Information

When physicists refer to information, they're not merely talking about conventional data such as letters, numbers, or binary code. Instead, it often pertains to the number of binary questions necessary to define the characteristics of a physical system completely. While examples like signals ensuring causality or quantum states (like qubits) represent information, they don't encapsulate all its forms. Information can also encompass:

• Signals that uphold causality.
• Quantum states (like qubits) for individual elements.
• Entangled quantum states among multiple elements.
• Any measure of entropy, a crucial physical quantity.

Entropy, a thermodynamic measure, is frequently misunderstood. Although often described as a measure of disorder, it can also quantify the number of possible configurations of a system's quantum state.

Consider two systems: 1. A room divided with one side containing hot gas and the other cold gas. 2. The same room with the divider open, allowing both sides to equalize in temperature.

Both systems have the same number of particles and total energy but vastly different entropies. The second system's entropy is higher, as numerous arrangements of energy distributions are possible. Greater entropy necessitates more information to describe the system fully.

Information and black holes

Burning a book doesn't destroy its information; it merely scrambles it. In theory, one could track every particle of paper and ink through the burning process to reconstruct the original content. Similarly, shattered glass or a scrambled egg can be analyzed to determine their initial states, provided the fundamental particles remain intact.

However, black holes complicate this notion. In General Relativity, black holes have no recollection of the particles contributing to their formation. Their only measurable characteristics are mass, charge, and angular momentum.

In the early 1970s, physicist Jacob Bekenstein grappled with this dilemma, realizing that the properties and entropy of the particles forming a black hole posed significant challenges. According to the second law of thermodynamics, entropy in a closed system cannot decrease. Yet, in pure General Relativity, black holes have zero entropy, creating a contradiction.

Bekenstein proposed that the information from infalling particles could become “smeared” across the event horizon, leading to the idea that a black hole's entropy is proportional to the surface area of its event horizon, now known as the Bekenstein-Hawking entropy.

Will that information get destroyed?

This conceptual breakthrough was short-lived. In 1974, Stephen Hawking introduced a groundbreaking insight. He demonstrated that standard quantum field theory calculations assumed flat space at quantum scales, a significant oversight in the vicinity of black holes.

Hawking realized that calculations needed to account for curved space dictated by Einstein's equations. His analysis showed that the vacuum state near a black hole's event horizon differs fundamentally from that far away. This led to the understanding of Hawking radiation, a continuous emission of blackbody radiation influenced by the curvature of spacetime.

Hawking radiation: - Exhibits a blackbody spectrum. - Comprises primarily massless photons. - Radiates at a temperature inversely related to the black hole's mass. - Evaporates over a duration proportional to the cube of the black hole's mass.

This revelation sparked new dilemmas. If Hawking radiation is purely blackbody, it lacks distinctions between matter and antimatter, or any other properties that would allow us to reconstruct the initial state of the particles that formed the black hole.

The essence of the black hole information paradox

So, where does the information vanish? This conundrum suggests that while information should theoretically be preserved, if black holes emit only blackbody radiation, the information that formed them appears lost.

• One possibility is that our understanding of information and entropy is flawed, and black holes do indeed erase information.
• Alternatively, even if the mechanism is unknown, there may be a relationship between the information on a black hole's surface and the outgoing Hawking radiation.
• It's also conceivable that the information becomes mixed within the black hole and is later encoded in the emitted radiation during evaporation.

Despite many claims that the black hole information paradox has been resolved, uncertainty remains. The fate of information—whether it's preserved, destroyed, or dependent on black hole dynamics—continues to elude us.

Research suggests that quantum entanglement may connect a black hole's interior with the emitted radiation, hinting at a possible method for understanding the encoding of information. Yet, we still lack the ability to calculate specific bits of information; we can only assess overall quantities.

Numerous theories are emerging, including ideas from string theory and concepts like complementarity and firewalls. These address the question of how information might be preserved during Hawking radiation emissions. However, the core issues persist—understanding how information from particles that create a black hole is encoded in the radiation produced during evaporation remains an unresolved challenge.

In summary, the black hole information paradox endures as an active research topic, and while progress continues, the ultimate solution remains uncertain.

Starts With A Bang is authored by Ethan Siegel, Ph.D., the writer of Beyond The Galaxy, Treknology, and The Littlest Girl Goes Inside An Atom. New publications, including the Encyclopaedia Cosmologica, are forthcoming!