J. Rogers, SE Ohio
Note on sources: quotations are given in the Cohen–Whitman translation of the Principia (1999) and from the General Scholium and De Gravitatione where noted. Latin is supplied where the wording is load-bearing. I have flagged the two or three places where I am working from memory and the exact phrasing should be checked against the text before publication.
Abstract
The received view holds that Newton posited an absolute space and time conceived as a fixed, rigid, detectable stage, and that Einstein refuted this by showing space and time to be relative. This paper argues that the received view is a strawman on both halves. Newton explicitly denied that absolute space and time are accessible to the senses, located them in God's duration and omnipresence, and directed natural philosophy to work with sensible relative measures. He then named and diagnosed a specific error — the substitution of measures for the things measured — and warned that this substitution produces philosophical mistakes. The modern claim that space and time are relative is that error, committed in his name. It takes a provable truth about measures (they are relative by construction, and by Lorentz invariance) and promotes it to a claim about the world. The paper distinguishes two opposite projections of our epistemic situation onto the world — reifying the measure, and reifying the limit — and argues they are the same error in different directions. Finally, it shows the central argument can be sustained without adopting Newton's substantivalism, and that the falsifiability objection to framework conditions misapplies a demarcation criterion as an existence test.
1. The received view and its function
The standard narrative in textbooks, popular science, and much of the philosophy of physics runs as follows. Newton held space and time to be absolute: a fixed, uniform, immovable container, the same for all observers, against which motion could be measured. Einstein demonstrated that this container does not exist and that space and time are relative. The moral is that Newton's absolutism was a metaphysical prejudice, corrected by the recognition that only relations are real.
This narrative performs a specific function. It supplies a clean before-and-after, it casts the later theory as the humbler one, and it provides the relationalist position with the appearance of having been established by physics rather than argued for. The last is the important one. Relationalism about space and time is a substantive metaphysical position, and it has serious difficulties — it has never adequately handled inertial effects, it strains against the reality of gravitational waves, and Mach's principle, its strongest physical expression, is not satisfied by general relativity. But if relationalism is what physics proved, those difficulties become puzzles rather than objections.
The narrative is not supported by the text. This section and the next three establish that.
2. What the Scholium says
Newton's discussion of space and time occupies the Scholium following the definitions at the opening of the Principia. The relevant passages are unambiguous and it is worth setting them out in order, because the structure of the argument is what has been lost.
He begins with the definitions:
"Absolute space, in its own nature, without relation to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces, which our senses determine by its position to bodies."
Note the asymmetry already present. Absolute space is characterised by the absence of relation to anything external. Relative space is characterised by its relation to bodies and by being determined by our senses. Relativity is not a property Newton assigns to space. It is a property he assigns to the measure, and he assigns it as part of the definition. The measure cannot fail to be relative; that is what it is.
The same structure applies to time. Absolute time, "of itself and from its own nature, flows equably without relation to anything external." Relative time is "the sensible and external measure of this duration, made by means of motion, which is commonly used instead of true time — such as an hour, a day, a month, a year."
Then the decisive passage. Having distinguished the two, Newton asks how we are to work with the absolute:
"But because the parts of space cannot be seen, or distinguished from one another by our senses, therefore in their stead we use sensible measures of them. For from the positions and distances of things from any body considered as immovable, we define all places; and then with respect to such places, considered as immovable, we estimate all motions."
The premise is that the parts of space cannot be seen or distinguished by our senses. This is not a concession added at the end. It is the stated reason we use sensible measures at all. The absolute is inaccessible, and the measures are what we have instead.
He then draws the methodological conclusion:
"And so, in place of absolute places and motions, we use relative ones; and that without any inconvenience in common affairs; but in philosophical disquisitions, we ought to abstract from our senses, and consider things themselves, distinct from what are only sensible measures of them."
The contrast is explicit: in common affairs we use relative measures without inconvenience; in philosophical disquisitions we are to abstract from the senses and consider the things themselves, distinct from the sensible measures. The measures and the things are different, and the difference is not merely a matter of precision. It is the difference between what our senses deliver and what there is.
Finally, on motion:
"For it may be that there is no body really at rest, to which the places and motions of others may be referred."
Newton states, as a genuine possibility, that no body is absolutely at rest. He is not assuming a detectable fixed reference. He is denying that one is available.
3. The vulgus and the error named
The passage that has been most thoroughly excised from the textbook tradition is the one that names the mistake:
"[Sensible measures] are what the vulgar (vulgus) use in place of the spaces and times themselves."
And the diagnosis:
"But because these measures are conceived as the quantities themselves, this leads to errors in philosophy."
(Latin, approximately: "sed sensibiles quasdam earum mensuras, quibus vulgus pro ipsis spatiis temporibusque utitur…" — verify wording.)
This is not a passing remark. It is a specification of a failure mode, offered in advance, with the mechanism identified. The vulgar error consists in taking the sensible measures for the quantities themselves. The consequence is error in philosophy. And the recommendation in the previous paragraph — abstract from the senses, consider the things themselves — is the remedy.
The word vulgus is doing work. Newton is not describing a naive error he expects his readers to avoid by sophistication. He is marking a contrast between the common conception and the philosophical one, and warning that the common conception is seductive precisely because it is all we have access to. The measures are what we use. The risk is forgetting they are measures.
4. The location of the absolute
Newton does more than deny access. He assigns the absolute to a domain we structurally cannot occupy, and this is the part the modern reading ignores most completely.
The General Scholium states:
"He endures forever and is everywhere present; and by existing always and everywhere, he constitutes duration and space."
And he is careful to distinguish constitution from identity:
"[God] is not eternity or infinity, but eternal and infinite; he is not duration or space, but he endures and is present."
In De Gravitatione the position is developed further: space is described as an emanative effect of God's being.
Whatever one makes of the theology, the philosophical function is clear. The absolute is not inaccessible because our instruments are insufficient, or because we have not yet found the right reference body. It is inaccessible because it belongs to God's being, and we are not God. The gap is not epistemic in the sense of awaiting closure. It is categorical.
This matters for the argument, because it means Newton left no room for the modern move. The claim "space and time themselves are relative" would not be a physics error on his view. It would be a category error, asserted before it could be evaluated. You cannot promote the measures to the reality when the reality has been placed where no creature can reach it. The promotion has nowhere to happen.
Dropping God removes the firewall. Once the absolute is either a physical hypothesis or a metaphysical posit, human inquirers have jurisdiction over it, and once they have jurisdiction, the measures can be declared to be the thing. That is what happened. The reification was not the result of a discovery about space and time. It was the result of an eviction.
5. The inference that does not follow
Set the theology aside. Grant nothing about God. The central argument still runs, and it runs on premises the modern reader should accept.
Premise 1. Our measures are relative. (Newton: relative space is defined by its relation to bodies; relative time is measured by motion. Also empirically: any measuring procedure returns frame-dependent values, per Lorentz invariance.)
Premise 2. We have access only to measures. (Newton's stated premise: the parts of space cannot be seen or distinguished by our senses. Also a general point about measurement: you cannot compare a measurement to a thing except through another measurement.)
Conclusion, which does not follow. Space and time themselves are relative.
The conclusion is a claim about the character of the thing measured. It does not follow from premises about the character and scope of the measuring. Newton makes the inference visible by denying the conclusion while affirming both premises, which is why the passage is so awkward for the received view.
What would be needed to license the inference is an additional premise: that there is nothing to space and time beyond what measurement yields, or that the question of what lies beyond measurement is meaningless or empty. That premise is available, but it is a metaphysical commitment, not a result of physics. It is exactly as unmeasured as the absolute it denies.
6. What general relativity actually relativizes
The modern position is usually taken to be the content of relativity theory. It is worth stating precisely what general relativity does and does not make relative.
Coordinates are relative. Yes, and they always were. Coordinate systems are conventions of description, and no result in physics depends on the choice. But coordinates were never the thing — they are measures, in Newton's sense. Relativizing coordinates relativizes the measures. It does not touch the question of the underlying structure.
The metric is not relative in the relevant sense. The metric is a dynamical field. It has degrees of freedom, it carries energy, it satisfies hyperbolic field equations, it supports wavelike solutions. Gravitational waves transport energy and momentum across regions of spacetime. In a binary merger, energy is carried away and the orbit decays accordingly. This is not bookkeeping. It is physics.
Causal structure is not relative. Every observer agrees on which events can influence which. Light cones are invariant. The distinction between timelike, null, and spacelike separation is frame-independent. There is no observer for whom two spacelike-separated events could be causally connected.
Mach's principle fails. The relationalist hope was that the distribution of matter fully determines geometry, so that geometry has no independent existence. General relativity does not deliver this. Vacuum solutions exist — you can have curvature with no matter anywhere in the spacetime. Gravitational waves propagate through empty space. So geometry is not exhausted by its relation to matter.
The theory credited with the relativization of space and time contains an absolute in the sense of a frame-independent, physically real, energy-bearing structure. Its absoluteness is not Newton's (fixed and immovable) but it is not relationality either. The honest description is that general relativity replaced a fixed absolute with a dynamical one, and relativized the coordinates. That is a different claim from the one in the textbooks.
7. Falsifiability and the status of axioms
A standard objection: positing an inaccessible absolute is unfalsifiable, and therefore illegitimate in physics.
This misapplies a demarcation criterion. Falsifiability distinguishes empirical hypotheses from non-empirical ones. It does not decide what exists. The criterion itself is not falsifiable, and neither is the framework within which falsification counts as a procedure. That is not a defect in Popper's proposal; it reflects the fact that a criterion cannot be applied to the conditions that make its application possible.
Newton's absolute functions as a framework condition, not a hypothesis. It is not a claim within a theory that could be tested and fail. It is part of what makes relative measures measures of something rather than free-floating numbers. The role is closer to that of an axiom than to that of a prediction. Axioms are not falsifiable, and demanding that they be is demanding that the framework justify itself in terms the framework supplies.
Two qualifications, in the interest of not overclaiming.
First, Newton offers what appears to be an empirical argument for the absolute: the rotating bucket, whose surface curves although the water is at relative rest with the bucket. If that argument is presented as an empirical demonstration, it is subject to empirical review, and the review has not gone entirely his way. But the bucket argument is a purported demonstration of a framework condition, and objections to the demonstration do not reach the condition. The condition would stand even if the bucket argument failed, because it rests on the inaccessibility premise, not on the bucket.
Second, "unfalsifiable" is sometimes used loosely to mean "not worth discussing." That is a rhetorical move, not an argument, and it is precisely the move this paper is describing.
8. Two directions of the same projection
There are two errors available, and they are mirror images.
Error A — reifying the measure. Our measures are relative; therefore space and time are relative. This takes a fact about our instruments and promotes it to the furniture of the world. It is the error Newton names in the Scholium.
Error B — reifying the limit. We cannot access the absolute; therefore there is no absolute (or the question is meaningless). This takes a fact about our access and promotes it to a fact about what exists.
Both place us at the center. Error A makes our cuts the ontology; Error B makes our reach the measure of what there is. Error A is confident; Error B is apologetic. Error B is more insidious, because it presents itself as humility. "We do not posit unobservables" sounds like restraint. But the claim is not restraint. It is a complete inventory of what exists, asserted from a finite vantage point inside a configuration we did not choose and cannot survey. That is a strong claim, and it is made in the register of modesty.
The only placement that inflates nothing is to hold the absolute with the whole and the measures with us. We are parts of a configuration. Our access is partial by structure, not by instrument. The measures are ours, and they are relative, and that is a fact about measures. What the measures measure has whatever character it has, and no measurement can settle the question, because measurement returns measures.
9. The argument without substantivalism
The central argument does not require Newton's metaphysics, and it is worth being explicit, because otherwise the position looks like a defence of the absolute against its critics.
Newton is a substantivalist: he holds absolute space and time to be real entities, distinct from bodies, and he argues for this (the bucket, God's duration). The argument of this paper does not require that. It requires only two things:
That the measures are relative, and we have access to nothing else. (Provable, and Newton's stated position.)
That premises about the character and scope of measurement do not determine the character of the measured. (A logical point.)
From these it follows that "space and time are relative" is not established by physics, and is instead a metaphysical commitment arrived at by an invalid inference. It does not follow that space and time are absolute. Nothing in the argument establishes substantivalism.
The resulting position is a refusal to close the gap. Neither the measure nor its negation is promoted. The question of what lies beyond measurement is held open — not as an awaiting-empirical-answer, but as a question whose status is not settled by the procedures that generated it. This is weaker than Newton's position and stronger than the relationalist's, and it cannot be dismissed as an untestable addition, because nothing was added. It is the observation that a gap exists and that filling it in either direction is a projection.
It is worth noting that this position has costs. It leaves a framework condition in place without a physical account of it. Some will find this unsatisfying, and the dissatisfaction is not unreasonable. But the alternative on offer is to close the gap with a claim sourced from the gap itself, and that is not a better answer. It is the same answer with the sign flipped.
10. What the reification costs
The reification is not merely a philosophical blemish. It has methodological consequences, and they are the ones visible in contemporary practice.
If the measures are taken to be the reality, then a mismatch between prediction and observation cannot indicate that the framework is wrong in kind. It can only indicate that something has been left out of the account. The response is to add a term: a planet, a parameter, a field, an epoch. Each addition closes the gap, and each closure confirms the framework, because the framework was never in question.
This is the structure Newton warned against, and it is worth being precise about why. The warning was not that measures are inaccurate. It was that measures are not the thing, and that mistaking them for the thing produces philosophical error. The methodological consequence of the error is that the framework becomes unfalsifiable in practice — not because it forbids testing, but because it can absorb any result. A framework that can accommodate every outcome by adding a term has no way to learn that it is wrong in kind rather than incomplete in detail.
The contrast case is a framework in which the gap is left open. There, a mismatch indicates that the description is inadequate, and the response is to examine the description rather than to supplement it. The distinction between an artifact of the method and a feature of the world becomes available, and the question of whether a residual is real can be asked and answered.
That distinction is unavailable when the framework is protected by the assumption that the measures are the reality. The protection is not stated as a premise. It is carried in the vocabulary — "law," "force," "rest mass," "the age of the universe" — each of which carries a structure of relations that presupposes the framework and makes the framework's failure unthinkable rather than merely unlikely.
11. Conclusion
Newton did not claim that absolute space and time are accessible. He claimed the opposite, explicitly and repeatedly, and he located the absolute in a domain he held to be beyond human reach. He directed natural philosophy to work with sensible relative measures, and he named the error of taking those measures for the things themselves, warning that it produces mistakes in philosophy.
The modern claim that space and time are relative is that error. It takes a provable truth about measures — they are relative by construction and by Lorentz invariance — and promotes it to a claim about the world. The promotion is not licensed by the premises, and it is not a result of physics. General relativity relativizes coordinates and replaces a fixed absolute with a dynamical one; it does not eliminate the frame-independent structure that does the physical work.
The correction is not to reinstate Newton's absolute. It is to notice that the inference was invalid, that it was invalid all along, and that the vocabulary of the debate has been shaped to conceal it. The measures are ours and they are relative. What they measure is not thereby determined. The gap that Newton left open was closed without argument, and it is worth asking what the closure was for.
Suggested additions before submission: (i) verify the Latin in §3 against the Cohen–Whitman text and the 1726 edition; (ii) a section on the Leibniz–Clarke correspondence, since Clarke's replies are where the Newtonian position was defended in its most explicit form, and Leibniz is the origin of the reading this paper contests; (iii) a section on Berkeley's De Motu and Mach's Science of Mechanics as the transmission path by which the strawman became canonical; (iv) engagement with Earman's World Enough and Space-Time and with the hole argument literature, both of which are the strongest contemporary statements of the relationalist case and deserve direct response.
