Abstract
An equation describing a one-dimensional model for the freezing of lakes is shown to be formally analogous to the Friedmann equation of cosmology. The analogy is developed and used to speculate on the change between two hypothetical "spacetime phases" in the early universe.
Highlights
The study of the freezing of water bodies in the natural environment has a long history [1,2,3,4,5,6,7,8,9,10], appearing in pedagogical [11,12,13] and popular [14] literature
This analogy would eliminate the problem of the big bang singularity at a = 0 by stating that in the early universe [when a(t ) is below the critical value a0] spacetime is in a different phase from the one we know today and it cannot be described by the classical Einstein-Friedmann equations
We point out the analogy between the freezing of lakes and spatially flat, radiation-dominated FLRW universes
Summary
The study of the freezing of water bodies in the natural environment has a long history [1,2,3,4,5,6,7,8,9,10], appearing in pedagogical [11,12,13] and popular [14] literature. The realistic problem of freezing of lakes in winter or in cold (for example, mountainous or polar) regions is difficult when factors such as the variability of atmospheric conditions, boundaries, and chemical impurities are taken into account [1,2,3,4,5,6,7,8,9,10], but it can be simplified considerably and reduced to a one-dimensional model under certain assumptions, which are best spelled out in the pedagogical literature [13]. The heat losses from the lake ice to the atmosphere due to convection and radiation are simplified and described by a single heat flux density linear in the difference between air and ice temperatures [13] and described by a single heat coefficient h. The Friedmann equation, which resembles an energy conservation equation for a conservative mechanical system, lends itself to analogy with equations arising in the study of many different and completely unrelated physical systems, ranging from particles in one-dimensional motion [15,16,17,18,19] to optical systems [20,21], condensed matter systems [22,23,24,25], the transverse profiles of glacial valleys [20,21,26], and equilibrium beach profiles [27]
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