FULafiaPhysics

Quantum mechanics is a lot to handle at first. However, let's remember that there are postulates that guide the madness!

First Postulate:
At each instant the state of a physical system is represented by a ket |ψ⟩ in the space of states.

Second Postulate:
Every observable attribute of a physical system is described by an operator that acts on the kets that describe the system.

Third Postulate:
The only possible result of the measurement of an observable A is one of the eigenvalues of the corresponding operator Â.

Fourth Postulate:
When a measurement of an observable A is made on a generic state |ψ⟩, the probability of obtaining an eigenvalue a𝘯 is given by the square of the inner product of |ψ⟩ with the eigenstate |a𝘯⟩, |〈a𝘯|ψ|².

Fifth Postulate:
Immediately after the measurement of an observable A has yielded a value a𝘯, the state of the system is the normalized eigenstate |a𝘯⟩.

Sixth Postulate:
The time evolution of a quantum system preserves the normalization of the associated ket. The time evolution of the state of a quantum system is described by
|ψ(t)⟩ = Û(t, t₀)|ψ(t₀)⟩
for some unitary operator Û.

Brownian motion :
The erratic random movement of microscopic particles in a fluid, as a result of continuous bombardment from molecules of the surrounding medium.

The random movement of particles suspended in a fluid resulting from their bombardment by the fast moving atoms or molecules in the gas or liquid, and there is no preferred direction for these random oscillations.
In 1905, Einstein published a diffusion equation that predicts the average distance a pollen grain travels through a liquid in a given time. The equation is much more complex than the typical equation:

d² = y(T/γu).(t/N)

d - the distance the pollen grain travel during time t.
N - no. of atoms in a specific volume of the liquid.
y - a numerical constant.
T - Liquid's temperature.
γ - radius of the pollen grain.
u - Liquid's viscosity, it's resistance to motion.

Einstein's diffusion equation predicts the average distance pollen grains travel for any values of four parameters: grain size, time, and the liquid's temperature and viscosity.
Einstein's insight was to figure out how far they travel on average. This is called a 'random walk' or a ‘drunken sailor problem'. Einstein found it takes four times as long to travel twice as far when each step is taken in a random direction.

HEAT ENERGY can leap across a few hundred nanometres of a complete vacuum, thanks to a quantum mechanical phenomenon called the CASIMIR INTERACTION.

In a new study, University of California, Berkeley, researchers show that heat energy can travel through a complete vacuum thanks to invisible quantum fluctuations. In the experiment, the team placed two gold-coated silicon nitride membranes a few hundred nanometres apart inside a vacuum chamber. When they heated up one of the membranes, the other warmed up, too, even though there was nothing connecting the two membranes and negligible light energy passing between them.

➡️ Vibrations of atoms or molecules, which carry thermal energy, simply can't travel if there are no atoms or molecules around. But a new study by researchers at the University of California, Berkeley, shows how the weirdness of quantum mechanics can turn even this basic tenet of classical physics on its head.
🔹This [Casimir] interaction is only significant on very short length scales.🔸
➡️ "Even if you have empty space—no matter, no light—quantum mechanics says it cannot be truly empty. There are still some quantum field fluctuations in a vacuum," - said King Yan Fong, a postdoctoral scholar at UC Berkeley and the study's other first author. "These fluctuations give rise to a force that connects two objects, which is called the Casimir interaction. So, when one object heats up and starts shaking and oscillating, that motion can actually be transmitted to the other object across the vacuum because of these quantum fluctuations."
➡️ Though theorists have long speculated that the Casimir interaction could help molecular vibrations travel through empty space, proving it experimentally has been a major challenge. To do so, the team engineered extremely thin silicon nitride membranes, which they fabricated in a dust-free clean room, and then devised a way to precisely control and monitor their temperature.
➡️ They found that, by carefully selecting the size and design of the membranes, they could transfer the heat energy over a few hundred nanometers of vacuum. This distance was far enough that other possible modes of heat transfer were negligible—such as energy carried by electromagnetic radiation, which is how energy from the sun heats up Earth.
➡️ "Because molecular vibrations are also the basis of the sounds that we hear, this discovery hints that sounds can also travel through a vacuum", said Xiang Zhang, the professor of mechanical engineering at UC Berkeley who guided the study.
© University of California - Berkeley