[EvaH (OP)]

Peter asks:

If light is said to have no mass, then why can it not move faster than 300,000 kps? Is it that the Higgs boson lends mass to the photon? If so then it truly does have mass...

What do you think?

[Halc]

If light is said to have no mass, then why can it not move faster than 300,000 kps? Is it that the Higgs boson lends mass to the photon? If so then it truly does have mass...

Light is energy, and energy is equivalent to mass (E=mc²), hence light has mass. This also makes the mass of a given photon frame dependent. What light lacks is proper mass (rest-mass).
So light thus has momentum and inertia, but lacking proper mass, it cannot meaningfully exist at any speed less than light since that velocity would be stationary in some inertial frame, which would mean light being at rest.

A Higgs boson has proper mass, and thus cannot be a component of light.

[jeffreyH]

The energy of a photon is given by E = hf. Where h is the Planck constant and f is the frequency of light. To expand upon what Halc said, the frequency of light is frame dependent and so therefore is any energy detected from measuring the photon. Thus red shifted light has lower energy than blue shifted light.

E = mc² requires rest mass which light does not have.

[Halc]

I stand corrected.
It seems that the general equation is E=√((m₀c²)² + (pc)²) where m₀ is proper mass and p is momentum.
For any object at rest, that reduces to E=mc².  For a photon which has no proper mass, it reduces to E=pc, which is almost mc² since momentum (p) is mv

[Janus]

I stand corrected.
It seems that the general equation is E=√((m₀c²)² + (pc)²) where m₀ is proper mass and p is momentum.
For any object at rest, that reduces to E=mc².  For a photon which has no proper mass, it reduces to E=pc, which is almost mc² since momentum (p) is mv

In the general equation, p is the relativistic momentum, which for something with a non-zero rest mass(m) is
mv/sqrt(1-v^2/c^2).
Again, since the m here refers to proper mass, it doesn't apply to a photon.  Instead, the momentum for a photon is found by
p = hf/c
And the general equation ends up giving you E= hf for the photon.

[Bill S]

Again, since the m here refers to proper mass, it doesn't apply to a photon.  Instead, the momentum for a photon is found by
p = hf/c
And the general equation ends up giving you E= hf for the photon.

I understand both equations (surprise!), but am not clear as to how p = hf/c becomes E= hf.

[jeffreyH]

Again, since the m here refers to proper mass, it doesn't apply to a photon.  Instead, the momentum for a photon is found by
p = hf/c
And the general equation ends up giving you E= hf for the photon.

I understand both equations (surprise!), but am not clear as to how p = hf/c becomes E= hf.

Energy is momentum times velocity. Here it is pc. Since hf/c times c cancels out the speed of light you are left with E = hf.

[Bill S]

Thanks, Jeffrey; got it,  there could be hope for me yet.

[Artur77]

A photon has no rest mass, and so it actually doesn’t rest, but nevertheless has a momentum that is frequency dependent.

The photon momentum was discovered experimentally by Arthur Compton, for this work he received the Nobel Prize in Physics in 1927.

[PmbPhy]

The energy of a photon is given by E = hf. Where h is the Planck constant and f is the frequency of light. To expand upon what Halc said, the frequency of light is frame dependent and so therefore is any energy detected from measuring the photon. Thus red shifted light has lower energy than blue shifted light.

E = mc² requires rest mass which light does not have.

The energy of a photon is E = pc where p = momentum (derived from classical EM). since p = mv and for photons v = c we have p = mc. (me defined this way is called relativistic mass). Substitute this into E = pc and we get E = mc^2. Note that has momentum has relativistic mass. Einstein proved light has rel-mass this this 1907 paper. This mass is aka relativistic mass, holds for tachyons (v = c) and tardyons (v < c).

The answer to the question "does light have mass" depends on what definition one means when they ask the question, i.e. proper mass or relativistic mass.

[Bill S]

Thanks, Pete. Different perspectives on any subject/problem are always valuable.  Sometimes, just a difference in wording can bring fresh enlightenment. A combination of #6 & #9 is just what I needed.

[Bill S]

In spite of being on 12 wks “house arrest” I’m having difficulty finding time for posting, but I really want to be sure I’ve grasped this, so comments on the following would be appreciated.

E= energy in Joules.
F = frequency in hertz =1/s.
h= Planck’s constant.
λ = wavelength = distance between crests in a wave cycle.

The momentum of a photon is given by the equation p = hf/c.  Energy is momentum times velocity; so, with velocity = “c”, energy = pc. 

So, Momentum: p = hf/c
Energy: Momentum times velocity: hf/c times c = hf. Thus; E=hf.

The equation E=mc² does not apply to the photon.  A “stationary” photon would have no mass, its energy would be dissipated, so it would not exist.

[alancalverd]

It's not intuitively obvious why p = hf/c unless you follow Einstein's derivation of photon momentum.
We know E = hf because Planck's model of the black body spectrum is vindicated by experiment.
Now if we have some photons in a hypothetical box, we can add up the energy of all the photons and divide by the volume of the box to get a figure for energy density.
We then note that energy per unit volume is equivalent to pressure i.e. force per unit area. Just like the gas laws.
So by analogy with the kinetic theory of gases, we can assign a momentum to a photon. In fact it's easier than gas mechanics because all photons move at the same speed.   

[Colin2B]

The equation E=mc² does not apply to the photon. 

Not strictly true. The problem is you are using the short form of Einstein’s equation. I think you will recall:
E_r² = (m₀c²)²+(pc)²
So where m₀=0 the equation reduces to E_r=pc and Alan neatly explains the other part of the energy momentum relationship

[alancalverd]

Energy is momentum times velocity; so, with velocity = “c”, energy = pc. 

Er, not quite!
Kinetic energy = ½mv²
Momentum = mv
You have to account for a factor of 2.
Hence Einstein's necessarily pedantic derivation: force is the rate of change of momentum, hence momentum = integral of force, and there's your multiple.
Dimensional analysis has an Achilles heel!
   

[Bill S]

Bugg’r!  Why do things always seem to become more complicated, just when I think I’m getting somewhere?
Thanks, anyway; it’s a bit more to think about, and thinking is probably a good thing to keep doing.

[Bill S]

Just checking.

M_o = rest mass.

The following two equations say the same thing.

1. Er² = (m₀c²)²+(pc)²     
2. E² = m² c⁴ + p² c²

E² = m² c⁴ applies to situations in which the object is considered as being at rest relative to the observer.
p² c² is added to the equation when the object is considered as being in motion relative to the observer.

[Colin2B]

Just checking.

Yes, that’s right.
Also, be careful not to fall into the trap many do of saying mass and energy are the same thing. An equivalence is not the same as 2 things being the same

[syhprum]

I am fascinated as to what the mass of a cubic meter of sunlight close to the Earth would be is it something we can calculate .
how many photons would it contain ?

[alancalverd]

The mass would be zero. But you can calculate its momentum since we know the irradiance at altitude is towards 1.5 kW/sq m, so the energy content of a cubic meter is the input power multiplied by the time it takes each photon to move 1 meter (1/300,000,000 s). You might assign an average photon energy of say 2 eV, and thus estimate the photon flux.

It is left as an exercise to the reader!