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Hi, I am thinking about acceleration. Let's think we have a force of $1$ N and a particle of $1$ kg, then acceleration will be $1$. So the speed gets higher every second and $c$ seconds later, in Newtonian mechanics, the particle will reach the speed of light. In relativity, of course, something like that cannot happen. So, what are the equations that describe acceleration in relativity?

Valter Moretti
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Layla
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1 Answers1

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Classicaly you have

$$ m\frac{\mathrm{d}v}{\rm{d}t}=F $$

In relativity, closer to speed of light the particle is, higher mass it gets. This increase of mass is expressed by gamma factor: $\gamma=1/\sqrt{1-v^2/c^2}$. See it is dependent on $v$. Therefore:

$$ \frac{\mathrm{d}(\gamma m v)}{\rm{d}t}=F $$

Le Hamburger
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    Very tempted to -1. It seems frowned upon on this site to use relativistic mass, and for good reason. It's more correct to say that its classical inertia increases as the velocity approaches $c$. –  Jan 17 '14 at 21:05
  • The question did not mention nothing about intertia so I did not want to complicate the answer introducing concept of intertia. – Le Hamburger Jan 18 '14 at 10:14
  • I thought that p/t=f not dp/dt=f – Layla Jan 18 '14 at 21:20
  • Is it clear that d/dt is derivative with respect to time? p/t = f is valid only in the case f is constant. – Le Hamburger Jan 18 '14 at 22:46