# A2 OCR B Advancing Physics Coursework - Research and Report - The development of a Theory of Gravity

The development of a Theory of Gravity.

What’s behind it and where does it stand in relation to the other forces?

Abstract:

The Theory of Gravity has been transformed through the last century, from an original and important classical framework to more recent relativistic and then quantum interpretations, eventually culminating in a specific requirement to link it all together with the other forces and create a unified theory of everything. The search for unification is currently very much dependent upon experimentation and raises questions as to the scientific validity of String Theory and whether it exists as science or philosophy – or indeed just an elegant, but meaningless, example of mathematical aesthetics.

1. Introduction

The ultimate goal for physicists is to devise a unified theory, which describes the universe all in one go. However, this proves difficult – there are partial theories which do not fit together, each predicting a limiting number of observations and neglecting others. Nevertheless the Standard Model exists as a framework for the coming together of partial theories.

1.1 The Basics of the Standard Model

In matter there appears to be four basic forces at work. Gravity is the weakest of the four but acts over great distances, binding stars and galaxies together. The electromagnetic force is stronger and is responsible for holding atoms and molecules together. As with gravity, its range is infinite. The weak force and strong force are, by contrast, limited in range, and operate only within the dimensions typical of an atomic nucleus. The weak force causes certain forms of radioactivity and underlies the nuclear fission reactions in the Sun. The strong force binds quarks and antiquarks together within the particles we observe. It seems to act in such a way that quarks are always locked inside more complex particles and are never observed on their own.1

The Standard Model incorporates quarks and leptons as well as their interactions through the strong, weak and electromagnetic forces. Gravity alone remains outside this model.

1.2 What’s wrong with Gravity?

The problem with Gravity is that through the development of its theory, its existence in situations of different scale is neglected. Newton proposed the first, classical, theory of gravity - but it failed to address some things – allowing crucial prediction but never offering an answer to why or how the universe worked like this. Einstein explained that Newton could provide only an approximation, revolutionising understanding with the theory of General Relativity. But he couldn’t explain what happened at a subatomic level, which is where quantum mechanics is applied. But quantum mechanics and general relativity are incompatible – the major aim in physics today being to develop a model for gravity which incorporates them both.2

2. Newton’s Theory of Gravity

An apple falls off a tree, landing on the head of a notable polymath - thus knocking the theory of universal gravitation right into the forefront of a brain otherwise contemplative of the nice weather for the time of year. Perhaps not, but in 1666, whatever the relevance of the popularised apple anecdote, Isaac Newton questioned why objects fall perpendicularly to the ground. What caused this downwards acceleration and was it the same for the rest of the universe?

2.1 Newton’s thought Experiment

Newton’s famous thought experiment, used to hypothesise that gravitation was indeed universal, became the key for predicting planetary motion. In the experiment a cannonball is fired from the top of a very tall mountain. If there is no gravity the cannonball would continue in a straight line, but as with the apple - this is not the case. The greater the velocity with which the cannonball is fired, the further it travels before hitting the ground – this effect being compounded as the surface of the Earth curves away under the flight of the cannonball. If the speed of the ball is equal to the threshold orbital velocity, it will continue circling the planet, like the moon. The constantly changing velocity (due to circular motion) means the object is accelerating. 3

2.2 Application of the Inverse Square Law

Formulated by Isaac Newton, the inverse-square law states that the force of gravity diminishes with the square of the distance between the source of gravity and the object being attracted. If you move twice as far away from the Earth, for example, only one-quarter as much gravitational pull will be felt. The inverse square law already stood for describing how light energy spread out from a source over increasing distances, but Newton applied this to the acceleration of the moon.

From the equation:

The acceleration of the moon towards the earth could be calculated. If the orbit time is 2.35 x 106s, and the distance (circumference of orbit) is 24.1 x 108m, simply using the fact that speed is distance divided by time, the velocity 1020ms-1 is calculated. This value squared and divided by radius 3.84 x 108m gives an acceleration of 0.0027ms-2. 4

Using the information that the radius of the Moon’s orbit is approximately 60 times the radius of the Earth, the acceleration due to gravity of an object falling towards Earth (9.81ms) should be 602 times the acceleration of the moon if the inverse square law can be extended to universal gravity. This is indeed the case as 9.81ms-1 divided by 602 is also 0.0027ms-2. The same equations could also be used to predict the orbit time correctly. Mathematical proof could back the concept of universal gravity with the existence of a universal gravitational constant, G. 4

Proposing that a universal force of gravitation F existed between any two masses, m1 and m2, directed from each to the other, proportional to each of them and inversely proportional to the square of their separation distance r, the following formula was created:

2.3 Prediction vs. observation

The universe was to be predicted like clockwork. However Newton was not entirely correct. Laboratories such as the McDonald Observatory in Texas have been gathering data ever since “retro-reflector” packages were placed on the moon in the 1969 Apollo 11 first manned lunar landing. The McDonald Observatory boasts data which can map the orbit of the moon, for example, exact to 1-3cm. But as this data improves in quality it becomes more obvious that Newton’s calculations are ultimately an approximation – calculations are out of synch by around 10 metres. 2

3. Einstein’s Theory of Relativity

At the time, Einstein did not have such observational data available to see the discrepancies between Newton’s predictions and the actual observations made, but he postulated using Special Relativity that Newtonian Laws of Motion break down at velocities approaching the speed of light. The Theory of General Relativity explains that Newton’s Law of Gravitation is also only approximately correct, breaking down in the presence of very strong gravitational fields.