Abstract
Using simple box quantization, we demonstrate explicitly that a spatial transition will release or absorb energy, and that compactification releases latent heat with an attendant change in volume and entropy. Increasing spatial dimension for a given number of particles costs energy while decreasing dimensions supplies energy, which can be quantified, using a generalized version of the Clausius-Clapyeron relation. We show this explicitly for massive particles trapped in a box. Compactification from N -dimensional space to (N - 1) spatial dimensions is also simply demonstrated and the correct limit to achieve a lower energy result is to take the limit, Lw → 0, where Lw is the compactification length parameter. Higher dimensional space has more energy and more entropy, all other things being equal, for a given cutoff in energy.
Highlights
We demonstrate explicitly that a spatial transition will release or absorb energy, and that compactification releases latent heat with an attendant change in volume and entropy
Compactification is an old idea [1] [2] where one reduces the dimension of space to account for observed symmetries and conservation laws
We focus on box quantization and specialize to massive particles, such as electrons
Summary
Compactification is an old idea [1] [2] where one reduces the dimension of space to account for observed symmetries and conservation laws. We demonstrate explicitly that a spatial transition will release or absorb energy, and that compactification releases latent heat with an attendant change in volume and entropy. We start by considering the energy levels of a massive particle trapped in a box or lattice in N = 3 versus ( N −1) =2 dimensional space.
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More From: Journal of High Energy Physics, Gravitation and Cosmology
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