# Does light have velocity?

1. Oct 14, 2014

### avito009

Firstly I know that light has a speed of 299 792 458 m / s. But does it have a velocity. Can this be plotted on graph that is (The velocity)?

Next if you derive the formula V2= 2Ek/ m. Where V2 is the velocity squared and Ek is kinetic energy and m is the mass. This is derived from Ek= 1/2 mv2.

So if we try to find velocity of a photon then the m would be zero and anything divided by zero is undefined. So why is the velocity of light undefined? V2= 2Ek/ 0= undefined.

2. Oct 14, 2014

### Matterwave

Certainly, light has a velocity since it's definitely moving some direction. Light (in vacuum) has a velocity $\vec{v}=c\hat{v}$ which is really easy since its speed is constant, the only thing you have to specify is the direction of travel $\hat{v}$.

The formula $E_k=\frac{1}{2}mv^2$ is only valid for $v \ll c$, and is only valid for massive particles where $m\neq 0$. For massive particles with speed close to $c$ the correct formula is $E_k=(\gamma-1) mc^2$. For a massless particle like the photon, we have to look towards quantum mechanics to give us the energy $E_k = hf$. The energy won't be speed dependent since all massless particles travel at the same speed, but it is rather the frequency of the massless particles that govern its energy.

3. Oct 14, 2014

### e.bar.goum

Yes, light has a velocity. I take a laser, I point it towards the ground, the photons have velocity c towards the ground.

Now, you cannot use Ek = 1/2 mv2. That is only correct in when v<<c, which, by your very question, is not the correct use of the definition. You must use the full relativistic equation for kinetic energy, namely:

Ek = sqrt(p2c^2 + m2 c4 ) - mc2

Be also aware that the kinetic energy is defined with speed not velocity - energy is a scalar, and my kinetic energy is the same if I'm travelling at 10 m/s south, or 10 m/s north.

ETA: Sniped by Matterwave.

4. Oct 14, 2014

### Matterwave

The reason I did not use the equation $E_k = \sqrt{p^2c^2+m^2 c^4}-mc^2$ is that for $m=0$ this reduces obviously to $E_k=pc$. Of course this equation is true, but the momentum of a mass-less particle will perhaps lead to just more confusion. And of course the next question is probably going to be "what's the momentum of a photon?" (which will get you right back to $p=h/\lambda=hf/c=E_k/c$).

5. Oct 14, 2014

### e.bar.goum

Amusingly, I used $E_k = \sqrt{p^2c^2+m^2 c^4}-mc^2$ for precisely the reason you didn't.

6. Oct 14, 2014

### avito009

You must note that the concept of frequency applies to waves only and not particles.

7. Oct 14, 2014

### Matterwave

This is not true, as was shown by de-Broglie in the early 1900's.

Light certainly has a frequency associated with it!

8. Oct 14, 2014

### Staff: Mentor

I believe there's also that small caveat about light being an EM wave too.

9. Oct 14, 2014

### sophiecentaur

De Broglie talks about the Wavelength of a particle and not a Frequency.

10. Oct 14, 2014

### Matterwave

I believe where you have a wavelength, you have a frequency $f=c/\lambda$. But even if that part of my argument is somehow wrong, light certainly has a frequency associated with it, and the formula $E=hf$ is certainly valid!

11. Oct 14, 2014

### sophiecentaur

E = hf applies to Photons but not to particles in general. For particles, P = h/λ is the relevant expression and that's what de Broglie was talking about - not involving frequency. The velocity of de Broglie waves cannot be c because there is mass involved.

12. Oct 14, 2014

### Matterwave

Ah, I see where my post was unclear. Sorry about that. I meant only for $E=hf$ to apply to light as a particle.

13. Oct 14, 2014

### David Carroll

Ironic. Matterwave is not merely justifying an argument, but his very username!

14. Oct 14, 2014

### avito009

Does the equation V2= 2Ek/ m for v<<c prove that, for the velocity to be higher either the mass has to be less or the kinetic energy has to be higher for the object to attain high velocity?

So does that prove that the more massive the object, the lesser will be its speed (Velocity) and if the speed has to be more then the object has to have more kinetic energy?

15. Oct 15, 2014

### Staff: Mentor

The equation is just showing a relationship between velocity, mass, and kinetic energy. If two objects are moving at the same speed then the one with more mass will have more kinetic energy. Two objects can have equal kinetic energy, yet have wildly different velocities if their masses are also very different.

16. Oct 15, 2014

### Matterwave

Mass is not something that will change in that equation, for a given particle. Only the kinetic energy and velocity may change. So higher velocity = higher kinetic energy. That's basically all that equation is saying.