Point Masses and the Speed of Light: An Exploration of Relativity

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SUMMARY

The discussion centers on the behavior of two point masses, each 1 kg and 1 meter apart, in relation to the speed of light as they are released. It is established that while gravitational force (Fg) approaches infinity as the distance decreases, relativity prevents these masses from reaching the speed of light (c). Instead, as their velocity approaches c, their mass increases, leading to infinite energy requirements without achieving infinite velocity. Additionally, the assumption of point masses becomes invalid as they approach each other, introducing quantum effects into the scenario.

PREREQUISITES
  • Understanding of Newtonian gravity and gravitational force (Fg)
  • Familiarity with Einstein's theory of relativity and the concept of mass-energy equivalence
  • Basic knowledge of limits in calculus, particularly in relation to velocity and distance
  • Awareness of quantum mechanics and its implications on particle behavior
NEXT STEPS
  • Study Einstein's theory of relativity, focusing on mass increase at relativistic speeds
  • Explore the implications of gravitational forces in general relativity
  • Learn about the concept of quantum effects in particle physics
  • Investigate the mathematical principles of limits in calculus, especially in physical contexts
USEFUL FOR

Physicists, students of theoretical physics, and anyone interested in the implications of relativity and quantum mechanics on particle dynamics.

mr200backstrok
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i was sitting here wondering about something, and I'm not sure, so ill ask.

suppose you take 2 point masses, say 1 kg each, 1 meter apart, and release them. Would they ever reach the speed of light? As they got very close, the [tex]F _{g}[/tex] would near infinity ( [tex]\lim _{distance \rightarrow 0} F_{g} = \infty[/tex] ), which means that it would accelerate at an infinite rate past the speed of light. but, relativity doesn't allow that, and would start reducing the acceleration as the velocity approached c. so, is [tex]\lim _{distance \rightarrow 0} v = c[/tex] (if v is velocity and c is the speed of light)?
 
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as particles increase in speed, they also increase in mass (and the mass can go to infinity). So the energy would, in fact, be infinite, but not the velocity
 
Another issue that has to be considered is that as the two particles get close to each other, the point assumption breaks down. Also quantum effects would begin to play a role.
 

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