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    <title>Interstellar on Sebastian Spicker</title>
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      <title>What Black Hole Images Actually Show (and Why a Wormhole Would Look Different)</title>
      <link>https://sebastianspicker.github.io/posts/black-hole-image-wormhole-shadow/</link>
      <pubDate>Mon, 17 Oct 2022 00:00:00 +0000</pubDate>
      <guid>https://sebastianspicker.github.io/posts/black-hole-image-wormhole-shadow/</guid>
      <description>The EHT images of M87* and Sgr A* are remarkable not because they surprised us, but because they confirmed a century-old prediction at microarcsecond precision. The more interesting question: what would a wormhole look like? Completely different — and we have never seen that.</description>
      <content:encoded><![CDATA[<h2 id="summary">Summary</h2>
<p>In 2019 and 2022 the Event Horizon Telescope released images of two supermassive black holes. Both
looked exactly like physics predicted they would. That precision — agreement to within a few
percent — is what makes them scientifically powerful. The ring is not merely beautiful; it is a
quantitative measurement of a metric.</p>
<p>The more interesting question, the one I want to spend time on here, is: what would a wormhole
look like? The answer is: radically different. Which means the images are also evidence — not just
confirmation of a black hole, but a <em>ruling out</em> of certain alternatives at those locations.</p>
<h2 id="the-images">The Images</h2>
<p>The Event Horizon Telescope is a planet-scale interferometer: radio dishes from Hawaii to the
South Pole, phase-locked to atomic clocks, synthesizing an effective aperture the diameter of
Earth. At millimetre wavelengths, this gives an angular resolution of around 20 microarcseconds —
enough to resolve a grapefruit on the Moon.</p>
<p>In April 2019 the collaboration published six simultaneous papers on M87*, the supermassive black
hole at the centre of the Virgo A galaxy
(<a href="#ref-eht2019a">EHT Collaboration et al., 2019a</a>, <a href="#ref-eht2019b">2019b</a>). The ring had an
angular diameter of \(42 \pm 3\) μas, consistent with a black hole of mass
\(M = (6.5 \pm 0.7) \times 10^9 \, M_\odot\) at a distance of 16.8 Mpc. The southern arc of
the ring was brighter — I will return to why.</p>
<p>In May 2022 the same team published results on Sagittarius A*, the Milky Way&rsquo;s central black hole
(<a href="#ref-eht2022">EHT Collaboration et al., 2022</a>). The ring diameter: \(51.8 \pm 2.3\) μas,
corresponding to a mass of \(\sim 4 \times 10^6 \, M_\odot\) at 8.18 kpc. M87* is roughly 1500
times more massive than Sgr A* and roughly 2000 times farther away — so the two apparent ring
sizes are within 25% of each other. The universe arranged the coincidence; the EHT exploited it.</p>
<h2 id="the-physics-of-the-ring">The Physics of the Ring</h2>
<p>The ring is not the black hole itself. You cannot image an event horizon: by definition, no
information escapes from it. What the EHT resolves is the <em>photon sphere</em> — the region of
unstable circular photon orbits — and its shadow.</p>
<p>For a non-rotating (Schwarzschild) black hole, the photon sphere sits at:</p>
$$
r_\text{ph} = \frac{3GM}{c^2} = \frac{3}{2} R_S
$$<p>where \(R_S = 2GM/c^2\) is the Schwarzschild radius. Light orbiting here is in unstable
equilibrium: a small perturbation sends it either spiralling inward or escaping to infinity. The
<em>critical impact parameter</em> — the perpendicular distance from the optical axis at which an
incoming photon just grazes the photon sphere — is:</p>
$$
b_c = \frac{3\sqrt{3} \, GM}{c^2} \approx 5.196 \, \frac{GM}{c^2}
$$<p>The angular diameter of the shadow as seen by a distant observer is therefore:</p>
$$
\theta_\text{shadow} = \frac{2 b_c}{D} = \frac{6\sqrt{3} \, GM}{c^2 D}
$$<p>Plugging in the EHT numbers for M87* (\(M = 6.5 \times 10^9 \, M_\odot\), \(D = 16.8\) Mpc):</p>
$$
\theta \approx \frac{6 \times 1.732 \times 6.5 \times 10^9 \times 1477 \, \text{m}}{16.8 \times 3.086 \times 10^{22} \, \text{m}}
\approx 40 \, \mu\text{as}
$$<p>The EHT measured \(42 \pm 3\) μas. Agreement within 5%. This is not a post-hoc fit; it is a
prediction that follows directly from general relativity and a mass independently constrained by
stellar kinematics.</p>
<p>The first numerical simulation of this image was done by Jean-Pierre Luminet in 1979, using punch
cards and an IBM 7040 (<a href="#ref-luminet1979">Luminet, 1979</a>). He computed the geodesics, rendered the
result by hand on photographic paper, and produced an image that looks startlingly like the
2019 photograph — forty years before the telescope existed.</p>
<h2 id="the-brightness-asymmetry">The Brightness Asymmetry</h2>
<p>The southern arc of the M87* ring is brighter. This is not an instrumental artefact. The
accretion disk — the superheated plasma spiralling into the black hole — orbits at mildly
relativistic speeds, \(v \sim 0.3\text{–}0.6 \, c\). On the approaching side of the disk,
synchrotron emission is Doppler-beamed toward the observer: intensity amplified, frequency
blueshifted. On the receding side, the flux is deboosted (<a href="#ref-eht2019b">EHT Collaboration et al., 2019b</a>).</p>
<p>In M87* the approaching side faces south, which implies — combined with the known orientation of
M87&rsquo;s large-scale relativistic jet — that the black hole spin axis points away from Earth. The
brightness asymmetry is, in effect, a spin measurement.</p>
<h2 id="interstellar-did-it-right">Interstellar Did It Right</h2>
<p>In 2014, the visual effects company Double Negative rendered the black hole Gargantua for
Christopher Nolan&rsquo;s <em>Interstellar</em>. They did this by integrating the actual geodesic equations for
a rapidly spinning (near-extremal Kerr) black hole. Kip Thorne, one of the producers, collaborated
on two companion papers with the visual effects team (<a href="#ref-james2015a">James et al., 2015a</a>).</p>
<p>The resulting image showed the accretion disk wrapping both above and below the black hole,
producing a characteristic double-arc structure — direct emission at the equator plus a secondary
image of the disk mirrored by gravitational lensing. This was not artistic licence. It was the
first photorealistic render of a black hole produced from first principles, and the physicists
found new results in the process: features of the lens map that had not previously been worked out
analytically.</p>
<p>The same team published a companion paper on the wormhole in <em>Interstellar</em>
(<a href="#ref-james2015b">James et al., 2015b</a>). That paper is where things get interesting.</p>
<h2 id="what-a-wormhole-would-actually-look-like">What a Wormhole Would Actually Look Like</h2>
<p>A traversable Morris-Thorne wormhole connects two regions of spacetime through a throat. An
observer near the throat would see <em>both</em> connected universes simultaneously — one on each side
of the throat boundary. The key visual feature, worked out in detail by Thomas Müller
(<a href="#ref-muller2004">Müller, 2004</a>), is this:</p>
<ul>
<li>Looking through the throat, you see the far-side universe compressed into a disk, bounded by
a bright Einstein ring at the throat.</li>
<li>Outside the ring, you see the near-side universe, heavily distorted by the wormhole&rsquo;s
gravitational field.</li>
<li>There is no <em>shadow</em> in the sense a black hole has — no region from which light cannot escape.
Instead, the ring acts as a portal: all light that reaches the throat passes through rather
than being absorbed.</li>
</ul>
<p>The James et al. (2015b) wormhole paper shows this explicitly. The <em>Interstellar</em> wormhole was
rendered as a spherical lens with a celestial hemisphere visible through it. The visual signature
is a double celestial sphere: your own sky distorted around the outside, and a compressed view of
a distant universe through the middle.</p>
<p>This looks nothing like the EHT images.</p>
<p>The EHT sees a <em>shadow</em> — a dark central region from which no emission escapes, surrounded by a
bright ring. A traversable wormhole at the same mass and distance would show a bright ring with
a <em>second universe</em> visible in the centre, not a dark disk. The topologies of the light-path
structures are fundamentally different.</p>
<h2 id="the-images-rule-something-out">The Images Rule Something Out</h2>
<p>This is the point I find underappreciated. The EHT results are usually discussed as confirming
that M87* and Sgr A* are black holes consistent with GR. That framing is correct. But the images
are also <em>falsifying evidence</em> against alternatives.</p>
<p>Several exotic compact object proposals — gravastars, boson stars, some wormhole metrics — predict
shadow-like features. But traversable wormholes of the Morris-Thorne type do not. The EHT image
morphology — shadow, photon ring, brightness asymmetry tracking Doppler beaming — matches the
Kerr metric quantitatively. An astrophysical wormhole of the type that appears in popular science
coverage would look observably different.</p>
<p>The constraint is not absolute. You could construct wormhole geometries whose photon-sphere
structure mimics a black hole&rsquo;s shadow. But those are not the wormholes that typically appear in
discussions of traversable shortcuts through spacetime, and the Morris-Thorne type — the
physically simplest case — is ruled out at M87* and Sgr A* by the EHT morphology alone.</p>
<p>For more on wormhole theory — ER bridges as time-reversal symmetry, the
Einstein-Rosen caterpillar, and Euclidean wormholes in single theories — see
<a href="/posts/try-to-relax-ironic-process-wormholes/">a later post</a>. The physics is rich and ongoing. But
a picture of a wormhole, if one were ever imaged, would not look like what the EHT published.
It would look like a portal.</p>
<h2 id="the-astonishing-thing-is-that-it-worked">The Astonishing Thing Is That It Worked</h2>
<p>I want to end on this. The ring around M87* was predicted in 1916 from a theory written down
without any observation of a black hole, by people who were not sure black holes existed, using
mathematics developed for entirely different purposes. Luminet computed the image in 1979 on
punch cards, and it matched a photograph taken in 2019 with a planet-scale interferometer.</p>
<p>The agreement is 5%. In astrophysics, where parameters routinely span ten orders of magnitude,
that is essentially exact.</p>
<p>The images are astonishing not because they surprised physicists — they confirmed what general
relativity predicted. They are astonishing because general relativity is apparently the kind of
theory that earns the right to be trusted at microarcsecond precision, at distances of 16.8
megaparsecs, around objects whose entire interiors are, by construction, hidden from us.</p>
<p>Peer review welcome. If you have a wormhole geometry whose shadow is indistinguishable from a
Kerr black hole at current EHT resolution, I would genuinely like to read the paper.</p>
<h2 id="references">References</h2>
<ul>
<li><span id="ref-eht2019a"></span>Event Horizon Telescope Collaboration et al. (2019). First M87 Event Horizon Telescope results. I. The shadow of the supermassive black hole. <em>The Astrophysical Journal Letters</em>, 875, L1. <a href="https://doi.org/10.3847/2041-8213/ab0ec7">DOI: 10.3847/2041-8213/ab0ec7</a></li>
<li><span id="ref-eht2019b"></span>Event Horizon Telescope Collaboration et al. (2019). First M87 Event Horizon Telescope results. V. Physical origin of the asymmetric ring. <em>The Astrophysical Journal Letters</em>, 875, L5. <a href="https://doi.org/10.3847/2041-8213/ab0f43">DOI: 10.3847/2041-8213/ab0f43</a></li>
<li><span id="ref-eht2022"></span>Event Horizon Telescope Collaboration et al. (2022). First Sagittarius A* Event Horizon Telescope results. I. The shadow of the supermassive black hole in the center of the Milky Way. <em>The Astrophysical Journal Letters</em>, 930, L12. <a href="https://doi.org/10.3847/2041-8213/ac6674">DOI: 10.3847/2041-8213/ac6674</a></li>
<li><span id="ref-luminet1979"></span>Luminet, J.-P. (1979). Image of a spherical black hole with thin accretion disk. <em>Astronomy &amp; Astrophysics</em>, 75, 228–235.</li>
<li><span id="ref-james2015a"></span>James, O., von Tunzelmann, E., Franklin, P., &amp; Thorne, K. S. (2015). Gravitational lensing by spinning black holes in astrophysics, and in the movie <em>Interstellar</em>. <em>Classical and Quantum Gravity</em>, 32, 065001. <a href="https://doi.org/10.1088/0264-9381/32/6/065001">DOI: 10.1088/0264-9381/32/6/065001</a></li>
<li><span id="ref-james2015b"></span>James, O., von Tunzelmann, E., Franklin, P., &amp; Thorne, K. S. (2015). Visualizing Interstellar&rsquo;s wormhole. <em>American Journal of Physics</em>, 83(6), 486–499. <a href="https://doi.org/10.1119/1.4916949">DOI: 10.1119/1.4916949</a></li>
<li><span id="ref-muller2004"></span>Müller, T. (2004). Visual appearance of a Morris-Thorne wormhole. <em>American Journal of Physics</em>, 72(8), 1045–1050. <a href="https://doi.org/10.1119/1.1758220">DOI: 10.1119/1.1758220</a></li>
</ul>
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