Dr Phill’s Science Made Simple

Relativity

Relativity has a reputation of being a difficult subject. Yes, the mathematics required to describe the general theory involves difficult differential geometry. It is possible to describe the concepts of relativity without complex mathematics.

Some of the concepts cen be difficult to grasp. They are often taught badly which doesn’t help.

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Isaac Newton

Isaac Newton is famous for his laws of motion and laws of gravitation. He and Gotfried Leibnitz independently discovered calculus. Newton used his influence to accuse Leibnitz of plagiarising his ideas. In fact they used different approaches to calculus and it is Liebnitz' notation that is used today.

It is important to state that a law of physics is one or more equations that describe a phenomenon accurately but makes no attempt to explain what or why it happens. Laws are accepted and rarely challenged. A theory of physics e-attempts to eplain what is happeneing and why. A theory is always being challenged and tested by physicists.

Newton’s Laws of Motion

An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line unless acted on by an unbalanced force.
The acceleration of an object depends on the mass of the object and the amount of force applied.
Whenever one object exerts a force on another object, the second object exerts an equal and opposite on the first.

Newton’s Laws of Gravitation

Newton is credited with the first great unification. He said that he was inspired by seeing an apple fall from a tree. He had the idea that a force of gravity caused the apple to fall. He then considered if gravity extended to the Moon. The force of gravity explained the centriptal force required to keep the Moon on orbit around the Earth.

Newton’s law of gravitation, states that any particle of matter in the universe attracts any other with a force varying directly as the product of the masses and inversely as the square of the distance between them.

\[F = \frac{GMm}{r^2}\]

F is the force due to gravity.
G is the gravitational constant.
M and m are the masses of the attracting objects.
r is the distance between the masses.

An apple falling from a tree experiences the force of gravity and accelerates. This means that it must be gaining kinetic energy. Newton reasoned that as energy has to be conserved, the kinetic energy must come from the gravitational field. This is called gravitational potential energy U at ditance r from the centre of mass M.

\[U = -\frac{GMm}{r}\]

For an object of mass m at height h from the Earth’s surface where the acceleration due to gravity at the Earth’s surface is g.

\[U = mgh\]

This states that work has to be done to lift an object against gravity to give it potential energy.

Newton’s law of gravitation is very accurate in most circumstances.

Reformulation and Issues

Now restate the law of gravitation adding an assuption that was assumed.

Time passes at the same rate everywhere.
Gravity is an attractive force between masses.
Objects have gravitational potential energy that beomes kinetic energy when they fall.

This very accurately describes gravity because it is in fact a very good approximation to what is actually happening.

There are a number of questions about the law.

Time doesn’t pass at the same rate everywhere. Atomic clocks run faster at higher altitudes, and slower if moving at higher speeds.
What causes the gravitational force and how is it transmitted?
When a meteorite falls to Earth, where did it get its potential energy?