TY - JOUR
T1 - Loop special relativity
T2 - Kaluza-Klein area metric as a line element for stringy events
AU - Davidson, Aharon
AU - Barkai, Nadav
N1 - Publisher Copyright:
© 2024 American Physical Society.
PY - 2024/7/15
Y1 - 2024/7/15
N2 - Let a physical event constitute a simple loop in spacetime. This in turn calls for a generalized loop line element (=distance2 between two neighboring loops) capable of restoring, at the shrinking loop limit, the special relativistic line element (=distance2 between the two neighboring centers-of-mass, respectively). Sticking at first stage to a flat Euclidean/Minkowski background, one is led to such a preliminary loop line element, where the role of coordinates is played by the oriented cross sections projected by the loop event. Such cross sections are generically center-of-mass independent, unless (owing to a topological term) the loop events are intrinsically wrapped around a Kaluza-Klein-like compact fifth dimension. Serendipitously, it is the Kaluza-Klein ingredient which, on top of its traditional assignments, is shown to govern the extension of the Pythagoras theorem to loop space. Associated with M4 - S1 is then a ten-dimensional loop spacetime metric, whose four-dimensional center-of-mass core term is supplemented by a six-dimensional Maxwell-style fine structure. The imperative inclusion of a positive (say Nambu-Goto) string tension within the framework of loop special relativity is fingerprinted by a low periodicity breathing mode. Nash global isometric embedding is conjectured to play a major role in the construction of loop general relativity.
AB - Let a physical event constitute a simple loop in spacetime. This in turn calls for a generalized loop line element (=distance2 between two neighboring loops) capable of restoring, at the shrinking loop limit, the special relativistic line element (=distance2 between the two neighboring centers-of-mass, respectively). Sticking at first stage to a flat Euclidean/Minkowski background, one is led to such a preliminary loop line element, where the role of coordinates is played by the oriented cross sections projected by the loop event. Such cross sections are generically center-of-mass independent, unless (owing to a topological term) the loop events are intrinsically wrapped around a Kaluza-Klein-like compact fifth dimension. Serendipitously, it is the Kaluza-Klein ingredient which, on top of its traditional assignments, is shown to govern the extension of the Pythagoras theorem to loop space. Associated with M4 - S1 is then a ten-dimensional loop spacetime metric, whose four-dimensional center-of-mass core term is supplemented by a six-dimensional Maxwell-style fine structure. The imperative inclusion of a positive (say Nambu-Goto) string tension within the framework of loop special relativity is fingerprinted by a low periodicity breathing mode. Nash global isometric embedding is conjectured to play a major role in the construction of loop general relativity.
UR - http://www.scopus.com/inward/record.url?scp=85199011573&partnerID=8YFLogxK
U2 - 10.1103/PhysRevD.110.026011
DO - 10.1103/PhysRevD.110.026011
M3 - Article
AN - SCOPUS:85199011573
SN - 2470-0010
VL - 110
JO - Physical Review D
JF - Physical Review D
IS - 2
M1 - 026011
ER -