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13:00in productionCh. 1 · A black hole entropy puzzle/ 13:00 · ceiling 15 min
Physics · Astronomy & space

Holographic principle

A puzzle about black hole entropy scaling with surface area, not volume, led to the idea that a region of space might be fully described by information on its boundary, and Juan Maldacena's 1997 conjecture gave that idea its clearest, still unproven, form.

Jacob Bekenstein noticed that a black hole's entropy scales with the area of its event horizon rather than its volume, and Stephen Hawking's later work on black hole radiation confirmed that black holes do carry finite entropy proportional to that surface area, an odd result given that entropy in ordinary physical systems scales with volume. Gerard 't Hooft proposed in 1993, and Leonard Susskind developed further using string theory, the idea that this could be explained if the description of a volume of space is actually encoded entirely on its lower-dimensional boundary, the holographic principle. Juan Maldacena's 1997 anti-de Sitter/conformal field theory correspondence gave this principle its clearest concrete mathematical example, showing that a theory of gravity in a particular curved space is equivalent to a quantum field theory living on that space's boundary, a paper that had accumulated over ten thousand citations by 2015. The correspondence remains a conjecture rather than a proven theorem, though it has found applications well beyond string theory, including in describing properties of quark-gluon plasma and certain condensed matter systems, while direct experimental tests of the holographic principle itself have so far come back negative or inconclusive.

Chapters & takeaways6
  1. 0:08
    A black hole entropy puzzle

    Jacob Bekenstein found that black hole entropy scales with the area of its event horizon rather than its volume, an odd departure from ordinary physical systems.

  2. 2:10
    Confirmed by Hawking's radiation work

    Stephen Hawking's work on black hole radiation confirmed that black holes carry finite entropy proportional to their horizon area.

  3. 4:20
    A boundary encoding a volume

    Gerard 't Hooft proposed in 1993, and Leonard Susskind developed with string theory, that a region of space might be fully described by information on its lower-dimensional boundary.

  4. 6:30
    Maldacena's 1997 correspondence

    Juan Maldacena's conjecture showed a gravity theory in a curved space is mathematically equivalent to a quantum field theory on that space's boundary, the clearest working example of the principle.

  5. 8:40
    Still a conjecture, not a proof

    Despite becoming one of the most-cited papers in high-energy physics, the correspondence has never been rigorously proved.

  6. 10:50
    Uses beyond string theory, tests that came back empty

    The framework has been applied to quark-gluon plasma and condensed matter physics, while direct experimental searches for holographic effects have not found the predicted signal.

Worth your time?

Yes. Study the whole thing.

4/ 5
What works
  • traces the idea back to a specific, well-defined puzzle about black hole entropy rather than presenting it as an abstract curiosity
  • is precise about Maldacena's correspondence being a conjecture, however well supported, not a proof
  • shows genuine applications outside string theory alongside genuine experimental null results
What does not
  • cannot claim the holographic principle has been directly experimentally confirmed
  • does not resolve whether AdS/CFT applies to our own universe, which is not anti-de Sitter space
Study it if
  • readers who want to see exactly what problem the holographic principle was invented to solve
  • anyone curious how an unproven conjecture can still be enormously useful in physics
  • people interested in where theoretical physics has actually been tested against experiment and where it has not
Skip it if
  • readers wanting the holographic principle presented as an established, experimentally confirmed fact
The written brief3 min read

A black hole entropy puzzle

The puzzle behind this idea starts with black holes. Jacob Bekenstein noticed that if black holes are to obey the second law of thermodynamics, which requires entropy to never decrease, they must themselves carry entropy, and he worked out that this entropy scales with the area of the black hole’s event horizon rather than with its volume. This was strange, because entropy in ordinary physical systems, a gas in a box for instance, scales with volume, the amount of space available for particles to occupy, not with the area of the container’s surface, so a black hole behaving this way suggested something unusual about how information is actually stored in a region containing a black hole.

Confirmed by Hawking’s radiation work

Stephen Hawking’s subsequent work strengthened rather than resolved the puzzle. Hawking showed that black holes are not perfectly black but emit radiation, and this work confirmed that black holes do carry finite entropy that is indeed proportional to the area of their event horizon, cementing what became known as the Bekenstein-Hawking relationship. This left physicists with a genuine question: why would the amount of information a region of space can contain be limited by its surface area rather than its volume, when every other physical intuition suggests volume should be the relevant quantity.

A boundary encoding a volume

Gerard ’t Hooft proposed an answer in 1993, suggesting that the description of a volume of space might, in some deep sense, be fully encoded on its lower-dimensional boundary, an idea he called the holographic principle by analogy with how an ordinary hologram encodes a three-dimensional image on a two-dimensional surface. Leonard Susskind developed this further using string theory, drawing on earlier observations by Charles Thorn from the 1970s that string theory itself seemed to admit lower-dimensional descriptions, giving the initially abstract proposal a more concrete theoretical foundation to build on.

Maldacena’s 1997 correspondence

The clearest working example of this idea came from Juan Maldacena, who proposed in late 1997 a specific correspondence between a theory of gravity formulated in a particular type of curved space, called anti-de Sitter space, and a quantum field theory living entirely on the lower-dimensional boundary of that space. The two descriptions, one including gravity and one not, are conjectured to be mathematically equivalent, meaning any calculation done in one framework should in principle give the same answer as the corresponding calculation in the other, a genuinely striking claim about two seemingly very different physical theories.

Still a conjecture, not a proof

Despite its influence, this correspondence has never been rigorously proved as a mathematical theorem; it remains, formally, a conjecture supported by a large body of consistent calculations across many specific cases rather than a settled, general proof covering every situation it is applied to. That has not limited its impact: Maldacena’s original paper had accumulated more than ten thousand citations by 2015, making it among the most-cited papers in high-energy physics, and the correspondence has become a standard working tool for exploring quantum gravity even without a complete proof of its validity sitting underneath it.

Uses beyond string theory, tests that came back empty

The framework has also found use well outside string theory itself, including applications by researchers such as Dam Thanh Son to modelling properties of the quark-gluon plasma produced in heavy-ion collisions, and by researchers including Subir Sachdev to certain condensed matter systems such as superconductors. Direct experimental searches for holographic effects predicted by related proposals, such as Craig Hogan’s suggestion of detectable holographic noise, have so far come back empty, with analysis of a gamma-ray burst finding no such signal at the predicted scale. The honest summary is a productive, widely used theoretical framework that remains, at its foundation, an unproven though well-supported idea.

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