1. Information and Local Realism: To prove that information is locally real, we need to define what we mean by "information" in this context. Let's consider a definition: Definition: Information is a measure of the state of a system that can be transmitted and received within the constraints of special relativity. Theorem: Information, as defined above, is locally real. Proof: a) Consider two spatially separated events, A and B. b) Let I_A be the information content at A, and I_B be the information content at B. c) By the principle of causality and special relativity, any change in I_B due to A cannot occur faster than the speed of light. d) Therefore, information respects locality. e) The state of the system carrying the information (e.g., particles, fields) has definite values before measurement, satisfying realism. f) Thus, information, as we've defined it, is locally real. 2. Dimensionality and Entropy: Hypothesis: 0D (dimensionless) entities are associated with perfect negentropy, while higher dimensions allow for the interplay of entropy and negentropy. Mathematically: In 0D: S = 0, N = maximum In R^n, n > 0: S > 0, N < maximum 3. Proving 0D is Non-Natural: Theorem: 0D entities are non-natural in the context of classical physics. Proof: a) Define "natural" as observable and measurable in classical physics. b) Classical physics operates in 3D space + 1D time (4D spacetime). c) 0D entities have no extension in space or time. d) Therefore, 0D entities are not observable or measurable in classical physics. e) Thus, 0D entities are non-natural in the classical physics framework. 4. Information in 0D vs. Higher Dimensions: In 0D: I = constant (perfect information preservation) In R^n, n > 0: dI/dt ≤ 0 (Second Law of Thermodynamics) Where I represents information content.
Great series I encountered. Nowhere to find a comprehensive lecture series. We met at ICTS this year.
1. Information and Local Realism:
To prove that information is locally real, we need to define what we mean by "information" in this context. Let's consider a definition:
Definition: Information is a measure of the state of a system that can be transmitted and received within the constraints of special relativity.
Theorem: Information, as defined above, is locally real.
Proof:
a) Consider two spatially separated events, A and B.
b) Let I_A be the information content at A, and I_B be the information content at B.
c) By the principle of causality and special relativity, any change in I_B due to A cannot occur faster than the speed of light.
d) Therefore, information respects locality.
e) The state of the system carrying the information (e.g., particles, fields) has definite values before measurement, satisfying realism.
f) Thus, information, as we've defined it, is locally real.
2. Dimensionality and Entropy:
Hypothesis: 0D (dimensionless) entities are associated with perfect negentropy, while higher dimensions allow for the interplay of entropy and negentropy.
Mathematically:
In 0D: S = 0, N = maximum
In R^n, n > 0: S > 0, N < maximum
3. Proving 0D is Non-Natural:
Theorem: 0D entities are non-natural in the context of classical physics.
Proof:
a) Define "natural" as observable and measurable in classical physics.
b) Classical physics operates in 3D space + 1D time (4D spacetime).
c) 0D entities have no extension in space or time.
d) Therefore, 0D entities are not observable or measurable in classical physics.
e) Thus, 0D entities are non-natural in the classical physics framework.
4. Information in 0D vs. Higher Dimensions:
In 0D: I = constant (perfect information preservation)
In R^n, n > 0: dI/dt ≤ 0 (Second Law of Thermodynamics)
Where I represents information content.