Photon Momentum: Massless but Impactful

[Parbat]

Photon has momentum but is massless.Doesn't that seem strange?

 

[Bob S]

If you write down the fully relativistic equation for momentum (in pc units) for any particle (including photons) of kinetic energy T, the quation is

(pc)² = (T + mc²)² - (mc²)²

= T² + 2(mc²)T

So, for a bullet use the second term; for a photon use the first (for mass = 0). So a massless photon has momentum.

Bob S

 

[jcsd]

Seems a bit strange of course when we've only encountered Newtonian physics as we're always taught p=mv, but relativirty shows that particles that travel at c can only have zero mass.

 

[maxverywell]

No it's not strange because photon has energy. So its momentum is $$p=E/c=h/\lambda$$

(ok it is little bit strange...)

 

[Bob S]

Seems a bit strange of course when we've only encountered Newtonian physics as we're always taught p=mv, but relativirty shows that particles that travel at c can only have zero mass.

No.

"Seems a bit strange of course when we've only encountered Newtonian physics as we're always taught p=mv, but relativirty shows that particles that travel at c [STRIKE]can only have[/STRIKE] may have zero mass".

Also, in Newtonian mechanics, p = sqrt(2mE) where E = ½mv²

Bob S

 

[jcsd]

No.

"Seems a bit strange of course when we've only encountered Newtonian physics as we're always taught p=mv, but relativirty shows that particles that travel at c [STRIKE]can only have[/STRIKE] may have zero mass".

Also, in Newtonian mechanics, p = sqrt(2mE) where E = ½mv²

Bob S

No, not 'may', 'must'. The four-momentum of a particle is tangent to it's wordline for a particle traveling at c this means it's four-momentum is always null. The mass of particle (in the absence of a rest frame to define it) can be taken as the norm of it's four-momentum which is zero for a particle with null four-momentum. Hence all particles traveling at c MUST have zero mass (unless we're going to allow particles to have undefined four-momentum and hence undefined momentum and energy).

In Newtonian mechanics a particles momentum is defined as p(t) = mv(t).

Your definition is clearly incorrect as momentum is a vector quantity whereas your definition defines a scalar quantity.

 

[Vanadium 50]

No, not 'may', 'must'.

Exactly.

$$v = c \sqrt{1-\frac{m^2 c^4}{E^2}}$$

 

[Bob S]

From jcsd:...but relativity shows that particles that travel at c can only have may have zero mass".No, not 'may', 'must'. The four-momentum of a particle is tangent to it's wordline for a particle traveling at c this means it's four-momentum is always null. The mass of particle (in the absence of a rest frame to define it) can be taken as the norm of it's four-momentum which is zero for a particle with null four-momentum. Hence all particles traveling at c MUST have zero mass (unless we're going to allow particles to have undefined four-momentum and hence undefined momentum and energy).

You are correct.

From Bob S: "but relativity shows that particles that travel at c [STRIKE]can only have[/STRIKE] may have zero mass".

My pocket calculator shows that a 3.5 TeV proton in LEP has a v/c =

β = 1-1/2γ² = 1-3.6·10^-8 = 0.999 999 964

For the 10²⁰ eV Oh My God cosmic ray proton

β = 1-1/2γ² = 1-5·10^-23 = 0.999 999 999 999 999 999 999 9 (more or less)

So any particle with mass >0 cannot have a velocity of exactly c. I was not careful enough in rounding off.

Bob S