PHY 101: Vector Integration

Image
What is Integration? Integration can be thought of as a continuous analogue of sum (\(\sum_{ }^{ }\)). We integrate or simply add infinitesimal small quantities together to form a continuous chain. Integration can be of 3 kinds rather I would call it 3 ways of integration. Linear, Area and Volume way. To show what each of them looks like here is a visual representation: $$\begin{aligned}& Linear \hspace{1mm}integration:\int_{ }^{ }f(x)dx\\ \\ &Area\hspace{1mm}or\hspace{1mm} surface\hspace{1mm} integration: \iint_S f(x,y)dxdy \\ \\ & Volume \hspace{1mm} integration: \iiint_V f(x,y,z)dxdydz \end{aligned}$$ You might have already noticed that the number of integration symbols (\(\int_{ }^{ }\)) increases with the increase in the number of variables. Hence, most books adopt the notation of calling these single, double and triple integrations. We at physics are creatures of simplicity and thus have kept it easy to remember. Let us talk about each in some detail! Single or Linear...

The Particle paradox of Quantum Duality

Duality of Particles

Early 1700s:

In early times people had the notion of particles namely photons or light as collectively to be either of wave nature or particle nature. Many scientists conducted various experiments to prove the existence of light as one of those natures. But one thing that they all observed was that light was acting as both particle as well as wave nature. This seemed moot for the genius minds of the time. How can light be a wave and a particle simultaneously? That is simply not possible.

To prove the particle nature of Light: The photoelectric effect was considered to be sufficient proof. The experiment basically shows that when a light of a certain frequency is greater than the threshold frequency of the material upon which it is incident, it causes the surface to give off electrons. The number of these electrons often called photo-electrons is proportional to the intensity/amplitude of the light. The excess energy is then transferred to the electrons as their kinetic energy which becomes the cause of their motion. This experiment was also worked on by Einstein himself and scientists of the time gave an equation which today is given in many books as:

h𝜈 = h𝜈0 + ½mev2


Where the v_0 is the threshold frequency while the entire term is considered as the work function (min amount of work to get the free electron out). What is so beautiful about this equation though? Well for starters this equation shows us that light is a particle. The light is made up of small packets of energy or quanta of energy, which are called photons.
Well, this experiment settles the debate then, right? Light is made up of particles.
Credit: Photoelectric effect
https://thescienceandmathszone.com/the-photoelectric-effect-photons-and-plancks-equation/

Um....NO! Then we had Young with his Double slit experiment in 1810, he showed us when a monochromatic source of light (like a laser with only one colour) was passed through two slits of order close to the wavelength of the light, instead of the image of two bands of light like that of the slits, we found an alternate pattern of light and dark bands. Odd....that was what everyone felt. How can light which is a particle show this interference pattern when it is not a wave. This could only lead to one solution that light is also a wave. Which stands correct, light is indeed both wave and particle in nature. It just so happens that the photons pass through both slits and interfere with each other. This duality of light poses many questions for other particles like that of electrons.

Single And Double Slit Pattern
Credit: Image of Single and Double Slit Diffraction and interference pattern  https://en.wikipedia.org/wiki/Double-slit_experiment


Now in present:
In the case of electrons we know for certain that it is a particle in nature, but here is when things start to take an interesting turn of events, electrons also show an interference pattern. And this is when physics starts to make no sense. With light, the photons are particles of relatively no mass, but electrons are different, in the case of electrons passing through the slits if unobserved show an interference pattern but if you keep a detector, then the electrons suddenly start to show their particle nature and the pattern disappears, this means under observation the nature of the particles changed as compared to when it had no observer observing it. This simple yet complex phenomenon is what scientists study under Quantum Mechanics!! 
Fun Fact: Tyndall effect is where light is scattered by particles of colloidal solution. How can particles scatter light? Shouldn't it lead to the fact that light is indeed made of particles? That is exactly the case we have seen countless times how light is also a wave. Thereby we can conclude that the duality of light is not just a made-up quantum effect but it does also exist and can be observed in real life too.
Credit: Observer effect on Interference pattern (electrons)
https://physics.stackexchange.com/questions/766346/how-are-electrons-distributed-on-the-screen-in-the-double-slit-experiment-with-a

Conclusion: While reading this small snippet you might have thought how is this related to space and astronomy, well it is. To understand the vast cosmic darkness you need to first get a grasp of what it is made of. The world around us is made of atoms and subatomic particles and their relation with the macroscopic world is what defines the space around us. While you think more about quantum mechanics and quantum physics here is a problem You might want to solve or at least try finding the solution to on your own. If light is indeed a wave/particle and we emphasize its wave nature how is it propagating in space? And if it is a particle then why does it lack mass like other particles.

Comments

Popular posts from this blog

Floating Rocks: A Quick read on space Rocks!

PHY 101: Vector Integration

PHY-101: Introduction to Vector Calculus