Understanding Cosmic Expansion and Relativity

According to accepted theories, the Hubble expansion of the Universe can result in objects that are sufficiently distant receding from us at speeds exceeding the speed of light (c).

However, this does not mean that these objects are moving towards us faster than the speed of light. In fact, they are not actually moving at all. The space between us and them is contracting, causing the distance between us and these distant objects to decrease.

The Role of Newtonian and Relativistic Velocities

Hubble's calculations rely on Newtonian space, which allows for unlimited velocities. This implies that outer galaxies can indeed recede at velocities exceeding one light-second per second by factors of over 50,000!

However, 'Relativists' deal with relativistic velocities, and the Lorentz transform must be applied when traversing space at a high velocity, implying a corresponding time dilation. Using the equation t/t √(1 - v/c2), we can derive the relationship between velocity and time dilation, leading to a modified formula to calculate the effective velocity.

Deriving the Effective Velocity

Given the relationship s/t v and s/t v, we can derive n √(1 - v/c2). Dividing both sides by v, we get 1/v √(1 - v/c2). Rearranging terms, we find v/v 1/√(1 - v/c2), which simplifies to 1/v √(1/v2 - 1/c2).

Since all velocities are considered relative to c, we replace c with unity: 1/v √(1/v2 - 1). Inverting both sides, we get nv 1/√(1/v2 - 1), which simplifies to v 1/√(1/v2 - 1).

Setting v 50,000, we calculate nv 1/√(1/2500000000 - 1). Due to the underflow, we apply the Binomial Theorem: (1 x)?≈ 1 nx for very small x. Thus, nv 1 - 0.5/2500000000 1 - 2E-10. In percentage terms, 2E-10 is 0.00000002, resulting in v/c 99.99999998.

Visual Phenomena and Sound Perception

Understanding that objects are not moving faster than light as perceived by our visual systems, we can extend this concept to sound perception. For example, if something was traveling away from you faster than its light was approaching you, it would appear to slow down visually, just as sound from passing trains sounds lower as it goes past you.

The Current State of the Universe Expansion

The current rate of expansion for superclusters is around 0.60c. Our supercluster, Virgo, is also moving away from the center at the same speed, meaning the distance between celestial bodies at both ends of the diameter increases at a rate of 1.20c. It is important to note that a contracting universe is not a viable concept. Instead, the universe appears to be heading towards its eventual thermal death.

By understanding these concepts, we can better appreciate the complexities and elegance of cosmic phenomena and the intricate relationships between space, time, and the expansion of the universe.