# How can a massless particle like a photon have transferable momentum? **URL:** \ **Category:** Factual Questions\ **Created:** [October 6, 2005, 5:21am UTC](https://boards.straightdope.com/t/how-can-a-massless-particle-like-a-photon-have-transferable-momentum/325011 "2005-10-06T05:21:38Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![astro](https://avatars.discourse-cdn.com/v4/letter/a/9dc877/32.png) [@astro](https://boards.straightdope.com/u/astro)\ **Post date:** [October 6, 2005, 5:21am UTC](https://boards.straightdope.com/t/how-can-a-massless-particle-like-a-photon-have-transferable-momentum/325011/1 "2005-10-06T05:21:38Z")
I never quite understood the quantum answer (next to last post linked thread below) given in this linked thread about how a photon can transfer momentum or “pressure” if it has no a mass. The Wikipedia article repeats the pressure without mass assertion. Could someone help me out? What’s hitting what to make the “pressure” or transfer of momentum happen? [Are neutrinos unaffected by black holes?](http://boards.straightdope.com/sdmb/showthread.php?t=44073) [From wikipedia](http://en.wikipedia.org/wiki/Photon) > [@](#): > > Unlike most particles, photons have no detectable intrinsic mass, or “rest mass” (as opposed to relativistic mass). Photons are always moving at the speed of light (which varies according to the medium in which they travel) with respect to all observers. Despite their lack of mass, photons have momentum proportional to their frequency (or inversely proportional to their wavelength), and this momentum can be transferred when a photon collides with matter (like a moving billiard ball transfers momentum into another ball). This is known as radiation pressure, which may some day be used for propulsion with a solar sail. ---
**Author:** ![Caligulas](https://avatars.discourse-cdn.com/v4/letter/c/a5b964/32.png) [@Caligulas](https://boards.straightdope.com/u/Caligulas)\ **Post date:** [October 6, 2005, 5:49am UTC](https://boards.straightdope.com/t/how-can-a-massless-particle-like-a-photon-have-transferable-momentum/325011/2 "2005-10-06T05:49:00Z")
Well, the key is right in that quote: “no rest mass”. That means that if a photon were to ever stop (which it can’t), it would not have any mass. However, thanks to you-know-who, we know that E=mc2, which means that (removing the c multiplier) energy (E) = mass (m). Therefore, the kinetic energy of its movement also gives it a “relativistic mass”. ---
**Author:** ![ambushed](https://avatars.discourse-cdn.com/v4/letter/a/3bc359/32.png) [@ambushed](https://boards.straightdope.com/u/ambushed)\ **Post date:** [October 6, 2005, 7:32am UTC](https://boards.straightdope.com/t/how-can-a-massless-particle-like-a-photon-have-transferable-momentum/325011/3 "2005-10-06T07:32:02Z")
> [@Caligulas](#): > > Well, the key is right in that quote: “no rest mass”. That means that if a photon were to ever stop (which it can’t), it would not have any mass. > > However, thanks to you-know-who, we know that E=mc2, which means that (removing the c multiplier) energy (E) = mass (m). Therefore, the kinetic energy of its movement also gives it a “relativistic mass”. And it’s the relativistic mass that transfers the momentum? ---
**Author:** ![Malacandra](https://avatars.discourse-cdn.com/v4/letter/m/45deac/32.png) [@Malacandra](https://boards.straightdope.com/u/Malacandra)\ **Post date:** [October 6, 2005, 9:15am UTC](https://boards.straightdope.com/t/how-can-a-massless-particle-like-a-photon-have-transferable-momentum/325011/4 "2005-10-06T09:15:29Z")
Hmm, this is interesting… e=mc[sup]2[/sup] Kinetic energy = 0.5mv[sup]2[/sup] But for a photon, v = c hence energy = 0.5mc[sup]2[/sup] Hence 0.5mc[sup]2[/sup] = mc[sup]2[/sup] Hence 0.5 = 1. ::wanders off, scratching head:: ---
**Author:** ![Mycroft\_Holmes](https://avatars.discourse-cdn.com/v4/letter/m/a5b964/32.png) [@Mycroft\_Holmes](https://boards.straightdope.com/u/Mycroft_Holmes)\ **Post date:** [October 6, 2005, 9:52am UTC](https://boards.straightdope.com/t/how-can-a-massless-particle-like-a-photon-have-transferable-momentum/325011/5 "2005-10-06T09:52:48Z")
> [@Malacandra](#): > > Kinetic energy = 0.5mv[sup]2[/sup] Only in Newtonian physics. In this calculation you would have to use the rest mass of the photon, which is 0, zo E = 0. An easier way to do it is: Momentum is mass \* speed, so p = mc so the Energy (mc[sup]2[/sup]) is: E = pc For a photon: p = h/λ (h = Planck’s constant; λ = frequency) so: E = hc/λ and since the frequency f is v/λ, and for a photon v = c we get f = c/λ, and thus: E= hf ---
**Author:** ![Malacandra](https://avatars.discourse-cdn.com/v4/letter/m/45deac/32.png) [@Malacandra](https://boards.straightdope.com/u/Malacandra)\ **Post date:** [October 6, 2005, 10:09am UTC](https://boards.straightdope.com/t/how-can-a-massless-particle-like-a-photon-have-transferable-momentum/325011/6 "2005-10-06T10:09:15Z")
Spoilsport. 😃 ---
**Author:** ![Mycroft\_Holmes](https://avatars.discourse-cdn.com/v4/letter/m/a5b964/32.png) [@Mycroft\_Holmes](https://boards.straightdope.com/u/Mycroft_Holmes)\ **Post date:** [October 6, 2005, 10:16am UTC](https://boards.straightdope.com/t/how-can-a-massless-particle-like-a-photon-have-transferable-momentum/325011/7 "2005-10-06T10:16:45Z")
> [@Malacandra](#): > > Spoilsport. 😃 Sorry! 😃 ---
**Author:** ![tim314](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim314/32/3468_2.png) [@tim314](https://boards.straightdope.com/u/tim314)\ **Post date:** [October 6, 2005, 10:42am UTC](https://boards.straightdope.com/t/how-can-a-massless-particle-like-a-photon-have-transferable-momentum/325011/8 "2005-10-06T10:42:32Z")
> [@Malacandra](#): > > Hmm, this is interesting… > > e=mc[sup]2[/sup] > > Kinetic energy = 0.5mv[sup]2[/sup] > > But for a photon, v = c > > hence energy = 0.5mc[sup]2[/sup] > > Hence 0.5mc[sup]2[/sup] = mc[sup]2[/sup] > > Hence 0.5 = 1. > > ::wanders off, scratching head:: Actually, that’s consistent with the following proof: Given a, b such that a = b ab = bb = b[sup]2[/sup] ab-a[sup]2[/sup] = b[sup]2[/sup] - a[sup]2[/sup] a(b - a) = (b + a)(b - a) a = b + a a = a + a a = 2a 1 = 2 Hence 0.5 = 1 ---
**Author:** ![Mycroft\_Holmes](https://avatars.discourse-cdn.com/v4/letter/m/a5b964/32.png) [@Mycroft\_Holmes](https://boards.straightdope.com/u/Mycroft_Holmes)\ **Post date:** [October 6, 2005, 11:16am UTC](https://boards.straightdope.com/t/how-can-a-massless-particle-like-a-photon-have-transferable-momentum/325011/9 "2005-10-06T11:16:39Z")
Should I be a spoilsport again and point out the fallacy in this part? 😃 > [@tim314](#): > > a = 2a > 1 = 2 Nope, I’ll let somebody else do it. Unless the fallacy hasn’t been pointed out within the next four posts. Then I’ll do it! ---
**Author:** ![BwanaBob](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bwanabob/32/2985_2.png) [@BwanaBob](https://boards.straightdope.com/u/BwanaBob)\ **Post date:** [October 6, 2005, 11:52am UTC](https://boards.straightdope.com/t/how-can-a-massless-particle-like-a-photon-have-transferable-momentum/325011/10 "2005-10-06T11:52:00Z")
How about this? a=2a a=0 ---
**Author:** ![Mycroft\_Holmes](https://avatars.discourse-cdn.com/v4/letter/m/a5b964/32.png) [@Mycroft\_Holmes](https://boards.straightdope.com/u/Mycroft_Holmes)\ **Post date:** [October 6, 2005, 11:54am UTC](https://boards.straightdope.com/t/how-can-a-massless-particle-like-a-photon-have-transferable-momentum/325011/11 "2005-10-06T11:54:32Z")
> [@BwanaBob](#): > > How about this? > a=2a > a=0 Bingo! In the next step, he divides both sides of the equation by a, which has to be zero to satisfy a=2a. Dividing by zero is a big no-no! ---
**Author:** ![Malacandra](https://avatars.discourse-cdn.com/v4/letter/m/45deac/32.png) [@Malacandra](https://boards.straightdope.com/u/Malacandra)\ **Post date:** [October 6, 2005, 12:09pm UTC](https://boards.straightdope.com/t/how-can-a-massless-particle-like-a-photon-have-transferable-momentum/325011/12 "2005-10-06T12:09:43Z")
There was another one which I liked, which began with For any a, b let a + b = 2c and ended up proving that a = b, consequently all numbers are the same. I can’t remember how that one goes, though. OP? We don’t need no steenkin’ OP!! 😃 ---
**Author:** ![carterba](https://avatars.discourse-cdn.com/v4/letter/c/85e7bf/32.png) [@carterba](https://boards.straightdope.com/u/carterba)\ **Post date:** [October 6, 2005, 2:16pm UTC](https://boards.straightdope.com/t/how-can-a-massless-particle-like-a-photon-have-transferable-momentum/325011/13 "2005-10-06T14:16:20Z")
> [@Mycroft Holmes](#): > > Bingo! In the next step, he divides both sides of the equation by a, which has to be zero to satisfy a=2a. Dividing by zero is a big no-no! Actually, the fallacy comes earlier than that: > [@](#): > > a(b - a) = (b + a)(b - a) > a = b + a He divided by b-a, but since a=b, b-a=0. ---
**Author:** ![Earthworm\_Jim](https://avatars.discourse-cdn.com/v4/letter/e/f07891/32.png) [@Earthworm\_Jim](https://boards.straightdope.com/u/Earthworm_Jim)\ **Post date:** [October 6, 2005, 2:30pm UTC](https://boards.straightdope.com/t/how-can-a-massless-particle-like-a-photon-have-transferable-momentum/325011/14 "2005-10-06T14:30:55Z")
> [@Caligulas](#): > > That means that if a photon were to ever stop (which it can’t), it would not have any mass. I thought some recent experiments **did** stop photons - From Wikipedia > [@](#): > > Light-slowing experiments > In a sense, any light travelling through a medium other than a vacuum travels below c as a result of refraction. However, certain materials have an exceptionally high refractive index: in particular, the optical density of a Bose-Einstein condensate can be very high. In 1999, a team of scientists led by Lene Hau were able to slow the speed of a light beam to about 17 metres per second, and, in 2001, they were able to momentarily stop a beam. > > In 2003, Mikhail Lukin, with scientists at Harvard University and the Lebedev Institute in Moscow, succeeded in completely halting light by directing it into a mass of hot rubidium gas, the atoms of which, in Lukin’s words, behaved “like tiny mirrors”, due to an interference pattern in two “control” beams. Others: [BBC News link](http://news.bbc.co.uk/1/hi/sci/tech/1124540.stm) [Wiki News link](http://en.wikinews.org/wiki/Light_stopped_for_over_a_second) ---
**Author:** ![Mycroft\_Holmes](https://avatars.discourse-cdn.com/v4/letter/m/a5b964/32.png) [@Mycroft\_Holmes](https://boards.straightdope.com/u/Mycroft_Holmes)\ **Post date:** [October 6, 2005, 2:43pm UTC](https://boards.straightdope.com/t/how-can-a-massless-particle-like-a-photon-have-transferable-momentum/325011/15 "2005-10-06T14:43:53Z")
> [@carterba](#): > > Actually, the fallacy comes earlier than that: > He divided by b-a, but since a=b, b-a=0. Hey, you’re right. So, in essence he’s dividing by zero twice. If two wrongs **did** make a right, the proof would be valid again. Also, since three lefts make a right, that makes two wrongs=three lefts. In that case, if left is wrong, then 2=3. _quod erat demonstrandum_ ---
**Author:** ![astro](https://avatars.discourse-cdn.com/v4/letter/a/9dc877/32.png) [@astro](https://boards.straightdope.com/u/astro)\ **Post date:** [October 6, 2005, 4:24pm UTC](https://boards.straightdope.com/t/how-can-a-massless-particle-like-a-photon-have-transferable-momentum/325011/16 "2005-10-06T16:24:57Z")
So… let me shift the question a bit - If the original mass is _nothing_, how does going C make it _something_. How does zero at rest become more than zero through speed? I appreciate the physics equations, but how about seeing if you can explain this in big crayon style thought balloons without using relativity equations. ---
**Author:** ![CalMeacham](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/calmeacham/32/35_2.png) [@CalMeacham](https://boards.straightdope.com/u/CalMeacham)\ **Post date:** [October 6, 2005, 4:40pm UTC](https://boards.straightdope.com/t/how-can-a-massless-particle-like-a-photon-have-transferable-momentum/325011/17 "2005-10-06T16:40:09Z")
How about looking at it this way – imagine that the photon had mass, but that it was moving slower than light. Now accelerate it to the speed of light. It turns out that acceleating an object of any mass to lightspeed requires an infinite amount of energy, and the relativistic mass asymptotically approaches infinity as well, regardless of how small the mass you started off with was. Far any value of v/c you can reduce the product of relativistic mass times relativistic velocity by making the mass smaller. The only limit that gives you a finite momentum for speed approaching lightspeed is mass approaching zero. ---
**Author:** ![SimonMoon5](https://avatars.discourse-cdn.com/v4/letter/s/9f8e36/32.png) [@SimonMoon5](https://boards.straightdope.com/u/SimonMoon5)\ **Post date:** [October 6, 2005, 6:20pm UTC](https://boards.straightdope.com/t/how-can-a-massless-particle-like-a-photon-have-transferable-momentum/325011/18 "2005-10-06T18:20:36Z")
> [@Caligulas](#): > > Well, the key is right in that quote: “no rest mass”. That means that if a photon were to ever stop (which it can’t), it would not have any mass. Here’s something I’ve been wondering about since a high school physics class some decades ago… Black objects are black because they absorb light, right? What happens to that light? I assume that black objects trap a large number of photons. If photons can’t stop, are they bouncing around inside a black object. Do black objects get heavier and heavier when you shine lights on them? What’s going on with the color black? ---
**Author:** ![CalMeacham](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/calmeacham/32/35_2.png) [@CalMeacham](https://boards.straightdope.com/u/CalMeacham)\ **Post date:** [October 6, 2005, 6:40pm UTC](https://boards.straightdope.com/t/how-can-a-massless-particle-like-a-photon-have-transferable-momentum/325011/19 "2005-10-06T18:40:05Z")
> [@](#): > > Here’s something I’ve been wondering about since a high school physics class some decades ago… > > Black objects are black because they absorb light, right? What happens to that light? I assume that black objects trap a large number of photons. If photons can’t stop, are they bouncing around inside a black object. Do black objects get heavier and heavier when you shine lights on them? What’s going on with the color black? They get hotter. Photons get absorbed by something (even if you have highly reflecting internal facets, as with the “light pump” in Theodore Sturgeon’s “Microscopic God” , you have a _huge_ number of bounces. Eventually, even with teeny absorption per bounce, it all gets absorbed). Some of the energy might get re-emitted as photons (of a different wavelength), but at least some and usually all of it ends up going into heating the object, so it gets hotter. The photons have momentum but no mass, so it doesn’t get heavier. Some of the heat re-emerges as infrared photons of vastly different wavelength. most of the heat ends up being conducted away by objects your black object is in contact with, or by the surrounding air. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [October 6, 2005, 7:00pm UTC](https://boards.straightdope.com/t/how-can-a-massless-particle-like-a-photon-have-transferable-momentum/325011/20 "2005-10-06T19:00:25Z")
> [@](#): > > The photons have momentum but no mass, so it doesn’t get heavier. Actually, all else being equal, a hot object _does_ weigh ever so slightly more than a cold object. The photon that got absorbed was massless, but in general, a system of photons does have mass, and a system of objects moving in different directions (as, for instance, a hot object) has a component of mass due to the kinetic energies of the individual particles. [Next page](https://boards.straightdope.com/t/how-can-a-massless-particle-like-a-photon-have-transferable-momentum/325011.md?page=2)