1. The theory must be "Relativistic". It must incorporate fully at every step Einstein's SPECIAL THEORY OF    RELATIVITY. This requirement stems from the fact that there is overwhelming supportive observational evidence all through physics that shows that nature does obey the laws laid down in this model.

2. The theory must incorporate the Principles of QUANTUM PHYSICS, again because there is overwhelming evidence that on the atomic, nuclear and elementary particle level physics is governed by quantum mechanics, a modification of the usual classical mechanics of moving objects that takes into account that our knowledge about the motion of objects depends on our ability to measure location and velocity of the object but that such measurement itself influences the behavior of the object and degrades previously acquired knowledge, leading to a probability description of the behavior of atomic and subatomic particles.

3. The Theory must satisfy a number of SYMMETRIES. That means, the equations that describe the behavior of the particles and forces between them must have structures that reflect the fact that in all processes between particles certain quantities remain CONSERVED.

In searching for general descriptions of all possible processes in science we orient ourselves on those aspects that do NOT change during the process. That strategy selects from an infinity of conceivable processes a subset of processes that can actually occur, satisfying the constraints imposed by CONSERVATION LAWS. What these conserved quantities are is derived from millions of observations of individual processes .

EINSTEIN's SPECIAL THEORY OF RELATIVITY provides a general scheme that allows to classify and write down all possible equations of motion for point like particles that are characterized by the mass of the particle and its SPIN, in the absence of any interactions between the particles.

The main task then was to find the right theories for these particles, including the proper description of their interactions, based on some Symmetries that reduce a conceivable infinity of possible force laws to the four we actually observe.

In 1954 YANG and MILLS discovered a general class of symmetries called LOCAL GAUGE SYNMMETRIES that automatically led to the correct mathematical description of the four forces. This unique principle, how nature structures forces represents a powerful principle of unification and led to the rapid development of the TREE of THEORIES, with ever more comprehensive and more unified description of particles and forces.

THERE WERE TWO PERSISTENT PROBLEMS throughout the development of these theories:

1. It appeared impossible to construct a theory of gravitation that incorporates fully the quantum principles in its relativistic form.

2. All Theories were plagued by calculational difficulties. Detailed calculations of collision processes between particles always seem to lead to infinite exchange energies in the process.

Each of these problem areas stimulated further developments. I will make some brief comments on each of these to indicate how these difficulties directed the further development.

THE PROBLEM OF QUANTUM GRAVITATION
This problem arises from the discordant description of gravitation as curvature of space in Einstein's theory of General Relativity and as the exchange of energy quanta in the quantum description, like in the theories for the other interactions. The suggestion arose: could one perhaps view and describe all forces in terms of curvature and is a quantum theory of curved spaces possible?

Already in 1919 Theodor Kaluza had introduced a fourth space dimension into Einstein's theory in addition to the three usual space dimensions. He had shown that in this way one could describe the gravitational and the Electromagnetic force in a unified way, both in terms of curvature.

But in the real world we see only three space dimensions, not four. So, what to do about that? From a far away distance a water pipe looks like a one-dimensional line. Only when one looks closely and makes a cross section of this line one can see that there is one large dimension extending along the pipe, and that there is a second dimension curled around this one direction making the interior of the pipe into a long stretched out space. The second extra dimension is "compactified" into a circle. Similarly it was assumed that the extra dimension in Kaluzas theory must be compactified to such small size that in all experiments one makes this dimension is too small to actually see. But it manifested itself as being the conveyor of electromagnetic signals.

This idea was revived in 1984. It was shown that, in order to represent all four forces in terms of space curvature one needed a total of eleven dimensions,

- one time dimension

- three extended dimensions for our ordinary space

- seven curled-up, compacted dimensions to represent the other three forces

In the figure below is shown a two-dimensional extended slightly curved space with additional two curled-up dimensions at each space point. We will see shortly how this idea got incorporated into our new way of visualizing the universe.

The quark or electron, up to this day, still looks point like in experiments. Ever larger energy accelerators were built to get closer and closer collisions to happen to perhaps detect that finite size of quarks, electrons, etc. With the largest accelerators built no real evidence of finite size of these particles has been seen yet. Instead, theory began to get ahead of experimentation.