PHY 101: Vector Integration

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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...

Exploring the Origin of the Universe: Unraveling the Big Bang Theory

Have you ever pondered the origins of the universe? The questions surrounding its inception, the unfolding of events, and the nature of its boundaries are thought-provoking and complex. Let's embark on a captivating exploration, step by step, beginning with the momentous revelation of the Big Bang theory.

The Red-Shifted Spectra: A Glimpse into Cosmic Motion

In the 1920s, scientists embarked on an astronomical journey that would revolutionize our understanding of the cosmos. Through the study of star spectra, researchers unveiled a significant phenomenon: redshift. As galaxies' spectra exhibited redshifts, indicating their movement away from us, a new perspective emerged. This revelation challenged the prevailing static model of the universe.

Hubble's Revelation and Cosmic Expansion

The findings of astronomer Edwin Hubble lent credence to the dynamic nature of the universe. His meticulous observations and calculations showcased a consistent pattern: the redshift of galaxies increased proportionally with their distance from us. This monumental discovery shattered the static universe paradigm, sparking a seismic shift in our comprehension of cosmic affairs.

Alexander Friedmann's Bold Assumptions

Amid this intellectual upheaval, Alexander Friedmann proposed audacious assumptions that laid the foundation for a new cosmological paradigm. He posited two key assertions: the universe's homogeneity (uniformity in all directions) and isotropy (uniformity throughout space). Though these assumptions don't hold entirely true, they offer a broader-scale framework for understanding the cosmos.

Cosmic Microwave Background Radiation (CMBR): Echoes of the Big Bang

In parallel with Friedmann's work, the discovery of Cosmic Microwave Background Radiation (CMBR) provided compelling evidence for the expanding universe. This residual radiation echoed the initial stages of the universe's evolution, further bolstering the arguments set forth by Friedmann. The harmonious synergy between theory and observation solidified the shift toward an expanding universe perspective.

Pondering the Center and Boundaries

As the concept of an expanding universe took hold, a tantalizing question emerged: Where is the center of the universe? Analogous to a balloon expanding, the notion of a central point evoked curiosity. However, exploring this question led to complex discussions involving boundaries, non-boundary conditions, and the nature of space-time curvature.

Friedmann's Model and the Singular Starting Point

Friedmann's models, although simplified, offered intriguing possibilities about the universe's fate. The common thread across these models was the notion of starting from a state of zero separation. This implied an infinitesimally dense and curved space-time, ultimately culminating in a singular point—a primordial moment of immense energy and expansion: the Big Bang.

Conclusion:

The journey through the universe's origins takes us from the red-shifted spectra of galaxies to the profound assumptions of Alexander Friedmann. With Cosmic Microwave Background Radiation affirming the expanding universe, the paradigm shift was undeniable. While questions remain about the universe's center and boundaries, one thing is certain: the concept of the Big Bang, a monumental explosion of energy and expansion, has forever transformed our perception of existence.

Comments

  1. Cosmos is something which is always very complex to understand but this blog gave me the first hand information about it. Very good information detailed in a very short manner. Keep posting and keep sharing more on this subject matter.

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