Lecture 1 | Quantum Entanglements, Part 1 (Stanford)

The paragraph discusses the intuitive ways humans and animals perceive the physical world, inherited through evolution. It emphasizes that our understanding of physics is often limited by these intuitions, which are not equipped to handle phenomena beyond our ordinary experiences, such as those addressed in quantum mechanics and relativity. The speaker uses examples like a lion chasing an antelope to illustrate how animals instinctively understand complex physics without formal education.

This paragraph delves into the peculiarities of quantum mechanics, contrasting it with the special theory of relativity. It highlights the difficulty in visualizing quantum phenomena like the motion of an electron or the uncertainty principle, which are outside the range of human experience. The speaker points out that physicists must 'rewire' their intuition to grasp these concepts, which are fundamentally different from classical bits of information.

The paragraph explains the concept of classical bits, which can be represented by zeros and ones, and how they can describe the state of a physical system. It introduces the notation of using brackets to denote the state of a bit, known as a 'ket.' The speaker also discusses multi-bits, where multiple coins (or bits) are lined up to represent more complex information, and the importance of understanding the number of possible configurations for these bits.

The focus here is on calculating the number of possible states in classical systems. The paragraph establishes that for a system of 'n' bits, there are 2 to the power of 'n' possible states. It also generalizes this concept to other systems, such as a die, which has six possible outcomes, and introduces the concept of measuring the amount of information in bits, using logarithms to base 2.

The speaker explores how real numbers and various physical quantities, like temperature, can be approximated and represented in terms of bits. It explains that by using base two representation, any real number can be expressed as a sum or collection of bits, which is crucial for digital computation and simulation of physical systems.

This paragraph discusses the representation of physical fields, such as temperature or electric fields, in terms of bits by discretizing space into small cells. It demonstrates that by knowing the state of each cell (e.g., whether it contains a particle or not), one can specify the configuration of a system throughout the space. The speaker also touches on the concept of using bits to represent the motion of particles within this discretized space.

The paragraph introduces the concept of 'laws of updating' or 'laws of motion' for systems described by bits. It shows how these laws can be visualized as a series of arrows in a state space, where each arrow represents a transition from one state to another. The speaker also discusses the possibility of having different types of laws, including those that are reversible or irreversible, and the importance of reversibility in physics.

The speaker provides an introduction to matrix algebra, explaining how matrices can be used to represent the time evolution of a system's configuration. It covers the multiplication of matrices by vectors to produce new vectors, and the concept of matrix multiplication to represent multiple updates. The paragraph also touches on the use of row vectors and the importance of matrix algebra in quantum mechanics.

In this final paragraph, the speaker encourages practice with matrix algebra, emphasizing its fundamental role in quantum mechanics. It mentions the importance of understanding matrix multiplication for both vectors and matrices to grasp the basic mathematics required for quantum mechanics. The speaker also addresses a question about the reversibility of matrices and their inverses, which is crucial for understanding deterministic and reversible laws in physics.