Quantum Theory from First Principles

In summary, the book "Quantum Theory from First Principles" by D'Ariano et al, recommended by @LittleSchwinger, is a concise and rigorous examination of the Hilbert space formalism of quantum theory and its relationship with information theory. It also provides a derivation of quantum theory from six information theoretic principles. The book does not focus on specific physical systems, but rather on the abstract formalism of quantum theory. The exercises are well-crafted and serve as a guided development of ideas from the text.
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Frabjous
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@LittleSchwinger recently recommended this book

LittleSchwinger said:
If you enjoy it D'Ariano et al's "Quantum Theory from First Principles" uses a similar diagramatic approach but is more concise and rigorous.

What are peoples thoughts on it?
 
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I fully agree with my own recommendations :wink:

Basically the book is divided into three parts:
  1. An examination of the Hilbert space formalism of quantum theory and how it generalises information theory.
  2. A discussion of information theoretic principles and how aspects of quantum theory are simply consequences of them
  3. A derivation of quantum theory from six information theoretic principles
Note: I say "quantum theory" to refer to the abstract formalism of Hilbert Spaces and operators on them. The book does not examine any physics as such, i.e. explicit systems like hydrogen atoms, harmonic oscillators, gases etc. It's an investigation of the abstract formalism.

The exercises are very well crafted and often take the form of a guided development of ideas from the text.
 
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FAQ: Quantum Theory from First Principles

What is Quantum Theory from First Principles?

Quantum Theory from First Principles refers to the approach of deriving quantum mechanics starting from a set of basic, fundamental postulates or principles, without assuming the traditional framework of quantum mechanics. This method aims to provide a deeper understanding of the foundations and logical structure of quantum theory.

Why is it important to study Quantum Theory from First Principles?

Studying Quantum Theory from First Principles is important because it helps clarify the foundational aspects of quantum mechanics, potentially leading to new insights and advancements in the field. It can also aid in resolving conceptual ambiguities and improving the coherence and consistency of the theory.

What are some of the key principles used in this approach?

Some of the key principles used in deriving Quantum Theory from First Principles include the principle of superposition, the principle of locality, the principle of causality, and the principle of measurement. These principles serve as the foundational axioms from which the rest of quantum mechanics can be logically derived.

How does this approach differ from traditional quantum mechanics?

This approach differs from traditional quantum mechanics in that it does not start with the established mathematical formalism, such as the Schrödinger equation or the wave function. Instead, it begins with a set of fundamental principles and builds the theory from the ground up, aiming to provide a more intuitive and logically coherent understanding of quantum phenomena.

What are the potential implications of deriving quantum theory from first principles?

The potential implications of deriving quantum theory from first principles include a better understanding of the nature of reality, the possibility of discovering new physical phenomena, and the development of more advanced quantum technologies. It may also lead to a more unified framework for quantum mechanics and other areas of physics.

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