Chapter 7
Gravitation by Condensation
Jonathan J. Dickau
Abstract For gravity to exert an influence, it must have a surface to act upon, or
something for its pull to push things against. With everyday objects made of ordinary
matter, the electromagnetic force acting through the electrons in atoms and molecules does all the pushing back. But in the degenerate cases, such as neutron stars
and objects even more dense; other forces come into play or predominate as massive
objects become more and more compact, until the gravitational limit sets the
absolute minimum size at the Schwarzschild radius. Dvali and Gomez suggest that
the event horizon of a Schwarzschild object is well modeled by the quantum critical
point of a Bose–Einstein condensate, which makes gravity a process of condensation. This fits well with thermodynamic or entropic theories of gravitation, such as
those proposed by Jacobson, Padmanabhan, and Verlinde, because condensation is
precipitated by cooling. This connection is also clearly represented in features at the
Misiurewicz point in the Mandelbrot Set near (À1.543689, 0i), which the author has
extensively studied, and these analogies offer many avenues for further research.
7.1 Introduction
Gravity is perhaps least understood of the natural forces, despite how sophisticated
our understanding has become. We know that gravity draws other massive objects
toward any center of mass, with a pull proportional to their combined masses and
inversely to the square of their distance from its center. With the refinement of
relativity, we learn this is an approximation because there is actually a radius of
gravitation defined by any mass—rather than a simple center of mass—as was
emphasized by Eddington (1920). With familiar and astrophysical objects, the
gravitational radius is a fraction of a massive body’s total volume. But when we
consider the case of a black hole devoid of charge or spin, the radius of gravitation is
at the surface, determining the object’s size, and is called the Schwarzschild radius.
J. J. Dickau (*)
Independent Researcher/ISGRG Member, Poughkeepsie, NY, USA
e-mail: jonathan@jonathandickau.com
© 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_7
67
Gravitation by Condensation
Jonathan J. Dickau
Abstract For gravity to exert an influence, it must have a surface to act upon, or
something for its pull to push things against. With everyday objects made of ordinary
matter, the electromagnetic force acting through the electrons in atoms and molecules does all the pushing back. But in the degenerate cases, such as neutron stars
and objects even more dense; other forces come into play or predominate as massive
objects become more and more compact, until the gravitational limit sets the
absolute minimum size at the Schwarzschild radius. Dvali and Gomez suggest that
the event horizon of a Schwarzschild object is well modeled by the quantum critical
point of a Bose–Einstein condensate, which makes gravity a process of condensation. This fits well with thermodynamic or entropic theories of gravitation, such as
those proposed by Jacobson, Padmanabhan, and Verlinde, because condensation is
precipitated by cooling. This connection is also clearly represented in features at the
Misiurewicz point in the Mandelbrot Set near (À1.543689, 0i), which the author has
extensively studied, and these analogies offer many avenues for further research.
7.1 Introduction
Gravity is perhaps least understood of the natural forces, despite how sophisticated
our understanding has become. We know that gravity draws other massive objects
toward any center of mass, with a pull proportional to their combined masses and
inversely to the square of their distance from its center. With the refinement of
relativity, we learn this is an approximation because there is actually a radius of
gravitation defined by any mass—rather than a simple center of mass—as was
emphasized by Eddington (1920). With familiar and astrophysical objects, the
gravitational radius is a fraction of a massive body’s total volume. But when we
consider the case of a black hole devoid of charge or spin, the radius of gravitation is
at the surface, determining the object’s size, and is called the Schwarzschild radius.
J. J. Dickau (*)
Independent Researcher/ISGRG Member, Poughkeepsie, NY, USA
e-mail: jonathan@jonathandickau.com
© 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_7
67