Relativistic space-time is described as a four-dimensional continuum comprising three dimensions of space and one dimension of time. In this framework, space and time are interwoven, forming an integrated space-time fabric. As time dilates due to relativistic effects, does this interconnected nature imply a dilation of space-time as a whole?
For context:
Cosmic Expansion: Describes how the distance between cosmic objects increases over time, which can be represented as:
t₀ < (t₀+Δt) = t₁ → (x₀,y₀,z₀,t₀) < (x₁,y₁,z₁,t₁)
Where (t₁ - t₀) = elapsed time.
Space-Time Dilation: Reflects how time dilation in relativistic contexts affects space-time coordinates:
t < t′ → (x,y,z,t) < (x′,y′,z′,t′)
Where t′ is dilated time
Given these representations, can the concept of space-time dilation be viewed as a form of space-time expansion in terms of their consequences?
