Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The two faces of the coin of Special Relativity   It is rarely emphasized in modern physics textbooks that our definitions of
space and time have to reflect their complete interdependence. Our intuitive
methods of always picturing one-dimensional space as a sum of unit-length rods
and of picturing one-dimensional time as consecutive ticks of a clock suggest
subconsciously that changes in space never alter time and vice versa. In this
paper, we present a compiled list of popular arguments against Special
Relativity, and we show how our erroneous intuitive conviction that the
definition of space is always independent of the definition of time and vice
versa is indeed the driving force behind these arguments. Once interdependence
between space and time is established within their respective definitions, it
is shown how such arguments are quickly resolved. Interdependence between space
and time is described in two different ways, which are mathematically different
but physically equivalent. We show how by assuming a time-independent
measurement tool for space, time should be defined in terms of space to reflect
their interdependence and this yields Lorentz Transformation. If we assume a
space-independent measurement tool for time, space should be defined in terms
of time, and this yields a different set of equations. Next, it is shown how
the two different faces of the coin of Special Relativity, while mathematically
different, are essentially equivalent from a physical point of view, and that
both yield the same laws of addition of velocity, length contraction and time
dilation effects. The apparent differences in physical interpretations between
the two sets of equations are attributed to the differences in the definitions
of space and time used in both cases.

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The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas