How a four dimensional motion mimics gravitation

Received: 20-Jul-2023, Manuscript No. PULJMAP-23-6595; Editor assigned: 24-Jul-2023, Pre QC No. PULJMAP-23-6595 (PQ); Reviewed: 07-Aug-2023 QC No. PULJMAP-23-6595; Revised: 24-Jan-2025, Manuscript No. PULJMAP-23-6595 (R); Published: 31-Jan-2025

Citation: Radhakrishnan MP. How a four dimensional motion mimics gravitation. J Mod Appl Phy. 2025;8(1):1-2.

This open-access article is distributed under the terms of the Creative Commons Attribution Non-Commercial License (CC BY-NC) (http://creativecommons.org/licenses/by-nc/4.0/), which permits reuse, distribution and reproduction of the article, provided that the original work is properly cited and the reuse is restricted to noncommercial purposes. For commercial reuse, contact reprints@pulsus.com

About the Study

Points to remembers

• An n+1 dimensional motion cannot be pictured in a single n dimensional plane. Example: A motion parallel to the z axis cannot be represented in a single (x-y) plane. Similarly, a motion in a 4D frame cannot be pictured in a single 3D R_(x,y,z) plane.
• Motion is always relative, not absolute.
• For a mass m’ moving away with a velocity v from another mass m, the reference point with which we measure the velocity is fixed at m. If we fix the reference frame at m’, the mass m will appear as it is moving away from m’ with the same velocity (Figure 1).

Figure 1: mass m’ moving away with a velocity v from another mass m.

• Centripetal force can mimic the effects of gravity (Figure 2).

Figure 2: Centripetal force.

An accelerating frame can also mimic the effects of gravity (Figure 3).

Figure 3: Accelerating frame.

Four dimensional motion and gravitation

We say ‘light travels with a speed c in free space’. What if it is not the light that travels with a speed c? What if everything in this space is traveling in a four dimensional R_(x,y,z)-ivt frame instead of the light?

Since a motion in the 4^th dimension cannot be observed in a single 3D plane, the difference in velocity of different masses in the 4D space appears as a gravitational pull in the observable 3D space.

Consider the linear motion of two masses m₁ and m₂ in a 4D frame with the velocities v₁ and v₂ respectively (Figure 4).

Figure 4: The linear motion of two masses m₁ and m₂ in a 4D frame
with the velocities v₁ and v₂.

The masses m₁ and m₂ can be represented in a 4 dimensional frame as (Figure 5).

Xx+Yy+Zz-iv₁t

X’x+Y’y+Z’z-iv₂t respectively.

Figure 5: masses m₁ and m₂ can be represented in a 4 dimensional frame.

The velocity range of different objects lies in between 0 to c depending on the masses of the objects. The heavier the object is, the lesser the 'v' will be.

This velocity difference in the imaginary velocity-time space also mimics time dilation in the real 3D plane. So the products v₁t and v₂t always appear as ct₁ and ct₂ near m₁ and m₂ respectively in the real space. Due to this apparent time delay near m₂, the mass m₁ appears as it is moving towards m₂ with an acceleration in the real 3D frame.

The motion possessing a momentum in the imaginary v-t frame is completely independent of any movement in the 3D plane. This is why light always appears as it is independent of any frame of references in the real space.

Centripetal force or an accelerating frame mimics the effects of gravity in the 3D space. Similarly, a velocity difference in the 4^th dimension appears as a gravitational pull around every independent objects in the real R_(x,y,z) space (Figure 6).

Figure 6: Centripetal force or an accelerating frame mimics the effects of
gravity in the 3D space.

Like a person experiencing artificial gravity inside an accelerating spacecraft, every layer of a spherical celestial object experiences an inward pull towards the center due to the difference in velocity of different layers.