#
Spring 2013 Meeting of the APS Ohio-Region Section

## Volume 58, Number 2

##
Friday–Saturday, March 29–30, 2013;
Athens, Ohio

### Session E4: Other Topics

11:00 AM–11:36 AM,
Saturday, March 30, 2013

Grover Hall
Room: E306

Chair: Martin Kordesch, Ohio University

Abstract ID: BAPS.2013.OSS.E4.3

### Abstract: E4.00003 : The Real Meaning of the Spacetime-Interval

11:24 AM–11:36 AM

Preview Abstract
Abstract

####
Author:

Florentin Smarandache

(University of New Mexico)

The spacetime interval is measured in light-meters. One light-meter means
the time it takes the light to go one meter, i.e. $3\cdot 10^{-9}$seconds.
One can rewrite the spacetime interval as: $\Delta s^{2}=c^{2}(\Delta
t)^{2}-[(\Delta x)^{2}+(\Delta y)^{2}+(\Delta z)^{2}]$.
There are three possibilities:
a)$\Delta s^{2}=$0
which means that the Euclidean distance $L_{1}L_{2}$ between locations
$L_{1}$ and $L_{2}$ is travelled by light in exactly the elapsed time
$\Delta t$. The events of coordinates (x, y, z, t) in this case form the
so-called light cone.
b)$\Delta s^{2}>0$ which
means that light travels an Euclidean distance greater than
$L_{1}L_{2}$ in the elapsed time $\Delta t$. The below quantity in meters:
$\Delta s=\sqrt {c^{2}(\Delta t)^{2}-[(\Delta x)^{2}+(\Delta y)^{2}+(\Delta
z)^{2}} ]$ means that light travels further than $L_{2}$ in the prolongation
of the straight line $L_{1}L_{2}$ within the elapsed time $\Delta t$. The
events in this second case form the time-like region.
c)$\Delta s^{2}<0$ which
means that light travels less on the straight line $L_{1}L_{2}$. The below
quantity, in meters:
-$\Delta s=\sqrt {-c^{2}(\Delta t)^{2}+[(\Delta x)^{2}+(\Delta
y)^{2}+(\Delta z)^{2}} ]$ means how much Euclidean distance is missing to
the travelling light on straight line $L_{1}L_{2},$ starting from $L_{1}$ in
order to reach $L_{2}$. The events in this third case form the space-like
region.
We consider a diagram with the location represented by a horizontal axis
$(L)$ on \textit{[0, }$\infty ),$ the time represented by a vertical axis $(t)$ on \textit{[0, }$\infty ),$
perpendicular on $(L),$ and the spacetime distance represented by an axis
($\Delta s)$ perpendicular on the plane of the previous two axes. Axis
($\Delta s)$ from \textit{[0, }$\infty )$ is extended down as $(-\Delta s)$ on \textit{[0, }$\infty ).$

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2013.OSS.E4.3