Random Thoughts.

In recent weeks, I have been reflecting on several topics that have been on my mind daily. In the following paragraphs, I will summarize my thoughts. 

Quantum physics is concerned with the behavior of matter and energy at the atomic and subatomic levels. Many scientists continue to be fascinated and awestruck by this field of study that has been around for more than a century. By taking into account the postulates of quantum physics, we can be able to explain the behavior of matter and energy in the quantum world. 

This section is devoted to explaining the seven postulates that form the foundation of quantum physics. In the first postulate of quantum physics, it is stated that every particle in the universe possesses inherent angular momentum, which is known as spin. Angular momentum can be defined as a quantity associated with a particle's mass that does not depend on the particle's motion. In other words, due to its quantization, angular momentum only has discrete values. As a result of this postulate, particles behave differently depending on the environment in which they are situated. 

Quantum physics' second postulate states that the wave function of a particle describes the probability that it will be found at any given location. The Schrödinger equation describes this wave function, which is a mathematical equation that describes the behavior of a quantum system. In other words, the wave function is a function of the particle's position and momentum. This method can be used to determine the likelihood of a particle being found at a particular location. 

According to the third postulate of quantum physics, an observer cannot observe a quantum system until it is observed by another observer that is not an observer; therefore, a quantum system can exist in a superposition of multiple states at the same time that is not observed before an observer first observes it. The 'uncertainty principle' was introduced by Werner Heisenberg in the 1920s and has become a standard notion within the scientific community ever since. In accordance with this postulate, a quantum system's "observable" properties, such as its position and momentum, can only be determined after an observation has been made. It is important to note that before an observation can be made, the system is in a superposition of multiple states and thus is indeterminate until it is observed. The concept of wave-particle duality is at the core of quantum physics. Physicists believe that particles are capable of acting as waves, while waves can also act as particles. In other words, it is impossible to predict what state a particle will be in prior to being observed. The famous double-slit experiment illustrates this concept, in which a particle passes through two slits and creates a wave-like pattern on the other side. It is clear from this that particles behave in a wave-like manner and that uncertainty exists. The third postulate of quantum physics has profound implications for our understanding of the universe. 

The fourth postulate of quantum physics states that the probability of an event occurring is equal to the square of the absolute value of the wave function of that event. This means that a particle's wave function is a mathematical representation of the probability of the particle being observed at a particular point in space and time. This postulate is one of the most fundamental laws of quantum mechanics, and it provides the basis for understanding the behavior of particles on the subatomic level. The fourth postulate of quantum mechanics can be used to explain a variety of phenomena, including the Heisenberg uncertainty principle and the wave-particle duality. It is also vital for understanding the behavior of electrons in their shells around atoms, as well as the behavior of photons in light. In addition to its fundamental implications, the fourth postulate of quantum mechanics has been used to develop various theories and models. For example, it is the basis of the Copenhagen interpretation of quantum mechanics, which states that an observer's knowledge of a system affects the system itself. This interpretation also led to the development of the field of quantum computing, which uses the fourth postulate to make calculations faster and more efficient. 

The fifth postulate of quantum physics states that the probabilities of observing the different possible outcomes of a measurement are determined by the quantum state of the system being measured. This means that the quantum state of a system completely determines the probabilities of observing different outcomes of a measurement. The fifth postulate is also known as the "collapse of the wave-function" or the "Copenhagen interpretation" of quantum physics. It states that when a measurement is made on a quantum system, its wave function collapses to a single discrete value, with the probability of each possible outcome being determined by the quantum state of the system. This postulate implies that the results of all measurements on quantum systems are fundamentally unpredictable. Because of this, quantum mechanics is sometimes referred to as a "theory of probability", since the outcomes of measurements can only be determined by a probability distribution over the different possible outcomes. This postulate has been experimentally verified and is the basis for our understanding of the quantum world.

The sixth postulate of quantum physics is known as the Born Rule. This postulate states that the probability of a system being in a certain state is proportional to the square of the absolute value of the wave-function of that state. In other words, the probability of a particle being in a certain state is proportional to the square of its wave-function. This postulate is based on the work of Max Born, who proposed that the probability of a particle being in a certain state is directly related to the magnitude of the wave-function of that state. The Born Rule has been an essential part of the development of quantum mechanics, as it is used to calculate the probabilities of different states for a particle. It is also crucial for understanding quantum phenomena such as tunneling and entanglement. The Born Rule has been used to explain the behavior of particles in experiments such as the double-slit experiment and to calculate the effects of quantum mechanical interactions. Despite its importance, the Born Rule still needs to be fully understood. It is one of the most mysterious postulates of quantum physics and has been the subject of much debate and discussion over the years. It is still the subject of much research, and its implications are still being explored. 

    The seventh postulate of quantum physics states that a quantum state is completely determined by its expectation values of observables. Any given quantum system can be described in terms of its average behavior. This postulate is closely related to the Heisenberg Uncertainty Principle, which states that it is impossible to measure both the position and momentum of a particle at the same time with absolute precision. The seventh postulate states that any observable quantity can be expressed as the expectation value of a quantum state, allowing for the calculation of average values for the system. This enables us to make predictions about the behavior of a quantum system. For example, if we know the expected value of a particle's momentum, we can predict its average behavior. This postulate is also closely related to the Schrödinger equation, which describes the evolution of a quantum system in time. The Schrödinger equation relies on the seventh postulate to determine the evolution of the system, as it uses the expectation values of the observables to update the system's state. The seventh postulate of quantum physics is a fundamental principle that underlies all of quantum mechanics. It is used to make predictions about the behavior of quantum systems. 

To conclude, perhaps, you are a Quantum system, have a wave function, and obey the Schrödinger equation. Or, you do not. 

 Hernández, Timothy Alexander, Left Turn, Tuesday, January 11th, 2023, Strings, Uptown