# Naked Science Forum

## Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: EvaH on 30/04/2020 12:20:04

Title: Does light have mass?
Post by: EvaH on 30/04/2020 12:20:04

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?
Title: Re: Does light have mass?
Post by: Halc on 30/04/2020 12:35:20
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.
Title: Re: Does light have mass?
Post by: jeffreyH on 01/05/2020 00:09:24
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.
Title: Re: Does light have mass?
Post by: Halc on 01/05/2020 03:45:35
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
Title: Re: Does light have mass?
Post by: Janus on 01/05/2020 16:24:22
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.
Title: Re: Does light have mass?
Post by: Bill S on 03/05/2020 10:38:31
Quote from: Janus
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.
Title: Re: Does light have mass?
Post by: jeffreyH on 03/05/2020 12:04:35
Quote from: Janus
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.
Title: Re: Does light have mass?
Post by: Bill S on 03/05/2020 12:15:43
Thanks, Jeffrey; got it,  there could be hope for me yet.
Title: Re: Does light have mass?
Post by: Artur77 on 03/05/2020 14:00:26
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.
Title: Re: Does light have mass?
Post by: PmbPhy on 03/05/2020 18:14:43
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.
Title: Re: Does light have mass?
Post by: Bill S on 04/05/2020 19:54:16
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.
Title: Re: Does light have mass?
Post by: Bill S on 08/05/2020 17:02:35
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.
Title: Re: Does light have mass?
Post by: alancalverd on 08/05/2020 21:40:02
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.
Title: Re: Does light have mass?
Post by: Colin2B on 08/05/2020 23:24:36
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:
Er2 = (m0c2)2+(pc)2
So where m0=0 the equation reduces to Er=pc and Alan neatly explains the other part of the energy momentum relationship
Title: Re: Does light have mass?
Post by: alancalverd on 09/05/2020 10:42:05
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!

Title: Re: Does light have mass?
Post by: Bill S on 09/05/2020 19:09:35
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.
Title: Re: Does light have mass?
Post by: Bill S on 10/05/2020 16:49:13
Just checking.

Mo = 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.
Title: Re: Does light have mass?
Post by: Colin2B on 11/05/2020 00:14:22
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
Title: Re: Does light have mass?
Post by: syhprum on 11/05/2020 07:08:16
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 ?
Title: Re: Does light have mass?
Post by: alancalverd on 11/05/2020 13:24:47
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!
Title: Re: Does light have mass?
Post by: syhprum on 11/05/2020 14:46:30
I did the calculation some while ago but I forget the answer now, I am amused by that song about lighting a penny candle from a star, pretty easy if you use our local star and a magnifying lens.
Title: Re: Does light have mass?
Post by: Bill S on 11/05/2020 19:38:50
might have trouble finding a penny candle, though.
Title: Re: Does light have mass?
Post by: PmbPhy on 11/05/2020 21:46:55
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!

You're wrong, Bill's right. See my post. Kiinetic energy s not 1/2 mv^2 in relativity it's K = E= E - E_0
Title: Re: Does light have mass?
Post by: hamdani yusuf on 12/05/2020 05:47:13
This mass is aka relativistic mass, holds for tachyons (v = c) and tardyons (v < c).
Quote
A tachyon or tachyonic particle is a hypothetical particle that always travels faster than light.
https://en.wikipedia.org/wiki/Tachyon
Quote
The term comes from the Greek: ταχύ, tachy, meaning rapid. The complementary particle types are called luxons (which always move at the speed of light) and bradyons (which always move slower than light); both of these particle types are known to exist.
Title: Re: Does light have mass?
Post by: Harryobr on 12/05/2020 12:03:23
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Title: Re: Does light have mass?
Post by: Bill S on 12/05/2020 20:56:51
Quote from: Pete
Bill's right

If I’m right, it would be good to know why.  Could you explain “K = E= E - E_0” please?
Title: Re: Does light have mass?
Post by: PmbPhy on 13/05/2020 21:32:18
Quote from: Pete
Bill's right

If I’m right, it would be good to know why.  Could you explain “K = E= E - E_0” please?

The total energy E is the sum of kinetic energy K and rest energy E_0, i.e.

E = K + E_0

solve for K to get

K = E - E_0

Title: Re: Does light have mass?
Post by: Bill S on 14/05/2020 14:41:11
Thanks Pete.  I know I'll never be a mathematician, but with a bit of patient encouragement, I can grasp some of the basics, I think. :)
Title: Re: Does light have mass?
Post by: alancalverd on 14/05/2020 17:15:45
All perfectly true, but E0 = 0 for a photon, so we are left with K = E = hc/λ. The question is how to derive p from E, knowing c.

On matters of relativity I defer to Pete - over!
Title: Re: Does light have mass?
Post by: Bill S on 14/05/2020 19:34:35
“And I am right,
And you are right,
And all is right as right can be!”

Title: Re: Does light have mass?
Post by: Bill S on 16/05/2020 14:09:26
I’m still juggling these equations in my head and wondering if there is something I’ve missed.

E = K + E0, solve for K to get:   K = E – E0.
E = K + E0, therefore, K = E – E0
For a photon, E0 = 0, so K = E – 0.  I.e. K = E.
We established earlier that Energy is momentum times velocity; given by the equation p = hf/c.
We also said that, because the velocity of a photon is “c”, hf/c times c = hf. Thus; E=hf.
If K = E, then K must = hf, in this scenario.
Title: Re: Does light have mass?
Post by: alancalverd on 16/05/2020 15:05:43
We established earlier that Energy is momentum times velocity; given by the equation p = hf/c.
It wasn't "established" but merely stated!
As I said, classical momentum pm = 2Km/vm where Km is the kinetic energy of a nonrelativistic particle m of nonzero mass.
For a photon vΦ = c, . The question is why pΦ = E/c and not 2E/c.
As this has baffled me from time to time since 1964, I call upon the right honorable Pete for enlightenment!
Title: Re: Does light have mass?
Post by: Bill S on 16/05/2020 18:37:58
Quote
I call upon the right honorable Pete for enlightenment!

Thank goodness you are not asking me!  I look forward to Pete's response, in the hope that I might understand it.
Title: Re: Does light have mass?
Post by: PmbPhy on 16/05/2020 18:43:59
I’m still juggling these equations in my head and wondering if there is something I’ve missed.

E = K + E0, solve for K to get:   K = E – E0.
E = K + E0, therefore, K = E – E0
For a photon, E0 = 0, so K = E – 0.  I.e. K = E.
We established earlier that Energy is momentum times velocity; given by the equation p = hf/c.
We also said that, because the velocity of a photon is “c”, hf/c times c = hf. Thus; E=hf.
If K = E, then K must = hf, in this scenario.

Seems okay to me.
Title: Re: Does light have mass? r eveything else?
Post by: alancalverd on 16/05/2020 22:30:42
Energy is momentum times velocity;
So why is E = pv for photons but ½pv for everything else?
Title: Re: Does light have mass?
Post by: PmbPhy on 17/05/2020 11:15:05
Energy is momentum
So why is E = pv for photons but ½pv for everything else?
By the way, I was wrong when I said Bill was right when he said "Energy is momentum." . The E = pc for EM radiation is a derived quantity from electrodynamics. Only  in In classical mechanics does kinetic energy = pv/2 = (1/2) mv^2. In relativity kinetic energy = (gamma - 1)m_0 c^2. Kinetic energy + rest energy = E = total inertial energy. When v << c  ->  E = mv^2/2 where m is rest mass.

Mind you that when we're talking about energy here it doesn't refer to total energy just inertial energy. Total energy = kinetic energy + rest energy + potential energy.
Title: Re: Does light have mass?
Post by: alancalverd on 18/05/2020 00:04:47
Hold on there pardner!
Quote
In relativity kinetic energy = (gamma - 1)m_0 c^2

Dang me if it ain't the fact that γ = 1/√(1-v2/c2)
Now yer photon critter is hi-tailin' thru the universe at v = c kinda by definition (curse that Limey Maxwell, denyin' the aether an' all)
Thus γφ = 1/√(0) which is one helluva lot, and (γφ - 1) ain't much smaller (see ole Bill's musin's on Cantor's infinities)
But m0 = 0 for them thar photons.
God-fearin' folk don't much approve o' Yankees multiplyin' the Good Lord's infinity by the Devil's zero, and puttin' in a dash o' Mr Einstein's c2 don't excuse such mathematical blasphemy.
I'm a-mindin' that y'all said E = K + E0 but ain't it the case that E0 = 0 'cause the photon bronco can't never stand still?
So Eφ = "anything you like" + 0?  No wonder New England heathens have fallen under the spell of Darwin.

(I have the entire "Big Bang Theory" on DVD, and when all else fails I look to Sheldon's mother for guidance.)
Title: Re: Does light have mass?
Post by: hamdani yusuf on 18/05/2020 04:19:29
Mind you that when we're talking about energy here it doesn't refer to total energy just inertial energy. Total energy = kinetic energy + rest energy + potential energy.
What is the potential energy of a photon? Can it have non-zero value?
Title: Re: Does light have mass?
Post by: PmbPhy on 18/05/2020 10:01:16
Hold on there pardner!
Quote
In relativity kinetic energy = (gamma - 1)m_0 c^2

Dang me if it ain't the fact that γ = 1/√(1-v2/c2)
That only applies to particles which move at speeds less than the speed of light.

I'm a-mindin' that y'all said E = K + E0 but ain't it the case that E0 = 0 'cause the photon bronco can't never stand still?
That's the reason I don't like to use the term "rest mass' do many relativists. I prefer the term proper mass defined as the magnitude of the 4-momentum of he particle divided by c^2, which is zero for photons.
Title: Re: Does light have mass?
Post by: PmbPhy on 18/05/2020 10:03:40
What is the potential energy of a photon?
Zero.
Title: Re: Does light have mass?
Post by: Bill S on 18/05/2020 19:00:08
Quote from: Pete
I was wrong when I said Bill was right when he said "Energy is momentum."

What I said was:

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

Is this wrong?
Title: Re: Does light have mass?
Post by: PmbPhy on 18/05/2020 21:52:47
Quote from: Pete
I was wrong when I said Bill was right when he said "Energy is momentum."

What I said was:

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

Is this wrong?

Yes. Kinetic energy is 1/2 pv for a particle when v << c. otherwise it's K = E - E_0