How does the holographic principle work in detail?

In one line

The rule

The holographic principle states: "All the information contained in a volume of space can be represented as information on the boundary of that space."

There is no single formula, but the idea is often shown using the Bekenstein-Hawking entropy formula for black holes: S = (k × A) / (4 × lₚ²) where:

• S = entropy (a measure of information)
• k = Boltzmann constant
• A = area of the event horizon (surface)
• lₚ = Planck length (very tiny unit of length)

Let's understand it simply

Imagine you are watching a cricket match on TV. The players look 3D, but the whole match is stored on a flat 2D screen. The TV does not need to be as big as the stadium. It just needs to store the right information.

Now, think about a pressure cooker. All the steam and food inside (the volume) can be described by what happens on the surface (the lid). The holographic principle says our universe might work like this: everything inside a space can be described by information on the surface, just like a hologram (a 3D image made from a 2D film).

How it works

1. Black holes and information: Scientists found that the amount of information (entropy) in a black hole depends on its surface area, not its volume.
2. Surface stores information: This means all the details about what is inside can be written on the surface, like writing all the details of a house on its walls.
3. Hologram analogy: Like a hologram stores a 3D image on a 2D surface, the universe's information can be stored on a lower-dimensional boundary.
4. Mathematics: In some theories, everything happening inside a space (like gravity) can be described by a theory on the surface (with no gravity).
5. Testing the idea: Physicists use special models (like AdS/CFT, a type of math) to check if this works for our universe.
6. Implication: If true, our 3D world could be a projection from a 2D surface, just like a movie projected from a film.

The story behind it

In the 1970s, Jacob Bekenstein and Stephen Hawking studied black holes. They found that the information (entropy) in a black hole is proportional to its surface area, not its volume. This was strange because we expect information to depend on volume.

In the 1990s, Gerard 't Hooft and Leonard Susskind took this further. They suggested that maybe the whole universe works this way. The idea became known as the holographic principle. One famous version is the AdS/CFT correspondence by Juan Maldacena in 1997, which gave a real mathematical example.

Where you see it in real life

• Black holes: The amount of information a black hole can hold is given by its surface area, not its volume.
• Holograms: A real hologram (like on your Aadhaar card) stores a 3D image on a 2D surface.
• Movie screens: A 2D screen shows a 3D world, similar to how information might be stored in the universe.
• Pressure cooker lid: The pressure and steam inside are controlled by the lid (surface), not the whole volume.
• Diwali rocket explosion: The energy released depends on the surface where the explosion happens.
• Computer hard disks: Data is stored on the surface of a disk, but we use it to create 3D games and movies.

Why it matters

• Quantum gravity: Helps scientists try to join quantum mechanics and gravity, which is a big unsolved problem.
• Black hole information paradox: Offers a way to solve the puzzle of what happens to information in black holes.
• String theory: Used in advanced theories like string theory to explain how the universe works.
• Future technology: Could change how we think about space, information, and even computers.

Worked example

Let's see how the entropy of a black hole depends on its area:

Given:  A = 4 × 10⁶ m² (area of black hole), k = 1.38 × 10⁻²³ J/K, lₚ = 1.6 × 10⁻³⁵ m
Step 1: Write the rule        S = (k × A) / (4 × lₚ²)
Step 2: Plug in the numbers   S = (1.38 × 10⁻²³ × 4 × 10⁶) / (4 × (1.6 × 10⁻³⁵)²)
Step 3: Calculate denominator (1.6 × 10⁻³⁵)² = 2.56 × 10⁻⁷⁰
Step 4: 4 × 2.56 × 10⁻⁷⁰ = 1.024 × 10⁻⁶⁹
Step 5: Numerator: 1.38 × 10⁻²³ × 4 × 10⁶ = 5.52 × 10⁻¹⁷
Step 6: S = 5.52 × 10⁻¹⁷ / 1.024 × 10⁻⁶⁹ ≈ 5.39 × 10⁵² J/K

This shows the entropy (information) depends on the area, not the volume.

Common mistakes

• Thinking it means the universe is flat: The principle says information is stored on the surface, but space can still be 3D.
• Confusing with normal holograms: Real holograms are just an analogy; the principle is about information, not light.
• Assuming it is proven for our universe: It is a strong idea, but not yet proven for our real universe.
• Believing it means we live in a simulation: The principle is about physics, not computer simulations.

Remember it

"Like a 3D cricket match stored on a 2D TV screen, the universe’s secrets may be written on its surface."