Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On time-interval transformations in special relativity   We revisit the problem of the Lorentz transformation of time-intervals in
special relativity. We base our discussion on the time-interval transformation
formula $ c\Delta t' = \gamma (c\Delta t - \vec{\beta} \cdot \Delta \vec{r}) $
in which $ \Delta t'$ and $ \Delta t $ are the time-intervals between a given
pair of events, in two inertial frames $ S $ and $ S'$ connected by an general
boost. We observe that the Einstein time-dilation-formula, the Doppler formula
and the relativity of simultaneity, all follow when one the frames in the
time-interval transformation formula is chosen as the canonical frame of the
underlying event-pair. We also discuss the interesting special case $ \Delta t'
= \gamma \Delta t $ of the time-interval transformation formula obtained by
setting $ \vec{\beta} \cdot \Delta \vec{r}=0 $ in it and argue why it is really
\textbf{not} the Einstein time-dilation formula. Finally, we present some
examples which involve material particles instead of light rays, and highlight
the utility of time-interval transformation formula as a calculational tool in
the class room.

9
The categories of this paper are: nlin
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
2
The categories of this paper are: math
37
The categories of this paper are: supr-con