Does Mass Increase as Velocity Approaches the Speed of Light?

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Discussion Overview

The discussion revolves around the concept of mass and momentum in the context of special relativity, particularly focusing on whether mass increases as velocity approaches the speed of light. Participants explore the implications of momentum equations and the limitations imposed by relativistic physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that as momentum increases and velocity approaches the speed of light, mass must also increase to account for this change, suggesting a relationship between momentum and mass.
  • Others propose that momentum in special relativity is described by the equation p = γmv, indicating that classical mechanics is an approximation and that relativistic effects must be considered.
  • One participant emphasizes that an object with mass cannot reach the speed of light, reinforcing the idea that momentum has no upper bound as velocity approaches c.
  • Another participant challenges the notion that momentum can be increased indefinitely, arguing that it is dependent on the limitations imposed by special relativity on mass and velocity.
  • There is a clarification regarding the definition of mass in relation to momentum, with a participant stating that if mass is defined as m = p/v, then it approaches infinity as velocity approaches c.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between mass, momentum, and velocity in special relativity. There is no consensus on how these concepts interact, and the discussion remains unresolved regarding the implications of mass increase as velocity approaches the speed of light.

Contextual Notes

Some limitations in the discussion include the dependence on definitions of mass and momentum, as well as the unresolved mathematical implications of the equations presented. The scope of the discussion is confined to theoretical considerations without practical applications being fully explored.

leftyguitarjo
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I just want to verify that I have the right mindset here on the subject:

p=mv

You can increase the momentum as much as you want, but when v reaches the speed of light, it cannot increase any more, but since momentum is still increasing, that means the mass must be the one to increase, for it is the only thing that can.
 
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Another way to think about it is that the momentum increases faster in special relativity than classically predicted, after all classical mechanics is only an approximation to special relativity. What we should write is,

p\approx mv

And,

p=\gamma mv

And just to clarify, an object with mass cannot reach the speed of light.
 
Last edited:
allright. Thank you.
 
leftyguitarjo said:
I just want to verify that I have the right mindset here on the subject:

p=mv

You can increase the momentum as much as you want, but when v reaches the speed of light, it cannot increase any more, but since momentum is still increasing, that means the mass must be the one to increase, for it is the only thing that can.
v can never reach the speed of light. There is no upper bound for the magnitude of momentum. As v approaches c, p approaches infinity. Therefore if one defines the mass of an isolated object then m = p/v m which approaches infinity.

Pete
 
Hello leftyguitarjo.

I think you have the mathematics back to front. You may not be able to increase momentum as much as you want because it is restricted by any limitations SR imposes on v and m. Momentum p is the dependent variable and varies when mass m and/or velocity v are changed. For a given mass you can increase the velocity at which it moves and so change the momentum. Of course the velocity is limited to less than c. It is not very practical to achieve the same result by holding v constant and altering m. There are other complications such as mass increasing with velocity.

Matheinste.
 
pmb_phy said:
v can never reach the speed of light. There is no upper bound for the magnitude of momentum. As v approaches c, p approaches infinity. Therefore if one defines the mass of an isolated object then m = p/v m which approaches infinity.

Pete
That was a bit confusing. I meant to write
Therefore if one defines the mass of an isolated object as m = p/v then m will approaches infinity as v approaches c.

Pete
 

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