Double special theory of relativity

Double special theory of relativity (DSTO) is a modified special theory of relativity , in which the concepts of Planck energy and Planck length are added. ^[one]

Content

DSTO postulates

The double special theory of relativity postulates that

the principle of relativity is true: all inertial reference systems are equivalent;
There are two quantities independent of the observer:
- speed of light $c$ ${\ displaystyle c}$ ;
- a certain value $\lambda$ ${\ displaystyle \ lambda}$ having the meaning of the Planck length , and at $\lambda \to 0$ ${\ displaystyle \ lambda \ to 0}$ DSTO goes to the service station .

History

The first attempt to introduce a length independent of the observer belongs to Pavlopulo (1967), who estimated it at about 10 ⁻¹⁵ meters. ^[2] ^[3] Giovanni Amelino-Camellia in the context of quantum gravity proposed ^[4] ^[5] what formed the basis of DSTO: Planck length invariance

\ell _{P}={\sqrt {\frac {\hbar G}{c^{3}}}}

{\ displaystyle \ ell _ {P} = {\ sqrt {\ frac {\ hbar G} {c ^ {3}}}}}

≈ 1.616199 (97) ⋅10 ⁻³⁵ m ^[6] ^[7] ^[8] ,

Where:

ħ is the Dirac constant ( h / 2π );
G is the gravitational constant ;
c is the speed of light in vacuum.

In 2001, the proposed idea was reformulated in terms of an observer-independent Planck length. ^[9] It was also shown that there are three modifications of the special theory of relativity, which make it possible to achieve Planck energy invariance either as maximum energy, or as maximum momentum, or both at once. DSTO is possibly related to the theory of loop quantum gravity in spaces with signature $(2;1)$ ${\ displaystyle (2; 1)}$ , either in $(3;1)$ ${\ displaystyle (3; 1)}$ .

Theory Problems

It is worth noting that DSTO has unresolved inconsistencies in the wording. ^[10] ^[11] In particular, it is difficult to restore the standard behavior of macroscopic bodies (“the problem of a soccer ball” ^[12] ). Of the other difficulties, it is worth noting that DSTO is formulated in momentum space . The wording in the coordinate space does not yet exist.

There are other models in which (unlike DSTO) the principle of relativity and Lorentz invariance are violated due to the introduction of privileged reference systems in . As examples, we can mention the effective field theory and the extended theory of the standard model

To date, there are no contradictions in predictions with SRT (see the search for violations in the Lorentz model ). Initially, it was assumed that SRT and DSTO will give different forecasts in the high-energy region, in particular, in estimating the energy of the Graisen – Zatsepin – Kuzmin limit , but this does not happen.

Notes

↑ Amelino-Camelia, G. Doubly-Special Relativity: Facts, Myths and Some Key Open Issues (English) // Symmetry: journal. - 2010 .-- Vol. 2 . - P. 230—271 . - DOI : 10.3390 / sym2010230 . - . - arXiv : 1003.3942 .
↑ Pavlopoulos, TG Breakdown of Lorentz Invariance (Eng.) // Physical Review : journal. - 1967. - Vol. 159 , no. 5 . - P. 1106-1110 . - DOI : 10.1103 / PhysRev . 159.1106 . - .
↑ Pavlopoulos, TG Are we observing Lorentz violation in gamma ray bursts? (Eng.) // Physics Letters B : journal. - 2005. - Vol. 625 , no. 1-2 . - P. 13-18 . - DOI : 10.1016 / j.physletb.2005.08.08.064 . - . - arXiv : astro-ph / 0508294 .
↑ Amelino-Camelia, G. Testable scenario for relativity with minimum length (Eng.) // Physics Letters B : journal. - 2001. - Vol. 510 , no. 1-4 . - P. 255-263 . - DOI : 10.1016 / S0370-2693 (01) 00506-8 . - . - arXiv : hep-th / 0012238 .
↑ Amelino-Camelia, G. Relativity in space – times with short-distance structure governed by an observer-independent (Planckian) length scale (Eng.) // International Journal of Modern Physics D : journal. - 2002. - Vol. 11 , no. 01 . - P. 35-59 . - DOI : 10.1142 / S0218271802001330 . - . - arXiv : gr-qc / 0012051 .
↑ The standard deviation is indicated in parentheses. Thus, the value of the Planck length can be represented in the following forms: $\ell _{P}$ ${\ displaystyle \ ell _ {P}}$ ≈ 1.616199 (97) · 10 ⁻³⁵ m =
= (1.616199 ± 0.000097) 10 ⁻³⁵ m =
= [1,616102 ÷ 1,616296] · 10 ⁻³⁵ m
↑ NIST 's “ Planck length ”, NIST's published CODATA constants
↑ Fundamental Physical Constants - Complete Listing
↑ Kowalski-Glikman, J. Observer-independent quantum of mass (Eng.) // Physics Letters A : journal. - 2001. - Vol. 286 , no. 6 . - P. 391-394 . - DOI : 10.1016 / S0375-9601 (01) 00465-0 . - . - arXiv : hep-th / 0102098 .
↑ Aloisio, R .; Galante, A .; Grillo, AF; Luzio, E .; Mendez, F. Approaching Space Time Through Velocity in Doubly Special Relativity // Physical Review D : journal. - 2004. - Vol. 70 . - P. 125012 . - DOI : 10.1103 / PhysRevD.70.125012 . - . - arXiv : gr-qc / 0410020 .
↑ Aloisio, R .; Galante, A .; Grillo, AF; Luzio, E .; Mendez, F. A note on DSR-like approach to space – time (Eng.) // Physics Letters B : journal. - 2005. - Vol. 610 - P. 101-106 . - DOI : 10.1016 / j.physletb.2005.01.01.090 . - . - arXiv : gr-qc / 0501079 .
↑ The Soccer-Ball Problem

Literature

Amelino-Camelia, G. Doubly-Special Relativity: First Results and Key Open Problems (Eng.) // International Journal of Modern Physics D : journal. - 2002. - Vol. 11 , no. 10 . - P. 1643-1669 . - DOI : 10.1142 / S021827180200302X . - . - arXiv : gr-qc / 0210063 .
Amelino-Camelia, G. Relativity: Special treatment (English) // Nature : journal. - 2002. - Vol. 418 , no. 6893 . - P. 34-35 . - DOI : 10.1038 / 418034a . - . - arXiv : gr-qc / 0207049 . - PMID 12097897 .
Cardone, F. Energy and Geometry: An Introduction to Deformed Special Relativity. - World Scientific , 2004. - ISBN 981-238-728-5 .
Jafari, N. (2006). "Doubly Special Relativity: A New Relativity or Not?". AIP Conference Proceedings 841 : 462-465. DOI : 10.1063 / 1.2218214 .
Kowalski-Glikman, J. Introduction to Doubly Special Relativity // Planck Scale Effects in Astrophysics and Cosmology. - Springer , 2005. - Vol. 669. - P. 131–159. - ISBN 978-3-540-25263-4 . - DOI : 10.1007 / b105189 .
Smolin, Lee. Chapter 14. Building on Einstein // The trouble with physics: the rise of string theory, the fall of a science, and what comes next. - Boston, MA: Houghton Mifflin, 2006 .-- ISBN 978-0-618-55105-7 . Smolin writes for the layman a brief history of the development of DSR and how it ties in with string theory and cosmology .

External sources

DSTO at arXiv.org

[1] Amelino-Camelia, G. Doubly-Special Relativity: Facts, Myths and Some Key Open Issues (English) // Symmetry: journal. - 2010 .-- Vol. 2 . - P. 230—271 . - DOI : 10.3390 / sym2010230 . - . - arXiv : 1003.3942 .

[2] Pavlopoulos, TG Breakdown of Lorentz Invariance (Eng.) // Physical Review : journal. - 1967. - Vol. 159 , no. 5 . - P. 1106-1110 . - DOI : 10.1103 / PhysRev . 159.1106 . - .

[3] Pavlopoulos, TG Are we observing Lorentz violation in gamma ray bursts? (Eng.) // Physics Letters B : journal. - 2005. - Vol. 625 , no. 1-2 . - P. 13-18 . - DOI : 10.1016 / j.physletb.2005.08.08.064 . - . - arXiv : astro-ph / 0508294 .

[4] Amelino-Camelia, G. Testable scenario for relativity with minimum length (Eng.) // Physics Letters B : journal. - 2001. - Vol. 510 , no. 1-4 . - P. 255-263 . - DOI : 10.1016 / S0370-2693 (01) 00506-8 . - . - arXiv : hep-th / 0012238 .

[5] Amelino-Camelia, G. Relativity in space – times with short-distance structure governed by an observer-independent (Planckian) length scale (Eng.) // International Journal of Modern Physics D : journal. - 2002. - Vol. 11 , no. 01 . - P. 35-59 . - DOI : 10.1142 / S0218271802001330 . - . - arXiv : gr-qc / 0012051 .

[6] The standard deviation is indicated in parentheses. Thus, the value of the Planck length can be represented in the following forms: $\ell _{P}$ ${\ displaystyle \ ell _ {P}}$ ≈ 1.616199 (97) · 10 ⁻³⁵ m =
= (1.616199 ± 0.000097) 10 ⁻³⁵ m =
= [1,616102 ÷ 1,616296] · 10 ⁻³⁵ m

[7] NIST 's “ Planck length ”, NIST's published CODATA constants

[8] Fundamental Physical Constants - Complete Listing

[9] Kowalski-Glikman, J. Observer-independent quantum of mass (Eng.) // Physics Letters A : journal. - 2001. - Vol. 286 , no. 6 . - P. 391-394 . - DOI : 10.1016 / S0375-9601 (01) 00465-0 . - . - arXiv : hep-th / 0102098 .

[Aloisio2004-10] Aloisio, R .; Galante, A .; Grillo, AF; Luzio, E .; Mendez, F. Approaching Space Time Through Velocity in Doubly Special Relativity // Physical Review D : journal. - 2004. - Vol. 70 . - P. 125012 . - DOI : 10.1103 / PhysRevD.70.125012 . - . - arXiv : gr-qc / 0410020 .

[Aloisio2005-11] Aloisio, R .; Galante, A .; Grillo, AF; Luzio, E .; Mendez, F. A note on DSR-like approach to space – time (Eng.) // Physics Letters B : journal. - 2005. - Vol. 610 - P. 101-106 . - DOI : 10.1016 / j.physletb.2005.01.01.090 . - . - arXiv : gr-qc / 0501079 .

[12] The Soccer-Ball Problem