On Inertial Reference Frames
| Scientific Paper | |
|---|---|
| Title | On Inertial Reference Frames |
| Read in full | Link to paper |
| Author(s) | Herbert Dingle |
| Keywords | inertial frame, coordinate system, clock paradox, Mossbauer effect, general relativity |
| Published | 1962 |
| Journal | Science Progress |
| Volume | 50 |
| No. of pages | 16 |
| Pages | 568-583 |
Read the full paper here
Abstract
It is the universal practice in physics, when describing the motion of a body, to choose a reference frame, i.e. some real or imaginary physical structure which is said to be "at rest", and then the motion of any other body is defined as its motion relatively to that. Of the various possible frames of reference, that known as an inertial system -- formerly, and still sometimes, called a Galilean or Newtonian system or frame of reference -- appears in the literature of relativity with a frequency unapproached by any other, and motion with respect to it is generally regarded as having a special significance. It is therefore of the first importance, both for theoretical reasons and on account of the possible effects in circumstances in which miscalculations may have dire results, that the meaning of the term, inertial system, shall be clearly understood, and that the term shall be used always in the same sense. Unfortunately, these conditions are far from being fulfilled. It is the purpose of this paper, first, to bring to light the widespread confusion that exists on this point; secondly, to show that existing ideas, notwithstanding their variety, are almost unanimously incompatible with the conception of inertial systems held by Einstein and regarded by him as indispensable for the proper understanding of his theories; and finally, to correct an outstanding example of this misunderstanding which might otherwise have unfortunate effects.
Overview
Herbert Dingle wrote this paper in 1962, in the middle of the long public controversy that would end with Science at the Crossroads. It is not, however, an attack on special relativity. It is a philological and philosophical audit of a single term — inertial system — and its central move is to defend Einstein's own usage against the physics profession that had inherited it. Dingle's thesis is that the phrase has drifted from a definition of a purely mental construct into a name for physical objects and physical conditions, and that most contemporary uses of it, if taken seriously, would refute the general theory of relativity outright.
The paper falls into two parts. Part I documents the confusion, sets out Einstein's own definition, and argues that four distinct popular conceptions of an inertial frame are each incompatible with it. Part II applies the result to a concrete case: C. W. Sherwin's 1960 Physical Review claim that rotating-absorber Mössbauer experiments had given "the first direct experimental verification" of Einstein's 1905 clock retardation prediction — a claim popularised in Britain by J. Bronowski on the television programme Insight. Dingle's conclusion is that Sherwin has misunderstood both Einstein and his own experiment, and that if Sherwin's reading were right, "Einstein's theories lie in ruins."
The argument
The evidence of confusion
Dingle opens with fifteen verbatim definitions or implied definitions of "inertial system" quoted from Nature, Science, Discovery, the Bulletin of the Institute of Physics, the American Journal of Physics, the Proceedings of the Cambridge Philosophical Society, the Australian Journal of Physics and the Journal of the British Interplanetary Society, all from 1956–1961. They range from "R remains at rest in an inertial frame, that is, he remains in a free path" to "there exists a unique absolute inertial system, such as the universe as a whole." He observes that no single definition can conform to all fifteen, and sorts the recurring assumptions into four:
- Inertial systems may be identified with particular objects in nature (e.g. the Earth, the universe).
- Inertial systems can exist only in certain circumstances, i.e. if certain natural conditions are realised.
- It is a fact of nature, and not a matter of choice, whether a particular object is "in" an inertial system or not.
- Inertial systems cannot be defined independently of some theoretical description of nature.
Einstein's definition, and why a coordinate system is a fiction
Against these Dingle sets Einstein's own words, from a little-read 1918 Naturwissenschaften dialogue: a Galilean coordinate system in the sense of the special theory is "ein Bezugskörper, relativ zu welchem isolierte, materielle Punkte sich geradlinig und gleichförmig bewegen" — a reference frame relative to which isolated mass-points move uniformly in straight lines. Whittaker's 1953 formulation is cited as equivalent.
The key inference is that an inertial system is a coordinate system, and therefore, on Einstein's repeated insistence, "something purely mental, quite independent of nature or of our observations of nature." Dingle quotes Einstein's Times article: "What has nature to do with our coordinate systems and their state of motion?" From this he draws the consequence that the motion ascribed to a single body is a fiction. The motion of A relative to B is an objective fact; the motion of A alone is a relation between A and an arbitrary framework, and is therefore itself arbitrary. That alone, he argues, disposes of idea (i).
The word doing the hidden work in Einstein's definition is "free". Dingle anticipates the objection that a free body is a piece of nature, so an inertial frame must after all depend on nature — and answers that there is no objective sign distinguishing a free body from an unfree one. His illustration is an apple detaching from a tree: neither apple nor Earth is subject to any observable force, yet at least one of them is not moving uniformly in a straight line. We do not conclude that inertial systems are unavailable; we say instead that a gravitational force acts. Newton's first law, on this reading, is not a discovery about nature but "a statement that he is going to use only inertial systems", and the admission of gravitational force is the price of that choice.
Newton's bucket and the accelerometer
The one thing that could privilege inertial systems is a phenomenon impossible to ascribe to anything but absolute acceleration — Newton's rotating bucket, Foucault's pendulum, and "accelerometers" generally. Dingle reproduces Einstein's disposal of this argument from the same 1918 paper. Einstein's example is a fast train brought to rest by collision and smashed, while a neighbouring church steeple is unharmed. The damage is caused not by the acceleration but by the impact of another body. Ascribe the acceleration to the steeple instead, and the steeple and the whole universe except the train suddenly move under a gravitational field which harms them no more than the Earth's field harms a falling apple — "only when the apple hits the ground is it bruised." The accelerometer therefore registers a relative acceleration between two bodies and does nothing to compel its assignment to one rather than the other. "The account of the phenomena changes with change of coordinate system, but the phenomena themselves remain the same."
Dingle reinforces this with Einstein's later statements: from The Evolution of Physics with Infeld, that "absolute motion is made possible only by the idea of an inertial system" and that "the ghosts of absolute motion and inertial coordinate systems can be expelled from physics"; and from the Autobiographical Notes, that with gravitational fields of arbitrary extension "the concept of the 'inertial system' becomes completely empty", together with Einstein's rebuke that keeping the narrower Lorentz group while basing gravitation on tensor structure "implies a naive inconsequence. Sin remains sin, even if it is committed by otherwise ever so respectable men."
The Mössbauer rotor experiments
Part II turns to the rotating-disc Mössbauer experiments of Hay, Schiffer, Cranshaw and Egelstaff (1960) and of Pound and Rebka (1960). Dingle takes the first, in Bronowski's own description: a six-inch aluminium disc carries a radioactive iron isotope on its spindle and a resonant iron absorber on its circumference, with a stationary counter beyond; the sharpness of the Mössbauer line permits comparison of process rates to one part in 1011, and the photon count differed significantly at fifty and at five hundred revolutions per second.
Dingle's first objection is historical. The prediction Sherwin claims to have verified is Einstein's 1905 remark that "a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles." Einstein himself withdrew it. The 1916 general-theory paper opens by revoking the assumption that the Lorentz transformation applies to a rotating body such as the Earth: no observation confined to a single body evidences its rotation, and the equatorial bulge — like the hypothetical clock effect — may equally be ascribed to external forces on a non-rotating body. A relative motion that can be transformed away cannot yield a physical effect from the Lorentz transformation. Ehrenfest's 1909 rotating-disc objection made the same point from another direction: every circumferential element moves along its length and contracts, every radial element moves at right angles to its length and does not, so the circumference shrinks while the radius does not — "clearly impossible." Solutions by Lorentz (1921) and Eddington (1940) gave an effect different in character and much smaller in amount than the one deduced from the Lorentz transformation. Hence Dingle's sharpest line: if Sherwin and Bronowski are right that the original prediction has been quantitatively verified, "Einstein's theories lie in ruins, and the unresolved dilemma of the rotating disc rises again, phoenix-like, from the ashes."
What the experiment actually shows
His second objection is analytical. Dropping the contested term altogether, he reduces the dispute to a clean issue: Einstein says no coordinate system is privileged, Sherwin says these experiments show that some are. Dingle then lists the five objectively distinguishable states of relative motion of two bodies A and B: relative rest; uniform relative motion at one velocity; at another velocity; relative motion with a given acceleration; and with another acceleration. A table of measured positions at successive times, in any coordinate system whatever, suffices to say which state obtains; so do the Doppler effect and accelerometers.
The rotor experiment, with A the source on the spindle and B the absorber on the rim, shows that the absorption rate differs at different speeds of revolution. That, Dingle says, "demonstrates only that there is an observable criterion for distinguishing between states (d) and (e), which stood in no need of demonstration. It tells us precisely nothing about the individual state of motion of either A or B." One remains free to choose a frame in which A is at rest, or moving round the Sun, or round the Galaxy, and the experiment is unchanged. The Pound–Rebka experiment likewise supplies a new criterion for distinguishing states (b) and (c) and no more. He also notes that Sherwin's own usage is internally unstable — the specimens "pursue independent paths ... in a common inertial frame" in the abstract, the travelling clock collects proper time "in several different inertial frames" later in the paper, and Bronowski says it is in no inertial frame at all — and that the resting specimen's frame is not inertial on Einstein's definition unless Newtonian gravitational force is granted, "for we may take it for granted that the specimen did not rest in mid-air." Accordingly the conclusions about the clock paradox drawn from these experiments are "without significance." A footnote is careful to add that Dingle offers no general comment on the experiments themselves, "which are of great interest and importance in relation to nuclear theory."
Assessment
The paper's strongest feature is its method. Dingle does not argue from intuition or from an alternative theory; he assembles fifteen dated, sourced quotations and shows that they cannot all be satisfied by any one definition. That is a genuine finding about the state of the literature, and the four idea-types he distils from it are a fair and useful taxonomy. His central logical point — that a coordinate system is a chosen framework, so that whether a body is "in" an inertial frame cannot be a fact discovered by an accelerometer — is correct as an exegesis of Einstein's own general-covariance stance, and the citations backing it (the 1918 Naturwissenschaften dialogue, the Times article, The Evolution of Physics, the Autobiographical Notes) are apt and largely unfamiliar even now. The "sin remains sin" footnote he unearths is exactly on target. Equally admirable is his refusal to overclaim: he explicitly declines to comment on the nuclear physics of the Mössbauer experiments, restricting himself to their bearing on the relativity of motion.
His criticism of Sherwin's terminology also lands. Sherwin does shift between "a common inertial frame", "several different inertial frames", and (in Bronowski's gloss) no inertial frame, and a rest frame identified by "the null reading of attached accelerometers" is not Einstein's frame in which free bodies move uniformly in straight lines. Dingle is right that at minimum two different concepts are in play under one name.
The difficulties lie in what he does with this. The step from "coordinate systems are conventions" to "inertial systems have not the slightest claim to special consideration" is asserted rather than derived, and it elides a distinction general relativity itself maintains: coordinates are arbitrary, but the invariants are not. Local inertial frames are picked out by the vanishing of the connection along a geodesic, which is a coordinate-independent statement, and the accelerometer reading Dingle dismisses is the norm of the four-acceleration — a scalar, the same in every coordinate system. Einstein's steeple argument shows that the description can be transposed, not that the invariant is undefined; Dingle's own footnote, conceding that it may be improper to give the fictitious field the same name as the fields of massive bodies, shows he half-sees this and declines to pursue it.
The historical claim about the 1905 clock prediction is likewise pushed further than the evidence carries. Einstein did withdraw the specific equatorial-clock deduction, and Dingle is right that the rotating-Earth case is entangled with the bulge; but the withdrawal concerned the applicability of the Lorentz transformation to a rotating extended body, not the differential ageing of separated worldlines as such. That the traveller's elapsed proper time depends on the path is a metric statement, not a statement about privileged frames, and it does not require the "objective existence" of inertial systems that Dingle and Sherwin are arguing about. The paper never engages the proper-time formulation, so its verdict that a positive result would leave Einstein's theories "in ruins" rests on a dilemma that the theory does not in fact face.
Finally, Dingle's own analysis of the rotor experiment is too quick. He is right that distinguishing his states (d) and (e) needs no new experiment; but the experiment measures the magnitude of the transverse time dilation against a quantitative prediction, and a null or wrongly-scaled result would have falsified something. Reducing it to a mere criterion for telling one acceleration from another understates what a one-part-in-1011 comparison was for. The verdict "without significance" is therefore stronger than his argument establishes, even though his complaint about the language in which the significance was announced is well founded.
Read narrowly — as a demand that a technical term be used consistently, and as a demonstration that in 1962 it was not — the paper is sound on its own terms and remains worth reading. Read as a refutation of clock retardation, it does not succeed.