Time and Space are of the Same Stuff
| Scientific Paper | |
|---|---|
| Title | Time and Space are of the Same Stuff |
| Read in full | Link to paper |
| Author(s) | Bernard Guy |
| Keywords | space, time, movement, relation-based thinking, quantum mechanics, three-dimensional time parameter |
| Published | 2011 |
| No. of pages | 23 |
Read the full paper here
Abstract
We propose to consider the concepts of time and space together. Both of these involve the same degrees of freedom of worldly elements and always work in tandem. In discussing their fundamental points, we need to use relation-based thinking, where each is defined in contrast to the other, instead of substance-based thinking, where each is defined by its own set of characteristics. We contrast spatial relations with temporal relations, or relative mobility with relative immobility. The boundary between the two is decided arbitrarily (there is a great deal of flexibility in definitions of associated time and space parameters), but such a decision runs into logical and conceptual obstacles similar to those encountered in quantum mechanics. Given this prospect, we need to revise the concepts of both time and space. Time does not flow, it is change in relation, it is movement; space is abstracted from constant relations or constant slices of movement. The relative movements that express these relations (changing or unchanging) always take both a spatial and a temporal aspect, like two sides of the same reality. More generally, we suggest seeing a spatial aspect (the distance separating the two terms of the relation) and a temporal aspect (travel along the path linking them) in every relation. On this basis, we propose a research program to examine a number of fundamental problems of contemporary physics and avenues for rethinking how we express time and space in the behavioral and social sciences, in culture, and even in everyday life.
Overview
Bernard Guy, a geologist and physicist at the Ecole nationale superieure des mines de Saint-Etienne, offers a conceptual rather than a mathematical paper. Its thesis is that time and space are not two things but one operation performed twice: both are abstracted from the same relations between elements of the world, and the line dividing "spatial" from "temporal" relations is drawn by us, not found. Time does not flow and is not a property of any point; it is change of relation, that is, movement. Space is what is abstracted from those relations we treat as unchanging — "constant slices of movement". Neither concept survives being defined alone. The paper is the English version of an article that appeared in Philosophia Scientiae 15(3), 2011, translated by Carolyn McBride Nafziger, and is deposited as HAL preprint hal-00651429.
The break with the standard account is not a claim that relativity's predictions are wrong but that its foundations are misdescribed. Guy argues that a spacetime built by coordinating measurements of independently conceived quantities is not the same as one built by unifying the concepts. Where standard physics adds a parameter t alongside x, y, z and declines to ask how t is constructed, Guy insists the construction is an arbitrary — though necessary — choice, structurally like a measurement convention, and that recognising this dissolves several puzzles: the twin paradox, the "problem of time" in quantum gravity, the question of the scale at which a temporal parameter may be assigned. His concrete proposal is that time should be built from three coordinates describing the motion of a reference point, not added as a fourth alongside them.
The argument
Substance-based versus relation-based thinking
Guy opens with two modes of thought. In substance-based thinking we act as if we could view the world from outside and pair each element with a definition drawn from an independent system of knowledge "hovering over the world like a sky of Platonic ideas". To think "horse" is to invoke a list of the horse's own characteristics; no cow or pig need be thought of at the same time. He traces the mode through Plato and Aristotle to Descartes, Newton and Kant.
In relation-based thinking, by contrast, we are inside the world and see only contrasts between its elements. To think "horse" is to make comparisons: "expressing what a horse is boils down to making a list of all the animals it is not." Guy dates the mode to Heraclitus and the pre-Socratics, and points to Edgar Morin, Francois Jullien and Michel Bitbol among contemporaries. He notes that modern phylogenetic classification already works this way — asking how many characters separate a horse from another animal rather than which characters are inherent in a horse. His claim is that time and space belong here: to imagine space one must contrast it with time, and the two "are imagined together, in contrast". He credits Mach, Whitehead, Barbour, Earman, Rossler and Assis with relational treatments, but says each takes the two concepts separately, without seeing that the same relations construct both.
Where the boundary between space and time is drawn
The core claim is developed through the practice of measurement. To build rulers and maps we fix boundary markers and triangulate; to build clocks we track the sun, a mechanical hand, or "the relative positions of a photon moving inside a box we call an atomic clock". In doing so, Guy says, we have already partitioned the world into a set of points treated as relatively immobile and a set treated as moving at constant speed. Nothing "positive" is asserted about either set; the partition is a relative point of view. Strictly, the first points merely do not move much relative to the second.
The arbitrariness is then made vivid by two thought experiments. If we lived far longer and more slowly, the mountains bearing our boundary markers would move like ocean waves and could serve to define time; if we lived briefly and fast, the grains of sand in an hourglass would not budge and could serve to define space. To the objection that we will eventually be able to stop and say "here is space, here is time", Guy's answer is flat: "Well, in point of fact, no!" There is no preexisting break in the continuum of relative motion, and no tool outside the world with which to find one — neither the observer nor the instrument can stop at an absolute boundary, so we are in a self-referential situation leading to undecidable propositions. What we do instead is halt an otherwise infinite regression by a "temporary" break, and Guy holds that this is exactly what the Lorentz relations of special relativity express. The current construction is light-based, taking c = constant; an older one took the sidereal rotation rate as constant. Each, he says, is internally coherent, though some are harder to implement.
The logical structure of the construction
Guy lists the features that follow from building concepts this way, and stresses their kinship with the structure of quantum mechanics:
- uncertainty — we cannot be sure whether a given material point is mobile or immobile, nor of the numerical value assigned to its velocity;
- incompleteness — the reasoning does not stand on its own;
- arbitrary choices — decisions such as "the velocity of light is constant" originate outside the reasoning they support;
- potentially contradictory constructs — several physical schemes can be built on different choices of which phenomenon has constant speed;
- recursive situations — words define each other, and the loop is broken only by showing something, without certainty that words and reality correspond.
He then sets out the conditions such thinking requires: an "empty stage" (a void distinguished from space, being simply the absence of relation); a separation of elements into classes, replacing the identity axiom with "A is not non-A"; equivalence relations within each class; and finally "the need to pose an absolute (at least temporarily)". This last is the crux. To judge two points mutually at rest one needs a constant-speed reference movement; to judge that movement constant one needs another; and so on. The regress stops only by declaring one phenomenon invariant — which Guy calls a return to substance-based thinking "but with the perception of its own insubstantiality". The absolute is relative to the model in which it is posed, and "assigning an absolute character is always subject to change." He notes that one could even imagine all material points expanding while the velocities of relative movements varied in proportion, with no observable effect.
Every relation has a spatial and a temporal aspect
From this Guy generalises. Wherever there is a relation there is space — the distance or amplitude the relation implies — and time — the traversal of the path linking its terms. "Every relation inextricably separates (space) and connects (time)." He applies the maxim beyond physics, for instance to biological classification, where the temporal aspect concealed in a relational taxonomy is evolutionary time. Substance-based thinking, by contrast, compares a thing with its word instantaneously and so has no time factor at all.
Consequences for physics
Guy makes two observations about contemporary physics: the problem of time has not been solved, only deferred by adjoining a parameter t to x, y and z — string theories add spatial dimensions but rarely revisit time — and the extensive literature criticising existing theories (he cites Selleri and Smolin) never contests the existence of time or its representation.
On quantum mechanics, he notes Rovelli's demonstration that the time parameter can be dispensed with in the formalism, and others' worry about whether time exists "at a certain scale". His response is that time exists at no scale, being only a marker, and that it is "ultimately absurd to want to assign individual particles their own 'proper' time, when time is relation." Discarding proper time removes the scale question entirely. The twin paradox is likewise defused: the age difference "corresponds to a different point of view with respect to a mobile frame of reference and not to an actual 'proper' age". He proposes reading the Lorentz relations themselves as uncertainty relations, the uncertainty being in the mobility or immobility of the material frames used to fix positions and times, expressible as a small unknown velocity between two geometric frames.
On the constancy of light speed — its constancy in time, its isotropy, the possibility of superluminal velocities — Guy's caveat is that the choices are conventional, must be made and honoured, but might have to be remade as circumstances require. "Nature does not impose its laws strictly." This makes him sceptical of theories postulating parallel universes governed by other laws, "as if these laws were prescribed independently of human choices", and he aligns himself with Poincare's theoretical pluralism.
On irreversibility, he reframes the question: the main problem with time "is not whether or not it is irreversible, but whether or not it exists." Irreversibility is the impossibility of some particles going backwards relative to others serving as a spatial reference — so one might as well speak of the irreversibility of space. Since frames of reference are always defined on material points, the reversibility of mechanics itself holds only to an approximation.
Time in culture, and the three-coordinate proposal
A long section applies the scheme to lived and cultural time. Because relations are multiple, times are multiple; a single "physical time" is defined on top of them purely for communication, and "basically has no significance for the way any one part of the world functions". Guy addresses the classical aporia — past no longer exists, future not yet, present a nothing between two nothings — by observing that the grammatical tenses concern the space-time set, not the mobile temporal slice alone. The mountain that has stood for millennia is "temporarily outside of time"; he proposes the terms "present past" and "present future" for its spatial mode of presence, reserving "past past" for the moment of its formation and "future future" for its eventual disintegration. He suggests a quasi-quantitative handle: a present that is "90% spatial and 10% temporal" indicates that a tenth of what the subject perceives is changing, and the "thickness" or duration of that present is a function of the proportion — a 90%-temporal present would be chaos and highly fleeting, a 10%-temporal one closer to the immobility of a desert.
The conclusion returns to physics with the paper's one operational proposal. Identifying time with movement leads to constructing time from three coordinates — not additional to the spatial ones but among them, being the coordinates of the specific moving point whose motion defines time in that frame. This yields "a renewed space-time that is more compact than the space-time of standard relativity, which links the measurements of space and time without unifying the concepts", with consequences for conservation laws, the Lorentz transformations, Maxwell's equations and the equations of gravity, which Guy says he began in earlier work. He is careful to separate himself from existing three-dimensional-time literature (Demers, Pappas, Ziino, Tsabary and Censor, Chen, Franco): those authors "have not grasped the real point, however, which is that time is not three-dimensional! It is a scalar that we construct to organize our events, but based on a movement that is marked by three coordinates". He notes that when the reference movement is a photon in an atomic clock, "the orientation of the device is not arbitrary and the temporal benchmark value incorporates spatial directions invisibly."
Finally he prefers the word composition to contrast: symmetry composes with dissymmetry, void with matter, boundary with its crossing, time with space. The pause needed to speak of them together is, in Aristotle's sense from the Physics, conventional and never definitive.
Assessment
The paper's real strength is that it identifies a genuine circularity and refuses to paper over it. The regress Guy describes — needing a constant-speed process to certify rest, and a further process to certify that constancy — is not a rhetorical device; it is the reason metrology proceeds by convention, and the 1983 redefinition of the metre from a fixed value of c is a textbook instance of exactly the "temporary absolute" he describes. His observation that the same relations underlie both the spatial and the temporal abstraction, and that the boundary between "does not move much" and "moves at constant rate" is one we draw, is a clean way of stating something usually left implicit in the operational definitions at the base of relativity. The distinction he draws between coordinating the measurement of space and time (which Minkowski spacetime does) and unifying the concepts (which he says it does not) is a fair and non-trivial point, and his warning about theories that legislate laws for parallel universes "as if these laws were prescribed independently of human choices" is a coherent extension of his own position rather than a slogan. The paper is also unusually honest about what it is: a conceptual programme with an acknowledged bibliography spanning physics, neuroscience, linguistics and hermeneutics, not a derivation.
The difficulties are of two kinds. The first is that the central proposal is announced rather than carried out. The three-coordinate construction of time is stated in the final pages, its consequences for conservation laws, the Lorentz transformations, Maxwell's equations and gravity are listed, and the reader is referred to Guy's own preprints. Nothing in this paper shows that the reformulation reproduces a single established result, let alone predicts anything new. The distinction he draws from other three-dimensional-time authors — that time remains a scalar constructed from a three-coordinate movement — is philosophically clear but leaves the formalism unspecified; it is not shown how a scalar so constructed differs, in any equation, from the ordinary t. Similarly, the "90% spatial, 10% temporal" present is presented as a way of giving "quasi-quantitative content" to the language of lived time, but no procedure for measuring the percentage is offered and none of the consequences drawn from it are testable.
The second difficulty is that the conventionalist reading is pressed further than the argument supports. That we choose which phenomenon to call constant is true; that all such choices are equally admissible is not, and Guy's own hedge — some constructs "might be more difficult to implement" — understates the case. A construction taking the sidereal rotation rate as the invariant does not merely inconvenience the physicist: it makes the laws of mechanics frame-dependent and the observed isotropy of physical processes a coincidence requiring explanation. The empirical content of the light postulate is not exhausted by convention. The one-way speed of light is indeed conventional, given the freedom in clock synchronisation; but the two-way speed is measured, and its isotropy has been constrained by Michelson–Morley-type and modern optical-resonator experiments to parts in 1017. Guy treats the isotropy question as one more open convention, citing Nodland and Ralston, without noting that the anisotropy claimed in that 1997 analysis of radio-galaxy polarisation was not confirmed by subsequent work.
The treatment of proper time is the sharpest instance of a conceptual move outrunning the physics. Saying it is "absurd to want to assign individual particles their own 'proper' time" is defensible as an ontological claim about what time is; it is much harder to sustain as a claim about what is measured, because proper time along a worldline is precisely what a decaying particle records. The differential decay rate of muons in a storage ring — measured to agree with the relativistic prediction to better than a part in a thousand in the CERN muon experiments — is a quantity attached to individual particles, and it is not obvious how a framework that treats time as "only a marker" with no proper-time content accounts for it. Guy's dissolution of the twin paradox has the same shape: calling the age difference "a different point of view with respect to a mobile frame of reference" rather than a real difference of elapsed proper time does not address the fact that the difference is one-way, permanent, and directly measured in the Hafele–Keating clock transport and in the daily corrections applied to satellite clocks. Reading the Lorentz relations as uncertainty relations, with the uncertainty carried by "a small unknown velocity", is an intriguing suggestion, but it is offered in a single sentence with a reference to earlier work; as stated it makes an exact transformation into an approximate one, which would have consequences the paper does not pursue.
Judged as what it claims to be — an angle of approach and the groundwork for a research programme, in the author's own words — the paper is coherent and its central observation about the shared origin of the two abstractions is worth taking seriously. Judged as physics, it is a promissory note. Its lasting value is likely to be as a clear statement of how much convention lies beneath the t that physics writes down without comment, rather than as a route to any replacement for it.