Why Might Space-Time Emerge From Quantum Gravity?

TL;DR

Space-time may be a useful classical approximation rather than a fundamental feature of reality. Attempts to quantize general relativity encounter serious problems, while black holes, Hawking radiation, information conservation, and holography suggest that quantum gravity contains non-local features and may need to be developed from an intrinsically quantum starting point.

Transcript

The emergence of space-time. That's right. Okay, so I thought space-time was fundamental. Yeah, I know. So this sort of dream that Einstein had, that everybody had, and everybody has of, you know, the theory of everything. So how do we build up from many worlds, from quantum mechanics, uh, a model of space-time, a model of gravity? Well, yeah, I me... Read More

Key Insights

• General relativity is a classical theory in which gravity is the curvature of space-time, represented by a field that pervades the universe and specifies how curved space-time is.
• Quantization is a procedure for promoting a classical theory into a quantum mechanical theory, and it was used to construct quantum electrodynamics despite initial problems involving quantities that became infinite.
• Quantizing general relativity produces problems more severe than those encountered with electromagnetism, and efforts starting from the classical theory have not yet yielded a successful theory of quantum gravity.
• Quantum gravity may not be a field theory because evidence from black holes, Hawking radiation, and information conservation points toward unusual non-local features that ordinary quantum field theories do not contain.
• An intrinsically quantum starting point may be necessary for quantum gravity, with researchers working backward to discover a classical limit instead of beginning with general relativity and attempting to quantize it.
• Locality is the principle that what happens at a point is directly affected only by what happens at neighboring points, while long-range influence develops through chains of local interactions across a field.
• Black hole evaporation creates a conflict involving locality because information about the material that formed a black hole should remain predictable under the Schrödinger equation, yet arguments suggest this cannot happen while locality is preserved.
• Holography suggests that information about a black hole's three-dimensional interior can be encoded across its two-dimensional horizon, indicating that locality and even space may be effective approximations rather than fundamental realities.
• More videos with Sean Carroll:
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Questions & Answers

Q: Why is a theory of quantum gravity considered necessary?

A theory of quantum gravity is considered necessary because general relativity describes gravity and curved space-time as entirely classical, while quantum mechanics provides a different framework for physical systems. Attempts to promote general relativity directly into a quantum theory encounter severe and currently insurmountable problems, suggesting that gravity requires a deeper formulation with potentially non-local features.

Q: Why has quantizing general relativity been unsuccessful?

Quantizing general relativity has been unsuccessful because the usual method of starting with a classical field theory and promoting it to a quantum theory produces problems more serious than those found when electromagnetism was quantized. The transcript says these difficulties remain insurmountable and may indicate that quantum gravity is not an ordinary field theory at all.

Q: What does locality mean in a field theory?

Locality means that what happens at one point in space depends directly only on what happens at points immediately next to it. Those neighboring points depend on their own neighbors, so an influence can travel across space through a sequence of local interactions. This principle is built into field theories, including classical general relativity.

Q: Why might locality not be fundamental in quantum gravity?

Locality might not be fundamental because black holes, Hawking radiation, and information conservation suggest that information can be distributed in ways that an ordinary local field theory cannot explain. If a black hole evolves according to the Schrödinger equation, arguments indicate that its information cannot remain conserved while strict locality is also preserved.

Q: How do black holes challenge information conservation and locality?

Black holes challenge these ideas because quantum mechanics indicates that they radiate and eventually evaporate rather than remaining completely black. If a black hole is formed from particular material, its later state should remain predictable under the Schrödinger equation. According to the discussion, preserving that information appears incompatible with preserving locality at the same time.

Q: What is holography in the context of black holes?

Holography is the idea that information about everything inside a black hole's three-dimensional region can be represented on its two-dimensional horizon. An observer falling inward may experience an apparently normal passage until reaching the singularity, while an outside observer can describe the incoming information as spread non-locally across the horizon.

Q: How could space-time emerge from an intrinsically quantum theory?

Space-time could emerge by beginning with a theory that is quantum from the outset and then working backward to find a classical limit. In that limit, familiar space-time, gravity, and locality would appear as effective descriptions. This reverses the usual approach of starting with classical general relativity and attempting to quantize it directly.

Q: What does it mean to say that space is an approximation?

Saying that space is an approximation means that spatial structure and locality may accurately describe ordinary classical conditions without being fundamental features of the underlying quantum theory. Holographic descriptions, in which a two-dimensional surface represents a three-dimensional interior, suggest that familiar space emerges only as a useful limit of deeper non-local quantum behavior.

Summary & Key Takeaways

• General relativity describes gravity classically as the curvature of space-time, using a field that extends throughout the universe. Although physicists can often construct quantum theories by quantizing classical ones, applying that procedure to general relativity creates problems more severe than those encountered when electromagnetism was quantized, with no successful result so far.

• Evidence from black holes, Hawking radiation, and information conservation suggests that quantum gravity may not be an ordinary local field theory. This possibility motivates an alternative strategy: begin with a theory that is intrinsically quantum, then work backward to identify the classical limit in which space-time, gravity, and locality emerge as useful approximations.

• Locality means that events at one point are directly influenced only by events at neighboring points, allowing effects to propagate across space through successive interactions. Holography challenges its fundamental status because information about a black hole's three-dimensional interior may be represented across its two-dimensional horizon, suggesting that space itself is approximate.