I Particles w/ 0 Inertial Mass Traveling Faster than Light?

[TerranIV]

I was just curious if there were any known (theoretical) particles with zero inertial mass that don't travel at light speed. Is this even possible?

 

[Orodruin]

Is this even possible?

No.

 

[TerranIV]

No.

Do we know why having 0 inertial mass causes particles to HAVE to travel at c?

I know it's true, but it doesn't seem intuitive to me. It makes sense why only zero inertial particles CAN travel at c, but I don't understand why they MUST travel at c.

 

[Orodruin]

The speed of a particle is given by $v = pc^2/E$, where $p$ is the momentum and $E$ the total energy. For a general particle $E^2 = m^2 c^4 + p^2 c^2$. If $m = 0$ then $E = pc$ and therefore $v = c$.

 

[PeterDonis]

Do we know why having 0 inertial mass causes particles to HAVE to travel at c?

Because they're the same thing: having zero inertial mass (actually "invariant mass" is a better term) is traveling at c. The geometry of spacetime forces them to be the same.

 

[PeterDonis]

Moderator's note: Thread moved to relativity forum.

 

[PAllen]

As a funny exception, one can have energy, momentum, and mass all be zero. Then velocity is not necessarily c. It is undefined. One may describe this as saying that a massless particle that doesn't exist, need not travel at c.

 

[PeroK]

As a funny exception, one can have energy, momentum, and mass all be zero. Then velocity is not necessarily c. It is undefined. One may describe this as saying that a massless particle that doesn't exist, need not travel at c.

For all particles that don't exist, it is vacuously true that they travel at $c$.

 

[Orodruin]

The classical mistake in topology is to forget about the empty set ...
"All open sets in $\mathbb R$ have an infinite number of elements."

 

[OCR]

Thread moved to relativity forum.

So now. . . it's fun and games in the relativity forum. .

.