What this is

A one-slider exhibit in special relativity, built on the real sky. You start on a hillside at night, climb out of the air, pick a speed, and — when you have seen enough — turn around and come home. Everything on the dashboard follows from the single number that slider sets.

The two clocks are the point. Yours is not simulated: it is your own device's clock, ticking at its ordinary rate, because going fast has never felt like anything from the inside. Earth's is the calculated one, and the growing gap between them is what the trip costs you. That gap only hardens into a single fact when the two clocks are back in the same place, which is what Return to Earth is for.

The sky is three real things, stacked. Underneath is a photograph — ESO's 360-degree panorama of the actual Milky Way, 120 hours of shutter time from the Chilean desert, sampled by galactic longitude and latitude so it sits exactly where the real sky does. Over that sit 9,096 catalogue stars at their real positions and real brightnesses. Filling everything, and invisible until you are going very fast indeed, is the microwave background. All three go through the same transform; nothing is swapped out for a different picture as you speed up.

Your motion does three things to all of it at once. Aberration changes the direction light seems to come from, so the sky crowds into the view ahead. Doppler shift changes its colour. Beaming changes its brightness. The last two are the same number — which is why colour and brightness can never drift apart here.

Star colour is not a free choice either. The catalogue gives a colour index, that gives a temperature, and a blackbody at that temperature has exactly one colour. A real star is not quite a blackbody — absorption lines and molecular bands pull its spectrum off the ideal curve, and interstellar dust reddens what reaches us before the catalogue ever measures it — so take this as a good approximation of a star's colour rather than a measurement of it.

Most movies get this wrong. There is no blue tunnel and there are no streaks: aberration moves stars, it does not smear them. And nothing twinkles — scintillation is something the atmosphere does, not something stars do.

The band across the sky is the Milky Way — not a picture behind the stars, but the combined light of the hundred billion or more of them you cannot pick out, going through the same transform. The dark shapes torn out of it are dust: the Great Rift, the Coalsack, the Pipe. It is nearly colourless to the eye, and the photographs of it you have seen in purple and gold almost always got that from a long exposure, not from anyone's eyes.

The equations

Everything below is live. The right-hand value under each formula is what that expression evaluates to at your current speed — leave this open, drag the rail, and watch them move. Nothing in the physics is fitted or tuned — no free parameters anywhere between β and the light arriving at your eye. The free choices all sit at the display end, where they have to: an overall exposure, a separate scale for the Milky Way's brightness, the tone curve that lands the result inside what a monitor can actually show, and — for the photographic layer only — a compressed stand-in for beaming, because no screen can carry the real thing over this range. That last one is a genuine departure rather than a scaling, and it is the reason the modelled star field and the photograph behind it are described separately under Scope, where all four are listed.

Wait — doesn't Earth see my clock as slow?

Yes. And Earth is not wrong. One word needs pinning down first, though: see. What you would literally see through a telescope is mostly about how long the light took to get to you — on the way out you would watch Earth's clock crawl, and on the way back you would watch it race, and neither of those is time dilation. Time dilation is what is left once you subtract the travel time of the light: not what a frame watches, but what it measures, after correcting for where the light started and how far it came.

Measured that way, while you are coasting, time dilation is completely symmetric — each of you measures the other's clock to be running slow, and both of you are right. That is reciprocity, and it is real physics, not an illusion.

The cluster on the left is showing Earth's clock in Earth's frame of reference, which is unambiguous. The comparison only becomes a single physical fact when the two clocks are back in the same place — which is what happens when you press Return to Earth.

What breaks the tie is that you changed reference frames and Earth never did, so there is no matching argument to run from your side. But the acceleration is only the tiebreaker; it is not what does the ageing. The size of the gap comes from the shape of your path: between the same two meetings, the straight, unaccelerated worldline is the one that accumulates the most proper time, and any detour accumulates less. Make the turnaround as brief and as violent as you like and the answer barely moves; make the trip longer or faster and it moves a great deal.

What just happened at home

Scope, and where the edges are

Your clock is not simulated. The traveler's elapsed time is your own device's clock, ticking normally, because that is the entire point: nothing about travelling fast feels like anything. Earth's clock is the calculated one.

Earth's elapsed time is ∫γ dτ along your path, accumulated every frame. That integral is exact for any speed history, including the ramps where the ship speeds up and slows down — so the numbers stay honest even while you are dragging the rail around.

This is special relativity only. Flat spacetime, no gravity, no gravitational time dilation. Accelerations are drawn as short ramps and their g-forces are ignored; the turnaround brings the ship to a full stop before it reverses, which is what makes each leg a plain constant-velocity problem.

What moves, and what does not. The simulation models the effects of velocity on the sky and clocks, while holding the underlying celestial sky fixed. Positional changes from travelling through the galaxy are omitted because they occur too slowly to matter during normal use.

The photographic sky stays, and it is one photograph. Every displayed ray is traced backward through the aberration equation, converted to galactic longitude and latitude, and used to sample ESO's all-sky panorama — so motion distorts the photograph itself rather than replacing it. It never twinkles. There is no rotation, crop or blend applied to it anywhere: the sky is pinned to the galactic frame and to nothing else, which means the photographed Milky Way and the catalogue stars drawn over it agree about where the band is.

What this replaced, since it matters. Until this revision the background was three images composited together — a front plate, a back plate and a soft filler panorama — joined by fitted per-channel gains and a speed-dependent feather, with the whole panorama rotated by a hand-picked angle so its band would line up with the front plate's diagonal. That rotation was a composition decision and it left the photographed Milky Way 38.6° from where the star catalogue put it. The filler panorama was also not a photograph: measured against a real all-sky plate its fine structure correlated at r = 0.06, below the floor set by comparing a real plate with a misaligned copy of itself, and it contained no Magellanic Clouds and no star bright enough to show a diffraction spike. It was almost certainly generated. The page claimed it was a photograph of the actual Milky Way. It was not, and that is why it is gone.

The transformed stars. 9,096 of them, from the Yale Bright Star Catalogue (Hoffleit & Warren 1991), J2000 — every star in it. The catalogue holds 9,110 entries, of which 9,096 are stars; the other 14 are novae and extragalactic objects kept only to preserve the numbering. It is drawn up to be complete to about magnitude 6.5 and its faintest entry here is 7.96, so the handful past 6.5 are a bonus rather than a survey. Real positions and real magnitudes throughout. Colour indices are real for all but 310 of them, which carry no measured B−V in the catalogue and are given its median (0.51, an early-G star) rather than an invented one. Positions are frozen at J2000: proper motion and precession are not modelled.

The Milky Way texture is photographic, not a catalogue. It supplies the visual depth of unresolved stars and dust. Its relativistic direction change is exact; its displayed Doppler colour and beaming are compressed into the range a monitor can show.

The four display parameters, named. Everything between β and the light arriving at your eye is computed. Four numbers past that point are chosen, and this is all of them: one overall exposure, set once so a first-magnitude star saturates its core and left alone at every speed; one separate scale for surface brightness, because a star's light lands in a sub-pixel point spread function and the Milky Way's is spread across degrees; one tone curve, 1 − e^−x, which rolls off highlights without ever clipping a channel. The fourth is the odd one out and the least defensible: the photographic layer raises brightness as D^1.28 rather than D⁴, capped at 60×, with a fitted colour balance. That is not an exposure — it changes the rate at which brightness grows with speed, so the photograph's response to beaming is qualitatively softened rather than merely rescaled. The modelled star field over it is not treated this way and carries the true exponent.

The microwave background is drawn. It fills the sky at 2.7255 K, which is far too cold to see, and for nearly the whole rail it contributes exactly zero — not a negligible amount, zero, because no visible photons survive the Wien tail at that temperature. Beaming raises it as D⁴ like any other surface brightness, and once the forward temperature passes about 700 K it appears as a dull red wash ahead and then climbs almost vertically: invisible at 0.9999 c, and roughly 200 times the Milky Way's peak surface brightness at 0.99998 c. That cliff is why the rung is there. Its brightness and colour come from the same Planck integral as everything else; the shader samples that result rather than recomputing it, so the two skies cannot disagree. At the top of the rail it saturates the view ahead to white, which is the honest answer — at that speed the blueshifted background is a genuine hazard, not a backdrop.

The opening view is fully dark-adapted. You begin with the sensitivity an observer would have after sitting in darkness, rather than waiting through that adaptation on the page. At this luminance the Milky Way is nearly colourless because rod vision dominates; Doppler colour appears as beaming makes the light bright enough for cone vision.

Colour. Planck's law integrated against analytic fits to the CIE 1931 colour-matching functions (Wyman, Sloan & Shirley 2013, not the published tables), converted to sRGB, gamut-mapped by desaturating toward white rather than clipping a channel. Tone-mapped once at the end. A monitor cannot reproduce a retina's absolute response, so the transformations and relative brightness are physical while the final display exposure is a calibrated representation. Assumes a reasonably dark room and an sRGB display.

The way home. Earth is held straight ahead as a black silhouette against the star field. Its apparent size grows as the range closes — it starts as a point you could miss and swells as you arrive — and it goes through the same aberration as everything else, so at high speed it is squeezed toward the middle of the frame along with the stars. Two deliberate departures: the disc is floored at a few pixels, because a light-minute out Earth really is smaller than one and a target you cannot see is not a target, and it is capped well short of the frame instead of swelling to fill the sky in the last moments. The Sun is intentionally kept out of this view so you can watch Earth approach.

Sources

The sky itself is a photograph by someone, and here is who. The all-sky panorama is The Milky Way panorama, credit ESO/S. Brunier — eso0932a, released by the European Southern Observatory under CC BY 4.0. Serge Brunier shot it from La Silla and Paranal between August 2008 and February 2009: about 300 fields, four exposures each, six minutes apiece, roughly 1,200 photographs and 120 hours of shutter time, assembled by Frédéric Tapissier. It is used here at 4096 × 2048 in galactic coordinates, and it is the only picture the exhibit shows you by default — everything else on screen at rest is computed. The thirteen plates behind the wavelength control are photographs too, and they are credited below.

Einstein (1905), Zur Elektrodynamik bewegter Körper, for all of the above. Ballesteros (2012) for B−V → temperature. Wyman, Sloan & Shirley (2013) for the colour-matching function fits. Hoffleit & Warren (1991) for the Yale Bright Star Catalogue. Fixsen (2009) for the microwave background temperature. Okun (2009) on why the words "relativistic mass" appear nowhere here. Bland-Hawthorn & Gerhard (2016) and Dwek et al. (1995) for the shape of the Galaxy, and the GRAVITY Collaboration (2019) for the Sun's 8.178 kpc distance from its centre. The magnitude-to-lux zero point (2.54 × 10⁻⁶ lux at V = 0) is the standard photometric conversion rather than a result from any of these.

The other thirteen skies. The plates behind the wavelength control are all-sky surveys served by NASA's SkyView (McGlynn, Scollick & White 1998), reprojected to galactic plate carrée: COBE/DIRBE zodi-subtracted mission average at 1.25, 2.2, 3.5, 4.9 and 240 µm (COBE Team); IRAS/IRIS at 12, 25 and 60 µm (Miville-Deschênes & Lagache 2005); the 100 µm dust map of Schlegel, Finkbeiner & Davis (1998); Planck 857 and 353 GHz (ESA/Planck Collaboration); the 408 MHz all-sky map of Haslam et al. (1982); and the ROSAT all-sky survey diffuse background (Snowden et al. 1997). All are public-domain or openly licensed.

What has been done to those plates, and why. Three things, none of them physics. The catalogue's stars are notched out of them. The exhibit draws the Bright Star Catalogue as a separate layer over the plate, and the star canvas is composited additively — so any star present in both was being drawn twice. Each catalogue star is found in the plate and its disc replaced with the local background, which removes about three quarters of the doubled light from the brightest stars; the photographic diffraction spikes of the very brightest survive, because taking those out would mean scrubbing a wide patch of real sky around each one. The IRAS plates have their gaps filled. IRAS surveyed about 96% of the sky, and the missing 3% is filled with the gap-free 100 µm dust map scaled to match — real structure, but from the wrong wavelength, and not a measurement at that wavelength. They are display-stretched, not linear. Each plate is an arcsinh stretch of the survey's intensity, chosen to keep faint structure visible without blowing out the Galactic plane, so these are pictures of the sky rather than calibrated intensity — the same standing as the visible photograph. Every band but the visible one is false colour: a single-channel measurement drawn as brightness.

The bands are not what you would see. They are what an instrument sees. Aberration and the Doppler factor are applied to them exactly as they are to the visible sky — that part is the same physics on the same code — but no speed on this rail turns an X-ray sky into something a human eye could receive. The wavelength control is the one place this exhibit shows you a sky you could not have.