They could not be same if one followed the conventional processes of scattering with point-like particles. But, if assumed that such structures were formed from string motion into space-time, then the figures would become topologically equivalent. This idea was proposed by Veneziano in 1968 and Yoichiro Nambu in 1970. This new idea did not gain much attention during that time, but in 1980’s, the weaknesses of super-symmetry and the failure of the standard model to unify gravity led to the reintroduction of string theory in a new form - the Superstring. Superstring Theory is a background based theory and needs the presence of a background space which can be perturbed by small amounts to study the effects. This theory has successfully unified gravity with quantum mechanics, but has some strange characters like having so many dimensions. A very successful result of the theory is that gravity is a consequence of low energy vibration of strings. Edward Witten, the leading string theorist, considers it the most beautiful consequence of the theory. The higher dimensions in string theory are embedded in our universe themselves in small loops. Every coordinate in the four dimension universe contains a structure which contains the extra dimensions.

Another very important theory is that of Loop Quantum Gravity Theory. This theory considers a discrete nature of space-time at a level known as Planck Scale. Max Planck had considered a scale in which speed of light, Planck’s constant and gravitational constant are 1. The unit of length in such a scale comes out to be around 10^-34 metres and the unit of time, 10^-43 seconds. It is easy to derive that Planck length = Ö(Gћ/c³).

While analyzing the relation between the actions of relativity and of quantum level, it was found that they became equivalent at the level of Planck scale. It is impossible to study the effect of gravity without introducing the quantum principles below this level. In loop quantum gravity, at Planck level, the world becomes quantized or composed of loops. There is no background space; space is almost absent there and the whole metric is present in the form of dirac-delta function on these loops. It was found that these Planck scales must be invariant under Lorentz transformation, which was not allowed under relativity (length contraction). So a new theory, Doubly Special Relativity, had to be introduced where there were two invariants instead of one - the Planck length and the speed of light. With these two invariants, a new form of relativity theory has emerged with a better promise of a ‘final law’. The leading theorist, Lee Smolin, has played a very vital role in developing the theory. He openly criticizes the very abnormal characteristics of string theory (a big reason why it has still been impossible to experimentally verify it) and considers this a very big drawback of the theory, even after the theory’s incredible success. The new experimental accelerator (Large Hadron Collider), being built in CERN, holds the promise of unveiling new mysteries of the world and observing many still mysterious particles like the Higgs Boson (a particle which  attributes mass to every other particle). A few years ago (end of 1980’s), a very powerful particle accelerator (Superconducting Super Collider) was proposed to be built, which would put an end to almost all the troubles (it had enough energy to produce the Higgs Boson). But, thanks to the government’s budget policies, it was never built; Steven Weinberg, in his book ‘Dreams Of A Final Theory’, has given a clear account of the issue (he was among the persons trying to persuade the government to pass the bill). The estimated cost of production had reached 12 billion dollars and the project was finally cancelled because the US could not afford this cost as well as the cost of NASA’s research (again, Einstein’s realm came in the path of quantum development).

Stephen Hawking is working similarly to develop something called the Euclidean Quantum Theory. Here, Riemannian manifold (the manifold in which the metric signature is always positive) is used instead of pseudo-Riemannian manifold (in which the metric signature may be negative or zero, like in Minkowski space). This is based on the concept of Wick Rotation. Wick rotation converts Minkowski space in Euclidean space by just making the time complex. It yields surprising result, with quantum mechanical equations, which becomes very much like the equations of statistical mechanics under Wick rotation. You can consider the universe to be made up of five dimensions, with two dimensions of time (real and imaginary). So, time is complexified and a simple rotation from our Minkowski world, lying on real time axis, to imaginary time axis will do the job.

Another theory is the Non-Commutative Geometry where the geometry is non-commutative. The metric tensor which is generally used is assumed to be symmetric and hence, follows the commutativity rule (g_ij = g_ji ). But, it is possible to have geometries where this assumption is dropped. In non-commutative geometry, the algebra defining the properties of various quantities on the manifold looses commutativity.

These theories have been able to come up as promising theories of quantum gravity, but they do not seem to care much about the problems of the interpretation of quantum mechanics. A complete theory must have this property because more than having a theory which has both quantum mechanics and relativity theory as its consequences, it is necessary to have something which can explain everything - not just the interactions. Now, the quantum state reduction is no longer the problem of quantum mechanics alone. Even gravitational energy has much to do with it. Also, the mysterious dark matter and dark energy need the explanation. Many other recently observed phenomena need explanations (like a very recent observation of change in the speed of light). Probably, we must wait for more experimental data (like those from Large Hadron Collider); who knows, may be, another Michelson-Morley experiment is going to take place for another clerk in some far away land.