# Does light have mass...?

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btw, how are you meant to do a multiplied sign in LaTeX? x doesnt work and * gives a star, are you meant to just leave it like xy to represent x multiplied by y?

\times

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all thats fine and good' date=' but HOW does it "transfer" this momentum if it has no mass?

its a bit like a ghost hitting a punch bag, it wont move unless it interacts or has Mass behind it.

THAT is the part Im trying to get at/understand.[/quote']

I think your difficulty is coming about because you are confusing mass and momentum. When something hits you, it is not the mass which is important but the momentum. A bullet, for example, has a pretty small mass, but firing it from a gun gives a big kick back.

Classically momementum p, mass m and velocity v are related by p=mv, so even a small mass object can have a large momentum if it moves fast enough.

For a particle with non-zero mass in relativity this equation becomes

$p = \frac{1}{\sqrt{1-v^2/c^2}}mv$

You can see that as $v \to c$ the denomenator becomes very small and the momentum tends to infinity. So no matter how small the mass is, as the particle approaches c it has a lot of momentum.

For a massless particle, the correct equation is $p=E/c$ (both this and the one above are derivable from the more general equation $E^2=m^2c^4+p^2c^2$). So the omentum is protortional to the energy and a high energy photon will have a high momentum.

Now, if a photon hits another particle and is absorbed it must transfer its momentum to the other particle. Let's say the other particle has mass m and is at rest before being struck. The photon has energy $E_\gamma$ and thus momentum $E_\gamma/c$. All this momentum goes into the stationary particle, which then has momentum $p=\frac{1}{\sqrt{1-v^2/c^2}}mv = E_\gamma/c$ and thus its velocity is

$v = c \frac{E_\gamma}{\sqrt{E_\gamma^2+m^2c^4}}$.

So you can see that a photon does indeed push the particle away.

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Hmmm... Im struggling with the formula here, I get so far in and then lost and have to backtrack,

stuff like that and I dont along very well you mention about when it gets absorbed, so that means its HIT something (like the punch bag) f=ma (I just about Understand this) .

surely if something has the speed of light, but no mass, it cant really "Hit" anything?

like firing a molecule at the punch bag, no matter how fast its unlikely to make it move much (it would probably penetrate deeply and get destroyed sure) but the overall would be little to nothing, now take the same speed and remove all the mass, it cant possibly effect it?

I sure am lost here imagine you were explaining this to a kid that asks? say a 10 year old, how would you explain it?

Ill work from there edit: I just had another idea that may help in explaining it, How big is a photon or rather what Volume does it occupy, what does it displace to assume this volume and what part of an atom does it strike when it hits (Im guessing the Electron cloud), and what happens when it imparts this "force" to the atom?

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Now I am wondering, if a photon has mass, exactly how much mass does it have?

Has it been measured?

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To calculate a photon's mass you'd need a formula which includes mass and is not referring to the rest mass. All the equations I can think of have m for rest mass, for a photon this is 0.

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YT, I see where you are coming from now. I can't really think how to explain it. How can you imagine or picture a massless particle?

If you're imagining things you can't think of body1 (photon) hits body2 (you) and the two physical things collide and momentum is transferred from to the other doesn't work because the photon isn't, in a sense, a physical thing, in that it doesn't have a rest mass.

You've probably just got to accept that a photon has momentum, and so when it hits something momentum must be conserved, it's a law of physics, and if the photon is absorbed by you the momentum must be transferred to you because there is no where else that momentum could go.

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YT2095 Think of the photo-electric effect.

Now I am wondering, if a photon has mass, exactly how much mass does it have?

Photon have no mass.

For a massless particle, the correct equation is $p=E/c$

Does that equation come from photo-electric effect mesurement or is it derived from theory ?

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It is very simply derived from the formula $E^2 = m^2 c^4 + p^2 c^2$

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A photon has energy (really, it is energy) and in transferring that energy, it also transfers momentum.

Just one more thing that behaves differently than everyday experience, which is why quantum and relativistic phenomena are difficult concepts - there are no common examples to which one may compare to make sense of what's going on. That's one reason physicists get used to looking at equations and use them to "see" what's going on.

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It is very simply derived from the formula $E^2 = m^2 c^4 + p^2 c^2$

Yes very simple to derive, but how this equation ($E^2 = m^2 c^4 + p^2 c^2$) was found ?

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Yes very simple to derive' date=' but how this equation ([math']

E^2 = m^2 c^4 + p^2 c^2

[/math]) was found ?

That's Special Relativity. It is really a statement that the length of a four-vector is invariant under a Lorentz transformation. This is exactly the same principle that the length of a space vector is invariant under a rotation.

Take a piece of string, hold it horizontally and measure its length - now hold it vertically and measure its length again. The two lengths are the same - can you tell me why? (I am neglecting gravity here.)

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Because like you said :

a space vector is invariant under a rotation.

OK I will try to understand the four-vector is invariant under Lorentz transform.

Explain how E=pc was found ?

four-vector is p in the E=pc

invariant = two length are the same

Lorentz transform: used to change reference frame.( Imply relative motion )

E can be seen as the kinetic energy an electron would acquire when hit by a photon. The relative velocity of the photon and the electron is c. I don't see how the Lorentz transform apply . Is it Einstein who found that equation ? When he was working on the photo-electric effect ?

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This is how I like to think about it: A photon is not a particle. A photon is not a wave. A photon is a photon. We just like to compare it other things that we can understand intuitively, like a moving billiard ball or the waves on the surface of water. Moving objects like billiard balls have momentum, so when they strike another object they transfer energy. They also happen to have mass. We can observe billiard balls with our own eyes and can understand their interactions with other objects intuitively.

Photons are "tiny" and move at great speeds so we never directly observe their movements with our eyes, and so we have trouble understanding their interactions with other objects intuitively. When we observe them transferring their energy to other objects by observing them with scientific instrumentation, we like to compare them to something we understand, such as a billiard ball that has mass. But it's not the mass that gives the object the ability to transfer energy; it's the momentum, which we know from the mathematical equations that we have developed, not an intuitive understanding.

Mathematical equations are constructs used to describe the observed and derived relationships of things. These equations describe the relationship in its purist form. Sometimes the information used to create the equations is gathered from scientific instruments that allow us to glimpse the universe in a way that we could never see with out natural senses so the relationships they describe are hard to understand.

Our bodies, and nature around us, have great mass compared to atomic particles and travel very slowly relative to light. Our senses have evolved to observe this limited part of reality and our brains have evolved to process it. Our brains have not had to deal with information gathered at the atomic level or with things traveling at the speed of light. Therefore when we encounter phenomena that occur at levels outside are normal reality we have trouble understanding them. Our modern instrumentation may help us observe these phenomena and we can use mathematics to record the relationships, but that does not mean that we can understand it intuitively. Momentum is a creature of mathematical equations and just because something like moving billiard balls, which we can understand and has mass like we do, has momentum, it doesn't mean that everything with momentum has to have mass as well.

Not sure if that helps at all.

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yes and no,

youve done a Fantasic job of explaining the problem I have with this sort of thing (much better than I could have done), and youre right, I cant grasp it intuitively or conceptualy, I like to have "frames of reference" so to speak.

I cant PART understand the idea that its just pure energy, then I trip up by likening it to electricity (Im still a "Chemist" at heart).

it almost begs the question, how can NOTHING have speed? if it has no mass, it cant exist (in "my" understanding) nor can it have Volume?

I can see its effects as I cant type in the dark, and I can get my head around the Wavicle (wave/particle) idea.

but then theres a hitch, if it has no mass, it cant be effected by gravity, as theyre intimately linked, and yet dense matter can curve a photons path, surely it should remain unaffected?

sorry if these questions are a bit simple, my understanding of it all is equaly simple (to not at all). and I really hope Im not infuriating anyone with my questions (it has happened). the way I figure it, if my little girl one day asks me the same question(s), HOW would I reply?

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four-vector is p in the E=pc

No' date=' the four-vector is a four-component vector whose zeroth (or fouth, depending on your notation) component is the Energy (over c) and the rest are the momentum. So i is (E/c,px,py,pz). The length of this four vector is [math']E^2/c^2 - p_x^2-p_y^2-p_z^2[/math] (the minus signs are because of the weird Minkowski metric). Under a Lorentz boost the energy and momentum change, but you can show that the length remains fixed, and is called the "mass".

Is it Einstein who found that equation ? When he was working on the photo-electric effect ?

It has nothing to do with the Photoelectric effect. It was derived by Einstein from the postulate that light has the same speed in all inertial reference frames. (Although I think it was first written down by Lorentz.)

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yes and no' date='

youve done a Fantasic job of explaining the problem I have with this sort of thing (much better than I could have done), and youre right, I cant grasp it intuitively or conceptualy, I like to have "frames of reference" so to speak.

I cant PART understand the idea that its just pure energy, then I trip up by likening it to electricity (Im still a "Chemist" at heart).

it almost begs the question, how can NOTHING have speed? if it has no mass, it cant exist (in "my" understanding) nor can it have Volume?

I can see its effects as I cant type in the dark, and I can get my head around the Wavicle (wave/particle) idea.

but then theres a hitch, if it has no mass, it cant be effected by gravity, as theyre intimately linked, and yet dense matter can curve a photons path, surely it should remain unaffected?

sorry if these questions are a bit simple, my understanding of it all is equaly simple (to not at all). and I really hope Im not infuriating anyone with my questions (it has happened). the way I figure it, if my little girl one day asks me the same question(s), HOW would I reply?[/quote']

A photon is a vibrational mode of an electromagnetic field. I don't know if that helps, but it's another way of looking at it.

Any charge has an electric field emanating from it, which causes interactions with other charges. There is energy stored in this field, and though it is massless, allows a force to be transmitted, which requires the transfer of momentum. Photons are quantized bundles of energy of/in a field when it is oscillating in a certain way. It's just that you can create that oscillating behavior in a number of ways.

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actualy it Does help a little "A photon is a vibrational mode of an electromagnetic field" although I dont entirely understand EM fields 100% (beyond that of RF in certain transmitters and its propagation) what you said makes some kind of sense in a usable way I still dont know what a photon IS or its structure, but what you said helps a little in defining HOW this "photon" may effect something.

half way there at least, Thnx )

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Lorentz wrote the Lorentz transform. E/c,px,py,pz

Does that 4-vec describe completely a photon ???

In relativity the fourth dimension is a dimension of time ???

Is E/c the time component or momentum is an other story ?

A photon move at c on x, px must be 0 under Lorentz lenght contraction ??

Thanks for your answers. I don't want to abuse on your time. It seam so clear for you!

Trying to imagine a photon I try to move in its reference frame . Length contraction eliminate the x spacial axis or maybe leave a plank length. All the length of the universe contracted to epsilon... That leave the y and z spacial dimension (maybe occupied by the electric and the magnetic field. A photon is a Flatlander ! The clock is stopped. Nothing happen.

Back in our frame can we mesure the lenght of a photon ?

Would it be a good analogy to figure the photon as a soliton ?

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I still dont know what a photon IS or its structure
No one knows what a photon's structure is as you can't actually see a photon (obviously everything you see is made of photons, but you can't actually take a single photon and do like a 360 viewing of it to reveal its structure).

A photon is a packet of energy, its a little lump of energy.

All we know about photons is this; originally we thought we light was made up of waves, this is partially true and can be experimentally proven. Then Einstein in the photoelectric effect noticed that light waves seemed to deliver their energy in little lumps. Rather than a continuous wave it came in packets.

A wave wouldn't arrive in lumps, only a particle would.

A photon isn't a particle, because then it wouldn't act like a wave, it would only act as a particle. A photon isn't a wave because then it would never act like a particle. A photon is something else which has charachteristics of both waves and particles.

One of the things we know from the Uncertainty Principle is that the more we know about the wave properties of a thing (ie. its momentum) the less we know about the particle properties of the same thing (ie. the position).

You can't imagine what a photon is, this is just part of QM. QM isn't something you can put into an everyday world of classical physics. Well you could imagine a particle moving in a wave shape, but as far as QM goes this is technically incorrect in almost every way!

So what is a photon? It's a thingy which explains why light energy arrives in lumps.

What's its structure? Who knows? It changes. In one experiment it behaves as a wave, in another it behaves as a particle. You can't stop it to look at it, you cant bounce light off it to observe it, we can't really answer your question!

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Does that 4-vec describe completely a photon ???

No, there are also other relevant Quantum Numbers. Spin, for example.

In relativity the fourth dimension is a dimension of time ???

The most common naming for the coordinates of spacetime are {time, x, y, z}. I suppose that´s a "yes" to your question.

Is E/c the time component or momentum is an other story ?

Energy is the time-component of (4-)momentum, yes.

A photon move at c on x, px must be 0 under Lorentz lenght contraction ??

I do not understand that question. But if a photon has a velocity vx > 0, then px>0, too.

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Thanks Ricker In that case' date=' how can these travel at light speed?

Anything with mass accelerated to light speed gains infinate mass and thus cannot travel light speed - am I wrong? This has been bugging me for a while, if I have made a mistake then pleas epoint it out Cheers,

Ryan Jones[/quote']

Photons doesn't accelerate, they always travel at c, from their creation to their destruction.

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Photons doesn't accelerate, they always travel at c, from their creation to their destruction.

I did not say that they did. I said that if you were to accelerate any object to the speed of light it gains infinate mass.

Heres another one for your guys - does light experience time or does time stand still at that speed?

Cheers,

Ryan Jones

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I do not understand that question. But if a photon has a velocity vx > 0, then px>0, too.

velocity of the photon vx=c

Can we move into the reference frame of the photon ? The gamma factor is 1/0. The Lorentz transform doesn't work. Lenght is contracted to zero.

I understood that the equation apply to reference frame with speed below c

I found a cool site on relativity lot of gif 4D rotating cube !!!

Cool relativity!

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I understand EXACTLY you question RyanJ.. Tonight I just wrote out an entire theory that explains everything!! I can almost swear by it. I am working on typing it out right now, but it explains the mystery of why light seems to have momentum and is massless.. it explains frigging everything!!! I understand not one of you beleive it right now. But here is kind of the thing.

Lets say einstien and my theory wre about an electrical charge and he wrote everything on the negetive aspect.. and I wrote everything on the positive aspect. We are both talking charge, but just opposites.. this simple problem can expain the reasons why when using math everythign comes out backwards to how it is in reality. I should have the post on here for tomorrow.

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velocity of the photon vx=c

Only if its direction is in x-direction. But ok, it´s "your" photon.

Can we move into the reference frame of the photon ? The gamma factor is 1/0. The Lorentz transform doesn't work. Lenght is contracted to zero.

Actually, it gets worse. Within relativity, there is no valid frame of reference in which a photon was at rest. That is due to the "pseudo" in the pseudometric used in relativity. Being in the frame of rest of a particle means that you take its movement direction as time direction. The base vector in time direction would have zero length in case of a photon which arises several problems, e.g. that you cannot normalize it and that it´s self-perpendicular.

The breakdown of the Lorentz Transformation is just a symptom of this which is caused by that Lorentz Transformations leave the lengths of vectors the same.

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I did not say that they did. I said that if you were to accelerate any object to the speed of light it gains infinate mass.

Heres another one for your guys - does light experience time or does time stand still at that speed?

Cheers' date='

Ryan Jones[/quote']

Ok, sorry for misunderstanding you. I thought that the part about mass being accelerated was an explanation to why you asked how speed can travel at c if they have mass. Sorry ## Create an account

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