Einstein's General Theory of Relativity | Lecture 1

Leonard Susskind introduces the concept of gravity, highlighting its unique association with the geometric properties of space and time through the general theory of relativity. However, in this lecture, the focus is on Newtonian gravity, which serves as a foundational theory for understanding gravity's further complexities.

Susskind starts with Newton's Laws of Motion, particularly emphasizing F=ma (force equals mass times acceleration) in an inertial frame of reference. He explains the concepts of vector quantities in physics and the conservation of mass in Newtonian physics.

The lecturer elaborates on the vectorial nature of physical quantities and explains that acceleration is the second derivative of position, commonly known as velocity when involving first derivatives. He underscores this with Newton's Laws of Motion.

Galileo's perspective on gravitational motion in a flat Earth approximation (where gravity is constant everywhere) is explored. This leads to the understanding that gravitational forces on an object are proportional to its mass, contrary to electrical forces, for example.

A further discussion on Galileo's experimental insights reveals the principle that in the absence of air resistance, objects will fall at the same rate under gravity, regardless of mass, illustrating a precursor to the equivalence principle.

The equivalence principle is elaborated on, emphasizing that in free fall, the effects of gravity on an object are indistinguishable from being in space. Leonard Susskind emphasizes this undetectability with various thought experiments.

The topic shifts to distinguishing mechanical effects in gravity, noting that the presence of a homogeneous gravitational field cannot be detected by mechanical means alone. Instead, external reference points or instruments are needed.

Susskind reiterates the independence of gravitational and electrostatic forces by exemplifying the lack of an equivalent universal force law for the latter, unlike gravity's mass-proportional force law.

Newton's law of universal gravitation is mathematically discussed, stressing the inverse square law for gravitational force. The smallness of the gravitational constant illustrates why gravity seems weak compared to other fundamental forces.

Susskind addresses common misconceptions about gravity's strength by illustrating its relative weakness compared to electrostatic or magnetic forces, reinforcing the importance of the universal attraction inherent in gravity.

The mathematical form of Newton’s law involving multiple masses and forces is introduced. The lecturer explains how gravitational forces aggregate in systems and how this leads to the derivation of the gravitational field concept.

A detailed explanation of how gravitational forces are summed across multiple interacting objects is provided, emphasizing that gravitational acceleration is independent of the test particle’s mass.

Susskind delves into the nature of tidal forces as a result of non-uniform gravitational fields and their effects on objects, using vivid analogies of stretching and compressing to explain astronomical interactions.

The discussion highlights real-world applications, addressing how gravitational fields impact stress and strain on bodies. This includes speculating on historical calculations such as lunar tides caused by gravitational interactions.

Through the concept of a gravitational field, the nature of gravitational interactions is explored further, illustrating how test particles can help visualize the field's effects and influence on different masses.

The mathematical framework for analyzing gravitational fields using Gauss's theorem is introduced. This involves divergence in vector fields, essential for understanding field spread and gravitational potential.

The concept of divergence is clarified through fluid dynamics analogies, helping illustrate how field lines and matter interact through divergence or convergence principles.

Susskind explains Gauss's theorem, which relates the behavior of vector fields over volumes to their behavior on surfaces, bridging mathematical theory with gravitational field computations.