Influence vs Signaling: The Key Difference
Audio Brief
Show transcript
This episode covers the critical distinction between causal influence and signaling in physics and cryptography.
There are three key takeaways. First, signaling requires statistical changes, while influence can exist silently. Second, a one-time pad proves influence can occur without signaling by masking data with noise. Third, this framework explains how quantum theories allow faster-than-light influence without violating relativity.
In cryptography, encrypting a message with a random key leaves the output looking completely random. While there is zero signaling to eavesdroppers, causal influence exists because the recipient can decode the message.
This principle also applies to quantum physics. Hidden variable theories feature superluminal influence, but local quantum noise washes out the signal, preventing faster-than-light communication.
Ultimately, understanding that physical connection can exist without statistical signaling clarifies how complex causal systems operate.
Episode Overview
- This episode explains the critical distinction between "influence" and "signaling," two concepts that are often conflated but are fundamentally different.
- Using the cryptographic concept of the one-time pad (Vernam cipher), the speaker demonstrates how causal influence can exist entirely in the absence of signaling.
- This distinction is highly relevant for anyone interested in physics, cryptography, and quantum mechanics, particularly in understanding how hidden variable models like Bohmian mechanics operate without violating relativity.
Key Concepts
- Signaling vs. Influence: Signaling is a stronger condition than influence. Signaling requires that a change in the input (plaintext) changes the probability distribution of the output (ciphertext). Influence, on the other hand, is a causal connection that must exist for communication to occur but can be obscured by noise.
- The One-Time Pad Demonstration: When encrypting a message with a truly random key (one-time pad), an eavesdropper gains zero information from the ciphertext because its distribution remains uniformly random regardless of the message. This means there is zero signaling to the eavesdropper. However, because the recipient can decode the message, a causal influence must exist between the plaintext and ciphertext.
- Washing Out with Noise: The reason influence does not always result in signaling is due to noise. When local noise is added (like a random key), it can completely wash out the observable signal while still preserving the underlying causal influence.
- Application to Bell's Theorem: This conceptual framework explains how hidden variable theories (like Bohmian mechanics) can feature superluminal (faster-than-light) influences to explain quantum entanglement, yet still comply with the laws of relativity because those influences are "washed out" by local noise, preventing any faster-than-light signaling.
Quotes
- At 0:01 - "So far in our discussion, I've been trying to distinguish influence from signaling... they really come apart; they're not the same idea." - setting up the core objective of the explanation.
- At 1:54 - "That's an instance where there's no signal from the plaintext to the ciphertext... but of course, there's a causal influence. Because if there were no causal influence, there'd be no way that the recipient could decode the message." - explaining the paradox of having causal connection without transmitting observable information.
- At 2:26 - "So signaling is stronger than influence... we have an influence, and furthermore, it's not being washed out by a noise source. But I can have influence with no signaling." - summarizing the relationship between the two concepts and the role that noise plays.
Takeaways
- Apply the distinction between influence and signaling when analyzing complex causal systems, recognizing that a lack of statistical variation (no signaling) does not prove a lack of physical connection (no influence).
- Use the cryptographic "one-time pad" as a mental model to understand how information can be securely transmitted through a causal link while appearing completely random to outside observers.
- Keep this framework in mind when evaluating quantum mechanics interpretations, noting how superluminal influences in theories like Bohmian mechanics avoid violating the theory of relativity by ensuring those influences cannot be used to send signals.
