Particles having nonzero rest mass can approach the speed of light

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Discussion Overview

The discussion centers around the behavior of particles with nonzero rest mass as they approach the speed of light, particularly focusing on concepts such as mass, energy, and the implications of relativistic mechanics versus Newtonian physics. Participants explore foundational ideas and challenge each other's interpretations of mass and energy in this context.

Discussion Character

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

Main Points Raised

  • Some participants assert that particles with nonzero rest mass can approach but not reach the speed of light, suggesting that their mass would become infinite at that speed.
  • Others argue that modern physics maintains that a particle's mass remains constant, and it is the energy that becomes infinite as the speed approaches that of light.
  • One participant questions the reasoning behind the assertion that mass becomes infinite at light speed, seeking clarification on the fundamental concepts involved.
  • Another participant emphasizes that while mass remains constant, the energy associated with a particle increases, leading to infinite energy at light speed, which is tied to kinetic energy's dependence on mass.
  • A later reply introduces the concept of four-vector mechanics in special relativity, arguing against the idea of using relativistic mass and suggesting that the relationship between force and acceleration cannot be simplified by merely substituting mass with relativistic mass.

Areas of Agreement / Disagreement

Participants express differing views on the nature of mass and energy at relativistic speeds, with no consensus reached on whether mass becomes infinite or remains constant while energy diverges. The discussion reflects multiple competing interpretations of relativistic mechanics.

Contextual Notes

The discussion highlights limitations in understanding the relationship between mass and energy, particularly in the context of Newtonian versus relativistic frameworks. Participants note the need for careful consideration of definitions and the implications of using different models.

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Particles having nonzero rest mass can approach, but not reach, the speed of light, since their mass would become infinite at that speed.

Can anyone expound upon this commencing with the very fundamental concepts (nonzero rest mass, mass, inertia, infinite mass etc.)?
 
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Modern physicists would say that the particle's mass is always the same, and that it is its energy which becomes infinite at the speed of light.

Because energy and mass are quite directly related, however, a particle with more energy behaves, in the framework of Newton's laws, as if it had more mass.

Newton's laws are not correct except at low relative velocities, however -- so rather than modifying them by assuming an "increased mass," it makes more sense to simply not use them at high relative velocities. They are replaced by relativistic mechanics.

Nowadays, when someone says "mass," they mean "rest mass" or "invariant mass," which is a fundamental and unchanging characteristic of the object under scrutiny.

- Warren
 
Why would the mass of a particle become infinite at the speed of light? That was the essential intention of my questions.
 
No, the mass will always be the same. If the mass is non-zero, however, the energy will be infinite at the speed of light. (Kinetic energy depends on mass.)

- Warren
 
Originally posted by chroot
Modern physicists would say that the particle's mass is always the same, and that it is its energy which becomes infinite at the speed of light. ... Newton's laws are not correct except at low relative velocities, however -- so rather than modifying them by assuming an "increased mass," it makes more sense to simply not use them at high relative velocities. They are replaced by relativistic mechanics.

Nowadays, when someone says "mass," they mean "rest mass" or "invariant mass," which is a fundamental and unchanging characteristic of the object under scrutiny.

- Warren

I agree, but with the exception that energy isn't divergent for massless particles which I'm sure you know and I would be careful about the following:

Because energy and mass are quite directly related, however, a particle with more energy behaves, in the framework of Newton's laws, as if it had more mass.

As mentioned in another thread the four vector law of motion for special relativity is four vector force equals mass times four vector acceleration
[tex]F^\mu = mA^\mu[/tex]
where the mass m does not change with speed. The relation "in the framework of Newton's laws" that you are probably considering is the relation between ordinary force and coordinate acceleration. In that case the relativistic behavior can not be described simply by replacing mass with relativistic mass in
f = ma
either. To speed up a particle most effectively you want all the force in the direction of motion and when you do that the relation will be two orders of [tex]\gamma[/tex] too big to be relativistic mass.
 

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