The concept of mass manifests in diverse forms, dimensions and configurations, and yet among all these manifestations, a unified origin is usually yearned for. This study aims to propose models that attribute the emergence of mass from fundamental quantities of physics, notably energy, space, and time. To this end, an operator is introduced, wherein these fundamental concepts serve as inputs, yielding functions that characterise mass. These functions are grounded in the domain of complex numbers, augmented by the incorporation of probabilistic elements, facilitating a nuanced depiction of mass modulation. Through investigation, it becomes apparent that a corollary energy field arises surrounding mass, facilitating its interactions within its surroundings. Ultimately, the comprehensive model of mass, inclusive of its associated field, gives rise to interactions with other masses, thereby engendering the genesis of larger and denser manifestations of mass, a phenomenon expounded within this framework.
References
[1]
HELM (2008) The Exponential Form of a Complex Number. https://www.ncl.ac.uk/webtemplate/ask-assets/external/maths-resources/images/Expo_form_complx_num.pdf
[2]
University of Winscosin-Madison (2008) Complex Numbers and the Complex Exponential. https://people.math.wisc.edu/~angenent/Free-Lecture-Notes/freecomplexnumbers.pdf
[3]
MIT Mathematics (2012) The Complex Exponential. https://math.mit.edu/classes/18.03/sup/sup6.pdf
[4]
Ackermann, G.K. and Eichler, J. (2007) Holography. Wiley-VCH Verlag GmbH & Co. https://onlinelibrary.wiley.com/doi/pdf/10.1002/9783527619139.app1
[5]
Δάρας, Τ.Ι. and Σύψας (2003) Στοχαστικές Ανελίξεις, Θεωρία και Εφαρμογές. Εκδόσεις ΖΗΤΗ.
[6]
Κοντογιάννης, Γ. and Τουμπής, Σ. (2015) Στοιχεία Πιθανοτήτων. Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών. https://repository.kallipos.gr/bitstream/11419/2810/3/final_h.pdf
The University of British Columbia (2024) 4.1 Gradient, Divergence and Curl. https://personal.math.ubc.ca/~CLP/CLP4/clp_4_vc/sec_graadDivCurl.html
[9]
North Dakota State University (2013) Curl and Divergence. https://www.ndsu.edu/pubweb/~micohen/oldlecturenotes/Lecture_Stokes_Thm_Div_Thm.pdf
[10]
Department of Physics-University of Texas at Austin (2024) Gradient, Divergence, Curl and Related Formulae. https://web2.ph.utexas.edu/~vadim/Classes/2024s-u/diffop.pdf
[11]
Lehman College (2010) Partial Differential Equations. https://www.lehman.edu/faculty/dgaranin/Mathematical_Physics/Mathematical_physics-13-Partial_differential_equations.pdf
[12]
Zurich, E.T.H. (2021) The Wave Equation. https://ethz.ch/content/dam/ethz/special-interest/itet/photonics-dam/documents/lectures/EandM/WaveEquation.pdf
[13]
Brown University (2024) Waves and the Wave Equation. https://www.brown.edu/research/labs/mittleman/sites/brown.edu.research.labs.mittleman/files/uploads/lecture02_0.pdf
[14]
Ακρίβης, Γ.Δ. (2008) Μερικές Διαφορικές Εξισώσεις. http://users.math.uoc.gr/~tertikas/pdes2.pdf
[15]
MIT Mathematics (2013) 18.03 PDE.3: The Wave Equation. https://math.mit.edu/~jorloff/suppnotes/suppnotes03/pde3.pdf