# Why Don't Photons have mass?
**URL:** https://boards.straightdope.com/t/why-dont-photons-have-mass/164600
**Category:** Factual Questions
**Created:** [March 27, 2003, 8:25pm UTC](https://boards.straightdope.com/t/why-dont-photons-have-mass/164600 "2003-03-27T20:25:28Z")
**Posts on this page:** 20
**Page:** 1
### Author:  [@Logical\_Phallacy](https://boards.straightdope.com/u/Logical_Phallacy)
#### Post date: [March 27, 2003, 8:25pm UTC](https://boards.straightdope.com/t/why-dont-photons-have-mass/164600/1 "2003-03-27T20:25:28Z")
I’m most interested in the topic question, though here’s a fun factoid for those of you that were nice enough to enter my thread:
According to the Theory of Relativity, photon particles have not aged a second since the Big Bang.
Source: The Elegant Universe, by Brian Greene
Feel free to comment on the above, but I’d also love to find out why photons can’t have mass, are they all of equal size?
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### Author:  [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)
#### Post date: [March 27, 2003, 8:27pm UTC](https://boards.straightdope.com/t/why-dont-photons-have-mass/164600/2 "2003-03-27T20:27:06Z")
Cause they’re not Catholic!
[sub]Sorry, couldn’t resist.[/sub]
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### Author:  [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)
#### Post date: [March 27, 2003, 8:32pm UTC](https://boards.straightdope.com/t/why-dont-photons-have-mass/164600/3 "2003-03-27T20:32:14Z")
Ok, seriously now. I read that book (excellent, by the way), and as I understood it, essentially everything in the universe is moving at the speed of light sharing that velocity in either space or time. Photons, being massless, only move in the space dimensions, and have no velocity “left over” to mive in the time dimension. Massive objects cannot move at the speed of light in space, and so are moving near the speed of light through time. It’s a bit confusing, and I don’t fully understand it myslef, but that’s the gist of it.
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### Author:  [@li\_l\_Dickie\_Dirtz](https://boards.straightdope.com/u/li_l_Dickie_Dirtz)
#### Post date: [March 27, 2003, 8:41pm UTC](https://boards.straightdope.com/t/why-dont-photons-have-mass/164600/4 "2003-03-27T20:41:37Z")
Because they don’t really exist?
Anyway, I believe they do have rest mass. If you could ever get one to stop.
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### Author:  [@SlickRoenick](https://boards.straightdope.com/u/SlickRoenick)
#### Post date: [March 27, 2003, 8:47pm UTC](https://boards.straightdope.com/t/why-dont-photons-have-mass/164600/5 "2003-03-27T20:47:39Z")
I wish I remember where I heard this, but I believe that photons do have mass to them–it’s just infinitely small. Something like 4 lbs of photons hit the eart in a _year_
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### Author:  [@TGWATY](https://boards.straightdope.com/u/TGWATY)
#### Post date: [March 27, 2003, 8:57pm UTC](https://boards.straightdope.com/t/why-dont-photons-have-mass/164600/6 "2003-03-27T20:57:06Z")
The masslessness of photons is a given. There is no real theory yet to explain the masses of the various particles in terms of something more fundamental.
That said, photons have to be treated somewhat differently than other particles within the theory of relativity. Whereas, the mass of an electron is truly a variable within the theory – a number that we have to plug in but could in principle take on any value – we cannot plug in anything except zero for photons without contradictions.
This can be summed up as _all particles that travel at the speed of light must have zero mass, and vice versa._
For example, in relativity theory the energy of a particle is
E = mc^2 (1-v^2/c^2)^(-1/2)
(that’s mc-squared divided by the square root of 1 minus v-squared over c-squared, c is the speed of light.)
which reduces to the familiar E= mc^2 for particles at rest.
Notice that if v=c, E is infinite. Unless m=0, that is. Mass must be zero for energy to be finite. (0/0 is undefined and can in some sense represent _any_ number.) For photons, v has to be c, because that’s what c is by definition – the speed of photons.
This is just one example. In short, if photons had non-zero mass, the theory of relativity would have to be redone from scratch.
What Muldoon is probably thinking of is that photons have **momentum**. Even though they are massless, the light from the Sun does exert a small push on the earth.
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### Author:  [@g8rguy](https://boards.straightdope.com/u/g8rguy)
#### Post date: [March 27, 2003, 9:16pm UTC](https://boards.straightdope.com/t/why-dont-photons-have-mass/164600/7 "2003-03-27T21:16:34Z")
**TGWATY** beat me to it, I see on preview. I’ll simply note that essentially, the reason that we say that photons are massless is because it seems that relativity is correct. Relativity tells us that if photons travel at the speed of light, then they must be massless, and of course it wouldn’t make a whole lot of sense to have photons which didn’t travel at the speed of light.
This, of course, just begs the question “why is relativity correct,” which is not one we can answer. Experiment seems to say that it _is_ right, but it will never tell us _why_ it’s right; that’s a job for philosophers.
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### Author:  [@mooka](https://boards.straightdope.com/u/mooka)
#### Post date: [March 27, 2003, 10:02pm UTC](https://boards.straightdope.com/t/why-dont-photons-have-mass/164600/8 "2003-03-27T22:02:28Z")
So can someone tell me if i understand this right…
Energy = mass. Thus we can’t travel at light speed, because we would need infinite energy to accelerate to this speed, as our mass would increase as our speed does.
Photons travel at light speed, so they possess velocity which equals energy. However they don’t possess mass. Thus energy doesn’t equal mass. Is the relationship more like mass = rest mass + (velocity x rest mass)? Thus it is possible to have a great deal of energy, but not have any mass.
I know i’m ignoring other types of energy here, i just want to understand the relationship between velocity and mass.
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### Author:  [@JasonFin](https://boards.straightdope.com/u/JasonFin)
#### Post date: [March 27, 2003, 10:31pm UTC](https://boards.straightdope.com/t/why-dont-photons-have-mass/164600/9 "2003-03-27T22:31:16Z")
One relationship which might help you think about these things is that potential energy = rest mass (This is precisely true in a system of units where c = 1). The definition of potential energy used here is that an object has potential energy equal to its energy in the inertial reference frame in which its energy is a minimum. If there does not exist such a reference frame, then the object’s energy can be made arbitrarily small by choosing an appropriate reference frame and its potential energy (and therefore rest mass) is zero.
This procedure is summarized by the equation E^2 = p^2 c^2 + m^2 c^4, which describes the relationship between energy, momentum, and mass which always applies for all particles. Note that when physicists say simply “mass,” they normally mean rest mass, which is also called invariant mass.
It has been determines by experiment that for a photon E = h f, where f is the photon’s frequency and h is Planck’s constant. It has also been determined that a photon’s momentum is p = h f/c. Together these imply that m = 0, which is in agreement with theory.
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### Author:  [@bonzer](https://boards.straightdope.com/u/bonzer)
#### Post date: [March 28, 2003, 12:30am UTC](https://boards.straightdope.com/t/why-dont-photons-have-mass/164600/10 "2003-03-28T00:30:00Z")
> [@](#):
>
> \*Originally posted by g8rguy \*
> Relativity tells us that if photons travel at the speed of light, then they must be massless, and of course it wouldn’t make a whole lot of sense to have photons which didn’t travel at the speed of light.
Not quite. The usual presentations of SR start from the two postulates that the laws of physics are the same in all inertial reference frames and that the speed of light is an invariant, i.e. a law of physics. But it’s also possible to replace the second postulate with one that states that there’s an invariant maximum speed. One then argues that _experimentally_ this appears to be the speed of photons. But one couldn’t rule out a **tiny** non-zero photon mass by this argument.
The better answer is gauge invariance. In an unbroken gauge theory, _all_ the masses have to be zero. One might almost argue that the photon is the natural case and the bigger problem has always been to explain why other particles have mass. Hence the importance of the Higgs mechanism.
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### Author:  [@eburacum45](https://boards.straightdope.com/u/eburacum45)
#### Post date: [March 28, 2003, 12:31am UTC](https://boards.straightdope.com/t/why-dont-photons-have-mass/164600/11 "2003-03-28T00:31:14Z")
‘Something like 4 lbs of photons hit the earth in a year’
Hmm… that would be light pressure, perhaps- the force that light imparts to an object when it hits it.
The light loses energy by this transaction and increases in wavelength…
but I would have thought it was a bit more than 4 pounds per year, or how are solar sails supposed to work?
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### Author:  [@g8rguy](https://boards.straightdope.com/u/g8rguy)
#### Post date: [March 28, 2003, 1:00am UTC](https://boards.straightdope.com/t/why-dont-photons-have-mass/164600/12 "2003-03-28T01:00:55Z")
> [@](#):
>
> \*Originally posted by bonzer \*
> **Not quite. The usual presentations of SR start from the two postulates that the laws of physics are the same in all inertial reference frames and that the speed of light is an invariant, i.e. a law of physics. But it’s also possible to replace the second postulate with one that states that there’s an invariant maximum speed. One then argues that _experimentally_ this appears to be the speed of photons. But one couldn’t rule out a tiny non-zero photon mass by this argument.**
Good catch. Thanks!
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### Author:  [@Ender\_Will](https://boards.straightdope.com/u/Ender_Will)
#### Post date: [March 28, 2003, 5:04am UTC](https://boards.straightdope.com/t/why-dont-photons-have-mass/164600/13 "2003-03-28T05:04:26Z")
I am by no means a physicist, so I’ll assume that everyone explaining how photons can’t have mass are correct. But, I do have a question for you. If light cannot escape a black hole due to its gravity, wouldn’t that require photons to have mass?
Fg=G(M1M2/D2)
So if a photon’s mass is zero, the whole equation would be zeroed, correct?
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### Author:  [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)
#### Post date: [March 28, 2003, 5:09am UTC](https://boards.straightdope.com/t/why-dont-photons-have-mass/164600/14 "2003-03-28T05:09:38Z")
I thought it was F=(G.M[sub]1[/sub].M[sub]2[/sub])/R[sup]2[/sup]?
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### Author:  [@Achernar](https://boards.straightdope.com/u/Achernar)
#### Post date: [March 28, 2003, 5:10am UTC](https://boards.straightdope.com/t/why-dont-photons-have-mass/164600/15 "2003-03-28T05:10:44Z")
Well, that’s a classical equation. You can’t use it to accurately describe:
a) photons, or
b) black holes, or
c) much less both at the same time.
But even classically speaking, yes, the gravitational force on a photon would be zero, but remember that F = ma. So you can cancel out the m’s and get:
a = GM/D[sup]2[/sup]
So photons will be accelerated just like everything else, regardless of mass. Classically, you define a black hole by setting the escape speed equal to the speed of light.
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### Author:  [@Logical\_Phallacy](https://boards.straightdope.com/u/Logical_Phallacy)
#### Post date: [March 28, 2003, 5:45am UTC](https://boards.straightdope.com/t/why-dont-photons-have-mass/164600/16 "2003-03-28T05:45:41Z")
Thank you all for your responses, but for some odd reason I haven’t been able to derive a logical explanation from the data here…I mean I don’t see how ‘it would mess up the equations we use’ is a legimate reason why some physical matter could conceptually have no weight…
And the posts are contradictory, ie “4 lbs of photons hit earth every year” is entirely the opposite of what others were saying about mass=0…
how can any physical thing not have mass? there is something fishy here.
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### Author:  [@Logical\_Phallacy](https://boards.straightdope.com/u/Logical_Phallacy)
#### Post date: [March 28, 2003, 5:53am UTC](https://boards.straightdope.com/t/why-dont-photons-have-mass/164600/17 "2003-03-28T05:53:59Z")
do photons have weight?
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### Author:  [@stypticus](https://boards.straightdope.com/u/stypticus)
#### Post date: [March 28, 2003, 5:55am UTC](https://boards.straightdope.com/t/why-dont-photons-have-mass/164600/18 "2003-03-28T05:55:29Z")
There was a recent experiment in which a physicist claimed to have _stopped_ light, held it in place for some length of time, then re-started it. Certainly the speed of light is reduced when it travels through different media; the speed of light in water is less than in air is less than in a vacuum. The constant _c_, however, is …uh, constant.
Seems to me a photon in any non-vacuum medium could have mass and not violate the infinite energy conundrum **TGWATY** presented.
Comments?
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### Author:  [@Achernar](https://boards.straightdope.com/u/Achernar)
#### Post date: [March 28, 2003, 6:05am UTC](https://boards.straightdope.com/t/why-dont-photons-have-mass/164600/19 "2003-03-28T06:05:21Z")
**Logical Phallacy** : It depends on what you mean by “mass” and “weight”. If you put a box full of light on a scale, it would read heavier than for an empty box. If you wanted to push an object, you could do so by throwing a bunch of photons at it. If the Earth were receiving radiation from the Sun and not giving off or reflecting any radiation, the Earth would gain mass at a rate of some 260,000 tons per year, just because of the light hitting it.
But none of these things is the same thing as having what physicists rather misleadingly call **mass**. So, the answer is no, photons do not have mass, but this might not mean exactly what you think it means. If you think that no physical thing can exist without mass, then I think that you are (understandably) confused about just what mass is.
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### Author:  [@g8rguy](https://boards.straightdope.com/u/g8rguy)
#### Post date: [March 28, 2003, 6:18am UTC](https://boards.straightdope.com/t/why-dont-photons-have-mass/164600/20 "2003-03-28T06:18:00Z")
About the posts being contradictory… Here’s some basic things you need to know about photons.
1. They have no mass
2. Thus, they travel at the speed of light
3. Nevertheless, they carry energy and momentum
4. They can transfer that energy and momentum to things that do have mass.
5. Because they travel through space and gravity is just space being bent, gravity affects them.
Okay, that being said… when we think without the wonders of relativity, mass tells us how things create gravity and how things respond to gravity. And without the wonders of relativity, photons are these rather dull little things that ignore gravity entirely.
Unfortunately, in the final analysis, mass really doesn’t tell us a whole lot, once we start talking about relativity. What matters then is energy and momentum. I have this vague premonition that your next question will be just how a massless object can carry energy and momentum, and explaining that requires someone who can phrase things a lot more clearly than me.
Switching over briefly to **stypticus** , the speed of light is reduced when it travels through different media, true. The speed of a photon isn’t. What’s happening is that a photon travels through the vacuum between molecules in the media at _c_, then gets absorbed, then some time later, gets emitted again with speed _c_, and so on, so that by the time it gets to the other end, it’s taken longer than you’d think it should; light has been slowed down. This is not to say that any single photon started moving at less than _c_.
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