system
Given the following post, respond as if you're commenting on Reddit:
human
why can't particles of zero mass be at the rest?

in a book I'm reading it says *the fact that a particle has zero mass means, in a way, that it cannot be at rest.* why is that?
gpt
Special relativity says that the following is true for **any** free particle:

**v**/c^(2) = **p**/E,

where **v** is the velocity, **p** is the momentum, E is the total energy, and c is the speed of light.

SR also says that for any free particle:

E^(2) = (mc^(2))^(2) + (**p**c)^(2).

For a massless particle, m = 0, so E = |**p**|c.

Taking the magnitude of the first equation and plugging in E = pc:

v/c^(2) = p/(pc)

v/c = 1

v = c.

Thus a particle with zero mass must always move at c. It cannot be at rest if it's always moving at c.