Does Quantum Entanglement Allow FTL Communication or Predetermination?

Quantum entanglement gives distant measurement results correlations that cannot be explained by ordinary local pre-determination. Yet those correlations do not let either observer control the distant result or send a faster-than-light message. These are separate claims: Bell’s theorem concerns which explanations can reproduce the correlations, while no-signalling concerns whether the correlations can transmit information.

Why entanglement is not a communication channel

Imagine two observers, Alice and Bob, who share a pair of spin-1/2 particles in the singlet state. Each chooses a direction and measures spin along it. If they measure along the same direction, their results are always opposite. If they choose different directions, the results remain correlated in a precise way.

Alice cannot choose whether her result is “up” or “down”: each is random, with probability one-half. Bob’s result is also random. Moreover, Bob’s local statistics do not depend on which direction Alice chose or what result she obtained. In the singlet state, for any settings and outcomes,

$$P(a,b\mid x,y)=\frac{1}{4}\left(1-ab\,x\cdot y\right),$$

where $x$ and $y$ are unit measurement directions and $a,b\in\{-1,+1\}$. Summing over Alice’s possible outcomes gives

$$P(b\mid x,y)=\sum_a P(a,b\mid x,y)=\frac{1}{2}.$$

The result at Bob’s detector is therefore equally likely to be either value, regardless of Alice’s setting. Alice cannot encode a bit by choosing a measurement direction, because Bob sees the same random distribution either way. To identify the correlations, they must later compare their records through an ordinary communication channel, which cannot exceed the speed of light.

What Bell’s theorem rules out

A local predetermined model supposes that each pair carries some shared information, often denoted by $\lambda$, that determines or helps determine the answers to the measurements. Locality means Alice’s answer does not depend on Bob’s setting, and vice versa. If measurement settings are statistically independent of $\lambda$, such models obey Bell inequalities.

One commonly used test is the CHSH inequality. Let $A(x,\lambda)$ and $B(y,\lambda)$ be the outcomes, each either $+1$ or $-1$, for settings $x$ and $y$. For any fixed $\lambda$, the combination

$$A(x,\lambda)B(y,\lambda)+A(x,\lambda)B(y',\lambda)+A(x',\lambda)B(y,\lambda)-A(x',\lambda)B(y',\lambda)$$

must be either $+2$ or $-2$. To see why, factor it as $A(x,\lambda)[B(y,\lambda)+B(y',\lambda)]+A(x',\lambda)[B(y,\lambda)-B(y',\lambda)]$. Since the two $B$ values are each $\pm1$, one bracket is zero and the other is $\pm2$. Averaging over $\lambda$ therefore gives the CHSH bound $|S|\leq 2$.

Quantum mechanics predicts a violation. For the singlet state, the correlation between outcomes measured along directions $x$ and $y$ is $E(x,y)=-x\cdot y$. Choose Alice’s directions to be perpendicular, and Bob’s directions halfway between them on either side. The resulting CHSH value has magnitude $2\sqrt{2}$, greater than 2. Experiments observe Bell-inequality violations consistent with quantum mechanics.

So a model in which the particles simply carry local answers fixed in advance cannot account for all the observed correlations, provided the assumptions behind the test hold. Bell tests have addressed important experimental loopholes, but the theorem’s logical assumptions still matter when interpreting what it rules out.

Does this mean influence travels faster than light?

Not in the sense of a usable signal. Bell-violating correlations are often called “nonlocal,” because they cannot be explained by local hidden variables satisfying Bell’s assumptions. That does not show that a controllable physical message travels between the detectors. The random local outcomes and the no-signalling result prevent that.

Interpretations differ about what lies behind the correlations. Some descriptions use a nonlocal influence or an instantaneous update of the quantum state; others do not treat the state update as a physical signal. Bell’s theorem does not select one interpretation. It establishes a constraint on theories that aim to reproduce quantum predictions.

Nor does it rule out every imaginable form of predetermination. A theory could be nonlocal, or reject the assumption that measurement settings are independent of the hidden variables (as in superdeterministic proposals). Such alternatives are not the simple picture of distant particles carrying independent, locally usable pre-written answers.

Common mistakes

• “No faster-than-light message” means “no nonlocality.” No-signalling and Bell locality are different conditions. Quantum correlations obey the first but violate the second.
• “Bell’s theorem proves outcomes are not predetermined.” It rules out local hidden-variable models under its assumptions, not every theory with predetermined outcomes.
• “The measurement on one side sends a chosen result to the other.” The result is random, and the other observer’s local statistics do not reveal the choice.
• “The particles must communicate after separation.” Bell violations constrain possible explanations; they do not by themselves establish a literal message or mechanism traveling between particles.