The discovery of Electron and the Plum Pudding Model

Before 1897, the atom model was believed to be a solid sphere. Thomson then disagreed with this idea. He conducted an experiment by producing a visible beam called a cathode ray in a tube. He also placed two plates with opposite charges around the beam and two magnets on either side of the tube. The result showed that:

• The particles are attracted by positive (+) charges and repelled by negative (−) charges, so they must be negatively charged
• They exist as a part of the atom and are less massive than atoms regardless of the source material
• These subatomic particles can be found within atoms of all elements

Electrons were found like this. He later proposed that atoms can be described as negative particles floating within a soup of diffuse positive charge. The model was known as the Plum Pudding model.

The Plum Pudding model, which was first proposed in 1904, played an important role in the early development of atomic theory. While it was a key step forward at the time, it has since been less noticeable compared to the later and more accurate models. Today, the planetary and the quantum model are the ones most commonly used in reference about atomic structure. However, the way the model was discovered and named is interesting.

Carbon, planetary model, and rocket fuel

Carbon, represented by the symbol C, is a non-metallic element with the atomic number 6 and a relative atomic mass of 12.011, typically ranging between 12.0096 and 12.0116. It is found in group 14 and period 2 of the periodic table, situated in the p-block, and has quantum numbers of 2, 1, 0, +1/2. At standard temperature of 298 K or 24.85 C, carbon exists as a solid and can appear in various forms. The most well-known is graphite, which is black and opaque, and diamond, which is transparent and colorless. The difference in color between these carbon forms reflects differences in their chemical structure, each carbon atom forms 4 bonds in diamond but only 3 in graphite, and the presence or absence of free electrons. These factors cause graphite to absorb visible wavelengths while they are not absorbed as photons do not have enough energy to excite electrons in diamond.

Carbon’s shell structure is 2.4, which indicates 2 electrons in its first shell and 4 in the second, which allows it to form covalent bonds with others and tend to fulfill 8 electrons to stay stable following octet rule. The electrons in the outermost also known as valence shell travel father, experience weaker pull from the nucleus, and have higher energy. This is the reason why the valence shell of an element determines its chemical properties.

However, it is important to remember that there are exceptions to octet rule where molecules having one or more atoms possess fewer or more than an octet of electrons. An example that does not follow this pattern is Hydrogen as Hydrogen has one valence orbital and tend to fill its valence shell with only 2 electrons instead of 8.

Chemical liquid rockets of bipropellant use liquid fuel such as liquid hydrogen (H2) and a liquid oxidizer such as liquid oxygen in the form of dioxygen (O2). Liquid hydrogen fuel is one of the most significant technical accomplishments in rocket science known for its light weight, high density, and high specific impulse.

If you are familiar with rocket science and understand why rockets are that large and have multiple stages, you might wonder whether there is an energy source capable of providing powerful thrust while being significantly lighter so that it could reduce the size of the rocket. There has been an idea that rocket fuel can be an alternative energy source like nuclear fusion, the one that is similar to burning of the Sun by fusing Hydrogen and Helium atoms. The idea has been around in rocket science and clean energy source with zero-emission research, and can be even found in the science fiction Iron Man Armor, the Arc Reactor, a compact nuclear reactor that fuses Palladium atoms to provide limitless powerful energy for advanced weapons and flight capabilities. However, while effective, exposure of power for a long time leads to poisoning that endangers the Iron Man’s life just as radioactive nuclear waste such as Plutonium, Uranium, or minor Actinides is highly poisonous for even thousands of years.

Schrodinger’s cat thought experiment and quantum mechanics

The statement of Schrodinger’s cat being “50% alive and 50% dead” is a simplification of a concept in quantum mechanics. In the famous thought experiment proposed by Erwin Schrodinger, a cat is placed in a sealed box with a radioactive substance, a Geiger counter, and a flask of poison. If the radioactive substance has an atom that decays, the Geiger counter detects it, triggers the release of a poison, and results in the cat’s death. If the substance does not have any atom that decays, the cat remains alive. According to quantum mechanics, until the box is opened and an observation is made, the atom exists in a superposition of decayed and not decayed state. As a result, the cat is also considered to be in a superposition of alive and dead state.

In quantum mechanics, the atomic orbitals of Hydrogen are solutions to the Schrodinger equation that describes the probability distribution of an electron around the nucleus instead of having it orbiting with a certain radius in planetary model. These orbitals are characterized by three quantum numbers: the principal quantum number 𝑛 indicating the energy level, the azimuthal quantum number ℓ determining the orbital shape, and the magnetic quantum number 𝑚 specifying the orientation in space. The wave function \(\psi_{n\ell m}(r, \theta, \phi) = R_{n\ell}(r) \cdot Y_{\ell}^{m}(\theta, \phi)\) is separable into radial and angular components with the radial part depending on 𝑛 and ℓ, and the angular part described by spherical harmonics dependent on ℓ and 𝑚. These orbitals define regions where the electron is most likely to be found and form an understanding of atomic structure of a Hydrogen atom in quantum mechanical model.

• Electron Scattering
• Photoelectric Effect
• Wave Interference, Diffraction
• Double-slit Experiment
• Wave-particle Duality

There is a common practice of firing a beam of particles through obstacles to study the behaviors and properies of them. Human can experience many phenomena directly with their naked eyes, however, many others can only be observed with the help of detectors.

Electron scattering experiment refers to the deflection of electrons from their original paths due to interactions with other particles or fields. In elastic scattering, electrons interact with nucleus or electron cloud without any loss of kinetic energy and only alter their direction. In inelastic scattering, electrons lose energy to nucleus or electron they encounter, which can lead to excitation or ionization. The interaction is mostly due to the electrostatic forces. Electron scattering helps us understand atomic structure even down to the level of subatomic particles known as quarks.

The photoelectric effect is a famous experiment where electrons are ejected from a material, for example a metal plate, when it is exposed to electromagnetic radiation such as UV or visible light. These emitted electrons are known as photoelectrons. When light of a sufficiently high frequency strikes a material, its photons transfer energy to the electrons within the material. If this energy exceeds the binding energy, the electron is likely ejected from the surface. Photoelectric effect is an example of particle-like behavior of light in the form of electromagnetic energy or photons.

You might notice the wave function takes the shape of the Trident of Atlan. Ocean and seashore are great places to observe waves in the form of energy tranfer when wind is blowing cross the surface. Waves can even be observed underwater. Internal waves are gravity waves that propagate along the interfaces between layers of different densities within the ocean. These density differences are typically from changes in temperature and salinity. Internal waves can be visualized as waves of energy on the surface if the density changes over a small vertical distance or being propagated both vertically and horizontally if the density is continuously changed.

Double-slit experiment might be inspired by surface waves. The double-slit experiment is a demonstration in physics that reveals the dual nature of particles and proves both particle-like and wave-like behavior of them. When particles such as electrons or photons are emitted one at a time toward a barrier with two slits, they are detected on a screen behind the slits as individual points. However, as more particles are emitted over time, these individual points collectively form an interference pattern characteristic of waves.

Many experiments other than these also demonstrate that under some circumtances, particles have the behavior of wave while behave as particle under other circumtances.

When Aquaman wields the Trident, a transfer of information occurs from neuron to neuron and an electrical or chemical signal, which is visualized as the orange light, travels through them, connects all the animals of the ocean, and grants him special abilities.

This was demonstrated when Arthur, the true heir of Atlantis, took the trident, and gained the ability to perfectly sense every creature of the ocean on the planet Earth and reach out to them all (including the savage Trench).
- Trident of Atlan, fandom.com

You can explore the movie on your own interest. I find these few minutes of the movie also contain useful information that reminds me of several concepts. The last but very important information is neuron. If you prefer an interactive approach, you can further explore the explorable explanation version of it here.

• Blackhole, event horizon, singularity
• Quantum entanglement, quantum computer, black body radiation
• General relativity spacetime curvature, gravitational lensing effect
• LHC particle accelerator

Moore’s Law gives us the idea that the density of transistors doubles every 18 months, roundly 2 years, in integrated circuit design. At the most fundamental level, physics and chemistry well explain how electrons are trapped and released to model the signal of 0 and 1. If transistors keep getting smaller and denser, will they break the laws of physics? Will the Dennard scaling effect no longer hold true? How small could a transistor be, down to the size of an atom? Will it be able to carry information at a single atom as in quantum mechanics. I used to think it could help in the development of quantum computers based on entanglement and superposition to create the next generation of computers capable and powerful enough to replace digital computers. But as it turns out, quantum computers only outperform digital computers in some specific tasks as they still face challenges that limit their applications.

The scene leverages many concepts in quantum mechanics and black holes. What comes first named the Phoson, a computer capable of extending to the size that could cover the entire planet when being unfolded in high dimensional space and collapsible to the size of single atom. The computer is most likely inspired by how a quantum computer works at quantum level. Four phosons, each pair is connected using the idea of quantum entanglement, in which the state of 1 phoson cannot be independent from the other regardless of their distance. Einstein refers to this as spooky action at a distance. The computer’s folding mechanism draws inspiration from a black hole, an extremely dense astronomical object formed during the gravitational collapse of a massive star after it exhausts its nuclear fuel. If the collapse of a star core results in a super dense giant ball of neutrons in type II supernova, the collapse of a massive star of typically around 25 to 30 and even up to 50 to billion times of solar mass can form a black hole. In such an object, the curvature of spacetime becomes so extreme that not even light can escape its strong gravitational field.

The artistic folding of the computer takes the shape of a funnel that depicts a few concepts related to black hole including event horizon, Schwarzschild radius, and singularity. To give an estimate of how large a black hole is and its visual, let’s start with singularity. Singularity is a point of infinite density and a maximum distance from this point forms a spherical region where any matter or radiation traveling at the speed of light cannot escape. This distance from the singularity is also referred to as event horizon with the radius known as Schwarzschild. If the escape velocity from a body with mass M and a radius R is given by the formula: \(V_{esc} = \sqrt{2GM / R}\), the Schwarzschild radius is easily calculated by replacing \(V_{esc}\) with c. As a result, a 3 times of solar mass black hole, the smallest ever discovered, will have a Schwarzschild radius of roundly 9 km. Matter and radiation within a black hole’s event horizon cannot escape its gravitational pull. Outside the event horizon, the black hole’s intense gravity bends and distorts the light from background objects, a phenomenon known as gravitational lensing, and allows telescope to detect and capture images of them.

LHC particle accelerator is the place to study particle physics. The LHC allows scientists to investigate the fundamental components of matter, explore the origins, and unlock the mysteries of the Universe. It accomplishes these by accelerating a beam of particles, for example protons, to near the speed of light and then let them collide to break the strong forces, one of the four fundamental forces holding subatomic particles together. One of the most significant accomplishments of LHC is the discovery of Higgs boson.

The writing borrows the idea from the method of extracting entities and their relations visually and conceptually after watching a video, then reconstruct and enrich new information with extra supplied sources of information if necessary. The method does not make use of vision language model so I need to handle the vision encoding myself. Different persons based on their own experience, memory, and at a unique point of time might have various interpretations of the video. The writing is also an attempt of using physics perspective to interpret the video as physics and technology have always been a source of inspiration for science fiction movies and novels.

How is the evidence of the Universe developed?

In the early years, the universe is small and extremely hot. All the matter existed as a dense plasma. Plasma—one of four fundamental states after solid, liquid, and gas—absorbed light, making the universe opaque (preventing light from traveling through, therefore not transparent). As the universe expands, so does the matter and energy inside it. What started as light released at that moment has now been stretched into the microwave region. Microwave radiation, WMAP can peer backward in time to when that radiation was emitted.

From 1989 to 1993, COBE tested many theories that predicted by the existence of a Big Bang and collected evidence to develop future questions. The data found agreed with the scientists’ predictions, it left a lot of questions unanswered. WMAP was launched on June 30, 2001, placed in six-month orbit around the Sun-Earth L2 Lagrange point, which is 1.5 million km from Earth. WMAP created an extremely precise full-sky map of the cosmic microwave background, improving upon the maps by COBE.

WMAP answered that the Universe started flat and aged 13.8b years ago. It also showed that dark energy is an unknown force that counteracts gravity, pushing galaxies away from each other rather than causing attract one another as we would expect if gravity were the only force at work. After 9 years of accumulation, WMAP also helped to prove that the Universe’s expansion is accelerating.

Dark energy was first discovered through the observation of Type 1a supernovae. Whereas, Galaxy rotation curve, X-ray observation of hot gas, and gravitational lensing all provide evidence for the existence of dark matter, the invisible substance that exerts gravity. Dark energy (70%) and dark matter (25%), while they do not fit into the Standard model, together contribute to 95% of the Universe model. The other component is ordinary or visible matter (atomic particle + small % of neutrino), which account for 5% only. Interestingly, dark matter and dark energy embody the philosophy of duality of opposing forces that coexist in many systems such as attraction and repulsion, matter and antimatter, order and disorder, positive and negative, Yin and Yang, and Han and Heung.

Additional Resources

• CERN record/2002395
• Standard Model
• Scale Of Universe
• Beyond Standard Model
• Atlas Opendata - Physics beyond the SM
• WMAP Matter/Energy
• Hubble Dark Energy
• Galaxy Rotation Curves
• Grand Unified Theory
• Theory Of Everything

Bullet Cluster (4b years ago)

The image depicts a duo of clusters of galaxies as observed through the Chandra X-ray observatory. The red shading represents the ordinary gas that has become hot, while the blue shading represents the presence of dark matter, which is figured out by looking at the gravitational lensing effect.

So why is it? Because the cluster of galaxies is basically an ocean of dark matter, which is supposed to keep the galaxies and gas inside. However, this gas is sort of outside of the ocean of dark matter. After some studies, it turned out that this was the aftermath of a collision of two clusters at an incredible speed of 45000 km/s.

During the collision of two clusters, the gas within them indeed interacts, leading to heating and friction, which causes them to decelerate and remain behind due to gravitational pull. However, dark matter continues to move as though unaffected by the collision.

Gravitational Lensing

Anything that has mass is subjective to gravity. Light does not have mass, so why does it get bent when passing near a massive object? The phenomenon of refraction suggests that light is bent when it passes through two different mediums in an optimal path. Therefore, the space around a massive object must prevent light from traveling in a straight line, which strongly supports the new definition of gravity as the result of distortions in spacetime. In general relativity, the stronger gravitational field stretches out time and makes it pass more slowly.

• Gravitational Lensing
• Cheshire Cat
• Gravity Warps Light
• Einstein Ring LRG-3-757

Black Hole

There was a young lady of Wight
Who traveled much faster than light
She departed one day
In a relative way
And arrived on the previous night
- Limerick, Stephen Hawking, A Brief History of Time

• Psychology Behind Remembering Music
• Astronomy Acrostics
• Poetry Examples
• HR Diagram Background
• Black Holes Explained
• First Image Of A Black Hole – Press Release
• How Scientists Captured The First Image Of A Black Hole

Fluorescence

Chemical compounds like fluorescent molecules are capable of being excited by absorbing light and achieving higher energy state from ground state. As the electron is unstable at high energy configuration and quickly transitions to lower energy states, light energy is emitted before reaching its ground state again. Because light is released at lower energy state, it has longer wavelength. This is the reason why fluorescent molecules allow the material to glow when they absorb UV light and emit visible light to the human eye.

Why do distant Galaxies look red? Is it because they are expanding?

An example with sound

A simple explanation comes from the pitch of sound. When an ambulance is passing in front of you the pitch is going up. Imagine an ambulance is approaching close to you, the pitch of the siren will be going up. When it passes through and far away (receding) from you, the pitch will be going down. From these observations, we can draw some comments:

• Approaching object gives away high pitch sound
• Receding object gives away low pitch sound
• Receding star gives away red color

Similarly, if a star is moving far away from the Earth, the light that a telescope captures from the star turns red.

This is called Doppler effect, and now comes the calculation:

• \(f’ = \frac{V}{V + v} \cdot f\) (when the object letting the sound out is moving)
• \(f’ = \frac{V - v}{V} \cdot f\) (when the object is moving, relative to the air)

Where:

• V is the speed of sound
• v is the speed of the object perceiving the sound.

Consider the example: a police car is moving west at 20m/s toward a driver who is moving east at 25m/s. The police car emits a frequency of 900 Hz. What frequency is detected by the driver? Given the speed of sound in air at 20C is 343m/s.

An example with light

\[ \lambda_{\text{observed}} = \lambda_{\text{source}} \cdot \sqrt{\frac{1 - \beta}{1 + \beta}} \]

\[ \begin{align*} &\text{Where:} \\ &\lambda_{\text{observed}} \text{ is the observed wavelength} \\ &\lambda_{\text{source}} \text{ is the emitted wavelength} \\ &\beta = \frac{v}{c} \text{ is the ratio of relative velocity over the speed of light} \end{align*} \]

The Doppler effect applies to all types of waves including sound, light, and water. Depending on the motion of the source and the observer, whether each is stationary, moving toward, or moving away from the other, there are 3 x 3 = 9 possible combinations to consider. This is the general expression for the Doppler effect for sound along with its specific form for every combination of source and observer motion. However, these forms are simplified under the assumption that the source and observer are moving along a straight line. In real world scenarios, the motion is often more complex, for instance, the observer may be approaching the source at a specific angle. Such cases will require including an angle variable in order to determine a precise result.

Yes, the Universe is expanding

The Universe is not static, it rather exists in 3 possible states: warp, twist, and expand. Today, more and more evidence, especially redshift, verifies the expansion theory throughout the observable universe. As a result, the Universe as a whole is getting bigger and, at the same time, getting colder. When returning to the past (Big Bang), it was smaller and hotter.

\[ E = h\nu = \frac{hc}{\lambda} \]

Revolution of the Earth

Ptolemy and the ancient observation

The ancient observation explains that we are at the center of the universe and any other star revolves around us. The observation is true for the Moon and Sun but wired for the other planets like Mercury, Venus, Saturn, and so on.

They saw that these planets also moves back and forth around us. In order to explain this, they added the concept of epicycle motion. Over time, they realized it is not true and trying to add more epicycle and making things more complicated. They started to think that the Universe cannot this be complex understanding and this idea is possibly right.

Copernicus and the modern observation

Copernicus, he believed that there is another simpler explanation and completely changed the idea of observation. He stated that the Sun is actually at the center and the Earth off-center along with other planets moving around the Sun in complete circles.

Let’s take Saturn as an example, because Earth and Saturn move at different speed where the Earth is faster, we would see the Saturn is a little bit falling behind. And when the Earth comes back from the other side, we see the Saturn is moving ahead.

Kepler and the Elliptical orbits

Everything still does not agree with the observations as the data collected are so precise. Kepler came up with another single concept that the orbits are elliptical and this very well explains the observations that meet all the criteria for a good physical theory.

1. Agree with observations and experiments
2. Has a unified description
3. And simple

Newton’s second law of motion and Universal law of gravitation in combination well explain the elliptical motion of a planet.

• \( F = ma \) means net force is equal to mass times acceleration.
• \( F = G \frac{Mm}{R^2} \) means the gravitational force (F) of two masses M (the Earth) and m (satellite/moon) is inversely proportional to the square of distance (R) between them.

Newton’s second law of motion describes how difficult it is to influence the course of motion. An example of this is when a car and a bicycle in stationary motion are provided the same push, it is more likely for the bicycle to move. The Universal Law of Gravitation shows how strongly it is pulled by the force of gravity. If m (a satellite/moon) gets closer to M (the Earth), the force (F) increases, and so does the acceleration (a).

Kepler’s three laws:

1. The orbit of every planet is an ellipse with the Sun at one of the two foci.
2. A line running from the sun to the planet sweeps out equal areas of the ellipse in equal times.
3. The square of the orbital period of a planet is directly proportional to the cube of the radius of its orbit.

If algebra represents the relationship between variables, calculus captures, for example, the rate of change in motion of planet as the Universe also exhibits non-linearity.

Earth-Moon system

As the Sun is extremely massive and accounts for 99,86% total mass of the Solar system, I also wonder if Kepler’s laws hold true in similar systems. If the ratio of mass between the Moon and Earth is established, 1.2%, we can easily come up with the idea that Earth-Moon system satisfies all the conditions to obey Kepler’s laws. However, thinking a small body in term of mass on a stable orbit hinders us from realizing that it is attracted by more than one body. In fact, it is, and one of them has the strongest and significant gravitational force over others that leads to the study of 2-body problem. This is a great reference as it also mentions the 2nd condition to consider due to n-body problem. The condition is what many resources do not explicitly point out perhaps because when describing planetary systems in Solar system, they assume that these systems are isolated. In this context, I prefer the phrase “nearly isolated” as one body is more or less still under gravitational influence of many other bodies.

1. The orbiting mass is small compared to the mass it orbits.
2. The system is isolated from other large masses.

Lagrange point

Lagrange point is a special point where a small mass is under gravitational force of 2 massive bodies. For every 2-body system, there are 5 points such that the gravitational forces and centrifugal forces get balanced and reach equilibrium. Bodies of small mass are gravitationally hovered in the region around these points and can exhibit nearly in-place, chaotic, or orbiting motion relative to observers on the 2 primary bodies. There are 2 stable points and 3 unstable points, and these have been the ideal positions to place artificial statellites for a long time.

L1, L2, L3

These points lie along the line connecting the 2 large masses. They are considered points of unstable equilibrium, which mean small masses placed here can maintain their position but require regular station-keeping to correct any perturbations. To maintain position near these points, small masses often adopt Halo or Lissajous orbits.

During the Apollo mission, the command module of Saturn V, named after the sixth planet in the Solar system, on its en-route the Moon gravitational influence experienced the balance of opposing gravity of Earth and Moon. It gradually drifted over this point and began to accelerate towards the Moon as the body’s gravity becomes increasingly stronger. The Universal law of Gravitation is an example of the famous Inverse Square law as it has a division by square of distance or \( \frac{1}{r^2} \) component and it well describes how strong the force is when a mass is closer to a body. Masses with the same center of gravity around this point accelerate at the same rate regradless of their mass as the gravitational field is different in space.

L4, L5

These points form the apex of 2 equilateral triangles with the large masses at their vertices. They are stable equilibrium points, which mean small masses can orbit around these points with a minimal configuration and additional help of coriolis force. This stability occurs when the mass ratio of the 2 large bodies (large over small) exceeds approximately 24.96 and the condition is met in systems like Earth–Sun and Earth–Moon.

• Lagrange Point

Earth-Moon-Sun system

According to the lunar orbit, the Moon requires 27.3 days to complete a full orbit around the Earth in a relative position. However, as the Earth also revolves around the Sun, the Moon actually needs 2.2 more days, a total of 29.5, to complete its 8 phases geometrically. If a line is drawn between the Earth and the Sun, an event known as the new moon occurs when the Moon aligns along this line. At this point, the side of the Moon facing Earth is not illuminated by the Sun and renders it invisible to observers on Earth. When the Moon reaches the position on the opposite side of the Earth, it becomes fully illuminated and creates the event known as the full moon.

On rare occasions, during a new moon and a full moon, the Moon’s orbit aligns precisely with the same plane as that of the Earth and the Sun. These 2 special alignments result in a lunar eclipse and a sun eclipse, where the Moon or Earth temporarily prevent sunlight from reaching the other. Outside of these specific alignments, the Moon is generally visible from Earth in different degrees and displays either a partial or full side depending on its position in orbit.

An interesting fact about the Moon is that it rotates on its axis at the same rate that it orbits the Earth. This synchronous rotation is the reason why only one side of the Moon is visible from Earth. To observe the far side of the Moon, a satellite must be deployed in lunar orbit to perform a full scan of its surface. As the Moon’s gravity is one-sixth that of Earth’s, you would feel less weight than you do on Earth.

The reason humans on Earth can observe the Moon with the naked eye is because the Moon reflects sunlight to observers from the Earth, its size is a bit more than one-fourth that of the Earth (approximately 27%), and it is relatively close compared to other natural celestial bodies in the solar system.

A bit of thermodynamics

Regarding the concept of isolated system, it reminds me of lessons about thermodynamics that deal with work, heat, energy, and open, closed, or isolated system using algebra-based physics in high school. Many of these can be easily experienced when preparing dishes as kitchen is the best chemistry lab after school. It is easily observed that closed and isolated systems have the distribution being shifted to higher velocity (higher kinetic energy) and flattened when temperature is increased. The ocean is a typical example of an open system, where energy from solar radiation and matter are exchanged with the atmosphere above.

Temperature, pressure, amount, and volume are closely related, and their interactions give rise to 4 fundamental laws of an ideal gas. Changes in one of these variables directly influence the others. In a closed or isolated system with a fixed volume, an increase in temperature yields higher kinetic energy and so forth pressure. If a closed system of liquid and gas produces additional gas particles as products but does not results in significant reduction of reactants in term of space that leads to higher density of gas, pressure also increases. These changes are not observable at the level of individual particles but happen when considering a large number of them, an example of emergent properties.

Going back to the thermodynamics example, high school lessons provide a conceptual foundation by introducing basic ideas such as temperature, heat, energy, and the laws of thermodynamics. These lessons help build intuition about how energy is transferred and transformed, and is often used in macroscopic systems like engines, refrigerators, or boiling water. However, they still lack the mathematical representation required to fully describe and predict the behavior of complex systems.

Nature is not that simple as we begin to see that not all particles in a thermodynamic system behave identically. In reality, systems consist of a large number of particles, each potentially having different values in properties such as energy and velocity. Especially in gas, the distance between particles is great and the attractive force is very weak, therefore, they move faster and have higher kinetic energy. This is where statistical mechanics becomes crucial. It provides, for example, a way to measure the motion of particles in a macrostate in relation to pressure, temperature, and entropy using probability and statistics. Maxwell-Boltzmann distribution is an example of these measurements. If you are familiar with ML, it is easy to understand that why entropy is to measure disorder in decision tree model and cross-entropy is to measure how different 2 distributions are in multiclass classification.

• https://astro.unl.edu/naap/atmosphere/animations/gasRetentionSimulator.html

Let’s take an example with an oil diffuser real quick. If you are close to an oil diffuser, the perfume is much stronger, whereas the smell becomes weaker as you move farther away. This is because the concentration of the diffused particles, essentially the aromatic molecules, is highest near the source and decreases with distance. This phenomenon can be explained by diffusion. If you take each air particle as a data point, you already have an excellent 3-dimensional space filled with data as the world we are living is also a 3-dimensional space. When the room temperature is high, particles propagate faster. So, what you are sensing is essentially an intuition of distribution of particles and how microscopic behavior results in macroscopic phenomena.

Phase transition, attractive force, and energy landscape

The discovery of Pulsars

One day, an astronomer student found something strange in her radio astronomy data. A very weak blip coming from one part of the sky that repeated every 1.3 seconds with incredible precision. She and her supervisor immediately figured that it was impossible for a message from aliens, but how else to explain such an astoundingly regular signal from space.

Other two astronomers developed their experiments to catch up with the theoretical explanation. By looking at the discovery of the sub-atomic particle called the neutron, they suggested that when an old large star runs out of nuclear fuel, it rapidly collapses under its own gravity. The star’s core suddenly transforms into a super dense ball of neutrons, and the outer layers of the star bounce off in a massive explosion of light and energy, a supernova. The dense core of neutrons that remains behind, forms a neutron star, would have the mass of two or three suns squeezed down into the size of a large city.

When a star suddenly collapses like this, two interesting things can happen. The star typically rotate like once every few days. The law of conservation of angular momentum suggests that when a star collapses the rotation speeds up. In case of neutron stars, it could spin at an incredible speed of ten or even hundreds of times a second. Like the Earth, a star has magnetic field and takes this incredibly intense field upon collapse. Charged particles in the super-hot plasma surrounding a neutron star would get funneled towards the stars magnetic poles and shot out into space as two intense beams like a lighthouse. Because the rotation axis is not aligned with the magnetic axis, what astronomers receive on Earth is the radio emission at a specific frequency.

The map of history of Unification and theory of Everything

Physics is a great framework to explore the world around us and unlock the mysteries of the universe. It is heavily based on mathematics to describe physical phenomena and can be used to understand other fields of science. For learning, HyperPhysics might be one of the best online references for physics concept definition.