Chapter 4
“Equat Causa Effectum”
Peter Enders
Abstract In contrast to the Newtonian force of gravity of a spherically symmetric
body (“cause”), the Kepler orbits (“effects”) are not spherically symmetric. Does this
contradict and thus disprove the metaphysical rule “equat causa effectum” (the effect
equals its cause)? I will show this contradiction to be resolved through taking into
account the initial conditions. Spherically symmetric sets of Kepler orbits are
constructed by means of the conserved quantities energy, angular momentum, and
Laplace–Runge–Lenz vector. The quantum analogs (Bohr orbitals) are considered as
well. The fact, that the Kepler hodographs and orbits are plane, is shown by means of
qualitative and intuitive arguing. The old rule “equat causa effectum” thus leads to
new insights due to another point of view. This should be exploited in teaching
physics, too.
4.1 Introduction
There are external frontiers:
• Space (“the final frontier”)
• Novel materials like graphene
• Quantum computing
• Novel experiments
• ...
and internal frontiers:
• Better understanding of what we know
• Improving existing experimental methods
• ...
This talk is rather about the latter ones.
The relationship between cause and effect is an old and lasting issue. “Aequat
causa effectum” (the cause corresponds to its effect) is originally a scholastic rule
P. Enders (*)
Taraz State Pedagogical University, Taraz, Kazakhstan
© Springer Nature Switzerland AG 2021
B. G. Sidharth et al. (eds.), Fundamental Physics and Physics Education Research,
https://doi.org/10.1007/978-3-030-52923-9_4
37
“Equat Causa Effectum”
Peter Enders
Abstract In contrast to the Newtonian force of gravity of a spherically symmetric
body (“cause”), the Kepler orbits (“effects”) are not spherically symmetric. Does this
contradict and thus disprove the metaphysical rule “equat causa effectum” (the effect
equals its cause)? I will show this contradiction to be resolved through taking into
account the initial conditions. Spherically symmetric sets of Kepler orbits are
constructed by means of the conserved quantities energy, angular momentum, and
Laplace–Runge–Lenz vector. The quantum analogs (Bohr orbitals) are considered as
well. The fact, that the Kepler hodographs and orbits are plane, is shown by means of
qualitative and intuitive arguing. The old rule “equat causa effectum” thus leads to
new insights due to another point of view. This should be exploited in teaching
physics, too.
4.1 Introduction
There are external frontiers:
• Space (“the final frontier”)
• Novel materials like graphene
• Quantum computing
• Novel experiments
• ...
and internal frontiers:
• Better understanding of what we know
• Improving existing experimental methods
• ...
This talk is rather about the latter ones.
The relationship between cause and effect is an old and lasting issue. “Aequat
causa effectum” (the cause corresponds to its effect) is originally a scholastic rule
P. Enders (*)
Taraz State Pedagogical University, Taraz, Kazakhstan
© Springer Nature Switzerland AG 2021
B. G. Sidharth et al. (eds.), Fundamental Physics and Physics Education Research,
https://doi.org/10.1007/978-3-030-52923-9_4
37