Tolman-R · Source catalogue

A Google Books scan of the University of California Press 1917 first edition (249 PDF pages, 248 OCR'd; title page p.8, contents p.12) [read]. Tolman, a physical chemist at Berkeley, presents Einstein's special relativity as a working tool for theoretical physicists. Chapters I-II survey Galilean/Newtonian space and time and ether theory; he accepts the relativity postulate 'as an experimental fact' (p.38), citing a long list of null ether-drift experiments (Michelson-Morley, Trouton-Noble, etc.), and argues against emission (Ritz-type) theories using the Comstock and de Sitter binary-star argument (pp.41-43). Chapter III (following Lewis and Tolman 1909) derives time dilation with a transverse light clock, Lorentz contraction with a longitudinal light round trip, clock-setting offset l'V/c^2, velocity composition (c+c=c; c/2 + c/2 = 4c/5), mass m = m0/sqrt(1-V^2/c^2) from a colliding-spheres argument, and Delta E = c^2 Delta m; Tolman says he lays 'no stress on mathematical elegance or logical exactness' there (p.45). Chapter IV obtains the Lorentz transformation 'by trial' from three conditions (Newtonian limit, V -> -V symmetry, invariance of x^2+y^2+z^2-c^2t^2). Chapters V-VII cover kinematic applications (Doppler, aberration, Fresnel drag), particle dynamics, mass-energy, systems of particles and a modified Lagrangian/Hamiltonian. Chapter VIII does relativistic statistical mechanics (Maxwell-type distribution, equipartition, a temperature scale). Chapter IX states a relativistic principle of least action with a kinetic potential H such that H/sqrt(1-u^2/c^2) is invariant. Chapter X builds relativistic elasticity: H = -E0 sqrt(1-u^2/c^2), stress transformations, energy and momentum density, an unsymmetrical stress tensor, and the angular-momentum 'right-angled lever' paradox, resolved by energy flow through the stressed lever. Chapter XI treats a moving thermodynamic system: entropy invariant, pressure invariant, temperature T = T0 sqrt(1-u^2/c^2), momentum and energy of a moving system and the hohlraum (black-body cavity). Chapter XII sets up Maxwell-Lorentz electrodynamics from a least-action principle (the Lagrangian is assumed, not derived; the deep read notes that the transformation of the last terms of eq. 217 into eq. 225 is 'a complicated one and it has not seemed necessary to present it here', p.185) and derives the field and charge-density transformations (227)-(229); Chapter XIII is Minkowski-Wilson-Lewis four-dimensional analysis. Appendices list symbols and vector notation. Deep-read check: SymPy and page-image reading found no mathematical errors in the printed equations checked across Ch. III-VI, VIII, X-XIII; expository gaps and roundings are noted in deep/. The rounding: Tolman writes 10^21 ergs for 1 gram (Ch. III 'approx.', section 105, and section 167 without 'approx.'), while section 77 eq. (87) gives 1 gram = 9 x 10^20 ergs and 8.99 x 10^20 follows from his own c. Several Step 1a digest errors were found and corrected by the deep reads (e.g. the c/2 + c/2 example is at p.70 not p.54; digest forms of eqs. 13, 17, 27, 168, 173, 204 are wrong); where digest and deep read differ the deep read governs. ADDED AFTER QE (deep reads of Ch. V, VI, VIII, XII, XIII): (1) Section 46 (PDF p.68, book p.51) proposes a time-dilation test: canal-ray atoms as 'little clocks', viewed at right angles to the beam, expecting lower frequency than light from atoms at rest; no number, apparatus or experimenter is given, and eq. (40) nu = nu0 sqrt(1-V^2/c^2) (section 54) gives a shift of -V^2/(2c^2) (about 2.1e-5 at V/c = 0.0065 [calc, deep read]). Ives and Stilwell (1938) later measured the same quantity longitudinally, with forward and backward lines [memory, medium-high; Ives himself favoured a Lorentz-type ether, memory, medium; web-check pending]. (2) Section 52 (p.71-72): a causal signal faster than light would give an effect before its cause in some frame, but Tolman words it cautiously ('might not be a logical impossibility') and allows non-causal superluminal 'motion' (blocks with alarm clocks). (3) Section 77 (PDF pp.101-102): Tolman says experimental proof of the mass-energy relation 'will be hard to find' and, outside the electron experiments (section 64, Comstock 1908 cited) and the energy-momentum relations of light, 'such evidence has not yet been forthcoming'; he suggests radioactive decay might account for 'the lack of exact relations between the atomic weights of the successive products of radioactive decomposition' (no numbers, a 'might'); footnote p.102: 'our theory points to the presence of enormous stores of interatomic energy which are still left in substances cooled to the absolute zero'. Section 78 (pp.102-104): a collision thought experiment shows elastic potential energy must carry mass for mass to be conserved. (4) Section 105 (PDF p.118): for particles of negligible mass E = 3nRT, twice the Newtonian (3/2)nRT; a mol at 300 K would have mass 3 x 8.31e7 x 300 / 10^21 = 7.47e-11 g (printed; 8.3e-11 g with c^2 = 8.99e20), 'a field of fascinating if profitless speculation'. Section 106: K = 12.4e7 T + (7.77/M) 1e-6 T^2 erg for one mol (M in grams), second term 3.5e-6 percent of the first for electron-mass particles at 300 K and 3.5e-4 percent at 30,000 K, so equipartition is 'substantially exact'; the deep read finds this follows for an ideal non-interacting classical gas, and Tolman's estimate is a lower bound (exact low-temperature correction about 1.9 times larger). Chapter VIII follows Jeans (1916) and Planck (1913), flags the ergodic assumption in a footnote, and states the exactly equipartitioned quantity is <m0 u^2/sqrt(1-u^2/c^2)> = 3kT, not the kinetic energy. (5) Section 159 (PDF p.189, quoted in full by the deep read): 'We also see that the electromotive force which acts on a charge moving through a magnetic field finds its interpretation as an electric force provided we make use of a system of coordinates which are themselves stationary with respect to the charge. Such considerations throw light on such questions, for example, as to the seat of the electromotive forces in homopolar electric dynamos where there is relative motion of a conductor and a magnetic field.' Three sentences; no equations, no Faraday disc, no experiment; the deep read notes that rotating conductor elements are accelerated and Tolman's transformations are for non-accelerated coordinates (his section 161), so the passage is a pointer, not a solution. (6) Sections 165-167 (PDF pp.193-198): eq. (235) E = (m0 c^2 + E0)/sqrt(1-u^2/c^2), with the integration constant fixed by the convention that zero energy goes with zero mass and phi(u) taken from the mechanical result (82); the system is inside a shell impermeable to radiation, and the 4/3 electromagnetic-mass problem is not discussed; section 167 concludes 'matter and energy are but different names for the same fundamental entity, 10^21 ergs of energy having the mass 1 gram'. (7) Sections 168-172 (PDF pp.198-204): Maxwell's equations in media and the moving-medium relations (245)-(250) (equal to Minkowski's relations [memory, high]); section 172 gives eq. (251) D_z = epsilon E_z + (V/c)(epsilon mu - 1) H_y for a dielectric moving along X in a magnetic field along Y. Tolman says it is 'in complete accord with the celebrated experiment of H. A. Wilson' (rotating hollow dielectric cylinder, axial magnetic field, electrometer); for permeability near 1 it reduces to (epsilon - 1)(V/c) H_y 'and this was found to fit the experimental facts'. He adds: 'It would be a matter of great interest to repeat the Wilson experiment with a dielectric of high permeability so that we could test the complete equation (251). This is of some importance since the original Lorentz theory led to a different equation, D_z = epsilon E_z + (V/c)(epsilon - 1) mu H_y.' The two forms differ by (V/c)(mu - 1) H_y, so Wilson's non-magnetic dielectrics could not separate them. Tolman gives no date, numbers or citation for Wilson; the deep reader's recollection that a later rotating-cylinder experiment with a magnetic dielectric (Wilson and Wilson, about 1913) favoured the Minkowski form is [memory, low-medium] and not web-checked. (8) Chapter XIII: Tolman uses a real time axis in a non-Euclidean four-space of signature (+,+,+,-) following Wilson and Lewis, not Minkowski's imaginary ict; (317) div T_m = 0 reproduces the Ch. X eq. (184) and the energy-conservation equation; (328)-(330) for the electromagnetic tensor were rebuilt in SymPy and are correct; Tolman defines a tensor by a divergence condition and does not prove the covariance of T_m and T_e (an unstated assumption); he warns that extension in time is not of the same nature as extension in space. (9) Preface (PDF p.21, from the QE read of the scan): Tolman deliberately leaves out accelerated frames and Einstein's latest work on gravity and acceleration. UNCORRECTED DIGEST ERRORS (the deep reads govern): c given as 2.9986 x 10^8 cm/s at digest p.27-28 (scan: 2.9986 x 10^10); '7.47 x 10^-8 grams' (printed 7.47 x 10^-11 g); K = '12.4 x 10^-12 T + (7.77/10^8) T^2' (printed 12.4 x 10^7 T + (7.77/M) 1e-6 T^2); the digest's (132) series with minus signs (all terms are plus); E = (1/(1-u^2/c^2))(mc^2 + E0) (printed (235): E = (m0 c^2 + E0)/sqrt(1-u^2/c^2)); '10^11 ergs ... 1 gram' (printed 10^21); Wilson equation with 'u(epsilon mu - 1)H_x' (printed (V/c)(epsilon mu - 1)H_y, field along Y); digest says equipartition 'approximately' holds for electron mass (Tolman: 'substantially exact'). The Ch. III-IV and X-XI digest errors listed earlier stand.

Key claims

• The speed of light is the same for all observers regardless of source motion, and absolute translatory motion is undetectable, so space and time measurements must be relative (the two postulates, pp.37-39); the book itself says the optical experiments that would decide between Einstein's and Ritz's theory 'have never been performed' (section 22, PDF p.43).
• A moving clock runs slow by the factor sqrt(1-V^2/c^2), and a moving rod is shortened by the same factor along the motion (Sections 25-27).
• Clocks synchronized in a moving system are out of step for a stationary observer by l'V/c^2 (Section 28, stated without derivation).
• Velocities compose as u = (V+u')/(1+Vu'/c^2), so no combination of sub-light speeds reaches c; c/2 + c/2 gives 4c/5 (Section 30; p.70).
• The mass of a moving body is m = m0/sqrt(1-u^2/c^2) (Lewis-Tolman colliding-spheres argument, Section 31; confirmed in Tolman's account by Kaufmann, Bucherer and Hupka electron experiments, p.56).
• Energy and mass are different names for the same entity: Delta E = c^2 Delta m (Section 32).
• The Lorentz transformation x' = kappa(x-Vt), t' = kappa(t-Vx/c^2) follows from the Newtonian limit, V -> -V symmetry and invariance of the light-sphere equation, and light speed is an upper limit (Sections 33-38).
• Relativistic particle mechanics follows from a modified Lagrangian with kinetic potential H such that H/sqrt(1-u^2/c^2) is Lorentz invariant (Chapters VII, IX).
• Momentum density equals energy-flow density divided by c^2, including energy carried by stresses, so a strained body moving along X has transverse momentum g_y = t_xy u/c^2 (eqs. 172, Section 139).
• A moving stressed right-angled lever needs an external turning moment F1 l1 V^2/c^2 to stay in equilibrium, because the energy flowing through it carries angular momentum (Section 136; the lever paradox of Lewis and Tolman 1909).
• The stress tensor of a moving elastic body is unsymmetrical, and p = t + g u is symmetric (eqs. 175-178), with Eulerian equation -div p = dg/dt (eq. 184).
• Entropy and pressure are Lorentz invariants (S = S0, p = p0), while temperature of a moving body transforms as T = T0 sqrt(1-u^2/c^2), i.e. T/sqrt(1-u^2/c^2) is invariant (eqs. 197, 200, 201).
• The momentum of a moving thermodynamic system is G = (E + pv)u/c^2, and for a hohlraum G = (4/3) a v0 T0^4 u/(sqrt(1-u^2/c^2) c^2) (eqs. 206, 208) (the 4/3 holds only for a cavity held by external pressure; for a closed system including its wall stresses G = E u/c^2, eq. 193).
• Maxwell-Lorentz field equations are taken as the basis of electromagnetism (the least-action Lagrangian is assumed, not derived); the fields and charge density transform by (227)-(229), with electric charge invariant because the density ratio equals the Lorentz-contraction ratio (sections 154-157; eq. 229 uses u_x, verified on the scan image p.186; the Gutenberg text misprints u_z).
• A system containing electromagnetic energy E0 behaves as a mechanical system of mass (m0 + E0/c^2)/sqrt(1-u^2/c^2), and its energy is E = (m0 c^2 + E0)/sqrt(1-u^2/c^2) (sections 166-167, eq. 235; the integration constant is fixed by convention).
• Equipartition of the quantity <m0 u^2/sqrt(1-u^2/c^2)> = 3kT holds for an ideal classical gas; the kinetic energy departs from (3/2)kT by about kT/(mc^2), which is negligible for electron-mass particles at 300 K and 30,000 K ('substantially exact'), while particles of vanishing mass have E = 3nRT, twice the Newtonian value (sections 100, 105-106).
• A direct test of time dilation is possible: atoms of canal rays viewed at right angles to their motion should emit light of lower frequency than atoms at rest, by the second-order factor sqrt(1-V^2/c^2) (section 46, eq. 40; proposed, no experiment cited).
• No causal signal can travel faster than light, because in some frame the effect would precede the cause (section 52, worded as 'might incline us to believe'); kinematic 'motions' carrying no energy may exceed c.
• Experimental proof of mass-energy equivalence 'will be hard to find' in 1917; only the high-velocity electron experiments and the momentum of light supported it, and radioactive decay might account for non-additive atomic weights (section 77); the theory points to 'enormous stores of interatomic energy' remaining at absolute zero (footnote p.102).
• The electromotive force on a charge moving through a magnetic field is an electric force in coordinates stationary with respect to the charge, which Tolman says throws light on the seat of the electromotive force in homopolar dynamos (section 159; three sentences, no equations or experiment).
• Tolman's moving-dielectric equations agree with H. A. Wilson's rotating-dielectric experiment, which used a permeability near 1; the permeability dependence (epsilon mu - 1) in eq. (251), which differs from the original Lorentz theory's (epsilon - 1) mu, was untested, and Tolman asks for a repeat with a high-permeability dielectric (section 172).
• The 'right-angled lever' and energy-flow results of Ch. X are restated by a single four-dimensional equation div T_m = 0 in a real-time non-Euclidean four-space (Wilson-Lewis method), and the Maxwell stress, Poynting vector and field energy follow from the tensor T_e (Chapter XIII).
• The hohlraum momentum G = (4/3) a v0 T0^4 u/(sqrt(1-u^2/c^2) c^2) holds only for a cavity held by external pressure; for a closed system including its wall stresses the momentum is G = E u/c^2, which is Tolman's own eq. (193) (stated in the arbiter's corrected claim 4).

Relevance: The project folder holds only this one book, a standard early textbook of special relativity written by a mainstream physicist. It is a primary source for how relativity was taught in 1917, with its derivations laid out step by step (useful for learning), and for Tolman's own relativistic elasticity and thermodynamics, including the moving-body temperature formula that later authors (Ott 1963, Arzelies 1965, Landsberg, van Kampen) disputed. It is not an alternative-science work by an outsider; the manifest gives no author-written commentary, letters or experiments by Tolman beyond the book. Why this book is in an 'Energy/Researchers' collection is not stated in the documents. Candidate answer (not established) to why a relativity textbook sits in this collection: section 159 touches 'homopolar' dynamos, a recurring topic in the Energy/Researchers collection, and section 77 (with its footnote on 'enormous stores of interatomic energy') treats rest-mass energy as a reservoir; the documents do not say why the book was included. Section 46 is the book's one explicit proposal for an experiment that was later carried out (Ives-Stilwell, 1938).

Mainstream conflict: None for the core of the book: special relativity, the Lorentz transformation, mass-energy equivalence, invariance of entropy and pressure, and energy-flow momentum are standard. Points where later work departs from Tolman: (1) the moving-body temperature T = T0 sqrt(1-u^2/c^2) (Planck-Einstein form, which Tolman follows) is one of several proposed rules: the gamma form T0/sqrt(1-u^2/c^2) is associated with Ott (1963), Arzelies (1965) and, by some accounts, Eddington and Moller; Landsberg (1966-67) proposed an invariant temperature; van Kampen and Israel used a rest-frame definition or a four-vector inverse temperature; there is no consensus [memory, high for the Ott/Landsberg/van Kampen attributions; medium for the Eddington/Moller attribution; not web-checked]; (2) 'relativistic mass' m = m0/sqrt(1-u^2/c^2) and 'transverse/longitudinal mass' language is mostly replaced by invariant mass in modern texts [memory, high]; (3) the Kaufmann electron-mass experiments are presented only as a triumph (p.56), without the earlier contrary reading: Kaufmann's first results (1901-1906) favoured Abraham's model rather than Lorentz-Einstein, Bucherer (1908) favoured Lorentz-Einstein, and Hupka (1910) said his result was not definitive; Zahn and Spees (1938) said the early experiments showed only a qualitative increase [web, secondary: https://en.wikipedia.org/wiki/Kaufmann%E2%80%93Bucherer%E2%80%93Neumann_experiments, as used by the reviewers; the primary papers were not opened]; (4) his unsymmetrical stress tensor is an older device compared with the symmetric stress-energy tensor [memory, medium-high]; (5) the book accepts the ether as superfluous and rejects emission theories, a position the alternative-science tradition often contests. Within the text [read: PDF p.43]: Stark-effect and sun-limb evidence bear on the first two emission variants only; Ritz's variant is opposed only by the Comstock and de Sitter binary-star argument; and Tolman writes that the optical experiments that would decide between Einstein's and Ritz's theory 'have never been performed'. A later extinction objection (Fox) to the binary-star argument is reported by the reviewers from one secondary source (Martinez 2004); Tolman's own 1910 paper said the possibility that the source-speed difference 'is destroyed near the earth is not entirely excluded' [read: research/2026-10-04-wikisource.md]; (6) the 'ether unnecessary' statement is an economy argument: a Lorentz-ether interpretation is empirically equivalent [reviewers], and Ives interpreted his 1938 result within a Lorentz-Larmor ether picture [memory, high per QE; web-check pending]; (7) the 4/3 factor in the hohlraum momentum applies only to a cavity held by external pressure (see claims).