Theoria

What Nolan’s film gets right about relativity, and what it quietly assumes about the metaphysics of time.

Contents

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I. Introduction

Regular readers will know that I have spent the past several months in an online dialogue with a physicist from UC Berkeley about the nature of time. The exchange began with the familiar tale of the twins: one flies off near the speed of light, returns to find his brother grey, and from the disagreement of their clocks my correspondent concluded that there is no overarching time at all, that time is relative and therefore subjective, and that any tensed alternative is unfalsifiable metaphysics. Somewhere in the middle of that conversation I rewatched Christopher Nolan’s Interstellar (2014), and it occurred to me that the film stages our entire dispute — twins, clocks and conclusions included — on a canvas the size of a galaxy.

It can do so because it is that rare blockbuster whose physics was built to survive scrutiny. Kip Thorne, the Caltech relativist who would later share a Nobel Prize for gravitational-wave detection, served as executive producer and scientific anchor, and he imposed two ground rules on the production: nothing on screen would violate firmly established physical law, and every speculation would grow out of real science rather than screenwriting convenience.¹ The discipline paid dividends beyond the cinema. The rendering code built to visualise the black hole Gargantua yielded genuinely new results on gravitational lensing by spinning holes, published in Classical and Quantum Gravity.²

Yet the film also advances a quieter claim, one no telescope can check: a claim about what time is. Here the ancient rivals are the A-theory, on which time genuinely passes, and the B-theory, on which time merely extends, a fourth dimension laid out as space is. I shall argue three things. First, the celebrated time-dilation sequences are metaphysically neutral: every reading of every clock is the common property of all serious interpretations of relativity. Second, the tesseract is not neutral: it is the B-theory rendered in production design. Third, nothing in relativity obliges that choice, and the quantum correlations at the heart of the film’s own plot device arguably pull the other way.

II. The physics on screen

II.1 A wormhole and a spinning black hole

The premise is agricultural apocalypse; the escape route is a wormhole parked near Saturn by parties unknown. The wormhole is the film’s one piece of frankly exotic infrastructure, and even it has a respectable pedigree: Thorne and his student Michael Morris showed in 1988 that traversable wormholes are solutions of Einstein’s field equations, though holding one open requires matter with negative energy density, something no laboratory has produced in the required quantities.³

The destination system orbits Gargantua, a black hole of roughly one hundred million solar masses whose horizon is comparable in radius to Earth’s orbit.¹ The enormous mass is not decoration. Tidal stresses at the horizon fall off as the inverse square of the mass, so a supermassive hole is gentle where a stellar-mass hole would shred a spacecraft and its crew. And the film’s most famous image, the glowing disc arching over and under the black sphere, is honest optics: light from the far side of the accretion disc is lensed above and below the shadow. Thorne concedes one deliberate inaccuracy, the suppression of the Doppler brightening that would make the approaching side of the disc far brighter than the receding side, sacrificed for visual legibility.¹

II.2 Miller’s planet and the arithmetic of dilation

Then comes the hour that costs seven years. Miller’s planet skims Gargantua so closely that its clocks crawl relative to those of the mother ship parked further out. General relativity supplies the bookkeeping. For a clock held at radius r outside a static black hole of mass M, proper time τ relates to the coordinate time t of a distant observer by:

dτ/dt = √(1 − 2GM/(rc²)) = √(1 − rₛ/r),   rₛ ≡ 2GM/c²

Nothing malfunctions on the slow clock. The crew on Miller’s planet age, think and tick at the perfectly ordinary local rate; the ratio concerns the metrical structure of spacetime itself, the comparative lengths of two worldlines, not the mechanics of any timepiece. Now run the film’s numbers:

7 years = 61,362 hours  ⇒  dτ/dt ≈ 1/61,362 ≈ 1.63 × 10⁻⁵
⇒  1 − rₛ/r ≈ (1.63 × 10⁻⁵)² ≈ 2.7 × 10⁻¹⁰

The naive calculation therefore parks the planet within about three parts in ten billion of the horizon, and there lies a snag: around a non-rotating hole no circular orbit, stable or otherwise, survives that deep, since stable orbits end at three Schwarzschild radii. Thorne’s solution was spin. A rotating hole drags spacetime around with it, and as the spin approaches its theoretical maximum the innermost stable orbit is dragged down towards the horizon. To buy one hour for seven years, Thorne computed, Gargantua must spin within about one part in one hundred trillion of the maximum — a hair’s breadth short of extremality.¹ The same ferocious gravity raises the planet’s mountain-sized tidal waves. The scene is as outlandish as it is outstanding and the arithmetic is perfectly accurate.

II.3 The twins on film, and the tesseract

Cooper and Murph are the twins of the thought experiment made flesh, father and daughter rather than brothers, with the added cruelty that the stay-at-home twin begins as a child. The resolution of the so-called paradox is the same on screen as in the textbooks: proper time is route-dependent. A clock measures the length of its own worldline through spacetime, and different worldlines between the same pair of events generally have different lengths. In the special-relativistic case the rule is:

Δτ = Δt √(1 − v²/c²),   γ ≡ 1/√(1 − v²/c²)

None of this is speculative. Caesium clocks flown around the world on commercial aircraft in 1971 returned measurably out of step with their earthbound counterparts, in the amounts relativity dictates,⁴ and the satellite clocks of the GPS constellation must be corrected by some thirty-eight microseconds per day, a combination of velocity and gravitational effects, or positional fixes would drift by kilometres within a day. Interstellar merely turns the dial: twenty-three years vanish during the excursion to Miller’s planet, the final slingshot through Gargantua’s grip costs another five decades, and Cooper is returned, barely older than when he left, to a daughter at the end of her life.

It is when Cooper falls through the horizon that the film changes significant direction. Inside Gargantua he is caught by the tesseract, a machine built by five-dimensional beings, strongly implied to be our remote descendants, in which the history of Murph’s bedroom is fanned out before him like a landscape. Every moment of the room exists, arranged along an axis he can traverse; he pushes books from shelves years before his own departure, encodes data in the second hand of a wristwatch, and discovers that he himself was always his daughter’s ghost. Thorne’s taxonomy is candid about the tier this occupies: the bulk, its fifth dimension, and the beings who inhabit it belong to disciplined speculation, constrained by science but not delivered by it.¹

III. Two theories of time

III.1 Tensed and tenseless time

Step back now from the screen to the concepts. In 1908, the very year Minkowski geometrised relativity, the Cambridge philosopher J. M. E. McTaggart published a classic analysis distinguishing two ways of ordering events in time.⁵ His A-series runs from far past through present to far future, and positions in it are forever changing: my writing of this sentence was future, is present, and will be past. His B-series orders the same events by the fixed relations of earlier and later, relations that never change: Minkowski’s lecture is earlier than Nolan’s film, always was, and always will be. From this distinction descend the two great rival metaphysics of time.

A-Theory (tensed time) — Temporal becoming is objective. Events are past, present, or future absolutely, and these determinations change: the future becomes present, the present slips into the past. In its presentist form, only what is present exists. B-Theory (tenseless time) — Temporal becoming is a feature of perspective, not of the world. All events are equally real, ordered only by the fixed relations of earlier than, simultaneous with, and later than. “Now” functions like “here”: an indexical, not a metaphysical spotlight. Note well — The A-theory is not the thesis that there is absolute, frame-independent time. Tense and absoluteness are separable claims, and conflating them is the cardinal error in this debate.

The standard form of the A-theory is presentism: only the present exists; the past has ceased and the future is not yet. The standard form of the B-theory is eternalism, the so-called block universe: all events, the Battle of Hastings, your reading of this essay, the heat death, exist tenselessly and on an ontological par, and the passage of time is something minds contribute, not something the world does.

III.2 Three faces of one theory: Einstein, Minkowski, Lorentz

How does relativity bear on this? Less straightforwardly than is usually supposed, and the history is instructive. Einstein’s original 1905 presentation of special relativity is a kinematics of rods, clocks and observers: ordinary three-dimensional objects enduring through time.⁶ It relativises simultaneity to inertial frames, and so abolishes Newton’s single universal time, but it nowhere denies temporal becoming; the theory as Einstein first framed it presupposes a tensed world. The tenseless reading arrived three years later, when Hermann Minkowski recast the theory as the geometry of a four-dimensional manifold and announced the new picture with the following flourish:

“Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.”⁷

On the Minkowskian interpretation, temporal becoming is an illusion; events sit tenselessly in spacetime as cities sit on a map. Einstein himself came to embrace something like this picture, famously consoling the family of his oldest friend Michele Besso, weeks before his own death, with the thought that for believing physicists the division into past, present and future is a stubborn illusion. But there is a third interpretation, the one I have been studying and defending: the neo-Lorentzian. On it there is a privileged foliation of spacetime, a fact of the matter about distant simultaneity, and the familiar relativistic effects of contraction and dilation are real dynamical effects of motion relative to that frame, effects which conspire to render the frame undetectable.⁸

The crucial point is that the Einsteinian, Minkowskian and neo-Lorentzian formulations share the same mathematical core and issue in the same empirical predictions; they are geometrically and observationally equivalent, differing only in the physical interpretation laid over the formalism. Nor does four-dimensional dress settle anything: Newtonian mechanics itself can be recast as a tenseless four-dimensional geometry, and a neo-Lorentzian can adopt Minkowski’s spacetime formalism without blushing. The geometry underdetermines the metaphysics.

III.3 Where the film stands

Where, then, does Interstellar stand? Every clock reading in the film, the seven years per hour, the twenty-three lost to Miller’s planet, the fifty-one to the slingshot, belongs to that shared core; all three interpretations certify the arithmetic, so the dilation scenes favour none of them. The tesseract is another matter. A past that exists, is arranged, and can be visited is eternalism in set design. The film, in short, is scrupulously agnostic where the physics is established and quietly partisan exactly where the physics turns speculative.

IV. Does relativity decide?

IV.1 The argument from the relativity of simultaneity

Is the partisanship forced by the physics? My Berkeley correspondent thinks so: the twins’ disagreeing clocks show, he says, that there is no overarching time, hence that time is relative and therefore subjective. The respectable version of this argument runs through the relativity of simultaneity. Under a Lorentz boost with velocity v:

t′ = γ(t − vx/c²),   x′ = γ(x − vt)

The term vx/c² is the whole story: two events with the same t but different x in one frame receive different t′ in another, so which distant events count as happening now depends on one’s state of motion. Rietdijk⁹ and Putnam¹⁰ sharpened this observation into an argument for the block. If whatever lies on some observer’s simultaneity hyperplane is real for that observer, then by chaining suitably moving observers one can catch any event whatever, your funeral included, on somebody’s plane of the present; whence, the argument concludes, all events are real and becoming is an illusion. Putnam did not undersell the result:

“I conclude that the problem of the reality and the determinateness of future events is now solved. Moreover, it is solved by physics and not by philosophy.”¹⁰

IV.2 What the argument assumes

The argument is elegant and, I shall now argue, doubly question-begging. Notice first the conflation on which the popular version trades: the A-theory is not the thesis of absolute time. These are separable claims, and history separates them, for Einstein’s own 1905 theory relativised simultaneity while presupposing a tensed world of enduring things. One cannot refute the A-theory by refuting Newton.

Notice next what the Rietdijk–Putnam argument must assume: that each frame’s simultaneity hyperplanes carry ontological weight, which is to say that reality is to be read off the Minkowski interpretation of the formalism. Against a neo-Lorentzian, for whom exactly one foliation is metaphysically privileged and the others are artefacts of clock synchronisation, this is not an argument but a stipulation. And since the three interpretations are empirically equivalent, the choice among them cannot be made in the laboratory; it must be made on philosophical grounds, by appeal to explanatory power and coherence with the rest of what we know (see my paper on Scientism).¹¹ The charge of unfalsifiability, incidentally, boomerangs: if a privileged foliation outruns all possible measurement, so does the tenseless block. Nobody in this debate has clean experimental hands.

The strongest objection to my side deserves stating plainly. Balashov and Janssen¹² press that an undetectable preferred frame is theoretically unmotivated: Minkowski explains contraction and dilation at a stroke, as perspectival effects of spacetime geometry, whereas the Lorentzian must postulate what looks like a dynamical conspiracy. It is a serious point, and I concede the geometrical story its economy. But dynamical explanation is still explanation, and a postulate ceases to be idle the moment it starts doing work elsewhere in physics. Whether it does is a question of fact, and it brings us to the laboratory after all.

IV.3 Entanglement and the return of simultaneity

Einstein, Podolsky and Rosen¹³ argued that quantum mechanics, if complete, commits us to a strange nonlocality; Bell¹⁴ turned the strangeness into an inequality that every local theory must satisfy; and experiment, from Aspect’s time-varying analysers onward, has found the inequality violated just as quantum mechanics predicts,¹⁵ a line of work crowned with the 2022 Nobel Prize. Send two entangled photons in opposite directions until they are separated by a spacelike interval, so that no signal at or below light speed can connect them. Measure one, say its polarisation, and the outcomes on the far side stand in correlations that no local common cause can underwrite: the distant photon immediately takes on the correlated value.

Here the interpretive bind tightens. If simultaneity is merely frame-relative, then the temporal order of the two measurements is itself frame-relative: there are frames in which the outcome runs ahead of the measurement that, in other frames, produced it. Treat the correlation as genuinely productive and you have causal influence running backwards in time relative to some frames, with all the pathological company that keeps, effects arriving before their causes. The no-signalling theorems keep the peace operationally, since the correlations cannot carry a message, but the ontology creaks. Bell himself, no friend of easy answers, mused that the “cheapest resolution” of the tension was “going back to relativity as it was before Einstein”, to the preferred frame of Lorentz and Poincaré, undetectable because our instruments are dynamically distorted by motion through it.¹⁶ A privileged foliation dissolves the ordering problem at a stroke: there is simply a fact about which measurement occurred first. It seems to me, as it seemed to Bell, that this is the least extravagant explanation on offer, and it is chiefly for this reason that I regard the neo-Lorentzian interpretation as enjoying a real, though defeasible, advantage. The reader should know that no-collapse interpretations tell the story differently; underdetermination, as ever, cuts many ways.

V. Cosmic time, causal loops, and the ghost

V.1 The universe keeps a clock after all

Special relativity, moreover, was never the last word; it has been superseded by the general theory, and when general relativity is applied to the universe we actually inhabit, something remarkable happens: a cosmic time emerges. On the largest scales the universe is homogeneous and isotropic, described by the Friedmann–Lemaître–Robertson–Walker metric:

ds² = −c² dt² + a(t)² [ dr²/(1 − kr²) + r²(dθ² + sin²θ dφ²) ]

The t appearing here is cosmic time: the proper time of observers at rest with respect to the expansion, ticking along worldlines orthogonal to the hypersurfaces of homogeneity. It is picked out not by anyone’s arbitrary labelling of events but by the matter content of the universe itself — which is why it functions as a parameter of cosmic history rather than a mere coordinate; and it is the same for every such observer regardless of position or state of motion, and in that sense frame-independent, absolute. When cosmologists report that the universe is about 13.8 billion years old,¹⁷ the figure is not Earth time parochially extended; it is the duration of the universe in cosmic time. Our planet simply happens to sit almost at rest in the relevant frame, moving at roughly 370 kilometres per second relative to the cosmic microwave background, a crawl that keeps terrestrial clocks within better than a part in a million of the cosmic rate, and successive instruments, the James Webb Space Telescope among them, keep sharpening our reckoning of that history. The irony should be savoured: the absolute simultaneity that special relativity was said to banish reappears, writ large, the moment Einstein’s mature theory meets the actual cosmos. The tensed theorist’s global now has a natural physical partner, and it is the very clock by which we date the universe.

V.2 Hume’s arrow, Gödel’s circles, and Cooper’s ghost

Finally, the ghost. The relation of cause to effect in time is among the oldest cruxes on record: Hume insisted that a cause must be prior to its effect, and argued for the priority, I have always thought, quite badly;¹⁸ Kant answered with the ball resting on the cushion, cause and effect simultaneous.¹⁹ Interstellar outbids them both: in the tesseract, effects precede their causes around a closed loop. Cooper was always the ghost; the data always arrived; the loop contains no contradiction, only a bootstrap. The physics literature knows this territory precisely. Gödel constructed rotating solutions of Einstein’s equations containing closed timelike curves and drew from them comfort for philosophers “who, like Parmenides, Kant, and the modern idealists, deny the objectivity of change”,²⁰ and the self-consistency of causal loops was analysed, delightfully, in a paper co-authored by Thorne himself.²¹

Two observations. First, Gödel’s universes admit no cosmic time; ours, on the evidence, does. Whether history can be toured is a contingent question about global structure, and the actual universe appears untourable. Second, consult the metaphysical ledger: on presentism the tesseract is impossible in principle, for there is no past bedroom left in existence to visit; on eternalism it is effortless, every moment of the room eternally in stock. Which is precisely my point about where the film’s allegiances lie. Let it also be noted that the independence runs both ways: a neo-Lorentzian spacetime can itself be given a tenseless four-dimensional formulation, so not even my preferred physics delivers the A-theory on its own. The tesseract is theatre, glorious theatre, but not theorem.

VI. Conclusion

Where does this leave us? With a film that is honest exactly where physics can speak and partisan exactly where it cannot. The dilation of time on Miller’s planet and the divergent ages of Cooper and Murph belong to the shared arithmetic of every serious interpretation of relativity, and Interstellar renders that arithmetic with a fidelity Hollywood had never before attempted. The navigable past of the tesseract is something else: a metaphysical thesis, the tenseless block, wearing the costume of physics.

And this is the moral I keep pressing on my Berkeley correspondent. The readings of the clocks, the violations of Bell’s inequality, the age of the universe: these are scientific data. Whether time therefore fails to pass, whether the A-theory dies with Newtonian absoluteness, whether an undetectable foliation is a vice or the cheapest sanity on offer: these are philosophical questions, and answering them badly while calling the answers physics is not rigour but its imitation. Most scientists, in my wider experience, are simply innocent of the philosophy their pronouncements presuppose. I say that respectfully, as an actual scientist; I just also happen to be a trained logician.

Let the film have the last word against itself. The reunion scene wrecks audiences for a reason. An old woman sends her father back to the stars, and what wrecks us is that the decades between them are gone, not stored two chapters back in a block but lost — unrecoverable, no longer real. On the tenseless view Murph’s childhood exists eternally, no more lost to Cooper than Berkeley is lost to a man standing in Boston. Nobody watching believes that in their bones. The tesseract preaches the B-theory; the tears confess the A-theory. Between the geometry and the grief? I suspect that grief is a better witness to what time is than what she first appears.

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References

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