[AntonioLao]

Georg Friedrich Bernhard Riemann (1826-66), within the short lifespan of 40 years, had achieved what 400 years of mathematicians cannot. Starting from his doctoral thesis at age 25, which is the foundation of complex analysis, he had written numerous foundational papers including what is to be the beginning of spacetime mathematics. The title of this particular paper is ‘On the Hypotheses which lie at the Bases of Geometry’. http://www.emis.de/classics/Riemann/WKCGeom.pdf He would have been the first to formulate the principle of general relativity but unfortunately his life was cut short by tuberculosis.

Roughly ten years after his death, the English mathematician William Kingdon Clifford, one of the few who realized the significance of Riemann’s opus, responded to the task of translating his papers into English. The rest of this story is history.

Although Riemann’s paper only talked about n-ply extended magnitude of space and manifold, his n-ply extended magnitude can easily and logically be applied to time. This is possible if and only if it is agreed that time, like space, can also be multidimensional. Furthermore that the multiple dimensions of time can only be found at the infinitesimal region of space, and this tiny region of space and time can truly be called a region of spacetime. The quantization of spacetime is a necessary outcome when both time and space are attributed with directional properties given by definitions of their respective unit vectors (and to satisfy the continuum hypothesis, these unit vectors become the null vectors when viewed globally). These spacetime quanta could never have been more lucidly described than by reading Max Jammer’s book ‘Concepts of Space: The History of Theories of Space in Physics’, 3rd and enlarged edition, pages 162-63, Dover, 1993.

[mkirkpatrick]

Interesting thread starter Antonio,if we know where space time begins,do we then know
where it ends? Or are they all an illusion?



regards michael.

[AntonioLao]

Originally Posted by mkirkpatrick are they all an illusion

If there is no meeting of events at the same time and the same place then it is an illusion or delusion.

[mkirkpatrick]

Originally Posted by AntonioLao If there is no meeting of events at the same time and the same place then it is an illusion or delusion.

The illusion I feel Antonio is that there are any events to meet?




regards michael

[AntonioLao]

Originally Posted by mkirkpatrick is that there are any events to meet?

In dreams I could meet and talk to people that are already dead.

[mkirkpatrick]

Originally Posted by AntonioLao In dreams I could meet and talk to people that are already dead.

That's right Antonio,its just that then you might well find out,that "they" are more alive
than you are?




warm regards michael.

[neutralino]

Originally Posted by AntonioLao He would have been the first to formulate the principle of general relativity but unfortunately his life was cut short by tuberculosis.

Not sure I agree with you on this point. Yes, Riemann invented the tools for the study of general relativity, but he was a pure mathematician. I'm not sure whether he would have made the conceptual leap that Einstein did in identifying the curvature of spacetime with gravity.

[AntonioLao]

Originally Posted by neutralino he was a pure mathematician

He could have been one of the greatest physicists if his health allowed him to live longer.