Conservation Laws

A conservation law is nothing but a statement that a particular quantity (energy, momentum etc.) stays constant during a process. There are at least 6 different conservation laws encountered in Physics, as follows:

Conservation of Mass

This law states that in any non-relativistic chemical or physical process(except nuclear processes), the total mass of an isolated system stays constant. In relativistic situations (and nuclear processes) mass is seen as a manifestation of energy associated with matter. In that case we consider the conservation of energy only and mass is represented by “mass energy“.

Conservation of Energy

The most popular of them all. It states that the total energy of an isolated system (including kinetic energy, potential energy, mass energy etc.) is the same before and after it undergoes a process. By isolated system we mean that it does not interact with its surroundings in any manner. Since the Universe as a whole is an isolated system(as far as we can say), the total energy of itself must be constant as well.

This law appears in many forms in different branches of Physics, e.g. as the first law of thermodynamics or as work-energy theorem in mechanics.

Conservation of Linear Momentum

This law is probably familiar to most of us in the form of Second law of motion. It states that the total linear momentum of a system stays constant if no external force acts on it.

Conservation of Angular Momentum

Analogous to the law of conservation of linear momentum, this one states that the total angular momentum of a system stays constant if no external torque act on it. (Torque ≡ moment of force)

Conservation of Charge

Electric charge is a fundamental properties of particles. Any particle which carries charge is either positively charged or negatively charged. e.g. protons carry net positive charge of 1 while electrons have -1. The law states that in any particle interaction, the net electric charge stays constant.

Consider the following decay of a pion into a muon and muon neutrino:

Total charge on the left hand side = +1(on pion)
Total charge on the right hand side = +1(muon)+0 (neutrino) = +1
Hence, total charge is conserved.

Conservation of Baryon Number

Baryons are a kind of fundamental particles such as protons and neutrons. Each of them has been assigned a particular Baryon Number (Baryons have +1 and antibaryons have -1, rest of the particles are assigned 0). The law states that in any particle interaction (strong, weak, electromagnetic or gravitational), the net Baryon number before and after the interaction remains unchanged.

Consider the following process:

Baryon number on left hand side = 0 (pion) +1(proton)
Baryon number on the right hand side = +1(lambda)+0 (Kaon)
Clearly, both baryon number and electric charge are conserved.

Conservation of Lepton Number

Elementary particles such as electrons, neutrinos etc (and their antiparticles) are known as Leptons. Just like Baryons, each of the Leptons has been assigned a Lepton Number (e.g. electrons have +1). The particles which are not leptons are assigned a lepton number of 0. The law states that the net Lepton number before and after a particle interaction stays constant.

e.g. consider the process of neutron decay:

Lepton number on left hand side = 0 (neutron)
Lepton number on right hand side = 0 (proton)+1(electron)-1(electron antineutrino)
Clearly, Lepton number is conserved in this process. Note that the Baryon number and electric charge are conserved as well.

Energy

Energy is a concept thrown around so much that we all have an intuitive idea of what it is about, but we can’t exactly define it. There are so many types of energy and they are closely related, yet different from each other. e.g. the Sun has energy because of the nuclear reaction going on in it. It radiates that energy towards us, in the form of heat and light. Plants utilize that light to synthesize food and we, humans get energy from eating those plants (or animals that eat plants). In the whole process, energy gets converted as Nuclear->Thermal & Radiation->Chemical. We, after eating food, are able to do work.

In fact, when you say that “I can’t do work, I feel tired and low on energy”, you are very close to the way it is defined in Physics. In mechanics, energy is defined as the ability to do work. This is the most agreeable definition we could come up with, at this level (In special relativity, Energy and matter are seen as equivalent).

As mentioned before, energy comes in many forms. It can transform again and again into different forms, either naturally or by an effort made by us. When you use electricity to power a light bulb, the energy in electricity gets converted to light (and heat). Some different forms of energy include:

• Thermal energy
• Nuclear energy
• Heat (Energy in transfer by virtue of a temperature difference)
• Chemical energy
• Potential energy
• Kinetic energy
• Gravitational energy
• Elastic energy
• Radiant energy
• Binding energy
• Rest energy etc.

Note that these terms are only defined in a particular context, and are related. e.g. Mechanical Energy is usually the sum of kinetic and potential energies.

Energy can also be understood abstractly as some quantity that stays constant in all the processes and reactions (except nuclear reactions, where the total of mass and energy stays constant). In other words,

Energy can neither be created nor be destroyed.

We may never know what Energy is, but we do understand how to utilise it to get our work done. If we also develop ways to optimize our energy usage, we can progress tremendously.

The youtube channel The Science Asylum has a great video on the topic if you want to learn more:

Resonant Frequencies

v_n = nth harmonic
n = integer
v₀ = fundamental frequency

We’ve all seen those opera singer references which claim that at a particular frequency, the singer’s voice can break a wine glass. The physics behind the trick is that of resonance.
Basically, anything that can vibrate has some fundamental frequency of vibration which depends on its physical properties. A fixed, vibrating string is the best way to visualize this. If you pluck it at just the right point, it starts to vibrate. The string vibrates in a manner that the fixed ends and the point you plucked(approximately) stay at their position while the rest of the string oscillates up and down. If it is one of those resonant frequencies, the vibrations will last for some time(ideally they should last forever). Otherwise they’ll dampen quickly.
The string prefers to vibrate at these resonant frequencies, the lowest of which is called the fundamental frequency. Every object has a fundamental frequency. If you put another object near it vibrating at one of the resonating frequencies, the first object will pick up the vibration as well. This is called resonance (e.g. a tuning fork and a pipe).

More info:
http://hyperphysics.phy-astr.gsu.edu/hbase/waves/funhar.html#c1

Some examples:

Difference between harmonics and overtone:

A beautiful experiment with salt:

For more equations in Physics, see Famous equations in Physics

Conductivity

Conductivity is the ability of a material (usually solid) to carry electric current. Since electric current is nothing but electrons in motion; more the electrons (or holes), more is the conductivity. Resistivity is the opposite of conductivity.

Origin of Conductivity

Atoms have electrons in different orbitals (energy levels). The outermost electrons are relatively loosely bound and can get detached if sufficient energy is supplied. This energy can be in the form of heat, light or other forms. These detached electrons are called conduction electrons and are the reason for conductivity of a material. The ones that stay bound to the atom are called valence electrons.

When conduction electrons get free, they leave a vacancy behind. A neighbourhood electron would try to fill in this void by occupying it, leaving another vacancy in its place(which then be occupied by its neighbour, and so on). It appears as if the vacancy is travelling on its own, from place to place. We call it a hole. In any semiconductor both electrons and holes carry current.

In any material there are many atoms. Since electrons are fermions, no two of them can occupy the same energy level. Hence, when many atoms come together, the energy levels of similar orbitals come close, but not coincide. They have slight difference in energy. A lot of atoms would thus have very slightly different energy levels, appearing as an energy band.

There is the valence band and the conduction band.

In metals, both bands overlap and thus electrons can easily move between them (hence excellent conductivity). In insulators, however, the bands are very distant and it takes a lot of energy for an electron to jump from valence band to the conduction band. In other words, metals have loosely bound electrons which can become detached easily. Insulators on the other hand have strongly attached electrons in their atoms and thus very few free electrons.

Semiconductors have in between energy band gap. Hence at room temperature or higher, some electrons can jump. By doping the material or supplying energy in other forms(heat radiation etc.) we can increase the no,. of conduction electrons.

A basic introduction to Physics

Actually, I should call it “Physics syllabus” instead, but bear with me.

Physics is the branch of science dealing with the properties and interactions between matter and energy in space-time.

Loosely speaking, Physics is the study of how nature works, as in how does the Universe evolve in space and time. The fundamental assumption here is that, there are certain laws or patterns in the various processes that occur in nature and if we know these laws, we can predict the outcome of any process in principle.

This does not mean that we can answer all the “why” questions. We can answer “how” questions quite comfortably but the “why” part on the fundamental level is not understood. For example physics can answer (in principle) how the matter clumped together to form stars and galaxies, but it cannot answer where did the matter come from in the first place. Physics can predict what happened during the first minutes of the Big Bang, but it cannot tell you why Big Bang happened.

In any case, attempting the “how” questions is a mind-boggling challenge in itself. We try to solve the hows by categorizing them into certain branches of physics, based on the scope and nature of the process involved:

1. Mechanics: How do things move?
2. Thermodynamics: How can we extract useful work from a system? What forms of energy can help us and how?
3. Electromagnetism: How charged particles (and bodies made of them) interact with each other?
4. Quantum Mechanics: How atomic structures form? Basically answers all “hows” except Gravity.
5. Relativity: How are mass and energy related on a fundamental level (not interactions among them, but the properties of mass and energy) and how does gravity affect them? What is spacetime really?
6. Particle and Nuclear Physics: What is everything made of? Why doesn’t a nucleus break apart when there is so much electromagnetic repulsion? Is “matter” all there is?
7. Condensed Matter Physics: What are the macroscopic structures of matter? How do these structures dictate the macroscopic properties of a material (solids mainly) and how can we enhance these properties to suit our requirements?

There could be many other ways to classify Physics, such as Physics at the microscale and Physics at macroscale. There is even Biophysics and Sociophysics.

But Metaphysics is not Physics, at least that’s what I think!