Why the Speed of Light Is the Maximum Speed

Spacetime is regarded as a medium consisting of spacetime quanta. Similar to the speed of sound in air or water, the vacuum speed of light is the intrinsic speed of spacetime. Because moving inertial systems are rotated into a fifth dimension, the speed of light is the same in all of them, and the principle of relativity holds.

1. Introduction

The script “Relativistic Dynamics and Energy in R5” [1] demonstrate and explain that the limitation of all effective velocities to the vacuum speed of light for bodies results in their having a velocity component in the fourth spatial dimension introduced there, which absorbs more and more energy during acceleration. The aim here is to answer the question of why such a limiting speed exists in the theory of relativity.

According to [1], the rest mass of a body remains constant even at relativistic speeds; therefore, it does not differ from its dynamic mass and, like the latter, will hereafter be referred to simply as mass m. It is equivalent to its kinetic energy E, which results from the translation of four-dimensional space in the direction of time at the speed of light. For a body at rest in three-dimensional space, E = m c². If a body moves with velocity v_x in the x-direction, then according to [1], it has the four-dimensional velocity v given by

v²= v_x²+ v_w² , (1)

where, for its component v_w² in the direction of the fourth dimension w, the following holds:

v_w= (γ / c) v_x²= v_x²/ √ (c²- v_x²) . (2)

For the angle ψ between vector v and the x-axis, the following holds:

cos⁡ ψ = √ (1 - v_x²/ c²) = 1 / γ . (3)

A moving body has the energy E = m c √ (c²+ v²) = m c v_E (4)

with the five-dimensional velocity v_E= √ (c²+ v²) . (5)

Fig. 1: Motion of a body with v_x = 0.5 c and four-dimensional velocity v, with the x-w-plane moving in the direction of time at the speed of light; resulting velocity vector v_E ; worldlines in R⁴ and R⁵ shown in blue; rest energy E₀ and total energy E as red lines, in the chosen unit of measurement m₀c, with magnitudes equal to those of the velocity vectors c and v_E .

2. Photons and Fields

Due to time dilation, for an observer in R³, time does not pass for objects moving at the speed of light—or, in other words, time stands still. This means that they do not participate in the universe’s journey through time. While they move through the universe, they remain at the time coordinate they had when they appeared in a flash at the measurement point in the universe. Therefore, they lack the velocity component c in the time direction.

Likewise, they lack the velocity component v_w in the direction of the fourth dimension. This is because, for objects with mass, the velocity component v_w arises from the absorption of acceleration work; however, since photons are not accelerated and already possess the speed of light, v_w must equal 0 for them.

A photon traveling along the x-axis is therefore not merely the projection of a photon supposedly moving in R⁵, as is the case with particles having mass (see Fig. 1). Since all bodies in this model move at the speed of light in the time direction, a photon emitted at an observer’s location thus remains in the past as it moves away. With the same scales, its worldline runs at an angle α = 45° from the t-axis to the x-axis.

Fig. 2: Motion of the universe over 1 second, with the worldline of a photon emitted from the origin (blue)

3. The Speed of Light as an Intrinsic Speed

The fact that the speed of light is simultaneously the speed of the universe’s motion and the limiting speed of all interactions is explained here by the assumption that spacetime is a medium with an intrinsic speed of propagation for interactions, just as air has the intrinsic speed of sound. The universe is then a wavefront that moves in the direction of time. From one spacetime quantum to the next, the displacement effect in the direction of time requires a characteristic time, the result of which is the vacuum speed of light. However, this is also the case for spatial movements (with the exception of the fourth spatial dimension, where superluminal speeds occur [1]).

Furthermore is assumed that every elementary particle is a specific motion pattern of spacetime quanta, e.g., a standing three-dimensional wave. Both the motion pattern and its propagation are based on collisions—on momentum transfers between spacetime quanta. Therefore, elementary particles—and thus all bodies—can move forward at most at the intrinsic velocity resulting from the collision time, which is the speed of light in a vacuum.

All interactions originating from a point—the origin in Fig. 2—at a speed lower than the speed of light proceed at angles α < 45°. If α > 45°, the speed of the interaction would exceed the speed of light. It would then also exceed the speed of light in the direction of time. The effect would then precede the universe as it moves through time. The effect would occur in the universe before the cause. This is impossible because of the universe's intrinsic speed.

4. Relativity Despite Intrinsic Speed

Light waves and all fields propagate as spherical waves. If a second reference frame S’ moves at a constant velocity v_x relative to the first reference frame S in R³ in the x-direction, then according to [1] and [2], it moves in R⁴ at an angle ψ with cos ψ = √(1 - v_x²/c²) = 1/γ relative to the x-axis in the direction of the fourth spatial dimension w (see Fig. 3). Since the y- and z-axes are omitted, the spherical wavefront appears as a circle that grows linearly in the negative time direction and thus forms a conical surface. The x’-axis of the direction of motion in R⁴ spans a plane with the t-axis; the line of intersection of this plane with the conic surface is the worldline of a photon emitted in the x´-direction in S’ at the point of coincidence of the systems at the origin. However, the opening angle of the cone, α, is the same for all angles ψ. That is, α is also 45° in S’, and the photon moves at the speed of light, even though S’ is already moving at relativistic speed relative to S. That is, the addition theorem for velocities applies and the speed of light is the same in all inertial frames moving relative to one another.

Fig. 3: In both reference frames S and S', the worldline of light (blue) lies on the bisector between the space and time axes; thus, light propagates at the same speed c (α = 45°), even though there is a relative velocity (here v_x = 0.6 c) between the frames. Representation of the light cone (light grey) in cavalier perspective

Viewed from S’, S moves at the same relativistic velocity, but the light in S still travels only at the speed of light. Despite the constant intrinsic velocity of action waves in R⁴, relativity arises due to the rotation by the angle ψ .

Even if a body starts at the origin with a relativistic velocity less than the speed of light—i.e., α < 45°—the angle α is not altered by the rotation of the spacetime plane by the angle ψ, again regardless of the direction of rotation. Consequently, the velocities determined in each case according to the addition theorem must also be equal. The principle of relativity thus applies generally in this model as well.

5. Summary and Outlook

To date, there is no explanation for the postulate that the speed of light is constant and that no higher speeds of action can exist. This script provides an explanation based on reasonable assumptions.

The speed of light is constant and the highest possible speed because it is the intrinsic speed of spacetime. It is determined by the coupling of spacetime quanta. Its independence from the reference frame and relativity in general are explained by the rotation of the moving reference frame into a fourth spatial dimension, as described in [1].

If the universe is expanding, the coupling of spacetime quanta must weaken, causing the vacuum speed of light to decrease. If such a decrease is measured, it serves as evidence for spacetime quanta and their intrinsic velocity, as well as for the expansion of the universe.

There is still no plausible hypothesis to explain why physical objects without mass move in space and at rest bodies move in time at this intrinsic velocity, whereas in spatial direction moving bodies do not.

References

[1] www.zenodo.org ; DOI 10.5281/zenodo.21429298

www.roland-sprenger.de: Relativistic Dynamics and Energy in R5

[2] www.zenodo.org ; DOI 10.5281/zenodo.17266293