# 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 the momentum is given by $P=mv$, where m is the mass and v is the 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.  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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### 80 Responses to Q: How can photons have energy and momentum, but no mass?

1. Elaine Puricelli says:

So…would photons….broken down to photoelectric ions…..yield (their light) to
a black hole in space? This speaks to the “mass” idea again. Even visible light, traveling at the speed of light as do photons, get swallowed up by the dense object itself (the black hole). The black hole’s gravitational field, I’m assuming, imprisons
light and photons (I think photons as well).
It’s easier to think of the photon as a wave; that is, easier to conceptualize a
mass-less entity such as the photon. I’m told that “rest mass” is used in mathematical
equations but doesn’t really portray the photon as it really is, and the rest mass of the photon is so near to zero that’s it’s generally thought of as zero.
Also I’ve come to realize that we’re grouping the photon into the gravitational
category…such as things in our everyday life that we know….weights of things.
Envisioning the photon as “burst” helps conceptualize. Also … speaking to the typical everyday use of man made photons such as diagnostic X-ray machines, it’s interesting to look at energies and follow the steps. The “punch” as I learned it, needed to power the quantity of the energy generated “the bundle,” of milliamps to create photons for
diagnostic use (the X-ray) is expressed in kiloVolts. So I automatically envision a “punch” of kiloVolts when dialing up settings for the X-ray machine as a dynamic
thing: the “punch” needed. However I think of the bundle of energy or the “dose” of milliamps just sitting there waiting for the kiloVolts to propel them as static.
Yet one doesn’t feel X-rays as one has a chest X-ray or any other diagnostic X-ray as the X-ray exposure is the amount of time the body part(s) is exposed to the radiation (photons) expressed as seconds. Maybe the ideas of dynamic and static energy relate to kinetic and potential energies. One would think that somehow we would, as X-ray subjects, feel that “punch” of the kiloVolts as the X-ray flows through our body. Yet we don’t feel a thing. Certainly on the scale used in our example, the X-ray appears to be without mass as no flesh was displaced or moved during the X-ray picture.
So energy begets energy….yet there is the mass of the electron…..hmmmm.
When one sticks a finger into an electrical outlet (alternating current) one feels a
“punch” then and we have a physical reaction. But on a much grander scale, when looking for photons on the Sun’s corona we don’t see mass bearing photons weighing down the Sun. Again, an expression of energy.

2. Elaine Puricelli says:

What about the energy of lightening. While I typically don’t see people (humans) providing a full body X-ray view when they are struck by lightenening, I know that
the energy certainly impacts a human body as if the body was stuck by a gigantic
imaginary baseball bat. The amount of energy in a lightening bolt as we know, is
hotter (not trying to exchange thermal heat for X-ray radiation) than the surface of the Sun….and of course..lightening must contain some other E-M components..
Is that any sort of incident of a mass bearing photon example or a far reaching example? Or are we getting closer? I am aware that science is not willing to
consider photons as mass bearing……

3. The Physicist says:

Lightning is probably poorly named. It’s not light, it’s just (lots of) electricity.

4. Elaine Puricelli says:

So…is that “electricity” quanta packets of energy within
the lightening’s make up itself? If I took a cross section
of that lightening would I find things such as quanta?
So photons are not similar to lightening in
any way? Photons are of course quanta, packets of energy.
I’m seeing a similarity but of course…it could be another
apples and oranges case as photons, as I’ve learned, are
better imagined as waves. I just don’t think (and it’s my
short-coming) of bremsstrahlung created photons as waves,
more like bursts out of the point where they were created.
I know that differences in static charges induce lightening
but I see the energy itself being similar to photons.
Help!
Speaking to the “debris” field that happens when a bremsstrahlung
created is spewed out, the “electron(s)” noticed in the debris field
must be reduced to ions from the original incoming electron that
caused the bremsstrahlung to occur as the electron approached the
target material? If that’s true then there is a photon which is known
and electron(s) (or their weakened resemblance of an electron)
in the debris field.

5. The Physicist says:

Electricity (including lightning) is just flowing charges, which is almost always electrons. The “quanta of electricity” is a single charge.
In all cases light is a wave, even when it’s a “burst” (the length of the burst puts certain restrictions on the range of frequencies involved, but doesn’t change the essential “waveness”).

6. Elaine Puricelli says:

O.K. ….so lightening (apparently flowing charges to the extreme) and not “light,”
is an apples and oranges situation. I was just equating the punch that lightening
gives to it’s victims (humans) to the possibility of a mass bearing photon. I knew that
lightening’s thermal heat was hotter than the surface of the Sun and I’m told that even the Sun is not a good potential breeding ground for mass bearing photons: I’m informed that a laser (very concentrated photon(s)) is our Earth-bound frame of reference for finding photons in their purest state. I keep harkening back to the
“debris field” idea that the photon is not the only product of conception of the
bremsstrahlung process. This “debris field” is apparently not well known. I wasn’t
told about a debris field (I guess I don’t need to quote myself) when I learned about how medically diagnostic X-rays are born. So apparently an “isotope” of the original incoming electron and random proton(s) along with the energetic photon are all the result of the bremsstrahlung action? And of course we can’t forget that an X-ray machine in a clinical (medical) setting has a filter built in to eliminate longer wavelength photons that are deemed useless in creating a latent image.
Hmm…..how did those longer wavelength photons happen? I would think that in a
vacuum tube photons of equal length would ensue. Apparently more than meets the eye, or at first glance, with those bremsstrahlung photons.

7. Paul moody says:

So , your saying that anything photonic, can’t contain mass, or…….that only that, which has mass is effected by the “higgs boson”? sorry, trying to get my mind around it is all! The higgs particle therefore only register’s itself against the subluminal, anything else it ignore’s? Does the higgs particle mediator lose influence over speed…..(Lorentz contraction, and temporal dialation)? Is this a divider effect between classical and quantum physics? Hell, I don’t know, is fascinating stuff though.

8. Elaine Puricelli says:

My idea has always been that a photon CAN be mass bearing but I’m corrected in my idea as I’m told to think of, in my example, bremsstrahlung created photons as energy, pure energy, seen as a wave, and moving at the speed of light.
However my frame of reference is Earth bound- using the example of a medical
diagnostic X-ray machine. I’m told that the purest photon(s) out there are those
contained within a laser beam. I’m assuming all along that a “photon” is a contracted
word, meaning photoelectric ion, but I’m not 100% sure of that.
The photon in my frame of reference lives in the X-ray band along the E-M spectrum.
I have not yet thought of an example of mass-bearing photons although I think it would only naturally occur in outer space. In the pure form of a laser beam, (photons in their purest state) I’m told there’s no mass present. Certainly laser beams act VERY similarly to mass bearing things in their effect: A laser beam can clearly cut through an object such as a mass bearing object, such as myself, could knock down a wooden post. And the “rest mass” value assigned to a photon is only a mathematical number and not seen in laboratory settings. The idea of mass bearing photons a curiosity for me. Perhaps a nuclear reaction could yield the elusive mass bearing photon. And, if photons are purely energy and not mass bearing objects, then what happens to them within a black hole in space? Does the ominous mass of the dense black hole swallow photons> If so then the photon is certainly affected by gravity, dense gravity in the case of a black hole.
I have learned that there is indeed a debris field that occurs with bremsstrahlung created photons so I am claiming a victory there: The victory there is that science books of which I’m aware, at least X-ray (medical X-rays) textbooks don’t speak about a debris field. I feel I am exclusive in that thinking. No where else have I read that anything but a photon is generated from a bremsstrahlung situation such as when X-rays are created to take an “X-ray picture” in a medical setting.

9. Elaine Puricelli says:

I would like a response please from the physicist on my last
(unfortunately lengthy) post, if possible.
Thanks! There may be hidden errors there that should
be exposed. Thanks again.

10. Elaine Puricelli says:

So…to summarize…electrons and positrons are “the debris field?”
That is…they are spewed out of the bremsstrahlung process along
with the photon. That’s what I’m getting from this discussion.
What lies in the debris field as the photon continues spewing
out along it’s merry way are: the electron and positron.
Again,……why is no one in the realm of X-ray technician
teachers telling students about a debris field that is created
simultaneously along with the humble photon?

11. Kirk says:

Physicist;
An antenna detects the energy of an EM wave.
The energy is related to the amplitude of the wave.
But at low frequencies, photons have very tiny energy. So how come I can have a very energetic wave at the same low frequencies? Can I relate amplitude increase of a wave with the number of photons?

What about information? A radio modulates the frequency and/or amplitude. But how do you modulate a frequency and/or amplitude of a photon? you can’t! so EM waves at radio frequencies are not photons???

12. Elaine Puricelli says:

Wait….The Physicist DID say that positrons and electrons are also created simultaneously with bremsstrahlung photons, right? Sounds like characteristic radiation at it’s best, ….. it’s
definition. Makes sense….an incoming electron encountering it’s own ionization
should have that outcome. So characteristic radiation (it’s by-products) would
be the “debris field” inhabitants (positrons, electrons ).

13. hasan msheik says:

if photons where massless and the equations of there ENERGY depends on P:MOMENTUM.and also on M:MASS where each is multiplied by other value and then added …in case of photon having M=0 AND P=MV ,where M=0 ALSO …then we would obtain E=0.therefore a photon would be massless and with no energy thus it would be nothing at all…plz reply

14. Elaine Puricelli says:

OOps…don’t forget the value assigned for rest mass of a photon.
If you’re doing a mathematical equation one can use the rest mass value
which is severely close to zero. Although in practical sense the photon
is never at rest so this “rest mass” idea is purely for math purposes.
This number exists and believe me, wasn’t created by me.

However, ….still waiting to hear a response from the physicist please:
Isn’t it correct that an ionized (formerly known as incoming electron) electron
will result in the byproducts? That’s known as characteristic radiation?
Basically an isotope of the incoming electron and it’s counterpart formed
from the reaction…the positron. I like to call this the “debris field” that results along with the
photon that was simultaneously created.

15. Elaine Puricelli says:

So….(physicist please)…in the context of medically diagnostic X-ray generation,
… I know that bremsstrahlung created photons constitute the majority of the X-ray beam. Characteristic radiation exists in this realm as well….so there are some photons in the mix that attribute their creation to that mode.
In light of my “debris field” idea….there would be a coexistence of bremsstrahlung photons spewing out from their creation (braking) point, photons via characteristic
radiation roaming about as well……AND the “debris field” products of the original incoming (now ionized) electron [ bremsstrahlung again] and its counterpart the positron. Wow……what a crowded environment!

16. The Physicist says:

Sorry Elaine, been running around a bit lately.
To the best of my knowledge, there are no, or very very few, electrons ejected from the metal during x-ray generation. Electrons that are ejected won’t make it very far in air.
There are definitely no positrons or electrons created.
X-ray machines just create a short burst of high-frequency light. Nothing special.

17. Elaine Puricelli says:

Thanks for the feedback! Looks like you have addressed the characteristic radiation that occurs simultaneously with the bremsstrahlung phenomenon.
However…I was assigning the name “debris field” to the bremsstrahlung
process: The products created along with the photon that is well known
in this phenomenon. So the “debris field” consists of by-products of the
bremsstrahlung phenomenon and there can be found the electron ( now an
ionized particle and no longer the same incoming electron in it’s former glory prior to
bremsstrahlung braking) And it’s counterpart the positron. Those two particles
are my debris field occupants which are separate from the photon that has gone
it’s merry way. The characteristic radiation that I mentioned doesn’t have a debris field but a product well known- the familiar photon. I’m not sure my “debris field” idea will be popular.

18. Elaine Puricelli says:

Perhaps this “debris field” scenario would play out better in a bigger
area: Possibly the lowly clinical X-ray machine is not powerful enough to
look for this “debris field.” Maybe higher energy machines are needed?

19. What happened when two photons collide ?
two photons with the same frequency and in opposite direction

20. John says:

What happened when two photons collide “with the same frequency and in the opposite direction” ??

21. Elaine Puricelli says:

As I’ve studied that accepted model of bremsstrahlung generated X-rays
(photons), I re-read the portion of my textbook that tells me what a small
portion of photons are created from this action: Most of the kinetic energy
transformation is given off in (thermal) heat.
Hmm..so it seems to start bremsstrahlung action and create photons
using enough very high energy to yield many more photons would be a
process of losing less energy to heat (given off by the photon production).
Of course…the aim here is to create many more photons but also enough
of the “debris field” to demonstrate a higher yield of positrons and
electrons (electrons altered by the bremsstrahlung action).
I’m guess we will need much thicker metal components in order to
complete this experiment: Thicker metals that the ones used in a
standard X-ray machine?

22. Elaine Puricelli says:

Oops, just saw a quote related to energy needed to create “pair production.”
It’s quoted as 1.22 or 1.24 MeV in order to create the electron and positron pairs,
and this is in the realm of gamma rays.
Not interested in those, I think there’s something more created during the bremsstrahlung action than the photon……we need a venue bigger than a
standard X-ray tube used in medical diagnostics. Can we keep this in the X-ray spectrum though? I know that this action of bremsstrahlung results in a very high
yield of thermal energy thrown off (heat) and substantially less photons when compared to the amount of heat given off. Hmmm…..I think this should be tried: Not leaving the X-ray range of the spectrum….to see what else spews out of the action more than just the photon.

23. Elaine Puricelli says:

Correction: Just re-read my previously cited information.
The minimum energy required in pair production is 1.022 MeV.
However, I’m not trying to present a scenario where a photon decomposes
into an electron-positron pain. I’m try to imagine a scenario where
a photon is spewed out via bremsstrahlung AND a “debris field” is
created simultaneously as well, all within the confines of the X-ray
range along the E-M spectrum (let’s leave gamma rays alone for now).
Is this science fiction to some? I just feel as if something else creates
simultaneously along with the photon as nature rarely creates a singe
thing during any reaction.

24. Elaine Puricelli says:

Perhaps we can’t see other products of conception in the X-ray/photon
making business because so much (predominantly so) heat is also
created when X-rays are made. Not trying to make a bad pun but the
heat production with bremsstrahlung created photons is a smokescreen
for looking deeper into this puzzle. We know that by this same process of
endeavoring to make X-rays, there are photons of unequal length and
that longer-waved photons are weeded out in order to make a more
efficient latent image, the X-ray image. I wonder why the length of photons
all created together varies in the same application of time? I’ll call them co-photons.

25. Pat says:

I’m sorry to weigh in with the ignorant vote, but I have to voice the opinion of the uneducated (high school only, and not a science major). I only understood a little of what I read, and maybe that is what the problem is, But, bottom line, to people like me, when you say it is massless and then start giving all these reasons why it works better or your equations if its massless, that just makes it sound like nonsense that is for your convenience.

You say that something that has no mass and no energy can’t exist, because it is nothing. In my mind, if it doesn’t have mass it is nothing, regardless of the energy factor. Even energy has been theorized to break down into particles of this and that, and every particle is a thing. It exists. If it is a thing that exists, what does it look like? It has to have some mass to be a thing that theoretically has a look, a shape, an ability to affect things. It just seems that it has to have some type of matter to it, and therefore has mass. You can call it antimatter, or something else, but it is still just a different form of matter; maybe not in scientific jargon, but for practical purposes of thinking about the “thing” simplistically.

You have now heard from one of the masses that thinks that something called a massless particle is illogical.

26. Elaine Puricelli says:

It is well known that a photon is massless, pure energy only.
There is a “rest mass” assigned to a photon which is VERY close
to 0 and exists only for mathematical purposes.
The photon moves at the speed of light, has momentum but
has not been found to have mass.

27. Elaine Puricelli says:

Back to my “….what else is created as a product of conception during bremsstrahlung besides the obvious photon” question.
I’m told lots of heat is created in the case of an X-ray tube used in medical diagnostics, majority of kinetic is converted to thermal energy (heat) but
there in the minority lies the photon.
Now outside the realm of the humble X-ray machine interests me.
I think at MUCH HIGHER ENERGIES for this same scenario, and staying
within the realm of the X-ray range along the E-M spectrum,…..we could
see a debris field consisting of something,……I just don’t the think the photon
is the only product of conception for bigger energies in a bremsstrahlung
situation….. Let’s leave the gamma rays out of this discussion.

28. Elaine Puricelli says:

I wonder if we would need a huge arena for this type of experiment.
Like the CERN in Switzerland? Isn’t that the size particle accelerator
we need?