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Mass of phonon; matter–dark matter conversion; string length; black body radiation; space energy theory

From Planck’s equation for black body radiation and de Broglie’s wave–particle duality relation, we can get a relation between the mass of a phonon and frequency of the emitted radiation. From this relation, we get the theoretical lower limit of the mass of a phonon and critical mass for matter–dark matter conversion. The maximum matter density and limit of the string length are also discussed in this respect. It is observed that there is a critical mass of the smallest particle, which is $7.367 \times 10^{−51}$ kg, above which we get normal matter and below, the dark matter. It is also observed that if phonon obeys the de Broglie’s equation, generation of an electromagnetic radiation of frequency less than 56638721410 Hz is not possible by thermal heating.

ARIJIT BAG¹

1. Division of Chemical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur, Nadia 741246, India

Published

1 August 2018

Manuscript received

3 March 2017

Manuscript revised

1 January 2018

Accepted

16 January 2018

Early published

Unedited version published online

Final version published online

29 June 2018