Newton and Einstein

Modern physics began with Isaac Newton's work on Classical Mechanics and the Universal Law of gravitation,

F = -GM₁M₂/|R|².

Newton provided the physical foundation for Kepler's 3 Laws of Planetary Motion ending a long chapter in the development of modern science (an exercise that stretched over 2,000 years). Today, Newton's laws and ideas are still valid when applied in the right situations; the astronauts were put on the Moon using Newton's laws.

Newton's Laws can, however, break down. Newton's laws have problems when objects travel at high speeds close to the speed of light, c (=300,000 km/s), and in the vicinity of strong gravitational fields.

Newton's laws break down because Newton assumed that events happen in rigid backgrounds of space and time where space is flat (unforced objects travel in straght lines) and time runs at the same rate everywhere (which means that speeds add). For example,

However, if the speeds are close to c, things change dramatically.

This is odd and can be true only if time runs differently for the different observers. Moving clocks run more slowly than stationary ones. These effects are part and parcel of Einstein's Theory of Special Relativity.

Special Relativity is based on two assertions:

• light travels at speed c for all inertial observers
• the laws of physics appear the same in all inertial frames

Einstein extended Special Relativity with the General Theory of Relativity (GR). In GR, accelerations are considered and gravity is not a force. (The effects of gravity can be mimiced using accelerated frames. This notion is embodied in the Principle of Equivalence.)

Einstein envisioned that when mass is embedded in space-time, it alters the shape of the Universe.

So, as objects move they follow paths defined by the local geometry of the space-time. They do not feel a force due to the embedded mass; the path they follow is curved because the space-time is curved.

In this world, the path of a light ray (or any particle) bends in a gravitational field --MACHOS, lensing, and black holes. This picture of how gravity works leads to some other interesting (and bizarre) situations (worm holes and Time Travel)!

Is GR correct? Tests of GR:

• Bending of starlight--yes
• The periastron advance of the orbit of Mercury--yes
• The gravitational redshift--yes

The above tests are for conditions where the mass that distorts space-time, and hence produces the gravitational effects, is not moving. The curvature is thus not changing with time. As a dynamic test, consider the following.

People posed the question of what happens if the embedded masses are in accelerated motion. In particular, what happens to the strength of gravity and how are these changes transmitted from the moving mass around the Universe? The suggestion is that gravitational waves are produced that play the same role electromagnetic radiation plays in transmitting the information that electric charges are in accelerated motion.