Test your understanding of quantum mechanics and relativity
In a Bell test experiment with entangled photons, what would violate the Bell inequality and confirm quantum entanglement?
A
Correlation coefficient ≤ 0.5
B
Correlation coefficient > 2√2
C
Perfect anti-correlation at 45°
D
Violation of the no-communication theorem
Correct!
The Bell inequality is violated when the correlation coefficient exceeds 2√2 (≈2.828), which is only possible with quantum entanglement (Option B). Classical hidden variable theories cannot exceed 2.
Explanation
The correct answer is B. Bell's theorem shows that any local hidden variable theory cannot produce correlations stronger than 2, while quantum mechanics predicts up to 2√2.
In the AdS/CFT correspondence, what is the minimum number of spacetime dimensions required for the bulk theory to have a consistent duality with a 4D conformal field theory?
A
5 dimensions (4+1)
B
10 dimensions (9+1)
C
11 dimensions (10+1)
D
26 dimensions (25+1)
Correct!
Option C is correct. The original AdS₅×S⁵ correspondence relates Type IIB string theory in 10D to a 4D N=4 supersymmetric Yang-Mills theory. The bulk must be 10D (9 space + 1 time).
Explanation
The correct answer is B. The AdS/CFT correspondence requires the bulk theory to be string theory in 10 dimensions (9 spatial + 1 temporal) to match the 4D boundary CFT.
When solving the Einstein field equations for a rotating black hole, what is the physical significance of the Kerr metric's inner horizon (r⁻)?
A
A coordinate singularity removable by transformation
B
A boundary where timelike becomes spacelike
C
A Cauchy horizon where determinism breaks down
D
A membrane encoding holographic information
Correct!
Option C is correct. The inner horizon represents a Cauchy horizon beyond which the future cannot be predicted from initial data, violating strong cosmic censorship.
Explanation
The correct answer is C. The inner horizon (r⁻) is a Cauchy horizon where solutions to the field equations become non-unique, violating determinism. This is a fundamental feature of Kerr black holes.
