The discovery of Electron and the Plum Budding 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.

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 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 year of accumulation, it also helped to prove that the Universe’s expansion is accelerating.

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 bends when it passes through two different mediums in an optimal way. Therefore, the space around a massive object must prevent light from traveling in a straight line, which leads to the new definition of gravity as the result of distortions in spacetime. In general relativity, spacetime is a 4-dimensional model in which anything exists in 3 spatial dimensions of space and 1 temporal dimension of time.

• https://pweb.cfa.harvard.edu/research/topic/gravitational-lensing
• https://chandra.harvard.edu/photo/2015/cheshirecat
• https://nasa.tumblr.com/post/187009797389/how-gravity-warps-light
• https://science.nasa.gov/image-detail/einstein-ring-lrg-3-757

Black Hole

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

Fluorescence

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’ = V / (V + v) x f (when the object letting the sound out is moving)

f’ = (V - v) / V x f (when the object is moving, relative to the air)

Where:

V is the speed of sound and 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.

In case of light

f’ = square root of((V - v) / (V + v)) x f where V is the speed of light and v is the relative speed between the object producing light and receiving light.

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 = hv = hc / lambda (h is Planck constant)

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(Mm)/square(R) means the gravitational force (F) of two masses M (the Earth) and m (satellite/planet) 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/planet) 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.

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 cases. 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 realising 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 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 balance each other and reach equilibrium. These have been the ideal positions to place artificial statellites for a long time.

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. Because open systems exchange matter and energy with their surroundings, they are considered non-equilibrium. 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 four 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.

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

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 early 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. This is where statistical mechanics becomes crucial. It also provides a measurement of behaviour of particle in the macrostate such as pressure, temperature, and entropy using probability and statistics. 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.

While the basic principles remain the same, the level of detail and the mathematical complexity increases significantly as we dive deeper by focusing on the underlying statistical distributions such as the Boltzmann or Maxwell-Boltzmann distributions that govern particle behavior in different complex systems.

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, a concept in thermodynamics and statistical mechanics. 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 are populated faster. So, what you are sensing is essentially an intuition of real-world distribution and how microscopic particle behavior results in macroscopic phenomena.