(zenodo.org)

Introduction

Based on the assumption that the de Broglie wave is most likely a spatial energy density wave (Dzen), we can conclude that space can have different energy densities. The energy density gradient in space may be a key factor in determining the trajectory of light. This may provide an alternative explanation for some observed phenomena such as gravitational lensing and redshift.

1. Relation of mass, energy and wavelength

Based on our reasoning about rest mass:

Where:

• E₂ is the energy of the object at rest,
• E₁ is energy at the speed of light,
• λ₁ is the wavelength of the object when travelling at the speed of light,
• h is Planck’s constant,
• c is the speed of light.

Here the rest mass of the particle depends on the wavelength at the limiting velocity. Since the speed of light is the maximum for a given medium, this indicates that the energy density of space affects the allowable range of frequencies.

2. Influence of energy density on frequencies

In this case the interaction of spatial waves of energy in space is considered. Since the de Broglie wave is most likely a spatial wave of energy, it is logical to assume that space itself can have different energy density on large scales. For example, gravitational force or electromagnetic force, all this can be considered as a space with a gradient of change of energy density in space

The higher the energy density of the medium, the higher frequency waves can exist in it. However, there are boundary frequencies that limit wave propagation. If the energy density changes, this leads to a change in the range of permissible frequencies and, consequently, in the possible velocities of wave propagation.

If the density of the medium determines the range of possible frequencies (i.e., the minimum and maximum boundary), then:

1. Frequency limits speed — if there is an acceptable range of frequencies for a given density, then the speed of wave propagation will also be limited.
2. The maximum speed in a given medium is determined by its properties — in a vacuum it is the speed of light c, but if the vacuum itself has «density», the speed can vary.
3. Relationship between density and velocity — if the density of the medium increases, high frequency waves travel better (this is similar to the behaviour of sound in dense media, but here we are talking about the fundamental level). Perhaps this is a hint that the speed of light may be variable.

3. Dispersion of light and its physical meaning

Dispersion is the dependence of the speed of propagation of a wave on its frequency within the same medium. That is, different wavelengths (frequencies) propagate at different speeds, but the frequency of radiation remains unchanged when crossing a boundary. What changes is the wavelength.

If we consider dispersion, the speed of propagation depends on frequency, which means that when some boundary frequency is reached, the angle of refraction can reach 90° or even more.

What does that mean?

1. The boundary frequency is the frequency at which light (or another wave) can no longer propagate in a given medium. It is similar to total internal reflection, but at a fundamental level.
2. If the angle of refraction reaches 90°, it means that the wave ceases to propagate further in that medium and is either reflected or absorbed by the medium.
3. Boundary frequency and space structure
   • If we imagine that the vacuum itself is a «medium» with variable density, then different boundary frequencies may exist in different regions of space.
   • This could explain why light can propagate in some conditions and not in others (e.g., near black holes or in special physical conditions).

Then, you might say:

The speed of propagation of light and particles in space is determined by the boundary frequencies, which depend on the density of the medium (or vacuum density), and when a certain frequency is reached, the wave is either completely reflected or disappears in the medium.

The dispersion effect shows that in media with different densities the speed of light depends on frequency. If the density changes abruptly, dispersion is observed, but if the density changes smoothly, light begins to move along a curve. This gives rise to centripetal force which does work. Since the law of conservation of energy must hold, this means that for light, a decrease in energy must mean a decrease in photon frequency.

4. Redshift and inhomogeneity of the Universe

If the Universe has a gradient of energy density, then light, passing through regions with different densities, loses energy. This leads to a decrease in photon frequency, which may explain the redshift effect. Moreover, if the energy density is not uniformly distributed, this can lead to local differences in the Hubble factor.

5. Gravitational lensing as a result of energy gradient

Gravitational lensing is traditionally explained by the curvature of space-time under the action of massive objects. However, if the energy density of space affects the speed of propagation of light, its trajectory can change without involving the concept of curvature of space. Near massive objects, such as black holes, lensing is observed, which can be associated with a sharp gradient of energy density in these regions.

Conclusion

If the space energy density gradient gradient assumption is true (I think gravity and the electromagnetic force are proof of this), then:

• Redshift is not an expansion of space, but an effect of changing the density of the medium.
• The universe may be more stable than is commonly believed.
• Perhaps dark energy is not needed at all, since accelerated expansion is simply a consequence of inhomogeneous density.

The energy density gradient can play a key role in the phenomena traditionally explained by gravitation. This provides an opportunity to take a new look at light propagation, the redshift effect and gravitational lensing. Possible ways to test this idea may include analyses of weak gravitational lensing and comparison with the predictions of general relativity.

This approach does not require the introduction of ether or new entities — only the consideration of energy density as a physical characteristic of space, making it elegant and conceptually simple.