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European Journal of Applied Sciences – Vol. 12, No. 5

Publication Date: October 25, 2024

DOI:10.14738/aivp.125.17550.

Tannous, S. (2024). Definition: Space-Time Interval. European Journal of Applied Sciences, Vol - 12(5). 57-68.

Services for Science and Education – United Kingdom

Definition: Space-Time Interval

Saliba Tannous

Independent research

saliboss.jony@gmail.com

ABSTRACT

The concept of spacetime interval is not clearly understood or defined in modern

physics. Here, I will present a clear and precise explanation and definition of the

concept of spacetime interval. This research is based on a different representation

of spacetime, Additionally, we will introduce and demonstrate a new physical

theory that will make all of modern physics more logical and easier to understand.

Keywords: special relativity, space-time, space-time interval.

INTRODUCTION

As a physics student. Like any studying physicist, I often leave lectures either lacking knowledge

or sometimes with facts contradicting straightforward logic. One of these things is the

spacetime interval (see Figure 1).

The definition of this concept is subjected to ongoing debate and remains unclear [1]-[13].

Therefore, I performed research on the subject, and indeed, I revealed a good result that defines

the term "spacetime interval" clearly and logically.

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Tannous, S. (2024). Definition: Space-Time Interval. European Journal of Applied Sciences, Vol - 12(5). 57-68.

URL: http://dx.doi.org/10.14738/aivp.125.17550

An inertial frame of reference must be a mass, i.e., mass with energy. Thus, a vacuum cannot

serve as an inertial reference frame because there is neither mass, energy, nor time.

Second:

In reality, there is a three-dimensional world �, �, � , where the time axis is imaginary

(simulated) and does not exist, and this is trivial and understandable because we do not see the

time axis.

SPACE-TIME

Figure 3: These illustrations taken from the professional literature do not describe space-time.

The representations in Figure 3 do not accurately depict spacetime. They are mathematical

descriptions of the Lorentz transformation, Minkowski spacetime interval, or spacetime events.

To visualize spacetime more intuitively, consider two spheres initially co-located, one red and

one black, as shown in Figure 4a. They move apart with constant velocity �. For simplicity, let

the black sphere be the stationary reference frame and the red sphere be the moving frame.

Let's calculate the Lorentz factor γ according to the formula � = *1 − (!

)! . After time �, the

coordinates of the stationary body will be (��, 0), In contrast, the coordinates of the moving

body will be ()*

+ , ��), remembering that there is a time dilation. Therefore, the position of the

two balls in the space-time will look as described in Figure 4b.