Imagine a particle of mass m, constrained to move along the x-axis, subject to some specified force F(x, t). The program of classical mechanics is to deter- mine the position of the particle at any given time: x(t). Once we know that, we can figure out the velocity (\( v=\frac{dx}{dt}\) ), the momentum (p = mv), the kinetic energy ( \( T=\frac{1}{2}mv^2 \) ), or any other dynamical variable of interest. And how do we go about determining x(t)? We apply Newton's second law: F = ma. (For conservative systems the only kind we shall consider, and, fortunately, the only kind that occur at the microscopic level---the force can be expressed as the derivative of a potential energy function, \( F=-\frac{\partial V}{\partial x} \) , and Newton's law reads \( m\frac{d^2x}{dt^2}=-\frac{\partial V}{\partial x} \) .) This, together with appropriate initial conditions (typically the position and velocity at t 0), determines x(t). Quantum mechanics approaches this same problem quite differentl
The Prophet Muhammad (peace be upon him) said, "Islam is built upon five pillars; bearing witness that there is no god but Allah, and Muhammad is the Messenger of Allah, establishing the prayer, giving zakat, fasting in Ramadan, and performing the pilgrimage to the House of Allah."
The Pillars of Islam are the obligatory acts of worship for every Muslim. One's Islam is not considered complete unless they believe in the obligation of these pillars and practice them all, as Islam is built upon them. Therefore, they are referred to as the Pillars of Islam.
The First Pillar: The testimony 'Lā ilāha illallāh' and 'Muḥammad rasūlullāh'
Allah the Almighty has stated,"
"Therefore, know that there is no deity worthy of worship except Allah." [Muhammad/47: 19]
Allah the Almighty also says,
"Indeed, there has come to you a Messenger from among yourselves. Grievous to him is what you suffer; [he is] concerned over you and to the believers is kind and merciful." [At-Taubah/9:128]
The meaning of the testimony "Lā ilāha illallāh" is that there is no true deity except Allah.
The meaning of the testimony "Muḥammad rasūlullāh" is to obey what he commanded, believe in what he conveyed, refrain from what he prohibited and warned against, and worship Allah only in the manner prescribed by him.
The Second Pillar: Performing the Prayer
Allah the Almighty has stated,"
"And establish the prayer." [Al-Baqarah/2:110]
Performing the prayer means observing it according to the manner prescribed by Allah the Almighty and as taught to us by His Messenger, Muhammad (peace be upon him).
The Third Pillar: Giving Zakat
Allah the Almighty has stated,
And give the Zakat." [Al-Baqarah/2:110]
Allah Ta’ālā decrees Zakat as a test of a Muslim's sincerity in faith, as an expression of gratitude towards their Lord for the wealth bestowed upon them, and as a means to aid the poor and needy.
Giving Zakat entails bestowing it upon those who are rightfully entitled to receive it.
The definition of Zakat is the obligatory right upon wealth once it reaches a certain threshold, then it is distributed to eight categories of recipients as mentioned in the Noble Qur'an, including the poor and needy.
The wisdom behind fulfilling Zakat is to manifest compassion, purify the character and wealth of a Muslim, bring joy to the hearts of the impoverished, and strengthen the bonds of love and brotherhood among fellow members of the Muslim community. Therefore, a virtuous Muslim will give it willingly and feel joyous in doing so, knowing that they bring happiness to others.
The rate of Zakat on wealth is 2.5% of the stored wealth in the form of gold, silver, money, and traded commodities for profit, if the value of the wealth reaches a specified amount and has been held for a full year.
Zakat is also obligatory on those who own specific livestock (camels, cows, and sheep) in a certain quantity, provided that the animals graze on natural vegetation for most of the year without being fed by their owner.
Additionally, Zakat is mandated on agricultural produce such as grains, fruits, mining products, and treasures if they reach a certain quantity.
The Fourth Pillar: Fasting during the Month of Ramadan
Allah the Almighty has stated,
"O you who have believed, decreed upon you is fasting as it was decreed upon those before you that you may become righteous." [Al-Baqarah/2: 183]
Ramadan, the ninth month in the Islamic lunar calendar, holds profound significance for Muslims worldwide. It is revered and distinguished among all other months. Observing a month-long fast during Ramadan is one of the five pillars of Islam, signifying the core principles and practices that every devout Muslim adheres to. This sacred month is an opportunity for believers to demonstrate their devotion, self-discipline, and spiritual reflection. It is a time for heightened acts of worship, increased acts of charity, and a deeper connection with the Quran, ultimately fostering a stronger sense of faith and righteousness.
Fasting during Ramadan is a form of worship to Allah that involves self-restraint from anything that nullifies it, from dawn until sunset, throughout the blessed month of Ramadan. During this period, Muslims abstain from food, drink, marital relations, and other activities that could break the fast, as a sign of devotion and loyalty to Allah. This practice reflects a deep commitment to cultivate spiritual qualities, strengthen self-discipline, and increase awareness of religious values and piety. By fasting during Ramadan, Muslims experience spiritual growth and draw closer to God in a state of sincerity and earnestness.
The Fifth Pillar: Performing the Hajj to the House of Allah
Allah the Almighty has stated,
Performing the Hajj pilgrimage to the House of Allah is a duty owed to Allah by all who can make the journey." [Ali 'Imran/3:97]
The obligation of performing the Hajj applies once in a lifetime for those who have the means to travel to the House of Allah.
The essence of the Hajj pilgrimage is to visit the Kaaba and the sacred sites in Makkah Al-Mukarramah to perform specific rituals at designated times. Prophet Muhammad (peace be upon him) undertook the Hajj, following the tradition of the prophets before him who also performed this sacred pilgrimage. The Hajj is a profound spiritual journey that signifies unity, submission to Allah's command, and a reaffirmation of the faith's fundamental principles. It serves as a powerful reminder of the ultimate goal of every Muslim's life - seeking closeness to Allah and striving for righteousness. This sacred journey leaves an indelible mark on the heart and soul of the pilgrim, fostering a deeper connection with the divine and a renewed sense of purpose in their faith journey.
Allah commanded Ibrahim (peace be upon him) to proclaim the call for Hajj to all of humanity, as mentioned by Allah the Almighty in the Noble Qur'an. Allah says,
And proclaim to the people the Hajj; they will come to you on foot and on every lean camel; they will come from every distant pass.
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