I know for most people this will bee too abstract, nevertheless ....
Today my new paper appeared on arxiv.org: On Conformal Infinity and Compactifications of the Minkowski Space
The story is this: studies the electromagnetic field and of the properties of light, which is close to what we think of as "pure energy", led Albert Einstein to his Special Theory of Relativity (STR). STR deals with uniform relative motions of reference frames. But in fact Maxwell's equations lead us naturally beyond STR - they have also the same form for uniformly accelerated motions. Einstein did not go there. He went straight into his General Relativity - a theory of (almost) arbitrarily moving observers. And yet he may have missed something. String theorists nowadays talk a lot about "conformal field theory". This is related to the avenue that Einstein has neglected. My paper deals with some special aspects of this avenue. Studying uniform accelerations (more precisely: conformal group of motions) we are led to the natural idea that our flat spacetime is not that flat. It has a real "infinity", like a "cap", which is not just a point, but which has its own structure. We may even have a natural doubling of both spacetime and infinity. Perhaps a separate world where matter reigns and another one for antimatter. Both are connected by the "infinity door".
So, here is a pictorial representation of this door taken from my new paper:
The two infinities have one common point in the middle, and they connect to the two worlds through the spherical doors indicated on the left and on the right.
(Of course, for the pictorial representation I had to skip one dimension.)
Today my new paper appeared on arxiv.org: On Conformal Infinity and Compactifications of the Minkowski Space
The story is this: studies the electromagnetic field and of the properties of light, which is close to what we think of as "pure energy", led Albert Einstein to his Special Theory of Relativity (STR). STR deals with uniform relative motions of reference frames. But in fact Maxwell's equations lead us naturally beyond STR - they have also the same form for uniformly accelerated motions. Einstein did not go there. He went straight into his General Relativity - a theory of (almost) arbitrarily moving observers. And yet he may have missed something. String theorists nowadays talk a lot about "conformal field theory". This is related to the avenue that Einstein has neglected. My paper deals with some special aspects of this avenue. Studying uniform accelerations (more precisely: conformal group of motions) we are led to the natural idea that our flat spacetime is not that flat. It has a real "infinity", like a "cap", which is not just a point, but which has its own structure. We may even have a natural doubling of both spacetime and infinity. Perhaps a separate world where matter reigns and another one for antimatter. Both are connected by the "infinity door".
So, here is a pictorial representation of this door taken from my new paper:
The two infinities have one common point in the middle, and they connect to the two worlds through the spherical doors indicated on the left and on the right.
(Of course, for the pictorial representation I had to skip one dimension.)
If it's not possible, no worries!