass

  7. [7]

    (103) In its original version (13) for Lagrangian function and without rel, this formula defines longitudinal mass

    Generalization of Abraham’s second formula: M := d2E (dv)2 rel . (103) In its original version (13) for Lagrangian function and without rel, this formula defines longitudinal mass

  8. [8]

    (104) It can be noticed that a change in the rest mass leads to relativistic mass regardless of the direction and value of jet velocity with the Lorentz factor for body velocity

    Thrust mass implies with (35) or (92): Mδm :=γ|δm|. (104) It can be noticed that a change in the rest mass leads to relativistic mass regardless of the direction and value of jet velocity with the Lorentz factor for body velocity

Show all 122 references
  1. [9]

    (105) Inertial mass favours transverse mass as it does not change during measuring (defining)

    A simple definition consistent with the Sandin lemma: M(v) = const ∧ a⁄= 0 ⇒ M := F a = F⊥ a⊥ . (105) Inertial mass favours transverse mass as it does not change during measuring (defining)

  2. [10]

    The Lobachevsky– Einstein Velocity Space

    Average longitudinal mass: M := 1 v ∫ v 0 µ‖(v)dv. (106) This definition allows us to easily calculate acceler- ation time with a constant force: F ∫ t 0 dt = ∫ v 0 µ‖(v)dv ⇒ t = Mv F , (107) which approaches∞ for v→c. And if we make the mistake of averaging the relativistic ma...

    2019

  3. [11]

    Mathematische Einf¨ uhrung in die Elektronentheorie (Mathematical introduction to the theory of electrons)

    A. H. Bucherer, “Mathematische Einf¨ uhrung in die Elektronentheorie (Mathematical introduction to the theory of electrons)”, Verlag von B. G. Teubner, Leipzig (1904)

    1904

  4. [12]

    A. H. Bucherer, “Messungen an Becquerelstrahlen. Die experimentelle Best¨ atigung der Lorentz-Einsteinschen Theorie. (Measurements of Becquerel rays. The Experi- mental Confirmation of the Lorentz-Einstein Theory)”, Physikalische Zeitschrift 9 (22), pp. 755–762 (1908)

    1908

  5. [13]

    Dynamik des Electrons (Dynamics of Electrons)

    M. Abraham, “Dynamik des Electrons (Dynamics of Electrons)”, G¨ ottinger Nachrichten, pp. 20–41, January 11 (1902)

    1902

  6. [14]

    Prinzipien der Dynamik des Elek- trons (Principles of the Dynamics of the Electrons)

    M. Abraham, “Prinzipien der Dynamik des Elek- trons (Principles of the Dynamics of the Electrons)”, Physikalische Zeitschrift 4 (1b), pp. 57–62 (1902)

    1902

  7. [15]

    Prinzipien der Dynamik des Elektrons (Principles of the Dynamics of the Electrons)

    M. Abraham, “Prinzipien der Dynamik des Elektrons (Principles of the Dynamics of the Electrons)”, Annalen der Physik 10, pp. 105–179 (1903)

    1903

  8. [16]

    Zur Theorie der Raketen (On the theory of rockets)

    J. Ackeret, “Zur Theorie der Raketen (On the theory of rockets)”, Helvetica Physica Acta 19, pp. 103–112 (1946)

    1946

  9. [17]

    Does mass really depend on velocity, dad?

    C. G. Adler, “Does mass really depend on velocity, dad?”, American Journal of Physics 55 (8), pp. 739–743 (1987)

    1987

  10. [18]

    Tests of Lorentz invariance at the Sudbury Neutrino Observatory

    B. Aharmim, S. N. Ahmed, A. E. Anthony, N. Barros, E.W. Beier, A. Bellerive, B. Beltran, M. Bergevin, S. D. Biller et al., “Tests of Lorentz invariance at the Sudbury Neutrino Observatory”, Physical Review D 98, 112013 (2018)

    2018

  11. [19]

    Powstawanie i wczesny odbi´ or szczeg´ olnej teorii wzgl¸ edno´ sci (Formation and early re- ception of special relativity)

    S. L. Ba˙ za´ nski, “Powstawanie i wczesny odbi´ or szczeg´ olnej teorii wzgl¸ edno´ sci (Formation and early re- ception of special relativity)”, Post¸ epy Fizyki 56 (6), pp. 253–267 (2005)

    2005

  12. [20]

    Review of problems of dynamics in the hyperbolic theory of special relativity

    J.F. Barrett, “Review of problems of dynamics in the hyperbolic theory of special relativity”, PIRT Conf., Im- perial Coll., London, Proceedings ISBN 1 873 694 07 5, PD Publications (Liverpool), pp. 17–30 (2002)

    2002

  13. [21]

    Gravitation and Relativity

    M. G. Bowler, “Gravitation and Relativity”, Pergamon, Elmsford, New York (1976)

    1976

  14. [22]

    Relativity Reexamined

    L. Brillouin, “Relativity Reexamined”, Academic Press, New York, London (1970)

    1970

  15. [23]

    A. Einstein, “ ¨Uber eine Methode zur Bestimmung des Verh¨ altnisses der transversalen und longitudinalen Masse des Elektrons (On a method for determination ratio of transverse and longitudal mass of electron)”, Annalen der Physik 21 (13), pp. 583–586 (1906)

    1906

  16. [24]

    ¨Uber die vom Relativit¨ atsprinzip geforderte Tr¨ agheit der Energie (On the inertia of en- ergy required by the relativity principle)

    A. Einstein, “ ¨Uber die vom Relativit¨ atsprinzip geforderte Tr¨ agheit der Energie (On the inertia of en- ergy required by the relativity principle)”, Annalen der Physik 23 (328/7), pp. 371–384 (1907)

    1907

  17. [25]

    G. von Buquoy, “Analytische Bestimmung des Gesetzes der Virtuellen Geschwindigkeiten in Mechanischer und Statischer Hinsicht (Analytical determination of the law of virtual velocities in mechanical and static terms)”, Breitkopf und Hartel, Leipzig (1812)

  18. [26]

    G. von Buquoy, “Exposition dun nouveau principe g´ en´ eral de dynamique, dont le principe des vitesses virtuelles nest quun cas particulier (Exhibition of a new general principle of dynamics, have the principle of vir- tual velocities is only a particular case)”, V Courcier, ...

  19. [27]

    Lorentz invariant relative velocity and rel- ativistic binary collisions

    M. Cannoni, “Lorentz invariant relative velocity and rel- ativistic binary collisions”, arXiv:1605.00569v2 (2016)

    2016 arXiv

  20. [28]

    From E = mc2 to the Lorentz transformations via the law of addition of relativistic velocities

    C. Criado, N. Alamo, “From E = mc2 to the Lorentz transformations via the law of addition of relativistic velocities”, European Journal of Physics 26, pp. 611– 616 (2005)

    2005

  21. [29]

    Electromagnetic mass, relativity, and the Kaufmann experiments

    J. T. Cushing, “Electromagnetic mass, relativity, and the Kaufmann experiments”, American Journal of Physics 49 (12), pp. 1133–1149 (1981)

    1981

  22. [30]

    Poincar´ e, the Dynamics of the Electron, and Relativity

    T. Damour, “Poincar´ e, the Dynamics of the Electron, and Relativity”, arXiv:1710.00706v1 (2017)

    2017 arXiv

  23. [31]

    Niezwykle szczeg´ olna teoria wzgl¸ edno´ sci. Roz. 3. Obr´ ot Thomasa–Wignera (Unusually special theory of relativity. Chap. 3. Thomas– Wigner rotation)

    A. Dragan, “Niezwykle szczeg´ olna teoria wzgl¸ edno´ sci. Roz. 3. Obr´ ot Thomasa–Wignera (Unusually special theory of relativity. Chap. 3. Thomas– Wigner rotation)”, monograph – lecture notes, www.researchgate.net/publication/265887295 (2012)

    2012

  24. [32]

    Half-page derivation of the 23 Thomas precession

    A. Dragan, T. Odrzyg´ o´ zd´ z, “Half-page derivation of the 23 Thomas precession”, American Journal of Physics 81 (8), 631 (2013)

    2013

  25. [33]

    Zur Elektrodynamik bewegter K¨ orper (On the Electrodynamics of Moving Bodies)

    A. Einstein, “Zur Elektrodynamik bewegter K¨ orper (On the Electrodynamics of Moving Bodies)”, Annalen der Physik 17, pp. 891–921, June 30 (1905)

    1905

  26. [34]

    Ist die Tr¨ agheit eines K¨ orpers von seinem Energieinhalt abh¨ angig? (Does the Inertia of a Body Depend Upon Its Energy-Content?)

    A. Einstein, “Ist die Tr¨ agheit eines K¨ orpers von seinem Energieinhalt abh¨ angig? (Does the Inertia of a Body Depend Upon Its Energy-Content?)”, Annalen der Physik 18, pp. 639–643, September 27 (1905)

    1905

  27. [35]

    Einstein Never Approved of Relativistic Mass

    E. Hecht, “Einstein Never Approved of Relativistic Mass”, The Physics Teacher 47, September (2009)

    2009

  28. [36]

    Defence of Relativistic Mass

    book was equivalent to d) and not c) (although it originally looked like b)). It is worth noting that even in 1935 Einstein propagated the formula c) (for c = 1), while formula d) actually ignored [25, 31]. Another element of Okun’s work was a formula for the force of gravity,...

    2004

  29. [37]

    Elementary Derivation of the Equivalence of Mass and Energy

    A. Einstein, “Elementary Derivation of the Equivalence of Mass and Energy”, American Mathematical Society Bulletin 41, pp. 223–230 (1935)

    1935

  30. [38]

    E = mc2: The Most Urgent Problem of Our Time

    A. Einstein, “ E = mc2: The Most Urgent Problem of Our Time”, Science Illustrated (The manuscript and reprints have survived) (1946)

    1946

  31. [39]

    Alternative realization for the composition of relativistic velocities

    M. Fern´ andez-Guasti, “Alternative realization for the composition of relativistic velocities”, Proc. of SPIE Vol. 8121, 812108 (2011)

    2011

  32. [40]

    The Feyn- man Lectures on Physics

    R. Feynman, R. B. Leighton, M. Sands, “The Feyn- man Lectures on Physics”, Vol. 1, Sec. 15-1 “The prin- ciple of relativity”, Sec. 15-9 “Equivalence of mass and energy”, Sec. 16-4 “Relativistic mass”, Addison-Wesley (1963, 2005), Basic Books (2011)

    2011

  33. [41]

    J. H. Field, ‘Einstein and Planck on mass-energy equiv- alence in 1905-06: a modern perspective”, European Journal of Physics 35 (5) (2014)

    2014

  34. [42]

    J. H. Field, ‘Feynman’s dynamical route to special rela- tivity via work-to-energy conversion and Newton’s sec- ond law”, Fundamental Journal of Modern Physics 11 (2), pp. 191–226 (2018)

    2018

  35. [43]

    Einstein’s 1935 Derivation of E = mc2

    F. Flores, “Einstein’s 1935 Derivation of E = mc2”, Studies in History and Philosophy of Modern Physics 29 (2), pp. 223–243 (1998)

    1998

  36. [44]

    The Theory of Space, Time and Gravitation

    V. Fock, “The Theory of Space, Time and Gravitation”, 1st ed. 1959, 2nd rev. ed., translated by N. Kemmer, Pergamon Press (1964)

    1964

  37. [45]

    The lack of rotation in a moving right angle lever

    J. Franklin, “The lack of rotation in a moving right angle lever”, European Journal of Physics 29, pp. N55-N58 (2008)

    2008

  38. [46]

    Relikt w fizyce – poj¸ ecie masy relatywisty- cznej (Relic in physics – concept of relativistic mass)

    J. Gluza, “Relikt w fizyce – poj¸ ecie masy relatywisty- cznej (Relic in physics – concept of relativistic mass)”, Fizyka w Szkole 5, 269 (1992)

    1992

  39. [47]

    Koczan, “Wyprowadzanie promieniowania Hawkinga: Cz¸ e´ s´ c II

    G. Koczan, “Wyprowadzanie promieniowania Hawkinga: Cz¸ e´ s´ c II. Mechanika kwantowa oraz statystyczna stan´ ow fotonowych (Derivation of Hawking Radiation: Part II. Quantum and statistical mechanics of photon states)”, Fo- ton 141 Lato, pp. 4–32 (2018), English version: www....

    2018

  40. [48]

    A Brief History of Time: From the Big Bang to Black Holes

    S. Hawking, “A Brief History of Time: From the Big Bang to Black Holes”, Bantam Books (1988)

    1988

  41. [49]

    The Universe in a Nutshell

    S. Hawking, “The Universe in a Nutshell”, Bantam Spectra (2001)

    2001

  42. [50]

    The illusion of time

    A. Jaffe, “The illusion of time”, Nature 556 (7701), pp. 304–305 (2018)

    2018

  43. [51]

    Electromagnetic Models of the Electron and the Transition from Classical to Rel- ativistic Mechanics

    M. Janssen, M. Mecklenburg, “Electromagnetic Models of the Electron and the Transition from Classical to Rel- ativistic Mechanics”, text from conference: The Inter- action between Mathematics, Physics and Philosophy from 1850 to 1940, Carlsberg Academy, Copenhagen, September 2...

    2002

  44. [52]

    Contents and commentary on William Moore’s A treatise on the motion of rockets and an es- say on naval gunnery

    W. Johnson, “Contents and commentary on William Moore’s A treatise on the motion of rockets and an es- say on naval gunnery”, International Journal of Impact Engineering 16 (3), pp. 499–521, June (1995)

    1995

  45. [53]

    W. Kaufmann, “Die magnetische und elektrische Ablenkbarkeit der Becquerelstrahlen und die scheinbare Masse der Elektronen (The magnetic and electrical de- flectability of Becquerel rays and the apparent mass of electrons)”, G¨ ottinger Nachrichten (2), pp. 143–155 (1901)

    1901

  46. [54]

    ¨Uber die elektromagnetische Masse des Elektrons (On the Electromagnetic Mass of the Elec- trons)

    W. Kaufmann, “ ¨Uber die elektromagnetische Masse des Elektrons (On the Electromagnetic Mass of the Elec- trons)”, G¨ ottinger Nachrichten (5), pp. 291–296, July 26 (1902)

    1902

  47. [55]

    Die elektromagnetische Masse des Elek- trons (The Electromagnetic Mass of the Electrons)

    W. Kaufmann, “Die elektromagnetische Masse des Elek- trons (The Electromagnetic Mass of the Electrons)”, Physikalische Zeitschrift 4 (1b), pp. 54–57, October 10 (1902)

    1902

  48. [56]

    ¨Uber die Elektromagnetische Masse der Elektronen (On the Electromagnetic Mass of Elec- tron)

    W. Kaufmann, “ ¨Uber die Elektromagnetische Masse der Elektronen (On the Electromagnetic Mass of Elec- tron)”, G¨ ottinger Nachrichten (3), pp. 90–103 (1903)

    1903

  49. [57]

    ¨Uber die Konstitution des Elektrons (On the Constitution of the Electrons)

    W. Kaufmann, “ ¨Uber die Konstitution des Elektrons (On the Constitution of the Electrons)”, Sitzungs- berichte der K¨ oniglich Preussischen Akademie der Wis- senschaften (45), pp. 949–956 (1905)

    1905

  50. [58]

    ¨Uber die Konstitution des Elektrons (On the Constitution of the Electron)

    W. Kaufmann, “ ¨Uber die Konstitution des Elektrons (On the Constitution of the Electron)”, Annalen der Physik 19, pp. 487–553 (1906)

    1906

  51. [59]

    A Test Theory of Special Relativity: I. Simultaneity and Clock Synchronization

    R. Mansouri, R. U. Sexl, “A Test Theory of Special Relativity: I. Simultaneity and Clock Synchronization”, General Relativity and Gravitation 8 (7), pp. 497–513 (1977)

    1977

  52. [60]

    Data Tables for Lorentz and CPT Violation

    A. Kostelecky, N. Russell, “Data Tables for Lorentz and CPT Violation”, Review of Modern Physics 83, 11 (2011), https://arxiv.org/abs/0801.0287v13 (2020)

    2011

  53. [61]

    On inert properties of particles in clas- sical theory

    B. P. Kosyakov, “On inert properties of particles in clas- sical theory”, arXiv:hep-th/0208035v1 (2002)

    2002 arXiv

  54. [62]

    Teoriya polya (The Clas- sical Theory of Fields)

    L. D. Landau, E. M. Lifshitz, “Teoriya polya (The Clas- sical Theory of Fields)”, Russian (1941, 1948), English: Addison-Wesley (1951), Pergamon Press (1959)

    1951

  55. [63]

    La physique des ´ electrons (The physics of electrons)

    P. Langevin, “La physique des ´ electrons (The physics of electrons)”, Revue g´ en´ erale des sciences pures et ap- pliqu´ ees 16 (6), pp. 257–276, March 30 (1905)

    1905

  56. [64]

    Special Relativity and Lorentz Invari- ance

    C. L¨ ammerzahl, “Special Relativity and Lorentz Invari- ance”, Annalen der Physik 14 (1-3), pp. 71–102 (2005)

    2005

  57. [65]

    A revision of the Fundamental Laws of Matter and Energy

    G. N. Lewis, “A revision of the Fundamental Laws of Matter and Energy”, Philosophical Magazine S. 6 Vol. 16 No. 95, pp. 705–717 (1908)

    1908

  58. [66]

    The Principle of Rela- tivity, and Non-Newtonian Mechanics

    G. N. Lewis, R. C. Tolman, “The Principle of Rela- tivity, and Non-Newtonian Mechanics”, Proceedings of the American Academy of Arts and Sciences 44 (25), pp. 709–726 (1909)

    1909

  59. [67]

    Simplified Theory of Electrical and Op- tical Phenomena in Moving Systems

    H. A. Lorentz, “Simplified Theory of Electrical and Op- tical Phenomena in Moving Systems”, Proceedings of the Royal Netherlands Academy of Arts and Sciences 1, pp. 427–442 (1899)

  60. [68]

    Electromagnetic phenomena in a system moving with any velocity smaller than that of light

    H. A. Lorentz, “Electromagnetic phenomena in a system moving with any velocity smaller than that of light”, 24 Proceedings of the Royal Netherlands Academy of Arts and Sciences 6, pp. 809-831 (1904)

    1904

  61. [69]

    Das Relativit¨ atsprinzip. Drei Vorlesun- gen gehalten in Teylers Stiftung zu Haarlem. (The Rela- tivity Principle. Three lectures held at the Teylers Foun- dation in Haarlem.)

    H. A. Lorentz, “Das Relativit¨ atsprinzip. Drei Vorlesun- gen gehalten in Teylers Stiftung zu Haarlem. (The Rela- tivity Principle. Three lectures held at the Teylers Foun- dation in Haarlem.)”, B. G. Teubner, Leipzig and Berlin (1914)

    1914

  62. [70]

    Die Mechanik in ihrer Entwicklung - His- torisch kritisch dargestellt (The Science of Mechanics - A Critical and Historical Account of Its Development)

    E. Mach, “Die Mechanik in ihrer Entwicklung - His- torisch kritisch dargestellt (The Science of Mechanics - A Critical and Historical Account of Its Development)”, first German (1883), first English (1893), fourth En- glish: T. J. McCormack, The Open Court Publishing CO. (1919)

    1919

  63. [71]

    The Concept of Mass

    L. B. Okun, “The Concept of Mass”, Physics Today 42 (6), pp. 31–36 (1989)

    1989

  64. [72]

    E = mc2

    K. A. Meissner, “ E = mc2”, multimedia lecture in National Centre for Nuclear Research May 23 (2011) and Faculty of Physics University of Warsaw (2014), https://www.youtube.com/watch?v= VDAy9zyvZ0 (2016)

    2011

  65. [73]

    Dinamika tochki peremnnoy massy (Dynamics of a point of variable mass)

    I. V. Meshchersky, “Dinamika tochki peremnnoy massy (Dynamics of a point of variable mass)”, Akademia Nauk, Peterburskij Universitet, St Petersburg (1897)

  66. [74]

    Uravneniya dvizheniya tochki pere- mennoy massy v obshchem sluchaye (Equations of mo- tion of a variable mass point in the general case)

    I. V. Meshchersky, “Uravneniya dvizheniya tochki pere- mennoy massy v obshchem sluchaye (Equations of mo- tion of a variable mass point in the general case)”, St. Petersburg Polytechnic University News 1, pp. 77–118 (1904)

    1904

  67. [75]

    Die Grundgleichungen fr die elektro- magnetischen Vorg¨ ange in bewegten K¨ orpern (The Fun- damental Equations for Electromagnetic Processes in Moving Bodies)

    H. Minkowski, “Die Grundgleichungen fr die elektro- magnetischen Vorg¨ ange in bewegten K¨ orpern (The Fun- damental Equations for Electromagnetic Processes in Moving Bodies)”, Nachrichten von der Gesellschaft der Wissenschaften zu G¨ ottingen, Mathematisch- Physikalische Klas...

    1908

  68. [76]

    A Treatise on the Motion of Rockets and An Essay on Naval Gunnery

    W. Moore, “A Treatise on the Motion of Rockets and An Essay on Naval Gunnery”, The Military Academy at Woolwich, G. & S. Robinson, London (1813)

  69. [77]

    On the question of the electromagnetic momentum of a charged body

    V. B. Morozov, “On the question of the electromagnetic momentum of a charged body”, Physics–Uspekhi 54, pp. 371–374 (2011)

    2011

  70. [78]

    First Test of Lorentz Invariant in the Weak Decay of Polarized Nuclei

    S. E. M¨ uller, E. A. Dijck, H. Bekker, J. E. van den Berg, O. B¨ oll, S. Hoekstra, K. Jungmann, C. Meinema, J. P. Noordmans et al., “First Test of Lorentz Invariant in the Weak Decay of Polarized Nuclei”, Physical Review D 88, 071901 (2013)

    2013

  71. [79]

    On Lorentz- invariant spin-2 theories

    A. Naruko, R. Kimura, D. Yamauchi, “On Lorentz- invariant spin-2 theories”, Physical Review D 99, 084018 (2019)

    2019

  72. [80]

    Philosophiae Naturalis Principia Mathe- matica (Mathematical Principles of Natural Philoso- phy) (Matematyczne zasady filozofii przyrody)

    I. Newton, “Philosophiae Naturalis Principia Mathe- matica (Mathematical Principles of Natural Philoso- phy) (Matematyczne zasady filozofii przyrody)”, Lon- don (1687), A. Motte (1729), J. Wawrzycki, Copernicus Center Press, Cracow (2011)

    2011

  73. [81]

    A. Nowik, “Prawda jest jedna, a g lupstw tysi¸ ace – uwagi do dyskusji o masie relatywistycznej (The truth is one, and the lies are thousands – remarks on the discus- sion about the relativistic mass)”, Fizyka w Szkole z Astronomi¸ a 4, pp. 33–34 and 37 (2016)

    2016

  74. [82]

    On the abuse and use of relativistic mass

    G. Oas, “On the abuse and use of relativistic mass”, arXiv:physics/0504110v2 (2005)

    2005 arXiv

  75. [83]

    Sur la dynamique de l´ electron (On the Dynamics of the Electron)

    H. Poincar´ e, “Sur la dynamique de l´ electron (On the Dynamics of the Electron)”, Comptes rendus hebdo- madaires des s´ eances de l’Acad´ emie des sciences 140, pp. 1504–1508, June 5 (1905)

    1905

  76. [84]

    Energy and Mass in Relativity Theory

    L. B. Okun, “Energy and Mass in Relativity Theory”, World Scientific (2009)

    2009

  77. [85]

    Mass versus relativistic and rest masses

    L. B. Okun, “Mass versus relativistic and rest masses”, American Journal of Physics 77 (5), pp. 430–431 (2009)

    2009

  78. [86]

    Energy in Special Relativity

    Z. Osiak, “Energy in Special Relativity”, Theoreti- cal Physics 4(1), pp. 22–25, Isaac Scientific Publishing (2019), www.researchgate.net /publication/322626086 (2018), first preprint 1512.0449 (2015)

    2019

  79. [87]

    How do you add relative velocities?

    Z. Oziewicz, “How do you add relative velocities?”, Group Theoretical Methods in Physics, Conference Se- ries Number 185, pp. 439–444, CRC Press (2004)

    2004

  80. [88]

    Ternary relative velocity

    Z. Oziewicz, “Ternary relative velocity”, arXiv:1104.0682v1 (2011)

    2011 arXiv

  81. [89]

    Relativity groupoid, instead of relativity group

    Z. Oziewicz, “Relativity groupoid, instead of relativity group”, International Journal of Geometric Methods in Modern Physics 04 (05), pp. 739–749 (2007)

    2007

  82. [90]

    Relativity without Lorentz group

    Z. Oziewicz, “Relativity without Lorentz group”, mono- graph, www.academia.edu/17230451 (2004, 2007)

    2004

  83. [91]

    The Road to Reality

    R. Penrose, “The Road to Reality”, Chap. 18.6–18.7, Jonathan Cape, London (2004–2007)

    2004

  84. [92]

    Variable mass systems dynam- ics in engineering mechanics education

    C. P. Pesce, L. Casetta, “Variable mass systems dynam- ics in engineering mechanics education”, Proceedings of COBEM, 19th International Congress of Mechanical Engineering, Brasilia (2007)

    2007

  85. [93]

    Das Prinzip der Relativit¨ at und die Grund- gleichungen der Mechanik (The Principle of Relativity and the Fundamental Equations of Mechanics)

    M. Planck, “Das Prinzip der Relativit¨ at und die Grund- gleichungen der Mechanik (The Principle of Relativity and the Fundamental Equations of Mechanics)”, Verh. D. Phys. Ges. 8, pp. 136–141, March 23 (1906)

    1906

  86. [94]

    M. Planck, “Die Kaufmannschen Messungen der Ablenkbarkeit derβ-Strahlen in ihrer Bedeutung f¨ ur die Dynamik der Elektronen (The Measurements of Kauf- mann on the Deflectability of β-Rays in their Impor- tance for the Dynamics of the Electrons)”, Physikalische Zeitschrift 7, pp...

    1906

  87. [95]

    On the Steady Motion of an Electrified Ellipsoid

    G. F. C. Searle, “On the Steady Motion of an Electrified Ellipsoid”, Philosophical Magazine 5, 44(269), pp. 329– 341 (1897)

  88. [96]

    Sur le mouvement dun systeme de corps, en supposant les masses variables (On the motion of a body system, assuming variable masses)

    S. D. Poisson, “Sur le mouvement dun systeme de corps, en supposant les masses variables (On the motion of a body system, assuming variable masses)”, Bull. Sci. Soc. Philomat. 60-2, Paris (1819)

  89. [97]

    Derivation of the relativistic momentum and relativistic equation of motion from Newton’s sec- ond law and Minkowskian space-time geometry

    K. R¸ ebilas, “Derivation of the relativistic momentum and relativistic equation of motion from Newton’s sec- ond law and Minkowskian space-time geometry”, Ape- iron 15 (3), July (2008)

    2008

  90. [98]

    Comment on Elementary analysis of the special relativistic combination of velocities, Wigner ro- tation and Thomas precession

    K. R¸ ebilas, “Comment on Elementary analysis of the special relativistic combination of velocities, Wigner ro- tation and Thomas precession ”, European Journal of Physics 34, pp. L55–L61 (2013)

    2013

  91. [99]

    Lorentz-invariant three-vectors and alter- native formulation of relativistic dynamics

    K. R¸ ebilas, “Lorentz-invariant three-vectors and alter- native formulation of relativistic dynamics”, American Journal of Physics 78, 294 (2010)

    2010

  92. [100]

    binary-ternary

    in the context of centripetal acceleration in quan- tum mechanics. Thomas precession surprised even Ein- stein himself [19] and, according to R¸ ebilas, he surprises physicists to this day [86]. Indeed, the physical phe- nomenon of Thomas precession in the face of the mathe- m...

    2004

  93. [101]

    Introduction to Special Relativity

    W. Rindler, “Introduction to Special Relativity”, Ox- ford University Press (1982)

    1982

  94. [102]

    Relativity: Special, General and Cosmo- logical

    W. Rindler, “Relativity: Special, General and Cosmo- logical”, Oxford University Press (2001, 2006)

    2001

  95. [103]

    Putting to Rest Mass Miscon- ceptions

    W. Rindler, M. A. Vandyck, P. Murugesan, S. Ruschin, C. Sauter, L. B. Okun, “Putting to Rest Mass Miscon- ceptions”, Physics Today, Letters 43 (5), pp. 13–14, 115, 117, May (1990)

    1990

  96. [104]

    What is mass?

    J. Roche, “What is mass?”, European Journal of Physics 26, pp. 1–18 (2005)

    2005

  97. [105]

    The Order of Time

    C. Rovelli, “The Order of Time”, Penguin Books (2018). 25

    2018

  98. [106]

    In defense of relativistic mass

    T. R. Sandin, “In defense of relativistic mass”, Ameri- can Journal of Physics 59 (11), pp. 1032–1036 (1991)

    1991

  99. [107]

    Gravitational Shielding and the Equiva- lence Principle

    L. A. Savrov, “Gravitational Shielding and the Equiva- lence Principle”, Gravitation and Cosmology 18 (4), pp. 270–278 (2012)

    2012

  100. [108]

    High-precision measurement of the atomic mass of the electron

    S. Sturm, F. K¨ ohler, J. Zatorski, A. Wagner, Z. Har- man, G. Werth, W. Quint, C. H. Keitel, K. Blaum, “High-precision measurement of the atomic mass of the electron”, Nature 506, pp. 467–470 (2014)

    2014

  101. [109]

    The derivation of the general form of kinematics with the universal reference system

    K. Szostek, R. Szostek, “The derivation of the general form of kinematics with the universal reference system”, Results in Physics 8, pp. 429–437 (2018)

    2018

  102. [110]

    Spacetime physics - intro- duction to special relativity

    E. F. Taylor, J. A. Wheeler, “Spacetime physics - intro- duction to special relativity”, W.H. Freeman and Com- pany (1966, 1992)

    1966

  103. [111]

    The velocity of light in uniformly moving frame, A dissertation

    F. R. Tangherlini, “The velocity of light in uniformly moving frame, A dissertation”, Stanford University (1958), The Abraham Zelmanov Journal Vol. 2, pp. 44– 110 (2009)

    1958

  104. [112]

    Motion of the spinning electron

    L. H. Thomas, “Motion of the spinning electron”, Na- ture 117, 514 (1926)

    1926

  105. [113]

    Issledovaniye mirovykh prostranstv reaktivnymi priborami (Exploration of world spaces by reactive devices)

    K. Tsiolkovsky, “Issledovaniye mirovykh prostranstv reaktivnymi priborami (Exploration of world spaces by reactive devices)”, A Scientific-Philosophical and Lit- erary Journal (in Russian) No. 5, St Petersburg May (1903)

    1903

  106. [114]

    Non-Newtonian Mechanics. The Mass of a Moving Body

    R. Tolman, “Non-Newtonian Mechanics. The Mass of a Moving Body”, Philosophical Magazine 23(135), pp. 375–380 (1912)

    1912

  107. [115]

    Special Theory of Relativity

    V. A. Ugarov, “Special Theory of Relativity”, Russian (1969), English Y. Atanov Mir (1979)

    1969

  108. [116]

    Thomas precession: its underlying gy- rogroup axioms and their use in hyperbolic geometry and relativistic physics

    A. A. Ungar, “Thomas precession: its underlying gy- rogroup axioms and their use in hyperbolic geometry and relativistic physics”, Foundations of Physics 27, pp. 881-951 (1997)

    1997

  109. [117]

    Gyrogroups, the Grouplike Loops in the Service of Hyperbolic Geometry and Einstein’s Special Theory of Relativity

    A. A. Ungar, “Gyrogroups, the Grouplike Loops in the Service of Hyperbolic Geometry and Einstein’s Special Theory of Relativity”, Quasigroups and Related Sys- tems 15, pp. 141–168 (2007)

    2007

  110. [118]

    Momentum in the Dynamics of Variable-Mass Systems: Classical and Relativistic Case

    J. Wolny, R. Strza lka, “Momentum in the Dynamics of Variable-Mass Systems: Classical and Relativistic Case”, Acta Physica Polonica A 135(3), pp. 475–479 (2019)

    2019

  111. [119]

    Historia fizyki – od czas´ ow naj- dawniejszych do wsp´ o lczesno´ sci (History of physics – from the earliest times to the present day)

    A. K. Wr´ oblewski, “Historia fizyki – od czas´ ow naj- dawniejszych do wsp´ o lczesno´ sci (History of physics – from the earliest times to the present day)”, PWN (2007)

    2007

  112. [120]

    Wst¸ ep do fizyki (Introduction to physics)

    A. K. Wr´ oblewski, J. A. Zakrzewski, “Wst¸ ep do fizyki (Introduction to physics)” Vol. 1, PWN (1976, 1984)

    1976

  113. [121]

    Extraction of the electron mass fromg factor measure- ments on light hydrogenlike ions

    J. Zatorski, B. Sikora, S. G. Karshenboim, S. Sturm, F. K¨ ohler-Langes, K. Blaum, C. H. Keitel, Z. Harman, “Extraction of the electron mass fromg factor measure- ments on light hydrogenlike ions”, Physical Review A 96, 012502 (2017)

    2017

  114. [122]

    Gravitational mass of composite systems

    M. Zych, L. Rudnicki, I. Pikovski, “Gravitational mass of composite systems”, Physical Review D 99, 104029 (2019)

    2019

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.