Why Superluminal Influences Are Philosophically Bankrupt

Superluminal influences are considered philosophically problematic when viewed through the lens of Leibniz's principle, which asserts that unobservable differences do not exist, making them inconsistent with our understanding of physics.

• Bell inequality violations suggest an issue with classical realism or local causality, not necessarily superluminal influences.

• Superluminal influences, though non-signaling, are philosophically problematic due to Leibniz's principle of indistinguishability.

• No-go theorems are crucial for challenging assumptions in quantum foundations by rigorously proving what cannot be explained under certain principles.

Superluminal influences, often proposed to explain Bell inequality violations in quantum theory, are deemed philosophically bankrupt because they violate Leibniz's principle. This principle states that if two things cannot be empirically distinguished, they are not ontologically different. While these influences do not allow for superluminal signaling, their unobservability makes them inconsistent with a robust understanding of causality and realism, highlighting the importance of no-go theorems in quantum foundations.

No-Go Theorems and Bell Correlations

• 00:01:09 When a phenomenon cannot be explained under a specific set of principles, it leads to a no-go theorem. The conventional framework for realism, known as the ontological models framework, assumes hidden variables, Bayesian probability, and local causality. However, quantum formalism violates the inequalities derived from these assumptions, leading to a contradiction. While some attribute this to superluminal influences, a more robust view suggests that the conventional framework for realism and causation needs revision, as these influences have been proven not to exist within a consistent classical explanation.

Superluminal Influence vs. Relativity

• 00:03:21 Models that explain Bell inequality violations by postulating superluminal influences, where Bob's outcome depends on Alice's setting variable across space-like separation, are often viewed as being in tension with relativity. Beyond the general feeling that influences should not travel faster than light, these models specifically violate Leibniz's principle. Since no experiment can detect information about Alice's settings in Bob's lab due to space-like separation, assuming an unobservable influence constitutes an ontological difference without empirical evidence, which Leibniz's principle rejects.

Influence vs. Signaling

• 00:10:04 Causal influence, where one variable affects another, is distinct from signaling, which implies an observable change in distribution. While inference is symmetric, causal influences are asymmetric, meaning a change in X impacts Y, but not vice-versa, as seen in projectile motion or the rooster and sunrise example. Special relativity allows for space-time regions that are causally disconnected, meaning there can be a fundamental speed limit to influences. Bell's argument relies on this specific aspect of relativity, stipulating that influences should propagate within light cones, thus defining space-like separated regions as having no influences between them.

The Vernam Cipher and Hidden Variables

• 00:12:50 The Vernam cipher, or one-time pad, illustrates how causal influence can exist without signaling. In this cryptographic method, plaintext causally influences ciphertext, but an eavesdropper cannot extract any information about the plaintext from the ciphertext due to the randomly generated key. This 'washing out' of influence by noise is a trick employed by hidden variable models like Bohmian mechanics to reproduce Bell inequality violations using superluminal influences without allowing superluminal signaling. However, this approach is problematic if one adheres to Leibniz's principle, as the unobservability of these superluminal influences means they should not be posited as existing.