PreprintHypothesisVersion 1Preserved in Portico This version is not peer-reviewed
Introducing the Framework of a "Dynamic" Higher Dimensional Spacetime. How Time behaves in It. Similarities with Quantum Mechanical and Relativistic Behaviour.
Alamanos, G. Introducing the Framework of a “Dynamic” Higher Dimensional Spacetime. How Time Behaves in It. Similarities with Quantum Mechanical and Relativistic Behavior. SSRN Electronic Journal 2024, doi:10.2139/ssrn.4742892.
Alamanos, G. Introducing the Framework of a “Dynamic” Higher Dimensional Spacetime. How Time Behaves in It. Similarities with Quantum Mechanical and Relativistic Behavior. SSRN Electronic Journal 2024, doi:10.2139/ssrn.4742892.
Alamanos, G. Introducing the Framework of a “Dynamic” Higher Dimensional Spacetime. How Time Behaves in It. Similarities with Quantum Mechanical and Relativistic Behavior. SSRN Electronic Journal 2024, doi:10.2139/ssrn.4742892.
Alamanos, G. Introducing the Framework of a “Dynamic” Higher Dimensional Spacetime. How Time Behaves in It. Similarities with Quantum Mechanical and Relativistic Behavior. SSRN Electronic Journal 2024, doi:10.2139/ssrn.4742892.
Abstract
The aim of the present work is to explore a different non-traditional approach to higher dimensional spacetime which differs from the usual approaches such as large extra space dimensions, warped extra space dimensions and multiple extra time dimensions. This approach will be referred to as "Dynamic" higher dimensional spacetime. By this term will be introduced a new kind of higher dimensional spacetime (more than the usual 3+1 dimensions), which behaves dynamically in the sense that time is not a fixed dimension but is the extra plus one dimension to the spatial dimensions of the phenomenon we are studying. For a higher dimensional phenomenon, the lower dimensional time will behave as space and the new time will be a plus one dimension, meaning if we study a 3-dimensional phenomenon then time is the usual 4th dimension but if we are studying a 4-dimensional phenomenon then its time will be an extra 5th dimension and for this phenomenon the 4th dimension will behave as space. All spatial dimensions are indistinguishable from each other and behave in the exact same way, which means that the important parameter is not the dimension we are studying (for example the 4th or the 5th) but the number of dimensions in which a phenomenon can interact and how higher dimensional phenomena interact with lower ones. This non-traditional approach to higher dimensional spacetime may appear confusing at first but will become clearer in the rest of the paper. For this reason, we will first associate the time dimension with propagation relative to space dimensions and change orthogonal to them in order to give the reader a better intuition. Following that, we will describe how higher - dimensional phenomena would appear to us, the 3 - dimensional observer and try to set some guidelines on how we should mathematically model higher - dimensional phenomena in order for us to make accurate predictions of their behaviour. Then we will express the general framework of a "Dynamic" higher - dimensional spacetime and turn our gaze to 4+1 – dimensional phenomena. We will explore how a mass term arises for 4 – dimensional waves by generalizing the frequency – speed – wavelength relation of 3D waves and give a basic description on a possible way to describe a 4+1 – dimensional disturbance in a scalar Energy Field in order to make accurate predictions on our 3+1 dimensional plane. In this framework we will derive the Klein – Gordon equation by generalizing the wave equation and ignoring all lower than 4+1 - dimensional disturbances and compere our mass term findings with the Klein – Gordon equation mass term and with results from gravity – induced quantum interference experiments. Lastly, we will describe how a "Dynamic" 5 - dimensional spacetime would appear in a 3D observer and examine whether our findings are compatible with quantum mechanics and the special theory of relativity.
Keywords
space; time; framework; higher dimensions; dynamic time; dynamic higher dimensional spacetime; quantum mechanics; relativity; special relativity; complex numbers; imaginary unit; Klein Gordon equation; gravity – induced quantum interference experiments; mass; emergent time; imaginary time; scalar energy field; time as space; 5 dimensional waves
Subject
Physical Sciences, Theoretical Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received:
5 March 2024
The commenter has declared there is no conflict of interests.
Comment:
The writer's exploration of "Dynamic" higher dimensional spacetime in the abstract is commendable. Their innovative approach challenges traditional perspectives, offering fresh insights into the dynamic interplay between dimensions and time. The clarity with which they articulate complex concepts and their dedication to exploring the implications of their framework are truly impressive. This work promises to inspire further inquiry and push the boundaries of our understanding of spacetime dynamics
The commenter has declared there is no conflict of interests.