## General Concepts

**Initial condition:** the exact condition at the start of the experiment. Essentially conditions at t0.

**Information never disappears:** While this concept has come into question, see Stephen Hawking, the general idea is that all the information of the system remains in tact. That we can understand how a system might have been in the past given a) current conditions and b) governing laws. Susskind defines information as the distinguishing aspect between things(https://www.youtube.com/watch?v=VvOZd_tbZ-w).

**Wave:** disturbance travelling through a medium. Electricity is a magnetic disturbance travelling through a medium. Water wave is caused by disturbance of the pebble dropped travelling through the medium in which it is dropped, water.

## Symbols

## Formula

### Hamilton’s Equations

### Maxwell Equations

### Einstein Field Equations

### Schrodinger Equation

## Classical Mechanics

### Hamilton’s Equations

These equations are everywhere and govern pretty much everything. The framework for all of physics.

### Maxwell Equations

Electromagnetism and such.

### Einstein Field Equations

Equations that explore the very basis of space and time, focus on gravity.

### Michelson and Morley’s Luminiferous Ether Experiment

## Quantum Mechanics

### General Concepts

A device that **measures** is also considered to have **prepared** a system in a given state.

Unit vectors in 3d space are represented with a hat symbol. So unit 3 vectors will be represented as, say, m-hat.

If we prepared a system in n, and then moved to m-hat, the result is that <sigma-m> = n dot product m. This means that m inherits the results of n to some extent???? (Do more here).

**and** and **or** statements are different in quantum mechanics than in classical. Take the following scenario:

A: sigma-z = +1

B: sigma-x = +1

(A or B)

If someone else where to complete the A measurement and it was found to be +1, then it would continue to be +1 if we measured it. However if someone else were to complete the A measurement and it was found to be +1 but we instead chose to measure B it would erase/reset their A measurement and we might find A to be -1. (Is this right???). Therefore, the order of the experiment matters. In the first case the statement A or B is always true, but in the second ordering of events A or B has a 25% chance of being false.

**General Readings and Resources**

Seven Principles of Quantum Mechanics – https://arxiv.org/pdf/quant-ph/0212126.pdf

The ultimate reading list for beginners – https://dornsife.usc.edu/assets/sites/1045/docs/qmreading2018.pdf

### Bra-ket Notation:

ket -> denotes a column vector |B> –. Is the original vector space.

bra -> denotes a row vector that is the conjugate transpose (also called hermitian conjugate) of column vector??? <A| – (a1^{*},a2^{*}). It is represented as a row vector simply to keep track of the fact that it belongs to the dual vector space rather than the single vector space of the ket vector.

bra-ket -> <A|B> means <A|⋅|B> which means the inner product of A and B.

<A|B> – <A| is (a1^{*},a2^{*}) and |B> is then <A|B> represents the inner union which is the first entry of A multiplied by the first entry of B, and so on. a1^{*}b1 + a2^{*}b2.

<B|B> – <B| is (b1^{*},b2^{*}) and |B> is then <B|B> represents the inner union which will be **POSITIVE** and a **REAL NUMBER**.

In application kets are associated with a specific state that can be measured. It can be up or down, Horizontal or Vertical, etc. Often these states are somewhat arbitrary in terminology because at such a small level Up and Down have little actual meaning, but there needs to be some terminology to differentiate them.

Two vectors <A|B> are orthogonal if the inner product is zero, <A|B> = 0.

### Bra-ket Multiplication:

<B|M = page 59

### Hermitiant Conjugation:

M|A> = |B>

Eigenstate/Eigenfunction: A wave function that, when acted upon by a general real-space operator, will multiply. In other words, it won’t ‘stretch’ in either direction. It scales uniformly.

Eigenvalue: The value by which the Eigenstate multiplies.

Self-Adjoint (Hermitian) Operator: ??? Represent physical observables in QM.

Born’s Rule:

Quantum Tomography: The measurement of the quantum state before measurement. As measuring will have a result on the system sometimes we are trying to figure out what that system looked like pre-measurement. This is what Quantum Tomography is for.

### Schrodinger Equation:

The quantum mechanics version of Hamilton’s equations

### The Problem of Time:

Ekatrine Moreva:

Time from quantum entanglement: an experimental illustration – https://arxiv.org/pdf/1310.4691.pdf

Quantum Time: experimental multi-time correlations – https://arxiv.org/pdf/1710.00707.pdf

Page and Wooters

### Causation in QM:

Milburn and Shrapnel – https://arxiv.org/pdf/1809.03191.pdf

### Wojciech Hubert Zurek:

Quantum Darwinism: https://arxiv.org/pdf/0903.5082.pdf

The idea is that there are pointer states that exist within a quantum system that can, or has a chance of, surviving when decoherence occurs.

Zurek also has intresting views on Maxwell’s demon and thermodynamic principles.