Q: How can photons have energy and momentum, but no mass?

Physicist: Classically (according to Newton) kinetic energy is given by E=\frac{1}{2}mv^2 and momentum is given by P=mv, where m is mass and v is velocity.  But if you plug in the mass and velocity for light you get E=\frac{1}{2}0c^2=0.  But that’s no good.  If light didn’t carry energy, it wouldn’t be able to heat stuff up.

The difficulty comes from the fact that Newton’s laws paint an incomplete (and ultimately incorrect) picture.  P=mv is very accurate for slow moving (compared to light) objects with mass, but it’s not true in general.  When relativity came along it was revealed that there’s a fundamental difference in the physics of the massive and the massless.  Relativity makes the (experimentally backed) assumptions that: #1) it doesn’t matter whether, or how fast, you’re moving (all physical laws stay the same) and #2) the speed of light is invariant (always the same to everyone).

Any object with mass travels slower than light and so may as well be stationary (#1).

Anything with zero mass always travels at the speed of light.  But since the speed-of-light is always the speed-of-light to everyone (#2) there’s no way for these objects to ever be stationary (unlike massive stuff).  Vive la différence des lois!  It’s not important here, but things (like light) that travel at the speed of light never experience the passage of time.  Isn’t that awesome?

The point is: light and ordinary matter are very different, and the laws that govern them are just as different.

Light and Matter: different

That being said, in 1905 Einstein managed to write a law that works whenever: E^2=P^2c^2+m^2c^4.  The same year (the same freaking year) he figured out that light is both a particle and a wave and that the energy of a photon isn’t governed by it’s mass or it’s velocity (like matter), but instead is governed entirely by f, it’s frequency: E=hf, where h is Planck’s constant.

For light m=0, so E=Pc (energy and momentum are proportional).  Notice that you can never have zero momentum, since something with zero mass and zero energy isn’t something, it’s nothing.  This is just another way of saying that light can never be stationary.

Also!  Say you have an object with mass m, that isn’t moving (P=0).  Then you get: E=mc2 (awesome)!

 

Unrelated tangent: It took a little while, but the laws governing the massive and the massless are even more inter-related than the ‘Stein originally thought.  He figured out that the energy of a photon is related to it’s frequency (E=hf), but why are photons so special?  Why do they get to have frequencies?  They’re not special.  Years later (1924) de Broglie drew the most natural line from Einstein’s various equations from light to matter.  mc^2=E=hf  So for a given amount of matter you can find it’s frequency.  Holy crap!  Everything has a frequency!

On the off chance that anyone out there got unduly excited about that last statement: the frequencies never go out of wack, you can’t tune them, more importantly they are utterly unimportant on the Human scale, or even the single-cell scale, and don’t ever buy a bracelet or anything else with “quantum” in the name.

No, no, no, no, no, no, no, no, no.

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227 Responses to Q: How can photons have energy and momentum, but no mass?

  1. Ross says:

    Thanks. Can you suggest reading materials to learn more about photons for a retired mechanical engineer? Too late for me to get another degree but I am fascinated with the subject.

    BTW, from the point of view of an ME not considering relativistic effects, if a rigid mass in motion strikes another identical mass (I’m thinking of the desk set of hanging ball bearings, for example), I recall that momentum can be transferred via the impact from one mass to another. However, that would be “relatively” (I now wince to use the term) instantaneous and without displacement during the impact. So I believe the energy is transferred w/o doing significant work (relative to the total energy transferred). Also, you said “when a photon HITS [my emphasis] a charged particle….” The term “hit” is interesting if the photon has zero mass. And I wonder if the consequences vary if the “impact” is to an electron in the spin direction vs against the spin direction? These details, if currently understood by science, are very interesting to me. Hopefully these kinds of questions don’t require calculus. Been close to 50 years since I had to use it. Thanks again.

  2. Al says:

    The photon has zero mass but has energy. So when the photon “hits” something it will be either reflected, absorbed, or absorbed and re-emitted. The latter two cases altering the (energy) state of the object that was “hit.”

  3. I am happy to have found this website for the first time this evening (10/21/2018). I read the above great response for the Physicist, and Al, thank you for your comment. I “discovered” that IR is reflected and re-emitted through a test in my lab at home when I received more “reflected” IR from a dull piece of aluminum than a highly polished piece of steel. I applied that discovery in the design of a consumer product with great success (I’m now more into medical device R&D). Ross, I too have had a 50-year career. Not since 1985, when I started using CAD, have I had to even use trigonometry. I have made a somewhat related to-the-subject discovery of my own. After 30-years of research, I have concluded there is an atemporal, massless particle at the functional center of every living cell which is responsible for all cell functions (through the DNA contained in the cell), it is also the repository of all memory and co-responsible for consciousness. I would love to hear from a physicist what the makeup of that particle might be.

  4. Anonymous says:

    The whole concept of a photon has no mass is bullshit if you accept E=MC squared. If M=0, the photon has no energy. Also, according to relativity, it takes infinite energy for any object with mass to travel at the speed of light. So if the photon has mass, it takes infinite energy for it to travel at c. WTF, I’m confused. All of Physics is screwed.

  5. Anonymous says:

    (P=0) for non (or slow) moving mass is not zero, it is P =1

  6. Rex R. Bahr says:

    X+xsq+(X+1) = (X+1)sq
    BTW I am 84 Y/O 8th grade education and not much of that
    I was born on a farm 7 miles South of Bassett Nebraska 07-23-1935 during the dirty thirties and the Doctors say my parents worry affected my brain.

  7. Elaine says:

    In reply to The Physicist’s comment (5/29/18), so “force carriers” of the E-M force. Hmm…..”When a photon hits a charged particle…” My first thought is an X-ray beam but we all know that simple, diagnostic X-rays are not felt. However, I believe that if we stand very close to the Sun (o.k. we’re wearing Sun-resistant suits so as not to be named Icarus) then the photons emitted from the Sun, an object larger than a controlled X-ray machine, we will sense the photon emission is the form of a mass-bearing force. So perhaps it depends on the size of the photo and the source from which it originated. By “size” of photon I think I am referring to a pure photon such as one that’s emitted from a large object (the Sun in this example) and not some X-ray machine emitted particle. So if we change the playing field in this example to a large photon emitter – the Sun- would we then notice a mass-bearing photon? Or a star bigger than our Sun perhaps?

  8. Carl says:

    If you accept E=MC2 then as a particle matter approaches the speed of light it is converted into energy the original mass being spread out infinitely as it is converted into energy. The reverse should also be true where as energy slows down by whatever mechanism the energy would revert to matter. This might explain how the matter in the universe arose from the Big Bang. As space, time and energy instantaneously unfolded the expansion caused a potion of the infinite energy to slow down and convert to mass. It will take time, but, one day a really smart individual may figure out the mechanism that allowed this to happen.

  9. Carl says:

    Sorry didn’t get to finish internet hiccuped. As the universe unfolded and energy slowed down converting to matter. The mass of the matter that was infinitely spread out was concentrated also. It makes for an interesting discussion.

  10. Elaine Puricelli says:

    Hi Carl, Sounds like you are in favor of my mass-bearing photon theory.
    I don’t get much support for my theory, but if one takes this to a mega-scale,
    it is possible to see that, for example, our Sun going nova, or a much larger sun’s nova event, that photons emitted from that spectacle could be mass-bearing photons. Just stand close enough to try and measure or you’ll be a charcoal briquet. I think my theory is sound because photons have the energy/momentum qualities at the least, in their favor. Would love to see the nova event done on a virtual scale to test this theory of a mass-bearing photon emission as one of a nova’s products.

  11. I am non-educated shlup,but have semi-figured out some questions including why a photon has energy without having mass,and if it ever runs out of energy or stops ? So a photon is outside of the mass is energy in concentration+ and energy is mass dispersed,then where in Einstein’s neat World does that fit a photon since it appears to be neither mass nor energy,so it more like Quantum Mechanics,you can know it exists,
    but not why,or how that’s possible,and last,if the universe is expanding,will it so,or when energy runs out ,will it start to contract faster+ faster,+ end up in a Big Bang + a new start ? Last what will happen to the photons if there not part of this normal universe?

  12. BurstBubbles says:

    Except for the fact that is not at all what happens or could have happened. “Infinite mass” is exactly what it sounds like it is: a mathematical error. It happens when you attempt to calculate an impossible real-world scenario. Like mass traveling at light speed.

    A photon would be nothing if it were at rest. So that’s why you never sss them that way. They are always going full speed. Movement creates kinetic energy which makes a photon something rather than nothing. If I weee to send a discrete packet of nothing at you at oh let’s say 300 million meters per second, what would it look like? Ahh. So now you get it. A photon doesn’t exist in a tangible sense. A photon must have energy as a source to be created however it does not take any energy from the source when it leaves.

    Photons are basically energy’s way to say “I’m here! Notice me!”

    Now, you are probably thinking “What about microwaves? Gamma rays? TONS of energy!”

    Yep, but a photon is a particle. Oh you want to talk waves? The frequency of a wave’s oscillation is a measure of more kinetic movement… not only is it moving at light speed-it is vibrating up and down as it does it, creating more kinetic energy-Again, the only energy it has.

    Confused? The double slit experiment which demonstrates the wave/particle duality nature of light is one of the most anti intuitive features of our universe.

    Your hypothesis isn’t ready for prime time, you have much to learn. Seek first to understand, then when you have a clear understanding of all the current information on a subject, hypothesize away!

  13. Tint Weezl says:

    Elaine I’m disappointed in you. All the carefully worded and painstaking posts myself and others made to clearly explain the nature of light and it didn’t make a dent. Proof after proof in example after example was laid out to explain the Higgs Field that imparts mass, the non-existence of light at rest (impossible if it had mass)… and nothing.

    Elaine… if light had mass you would be SCREAMING RIGHT NOW

    IT WOULD HURT

    IT WOULD FEEL LIKE BEING SANDBLASTED

    My God, drop the crazy impossible dream of an idea you want to be right about, end the obvious cognitive dissonance that threatens you and GROW. Learn something. Understand instead of fight.

  14. laird wolfe says:

    if massless particles are “doomed” to travel the speed of light. how can quarks and gluons which are stationary travel ate speed of light

  15. laird wolfe says:

    if massless particles are “doomed” to travel the speed of light. how can quarks and gluons which are stationary travel at the speed of light

  16. Elaine Puricelli says:

    Tint Weezl. Try to contain your disappointment. You see, I can speak to theoretical themes all day long. Of course your argument is flawed: We are not sandblasted by our light from OUR Sun because we’re too far away. And by the way, the sandblasting thing reminded me of Lot’s wife in the Bible. She was turned to a pillar of stone when she looked back onto the land she and Lot fled, so that was some targeted sandblasting! My point is, if you’re ignoring what happened to Icarus, and you decide to take a road trip to the Sun (I love a road trip), then my point might be made more clearly. Certainly we (yes, we’re riding together) steel ourselves for the blast of photons radiating out of the Sun, and we survive this journey. Tell me how we would not be irradiated then? We would be wearing out super-photon protective goggles and notice that the photons appear to be coming directly at us (like with snow when you’re driving) . So we’ll take a side angle to better observe the photon fun. Of course the photons will be moving at the speed of light so be mindful that we’ll need our full concentrative abilities. We may then know if those wave-behaving photons are mass bearing. Maybe we can take a Geiger counter? No…too many other rays coming at us. And we’ll need reflective clothing. I think if you look at my theme in the context of Sun observing light-show scientists, you may decide that my theory is not so flawed. Let’s step out of our Earth bound point of view and enter the Sun’s near-atmosphere for our observation.

  17. Elaine Puricelli says:

    Anonymous. Another neigh sayer?? You do realize that photons have been assigned a mass by physicists? I’m told, (o.k., I’ve read), that the quantity of mass assigned to the humble but brilliant photon is for the purpose of mathematical equations. So why were physicists so enthralled by the photon they someone decided to assign a quantity of mass? Were scientists sitting around a room and one scientist caved to another scientist’s claim of mass-bearing photons or was it taken to a majority-rules vote?? Therefore, technically “p” does not = 0. The humble photon needs a cheerleader like myself.

  18. Elaine Puricelli says:

    Here’s another perspective: I originally became interested in photons when I was taking a class on X-rays (diagnostic, not therapeutic)..
    When we receive an X-ray in a clinical setting, we’re not able to detect the X-ray radiation (photons directed straight into whatever site on the body is to be examined). The “dose” of X-ray radiation is carefully ascribed based on our body type/thickness of the part to be examined. But if we stood directly at the Sun, we would experience many types of photon emissions so selecting only the X-ray photons by their wavelength compared to the wavelengths of other photons, wouldn’t we then observe mass-bearing photons as the amount of radiation has been ramped up by our journey to the Sun, our proximity to the Sun?

  19. Tintweezl says:

    They don’t.

  20. TintWeezl says:

    Elaine,

    Whatever are you babbling on about?

    The sandblasting joke was to elucidate the repercussions of assigning mass to little bits of light.

    Matter can never be created or destroyed.

    Where does the matter go, then?

    I mean just stop. And the Bible is a book of myths.

  21. Elaine Puricelli says:

    I really believe that one can observe a mass-bearing photon if one stands directly in front of the Sun. Maybe the mythical Icarus thought the same thing. However, our experience with photons on Earth cannot compare to a photon strike on our photon counting machine when the photons are emitting from the Sun at the time of our real-time experiment. If I could do this in person (with the Sun) I would but I don’t have a photon counting machine nor oven mitts that would allow me to stand directly in front of the Sun. On Earth, when getting a diagnostic X-ray, of course we don’t feel the photons passing through our body. But if you ramp up your photon strikes with the photon counting machine while standing in front of the Sun you may experience PURE photons and not just manufactured photons that you would get here on Earth – the Sun’s photo-bearing rays not withstanding. I’ll bet you could hardly lift a photon emitted from the Sun when trying to put a photon in your space ship for travel back to Earth for the photon’s weigh- in! So we know photons have energy and travel at light speed, and they have momentum AND they are assigned a mass “of sorts” for the purpose of mathematical calculations. So why all the neigh saying about mass-bearing photons?

  22. Tintweezl says:

    <<>>

    Your belief is based on something you thought of in your head that you want to be correct or at least remain disprovable (to you, it already has been to anyone who understands and accepts experiments proving the massless nature of light.

    <<>>

    A mythical figure is an excellent analogy.

    <<>>

    Two points to process here. You suggest:

    1) experience with photons on earth is fundamentally different than those emitted from the source, the Sun
    2) you believe a “photon counting machine” would show this difference

    Since the surface of the Sun is not a place we have the technology to conduct experiments on, this is how you protect yourself from direct refutation of your theory. You have decided this is the only way you will accept as proof because you know it is not possible. So no matter what else happens, nothing can reach this bar and you never have to give up your fanciful ideas.

    <<>>

    See above response.

    <<>>

    We experience pure photons on our skin all day long on Earth and photon detectors register them the same way as “manufactured” photons. The laws of thermodynamics tell us that heat is energy and a byproduct is light, pure energy by virtue of kinetic momentum. The Sun creates heat and thus, light. X-ray machines on Earth generate X-rays by sending an electron stream through a cathode tube which results in 99% heat and 1% light resulting from that heat. The light is in the X-radiation part of the spectrum based on the energy of the electron beam. Lower mA electron beams would result in a light emission further down the electromagnetic spectrum.
    We can’t manufacture photons, all we can do is replicate situations in which they naturally occur. Photons all share the same massless quality and only vary in their energies manifested as frequency, meaning higher energy photons move around a lot more up and down while traveling. They are more “energetic”.

    <<>>

    What do you propose happens to all this mass between the Sun and Earth where a trillion trillion of them hit everything outside every second?

    <<>>

    Your spaceship would be destroyed by all the trillions of photons hitting the ship on the pick up of the photon detector (the detector would be destroyed as well) if photons had mass.

    <<>>

    The momentum IS the energy. That energy has a mass equivalent but not as rest mass. This is important. Light has energy which equals mass while it’s moving. So if that’s what you want to make the point of, you’re right: light has energy and energy is mass. Photosynthesis works this way. Ever notice how the dirt level in a pot with a plant never needs topping up even as the sprout grows into a huge ficus tree? Where is that mass coming from? Photosynthesis is light being converted to mass. Yes! Vegetables are just light mass. So there you go. When you bite into a plum, know you were right in your theory but a touch off in your details.

    <<>>

    Because all photons are equal in terms of having no rest mass. If you could stop light in its tracks, there wouldn’t be anything there because it isn’t anything except traveling energy and that energy is created by the traveling. I know it sounds weird like well, what was it before it started traveling? When you realize that light isn’t even a particle until you decide to see if it’s a particle, it gets even weirder. But let’s stick to basics for now. There is nay saying because all objective equations and experimental data have shown to a virtually infinite degree that the (rest) massless nature of light is, and must be, the case while the alternative can not be.

  23. Paul Crandall says:

    TO: BurstBubbles: September 28, 2020 at 3:26 am

    I’m confused. You state that a photon does not take any energy from a source when it leaves. If an electron moves from a higher state to a lower state by expelling a photon isn’t that taking energy away from the source?. (Just trying to wrap my head around this stuff.)

  24. Serge Petelin says:

    Elaine, I’m afraid Tinwzl (whatever) and others are correct. A Photon is Photon is Photon regardless of where it comes from, and how close you are to it.
    If any Photon did have a rest mass , no matter how small, it would require an infinite amount of energy to reach light speed.
    Which is why nothing with mass can get to light speed.

    Looking at you concept upside down, if one your photons happened to have mass (impossible) and was able to travel at light speed, it would not only strip the paint off your space ship, it would destroy the universe with the burst of its infinite Energy.
    And there would be no one around to enjoy the spectacle.

    In fact, its apparently considered to define the apparent mass of a moving chunk of light to have Kinetic Energy, rather than the classical property of mass.

  25. Anonymous says:

    Tintweezl Plants don’t turn light into mater. Plants are made of Carbon, and they grow by taking it from the CO2 in the air.

  26. Elaine S. Puricelli says:

    Well, if Icarus reincarnates and plans yet another trip to the Sun, and he is an optimist, then I will have to hitch a ride with Icarus. I want to see for myself if sidling up alongside the Sun (once my spacesuit is proven to resist gamma rays) shows me that the beleaguered and misunderstood photon contains mass. Wait! Will the gamma rays blasting me at full speed from our Sun cloud my judgement or just burn up my spacesuit with radiation? Too late to replace the spacesuit at that moment. I’ll set my Geiger counter, or equivalent, for photon counting only. Gamma rays be damned! Or perhaps I’ll pick a more powerful star for my field experiment – our Sun seems a bit lackluster these days.

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