Chapter 17
The Twin Paradox
The twin paradox is certainly one of the most provocative consequences with which
Special Relativity confronts us. It is a challenge to everybody’s ‘common sense’.
One can however also see this from various viewpoints. The unpretentiousness and
indigence of our common sense which we so desperately need and the loose ground
on which our indisputable facts of everyday life are built on crumbles away in the
face of the twin paradox. If one can be certain about one fact, then that twins always
have their birthdays on exactly the same day, even if they have completely different
lifestyles and have lived completely different lives. However, this is not exactly true.
1
What is the problem here? Both twins, let us call them brother A o and twin A go on a
journey. To be more precise, brother A o finds himself in the reference system o and
his twin A in the reference system
, so that A moves away from A o with the uniform
velocity v and correspondingly that A o moves away from A with the velocity −v.
Both of them should be equipped with a sufficient number of our described clocks and
measuring-rods. At their point of departure found at the common coordinate origin,
event O, where (x = 0, t = 0) in o and also (x
= 0, t
= 0) in
, the clocks they
both carry, let us determine them as the clock U
A
o of brother A o and the clock U
A
of his twin A that they both show the reading zero. This situation corresponds to
our Fig.12.3, which we have reproduced here with different labelling, because of the
different objective; see Fig. 17.1.
Using these ‘personal clocks’, the twins measure the time since their point of
departure at event O. The personal clocks, the pulsating breathers, show how much
1 From now on, we will talk about persons. Here, we have the situation inside of the crystal in front
of us, in other words, we consider the internal observers. For us, clocks are breather solutions of
sine-.Gordon equation which have the possibility of moving through the crystal with the velocity
|v| < c o . The number of oscillations of such a breather determines its ‘personal life span’. We could
replace the twin brothers anytime with ‘twin breathers’.
© The Editor(s) (if applicable) and The Author(s), under exclusive
license to Springer Nature Singapore Pte Ltd. 2020
H. Günther, Elementary Approach to Special Relativity,
https://doi.org/10.1007/978-981-15-3168-2_17
167
The Twin Paradox
The twin paradox is certainly one of the most provocative consequences with which
Special Relativity confronts us. It is a challenge to everybody’s ‘common sense’.
One can however also see this from various viewpoints. The unpretentiousness and
indigence of our common sense which we so desperately need and the loose ground
on which our indisputable facts of everyday life are built on crumbles away in the
face of the twin paradox. If one can be certain about one fact, then that twins always
have their birthdays on exactly the same day, even if they have completely different
lifestyles and have lived completely different lives. However, this is not exactly true.
1
What is the problem here? Both twins, let us call them brother A o and twin A go on a
journey. To be more precise, brother A o finds himself in the reference system o and
his twin A in the reference system
, so that A moves away from A o with the uniform
velocity v and correspondingly that A o moves away from A with the velocity −v.
Both of them should be equipped with a sufficient number of our described clocks and
measuring-rods. At their point of departure found at the common coordinate origin,
event O, where (x = 0, t = 0) in o and also (x
= 0, t
= 0) in
, the clocks they
both carry, let us determine them as the clock U
A
o of brother A o and the clock U
A
of his twin A that they both show the reading zero. This situation corresponds to
our Fig.12.3, which we have reproduced here with different labelling, because of the
different objective; see Fig. 17.1.
Using these ‘personal clocks’, the twins measure the time since their point of
departure at event O. The personal clocks, the pulsating breathers, show how much
1 From now on, we will talk about persons. Here, we have the situation inside of the crystal in front
of us, in other words, we consider the internal observers. For us, clocks are breather solutions of
sine-.Gordon equation which have the possibility of moving through the crystal with the velocity
|v| < c o . The number of oscillations of such a breather determines its ‘personal life span’. We could
replace the twin brothers anytime with ‘twin breathers’.
© The Editor(s) (if applicable) and The Author(s), under exclusive
license to Springer Nature Singapore Pte Ltd. 2020
H. Günther, Elementary Approach to Special Relativity,
https://doi.org/10.1007/978-981-15-3168-2_17
167