Understanding Relativistic Energy Equations: Are They Linear?

[jaketodd]

Are Einstein's energy equations for relativistic speeds linear? For example, if you had something going at relativistic speed and then slowed it, but still had it at relativistic speed, would the decrease in energy be directly proportional to the amount you slowed the thing down?

Thanks,

Jake

 

[jtbell]

Relativistic energy:

$$E = \frac{m_0 c^2}{\sqrt{1 - v^2 / c^2}}$$

Work out an example or two for yourself, and see what you get.

 

[yuiop]

You can also use:

$$E = \sqrt{(m_0 c^2)^2 - \frac{(m_0 v c)^2}{(1-v^2/c^2)}} = \sqrt{(m_0 c^2)^2 - (p c)^2}$$

Where p = relativistic momentum. This form has the advantage that it can be used for particles with zero rest mass like photons.