Soumendra Nath Thakur
January 17, 2025
Light becomes unreachable from sources at distances beyond what light could travel in 13.8 billion years, particularly when the relative recession speed between the source and observer exceeds the speed of light.
Additionally, the expansion of intergalactic space—driven by dark energy—increases the physical distance between distant sources and observers. Photons expend additional energy to traverse this growing separation. Over time, cumulative energy loss diminishes photons' ability to propagate as electromagnetic waves at their inherent speed, rendering them incapable of reaching us. The observed 46-billion-light-year horizon of the universe may be linked to this energy dissipation.
Scientific and Mathematical Consistency
1. Hubble's Law and Physical Distance (d):
Hubble's Law, v = H₀⋅d, describes the recession velocity (v) of galaxies in terms of the Hubble constant (H₀) and the distance (d) between objects.
• For distant galaxies, v can exceed the speed of light (c) due to the expansion of space, making their light unreachable.
• Here, d represents measurable physical separation, consistent with classical mechanics, rather than an abstract "stretching of space."
2. Dark Energy and Increasing Separation:
While Hubble's Law treats d as static, the repulsive effects of dark energy dynamically increase physical separations, causing galaxies to recede and inducing the observed cosmic redshift.
3. Redshift and Distance:
The cosmological redshift (z) arises from the increasing separation between galaxies, with the wavelength stretching proportionally:
1 + z = λᴏʙꜱᴇʀᴠᴇᴅ/λꜱᴏᴜʀᴄᴇ.
This redshift reflects physical motion, consistent with classical mechanics.
4. Photon Energy Loss in Expanding Space:
The energy of a photon (E = h⋅f) diminishes as its frequency (f) decreases with increasing z:
f ∝ 1/ (1+z).
This represents the cumulative energy loss as photons traverse expanding distances.
5. Observable Universe and Energy Limits:
The observable universe's radius (~46 billion light-years) corresponds to the farthest distance light has travelled since the Big Bang, incorporating the cumulative effects of dark energy-driven expansion.
6. Mathematical Horizon:
The radius of the observable universe can be expressed as:
dᴏʙꜱᴇʀᴠᴀʙʟᴇ = c ∫(0 to tₚᵣₑₛₑₙₜ) {1/a(t)H(t)} dt,
where a(t) is the scale factor and H(t) is the Hubble parameter. This integral reflects the influence of cosmic expansion on photon travel.
7. Consistency with Hubble's Framework:
• v = H₀⋅d remains valid, with d interpreted as dynamic physical distance.
• Dark energy's repulsive effects reconcile the equation with modern observations, without invoking additional variables for "space stretching."
Logical Implications
1. Unreachable Light:
Light from sources receding faster than c due to cosmic expansion becomes undetectable.
2. Dark Energy's Role:
Dark energy accelerates cosmic expansion, increasing separations and stretching photon wavelengths, leading to redshift and energy loss.
3. Energy Depletion and Photons:
Over vast distances, cumulative energy loss renders photons incapable of maintaining wave properties, explaining the limits of the observable universe.
Conclusion
This analysis integrates Hubble's Law, redshift, and dark energy effects into a cohesive framework, explaining why light from extremely distant sources becomes unobservable. It preserves the classical mechanics foundation while aligning with modern cosmological observations, highlighting the interplay between energy loss, cosmic expansion, and the observable universe's horizon.
#observableuniverse #cosmicexpansion
