Relativity That Ordinary People Can Understand

-Relativity Is Not That Mysterious

Special Relativity:

The basic principles of special relativity are based on the assumption of flat spacetime, without considering the discussion of spacetime elasticity found in general relativity.

1. Light speed is absolute and not additive – The absoluteness of the speed of light in special relativity does not take into account gravitational effects or equivalent gravitational time dilation as discussed in general relativity. In other words, it doesn't consider how spacetime metric variations modulate local time. A more precise way to state this is that the speed of light cannot be added vectorially.

2. Space is isotropic

With these two fundamental assumptions, the Lorentz transformation can be derived. Understanding the 2D Lorentz transformation only requires the Pythagorean theorem. Anyone who understands the 2D version already grasps that the Lorentz factor formula comes directly from applying the Pythagorean theorem to the difference in light paths — it's essentially a problem in plane geometry, nothing mysterious at all. As for the 3D Lorentz transformation, it indeed benefits from tools in higher algebra. However, once you understand the 2D case, you’ve already understood the core principle of special relativity.

The classic examples of time dilation and length contraction in special relativity are fundamentally observational perception effects. When an observer measures time and length in a frame moving relative to them, their measurements differ due to relative motion. Special relativity does not involve spacetime curvature or time modulation caused by such curvature; those phenomena belong to general relativity under its deformable spacetime framework. This is often a source of confusion in popular science articles.

The essential principle behind Lorentz transformations is observer perception differences — the differences arise because of the light path differences between observers and moving objects. Since time and length measurements depend on the light path between the observer and the observed object, dynamic changes in light paths due to the non-additive nature of light speed correspond precisely to the Lorentz covariance formulas.

General Relativity:

General relativity introduces a deformable (elastic) spacetime paradigm. Experimental evidence and cosmological observations support this view. The most direct confirmation is the smooth curved trajectory of light near black holes.

Under the elastic spacetime framework of general relativity, space behaves like an elastic medium. Changes in spatial metrics (i.e., deformation) modulate time. Let me explain this time-modulation mechanism using my own analogy: imagine a spring with a mass attached to it — when loaded, the spring’s resonant frequency decreases. Similarly, in general relativity, gravity or any equivalent form of acceleration leads to time dilation.

Not only does gravity cause spatial deformation, but any energy fluctuation, including object motion and electromagnetic interactions, can also lead to metric changes, which in turn modulate the local resonant frequency — this is what we observe as time dilation under the equivalence principle.

General relativity also introduces the concept of geodesics — when spacetime is deformed, physical trajectories are influenced by this deformation. These altered paths are called geodesics. As mentioned above, the motion and mass of objects themselves contribute to spacetime deformation (metric variation), so there exists a mutual interaction between matter and spacetime. This mutual influence forms a differential equation — the geodesic equation.

If you study theoretical mechanics or analytical mechanics at university, you'll find that the geodesic equations in general relativity are mathematically equivalent to the principle of least action — they describe the same physical law.

Now I will discuss something not explicitly stated in general relativity, but which I believe is inherently implied by it:

Looking at the metric field equations, I interpret them as suggesting that matter and spacetime are one and the same. Matter itself is a localized concentration of energy excitation within space. The motion of matter is essentially a wave propagating through space. Only under this interpretation can we better visualize how mass-generated gravity spreads spherically and symmetrically. Moreover, if matter and space were separate entities, then the movement of matter would necessarily disrupt the topological structure of space. This contradicts general relativity’s assumption of differential topological invariance. Also, since the bending of light near a black hole follows a smooth arc even under extreme gravitational conditions, this strongly suggests that matter must be part of space itself.

In fact, many people today recognize that the idea of spacetime-matter unity is more consistent with observed physical phenomena. Some new formal physics models reflect this perspective, and personally, I believe general relativity has already made this point clearly.

Full text of the paper: https://doi.org/10.5281/zenodo.14788393