Expansion of the Universe and the Limitations of Hubble's Law

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SUMMARY

The discussion centers on Hubble's Law, which states that the velocity of recession of galaxies is directly proportional to their distance, expressed as v = H0.r. However, the theory of relativity introduces time dilation, represented by the equation t = t0√(1 - v²/c²), suggesting that as velocity approaches the speed of light (v → c), time (t) approaches zero. This implies that the universe's expansion may reach a limit of approximately 2 x 10^10 light-years, beyond which galaxies would appear to slow down relative to an observer. The conversation emphasizes the impossibility of exceeding the speed of light and the implications of time dilation on cosmic expansion.

PREREQUISITES
  • Understanding of Hubble's Law and its mathematical representation
  • Familiarity with the theory of relativity and time dilation concepts
  • Knowledge of the speed of light as a universal constant (c)
  • Basic grasp of astrophysical distances and their significance in cosmology
NEXT STEPS
  • Research the implications of time dilation in relativistic physics
  • Explore advanced concepts in cosmology, such as dark energy and the accelerating universe
  • Learn about the limitations of observational cosmology and the role of redshift
  • Investigate the mathematical derivations of Hubble's Law and its applications in modern astronomy
USEFUL FOR

Astronomers, physicists, and students of cosmology who are interested in the dynamics of the universe's expansion and the interplay between Hubble's Law and relativistic effects.

.ultimate
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According to Hubble's law, Velocity of recession of galaxies is directily proportinal to distance between them

ie v=H0.r

But, according to theory of relativity

Time diliation

t=t0.(underoot 1-v^2/c^2)

as v->c

t=0

That means the universe will expand upto a certain distance ( if the law hold correct) i.e 2.10^10 l.y

After that the galaxies will slow down to the observer

as
 
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.ultimate said:
But, according to theory of relativity

Time diliation

t=t0.(underoot 1-v^2/c^2)

as v->c

t=0
Here i don't think its possible that v>c.Also if it were to be so you would get \gamma as a complex number!
 
I meant as v is almost equal to speed of light, will the recession of galaxies slow down? because t~0
 

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