Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.22025 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914996907147264 |
|---|---|
| author | Acton, David Doyle, Owen Tuite, Michael P. |
| author_facet | Acton, David Doyle, Owen Tuite, Michael P. |
| contents | We consider real linear transformations between two inertial frames with constant relative speed $v$ in a $d$-dimensional spacetime where light moves with constant speed $c=1$ (for some chosen units) in all frames. For $d=2$ we show that the standard relative velocity formula holds and that any associated anisotropic conformal factor is multiplicative under composition of inertial transformations for $|v|\neq 1$. Assuming that the inertial transformation matrix is continuous in a neighbourhood of $v=0$ and differentiable at $v=0$, we determine the conformal factor for all $|v|\neq 1$. For an isotropic spacetime, the general solution reduces to the standard $d=2$ Lorentz transformation for $|v|<1$ or to a Tachyonic transformation for $|v|>1$, first described by Parker in 1969. For $d>2$ we show that no Tachyonic-like inertial transformations exist which are compatible with constant light speed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22025 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inertial Transformations and the Nonexistence of Tachyons for Spacetime Dimension Greater than Two Acton, David Doyle, Owen Tuite, Michael P. High Energy Physics - Theory We consider real linear transformations between two inertial frames with constant relative speed $v$ in a $d$-dimensional spacetime where light moves with constant speed $c=1$ (for some chosen units) in all frames. For $d=2$ we show that the standard relative velocity formula holds and that any associated anisotropic conformal factor is multiplicative under composition of inertial transformations for $|v|\neq 1$. Assuming that the inertial transformation matrix is continuous in a neighbourhood of $v=0$ and differentiable at $v=0$, we determine the conformal factor for all $|v|\neq 1$. For an isotropic spacetime, the general solution reduces to the standard $d=2$ Lorentz transformation for $|v|<1$ or to a Tachyonic transformation for $|v|>1$, first described by Parker in 1969. For $d>2$ we show that no Tachyonic-like inertial transformations exist which are compatible with constant light speed. |
| title | Inertial Transformations and the Nonexistence of Tachyons for Spacetime Dimension Greater than Two |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2410.22025 |