# Talk:Photon/Photons and Mass Debate2

## Breaking some people's bubbles?

"In some respects a photon acts as a particle, for instance when registered by the light sensitive device in a camera."

A massless "particle" could not possibly contain enough "information" to render color or even shading onto film. Only a wave function could effect that.

Photons cannot be particles, simply because if they are without mass they would be nothing. If they have mass, they violate the General Theory of Relativity. If energy directly equals mass, as E=MC2 represents, then a photon must have mass as it is capable of doing work (read as having energy). An item of mass that would be traveling at the speed of light would become infinitely massive, said Einstein, and we all know that our universe is not one infinitely massive photon. The only solution for this quandry is to realize that photons do not exist. Light is only a wave function.

I am going to take this one step further and invalidate almost all of the calculations made within this discussion thread. As light is not a particle, and only a wave function carried through mass, light cannot travel through a true vacuum of relatively large volume. C cannot be a constant, because it specifies that light has a set speed within a vacuum, but if light can't travel through a vacuum, then how can the constant be valid? It can't be. There are no human beings that can prove me wrong on this either, as there exists nowhere in the universe a true vacuum of relatively large volume. (yes, there is true vacuum everywhere, as the space in between all singularities, but the distance between massive objects is still relatively small. Massive objects meaning all items of mass, such as single atoms.) All of modern physics is built upon a theory that is not proven, or provable, but can be proven wrong. Theories are not fact. Facts are facts. You cannot build fact using parts that are still only theories.

Kevin E. Carman 11-18-05

Sorry, but you just don't know enough physics to make a cogent argument on this issue. Pretty much everything you are saying is incorrect, but I'm not going to spend the next two hours writing a detailed rebuttal. Go take a course in modern physics.
Clue: in modern notation E≠mc2, and mass does not increase with velocity (that would not work with General Relativity). Massless particles carry momentum and energy just fine.--Srleffler 08:06, 23 November 2005 (UTC)

Inertia increases with velocity, and at C mass would have infinite inertia. Massless particles could not carry energy at all, as E=MC^2 means that energy equals mass. The simplest logic would also dictate that something without mass, would actually be nothing. If energy is mass, and vice versa, something without mass could have no energy. If you would like to discuss relativistic mass versus mass at rest, you would have to assume that at some point the photon would have mass in either state of motion. By description, photons cannot have mass, and therefore they cannot actually be able to do any work (aka have energy). I can provide upwards of 2 dozen very strong logical arguments against the existence of the photon, but I suspect your logic would not be strong enough to make the connections I would provide, based on your reply to my comment. If you choose to correct me on using E=MC^2, I only used it because everyone is familiar with it. The real equation is E=M, because energy would be a direct conversion. The speed of light has no bearing on this conversion factor, and thereby not be necessary. For example, 1amu would be capable of X amount of work, if it were to be a complete conversion. (IMHO, I completely disagree with the premise of the formula itself, as it implies that mass can actually "change" into something other than simple kinetic energy, and it can't. Mass does not simply go away, as many assume.) Have scientists actually "captured" a photon? Nope. They can't because they do not exist. If you doubt me, provide us proof of humans capturing a photon in it's energetic state. I feel pretty safe that you cannot.

Kevin E Carman

You argue that photons can't be particles because they have no mass. Note that photons have relativistic mass but no rest mass. At the speeds that photons travel, one could conceivably think of them as a tiny particle (like a neutrino which was previously thought to be massless, but have been since found to have a rest mass). As long as the particle is moving, it exerts a gravitational field and has momentum - just like any mass would. The quote "light is massless" is thrown around too freely, and people who hear it most likely don't understand the difference between rest mass, and relativistic mass. Fresheneesz 22:40, 7 April 2006 (UTC)

Kevin, here is where your error arises from, in fact this is a common error a lot of people make in relation to the whole E = mc^2 thing, the complete equation for this is E^2 = (pc)^2 + (mc^2)^2, where E,m and c have the usual meaning and p is the momentum of the particle, which in the case of light is expressed by the de Broglie expression i.e wavelength = h/p. Now as you see a particle need not have a rest mass (m) to be able to exert a force (so to speak). I could have just said "two words, photoelectric effect" but that I thought might be inappropriate, also this would clear it up for you and help your understanding of the matter (no pun intended :-P ). Hope this helped. Pubuman 16:24, 10 August 2006 (UTC)

## Photon mass

I hesitate to write this after the section above, which frankly looks crankish to me, but there doesn't seem to be any other place to put it.

What is the status of the possibility that photons have nonzero rest mass? I remember seeing an old Scientific American article on it, showing how Maxwell's equations would have to change, among other things. As I understand it, current observations have put an upper bound on photon rest mass, but have not ruled out its existence. However, supposedly (I don't understand why), the discovery of a magnetic monopole would refute a nonzero rest mass for photons.

Anyone know anything about this? Have there been any theoretical or experimental developments that bear on the question since the article I remember (which probably would have been from the '70s or so)? --Trovatore 00:23, 23 November 2005 (UTC)

If a photon were to have mass while it was at rest, it would defy the theory of general relativity. If a photon were to have mass while it was in motion, it would also defy GR. Mass would require infinite energy to accelerate it to C, so if photons existed as mass before they were emitted from electrons and such, then it would have required infinite energy to "propel" that photon to C. We know that electrons do not lose energy, and certainly not infinite energy, when they emit photons. Therefore, to stay within the parameters GR sets out for mass and velocity, photons can never within their lifetimes have mass. This also means that because they can never have mass, they can never represent energy.

The only possible exception to this would be the ability of a body of mass actually going at C and emitting an object of mass. The energy to accelerate that body of mass to C was already invested in the mass itself, so it would take no further energy to emit something at C. The problem is that no mass can go C, within the parameters of GR. Photons cannot accelerate themselves, and since no objects of mass can go C to emit something at C, there is nothing that can propel them to C.

Kevin E Carman

I'm afraid I don't believe you know enough physics to give a useful answer to my question. For those who are interested, the question is discussed at Wikipedia:Reference desk/Science#photon mass. (I don't know how long the discussion will stay there or whether it will eventually be archived.) --Trovatore 19:17, 6 December 2005 (UTC)

You haven't provided any substance to back up your claim that I do not know enough physics to back up my commentary. You assume that GR is valid, and what I am saying is that it is atleast partially invalid. Light only travels in wave form. The only reason why you cling to the idea of the photon is because most of GR "needs" it to exist to propogate energy without a carrier of some source. If you are willing to not insult me with snide remarks that imply I do not know about what I speak of, I can enlighten you to a complete unified field theory that is far more functional, and logical, than what GR offers.

Please enlighten us with your complete unified field theory. Even better, you could submit it to a peer-reviewed scientific journal for publication. Best of all would be to provide us with a citation of an existing article in such a journal where we can all read about it. -- ALoan (Talk) 20:07, 6 December 2005 (UTC)
I plan on publishing it. I am currently writing it for exactly that. Kevin Carman

The discussion at the reference desk has been archived at Wikipedia:Reference_desk_archive/Science/December_2005#photon_mass. Someone might like to incorporate the information from there into the article. --Trovatore 19:19, 2 January 2006 (UTC)

## Mass

Mass. Photons haven't got any. As this is an article about photons, the article should (and does) say so.

I think the text you reverted was there to take care of a possible terminological confusion. Contemporary physicists usually use "mass" to mean "rest mass", but this has not always been so. To someone expecting "mass" to mean "relativistic mass", the current text is possibly misleading.
Moreover, as I understand it, even a nonzero rest mass for the photon has not really been ruled out on theoretical grounds; all that has been determined is an upper bound, which is explained in the paragraph immediately following the one you edited. The two paras are currently a bit at cross purposes; perhaps the first one should be edited to explain that physicists generally assume photons have zero rest mass, but etc etc etc. --Trovatore 01:48, 12 February 2006 (UTC)
Yep. Worse, current popular science books sometimes use "relativistic mass", despite the fact that this is no longer current scientific usage. I didn't revert his change, though, because perhaps this unfortunate usage should not be encouraged. The article on mass which is linked there does explain this issue.--Srleffler 02:03, 12 February 2006 (UTC)
The obsolete term "relativistic mass" is synonymous with the non-confusing term "energy". Use of "relativistic mass" should never be encouraged. Zero photon mass is theoretically necessary due to gauge invariance; however, one can never be totally certain that it's exactly zero. Current experimental bounds are really small: less than 10−16 eV. It might be nice to work that into the article somewhere, but it's really only of interest to the small group of physicists working to make the bound ever-smaller. Feel free to bet the farm that it's exactly zero. -- Xerxes 03:06, 12 February 2006 (UTC)
You don't have to encourage the use of "relativistic mass", but you ought to have language that explains the situation to readers who might be confused. There already is text about an upper bound for photon rest mass; what's needed is a better transition from the previous para, which claims photons have "no" mass. Quibble on that: Of course they have a mass, even if it's zero. So "zero (rest) mass" would be a better way of putting it. --Trovatore 03:10, 12 February 2006 (UTC)
I think the term is dead enough now that merely mentioning it confuses the non-confused and does little to alleviate confusion amongst the confused. I do agree on "zero" versus "no"; duly changed. -- Xerxes 03:27, 12 February 2006 (UTC)
We don't need to mention relativistic mass. We can simply say that light is affected by gravity, has momentum, and has inertia. Quite simply, if we weighed a photon the same way we weigh ourselves, we would find that it has mass.
Another thing to note is that it is still in question whether photons actually have zero rest mass, or whether they are simply very very very light. This is noted on the page that the consensus upper limit on photon mass is 6*10^-17 or something. Fresheneesz 23:40, 7 April 2006 (UTC)

## Photons exerting gravity

• "Photons have zero mass and zero electric charge, but they do carry energy, momentum and angular momentum."

I wanted to change this sentence a bit, not only to reflect that photons are not for sure 100% massless, and also to note that they do everything mass should do - exert gravity, are affected by gravity, and exert a force on particles they hit. I wanted to make sure that I was correct in those assumptions.

• "Photons are deflected by a gravitational field twice as much as Newtonian mechanics predicts for a mass traveling at the speed of light."

? How would newtonian mechanics predict anything for a supposedly massless object? Fresheneesz 23:46, 7 April 2006 (UTC)

Absolute certainty is not part of science. Photons are massless to within very tight experimental constraints, and there are solid theoretical reasons to think they must be exactly massless. There is no point in obfuscating the situation by adding weasel-words. Newtonian mechanics predicts that everything falls at a constant rate, independent of mass; one may assume that this also holds in the massless limit. -- Xerxes 17:15, 8 April 2006 (UTC)
Thats not my point. This article already addresses the uncertainty of a photons mass. However, I was still making sure that the reset of my assumptions are correct. It is a very common mistake with people to be confused by the descrepensies of saying light is "massless" when it interacts with things like a mass should. People think "why does light bend if it has no mass?" or "how can light push a solar sail if it has no mass?" people don't understand that light has properties that act exactly as if it had mass. I think this very common misconception should be emphasized in this article.
I was particularly confused with my second bullet pointed quote. Fresheneesz 03:55, 10 April 2006 (UTC)
People's misunderstanding of general relativity is not really a topic for the photon article. In any case, it has little bearing on whether or not photons have mass. In particular, a photon does not act "exactly as if it had mass"; it acts exactly as if it had zero mass, because it has zero mass. Momentum and energy are properties wholly independent from mass. -- Xerxes 04:38, 10 April 2006 (UTC)
No, people's misunderstanding of LIGHT *is* really a topic for the photon article. People associate mass with gravity, bounching, momentum, etc. Light HAS momentum, and can bounce, and is affected by gravity. This should be noted in order for people to more fully understand what it means for light to be massless. This isn't about making things too specific, or expanding an unrelated issue into an article where it doesn't belong. Light is misunderstood, and this article should address that. Fresheneesz 19:33, 10 April 2006 (UTC)

## "...deflected by ..gravit[y] .. twice as much as Newtonian mechanics predicts..."

• "Photons are deflected by a gravitational field twice as much as Newtonian mechanics predicts for a mass traveling at the speed of light."

Since this isn't getting answered in the above post, I'll reitterate this. This sentence doesn't make sense to me. How does Newtonian mechanics predict the deflection of light by gravity? And what "mass" is it talking about (since the article says light is massless)? Fresheneesz 19:37, 10 April 2006 (UTC)

To reiterate the answer (posted above), Newtonian mechanics predicts a deflection that is independent of mass. (For a detailed derivation, see Newtonian gravitational deflection of light revisited.) In that sentence "mass" is being used figuratively to mean "test particle" (often called a "test mass" in gravitational contexts). -- Xerxes 20:04, 10 April 2006 (UTC)
Yea that link doesn't help. How can deflection of gravity be independent of mass - especially in newtonian physics? What *was* it dependent on? Fresheneesz 10:19, 20 April 2006 (UTC)
Could you be more specific? What about the detailed derivation of the appropriate equations is not helpful? Note that the deflection does depend on the mass of the deflector, it just doesn't depend on the mass of the deflected object (the light, in this case). To be really perfectly fair, there ought to be a teeny-tiny correction due to the deflector being nudged by the gravity of the deflected object. Since the deflector is usually a star, it doesn't move very much. However, such a term would depend on the mass of the deflected object. -- Xerxes 14:24, 20 April 2006 (UTC)
Ahh, I see, maybe you're right. I don't have time to read it again (I only skimmed it the first time), but i'll see if I can make sense from it. In any case, that part in this article isn't very clear since most people aren't familiar with newtonian bending of light. Is there a page on that on wikipedia? I'm going to red link "Newtonian mechanics predicts" for now. Fresheneesz 21:57, 20 April 2006 (UTC)

To a first approximation (in general relativity), the gravitational force exerted on an object moving transversely (perpendicular to the radial direction) by the Sun is proportional to E+P·V where E is the energy of the object (including both the energy of its rest mass (if any) and its kinetic energy), P is its linear momentum, and V is its velocity (transverse). If the object is moving at the speed of light, then P·V is equal to E which is why you get a doubling. A more complex expression is needed, if the motion is not transverse. JRSpriggs 03:52, 10 August 2006 (UTC)

## Photons have relativistic mass - ie gravitational attraction and momentum

People are *always* confused about the "masslessness" of light. Light does have the property of the outdated concept of relativistic mass. I want to write a little blurb - not on relativisitic mass (which everyone says is a bad concept) - but on the gravitational attraction and momentum of light. I would also like to mention the "effective mass" of light, which is derived from its gravitational attraction and momentum - like any other mass is.

I don't think anyone can really understand light without knowing that *while moving* it acts like it has mass. I have a couple sources I could site to support this view:

Anyone like to give me the thumbs up? - Fresheneesz 06:28, 8 May 2006 (UTC)

Absolutely not. "Acts like it has mass" is meaningless nonsense. Photons act exactly as if they have zero mass; they do have zero mass. -- Xerxes 15:17, 8 May 2006 (UTC)
Did you not read what I wrote? I was not talking about rest mass. The *only* way humans can detect somethings mass is through detction of momentum and gravity. Photons have both of these properties while in motion. Please read what I write if you're going to call it nonsense. Fresheneesz 01:36, 9 May 2006 (UTC)
This is also nonsense. General relativity indicates that objects are deflected according to the geodesic equation for a metric determined by the stress-energy tensor. Mass is only a small part of the stress-energy tensor; gravity is due to many things other than mass. The way you actually determine mass is by the root squared difference between energy and momentum. -- Xerxes 16:18, 9 May 2006 (UTC)
What is a "root squared difference"? The bottom line is that photons have momentum and are effected by gravity, and that isn't addressed very well in this article. Like I have said before, there are millions of people that simply *do not* understand that photons can be "massless" *and* be effected by gravity, or push things. Fresheneesz 05:28, 10 May 2006 (UTC)
Root squared difference: ${\displaystyle m={\sqrt {E^{2}-p^{2}}}}$. I think the article is very clear that photons are affected by gravity. Associating that effect with mass only served to propagate a falsehood. -- Xerxes 16:50, 10 May 2006 (UTC)
Do you deny that photons bouncing around in a box will make the box heavier than if it had no photons inside? Fresheneesz 05:28, 10 May 2006 (UTC)
While a box full of photons may have mass, a single photon does not. Since boxes of photons are not everyday sorts of objects, they are not mentioned in the article. See, for more detail, photon gravity on the topic of boxes of photons. -- Xerxes 16:50, 10 May 2006 (UTC)
Of course you don't really need the box; two photons, not going in exactly the same direction, constitute a system having nonzero invariant mass. That seems like a fairly "everyday object" to me. I would think it might rate a mention here. --Trovatore 17:05, 10 May 2006 (UTC)
It's interesting, but is it about photons? I'd say it's something that belongs in an article about mass or binding energy or some other relativistic phenomenon. I mean, you could say the same thing about a box of neutrinos (modulo neutrinos actually having a tiny mass). -- Xerxes 19:40, 10 May 2006 (UTC)
Neutrinos do have mass though, which makes anyone considering it be less than confused about why it interacts with gravitational fields etc the way it does. Photons are the *only* thing in science that most people have heard of that has no invarient mass. Given that it involves photons, it deserves at least a mention on this page, and like you said, probably on pages involving relativistic phenomenons, and articles about mass. People aren't going to read the entire wikipedia, so multiple mentions of the same thing should appear whereever relevant. And I think it is relevant in this case. Fresheneesz 10:34, 11 May 2006 (UTC)
BTW, I like the link you gave - it says very nicely exactly what I was trying to say. Fresheneesz 10:35, 11 May 2006 (UTC)

## Last batch of edits

This certainly did not meet any set of standards we discussed here on the topic of light and gravity. The most glaring error was the incorrect use of the term "effective mass". Please refrain from adding bad physics to the article. -- Xerxes 21:10, 14 May 2006 (UTC)

Yes, I did some research to try and justify the much less used (or incorrectly used) definition of "effective mass". I found a couple cases, but over all, I realized I shouldn't have used that particular phrase. Relativistic mass is looked down upon, and so I tried a different term - which I hadn't realized had a precise scientific meaning.
However, I had many other edits that I think are relevant and helpful. Please discuss other "glaring error"s that you have issue with. Fresheneesz 18:43, 15 May 2006 (UTC)
I also noticed that you reverted my edits en-masse. I would very much appreciate if you discriminate between my good edits and my bad edits, and take out the crap - but not the good stuff. I hardly can think that all of my edits were bad. Reverting en-masse is an action taken far too often. I would ask that you please revise your edit, and discuss the issues you have with what you actually want reverted. Fresheneesz 18:48, 15 May 2006 (UTC)

## mass of photon and "gas"

Xerxes, you put the phrase "gas of photons" under that header, and I think thats just a bit misleading. Some people might misinterpret that to mean that photons constitute a gas. In the most common sense of the word, photons don't make up a gas. Comments? Fresheneesz 02:49, 24 May 2006 (UTC)

Photon gas is a perfectly cromulent physics concept. See, for example, these hundreds of papers in the arXiv. -- Xerxes 03:30, 24 May 2006 (UTC)
Ok, I created a page explaining somthing about a photon gas, and linked to it. Fresheneesz 17:34, 24 May 2006 (UTC)
I guess our theme-song for the box of photon gas wouldn't be by Mason Williams....
Seriously this is over-complicated. One of the reasons a single photon has no invariant mass is that you can change its energy to anything you like, just by jumping to a different inertial frame. So what invariant mass would it have, if it had one? You can make its energy go as close to zero as you like.
The nifty and tricky thing about PAIRS of moving objects, so long as they aren't co-moving (they have some relative velocity) is that there's no reference frame you can pick, to make all their energy go away. You're always STUCK with some, no matter which single frame you pick. All you can do is find the frame where the total energy of the two particles is MINIMIZED. In that frame, you'll find each particle headed away from you (or toward you, one or the other) with exactly the same MOMENTUM. So the total system momentum is zero. In that frame, energy is the least. And in that frame, the total mass of the system is the invariant mass. Multiply by c^2 and you have the "rest energy" of the system, which is also the total energy of the system (since momentum is zero). It's the minimal energy you can't avoid, because it's a system. Notice that it includes the sum of the rest energies of the particles, plus some kinetic energy you can't get rid of by changing inertial frames.
Now for the fun part. This is also true for two photons. For every pair of photons (let's pretend they start from the same point), so long as they aren't headed the same exact way, there's some inertial frame where both photons are headed "exactly" away from (or toward) the observer, and both have the same frequency, and the same momentum. *That* is the frame in which the energy of the PAIR is the least. And in that frame, the pair of photons have a mass, and that mass is the "invariant mass" of the pair. Their momenta cancel, and are zero. Which means their mass is their [combined energy in that frame]/c^2. Just as advertized. You don't need a box, but if you had one, that box would force both photons into bouncing around until the zero-total momentum frame was very close to the initial rest frame of the box. In that frame, that's how much extra the box would weigh, by comparison with empty (on average, after many photon bounces transfer momentum to the walls). See below for detail.
Actually, if you have box, you can weigh just ONE photon. Does that mean the photon has a mass? No. It means you still are stuck with a SYSTEM of two objects (box + photon), which you can look at from many inertial frames, until you find one in which the total momentum of the two is zero. What would that look like? In that frame, if the photon is moving the right with momentum p = E/c, then the box is moving to the left with the same momentum m*v. Obviously v will be small. When the photon bangs off the other side, they trade directions. If you weigh this collection you see it jumps from side to side (jiggles) as the photon hits, but the net downward force can be calculated, because the one photon suffers aberration in a g field, and hits each wall at a slightly downward angle. Downward momentum transferred gives you extra weight, and over and above the m*g of the box, you find that this extra weight is [E/c^2]*g where E is the energy of the photon in your zero-momentum frame. So the single photon seems to act like it has mass of E/c^2, but only because of your prejudice that the weight of a box has to equal the sum of the rest masses of the things in it. It doesn't. In a sense, you're not weighing the photon, but weighing the photon's kinetic energy. If the box was full of gas molecules you'd weigh their kinetic energies in the same way, along with their rest masses. But kinetic energy is all the photon has. No rest mass. Still, you weigh just the energy, and you can do it for ONE photon, so long as it's part of a zero-momentum system. Sbharris 04:25, 9 June 2006 (UTC)

I had writen that a single photon can't turn into a particle or particles with rest mass, for the reason that the energy of a single photon is not defined, it's rest mass is zero, and rest mass (invariant mass) is conserved in reactions. However, I neglected to mention that of course single photons can turn into particles with rest mass by interaction with another particle. In that case, it is because the photon provides an extra invariant mass to the system which IS defined.

This is very much the same case as a single photon in the box, above. The photon and the box now defines a 2-object SYSTEM, in such a system has increased invariant mass due to the photon, and so the energy available from the photon to produce rest mass (in the form of other particles) is now defined. In the case of a photon interacting with a nucleus or other charged object in pair production, much the same thing happens. Since we have a system, the single photon's energy can be defined: if it's 1022 kev in the center of momentum frame of the 2-particle system, that's enough to make an electron-positron pair. If it's less than that, it can't happen. That second particle is necessary not just to absorb the extra momentum when the photon offloads its energy, but also acts as an objective guage to how much "rest-mass convertable" energy the photon "has." Otherwise it's just a matter of observer.

Single particles with rest mass can decay all by themselves, because they have some store of minimal energy which isn't kinetic. For a photon there's no such thing, so in a sense they all need "help" from an external reference to tell how much "kinetic" energy they have. Sbharris 22:41, 9 June 2006 (UTC)

For a single photon... what you're saying here seems right. For two photons, you *can* create particles with rest mass... it's done all the time at the B-factory here (this is my third edit to this section - I am finally satisfied with this link I provide here :D ). I know it may seem like fantasy that from two massless Bosons you can create positive-mass Leptons and Hadrons but it's done all the time. At the PEPII B-factory (link above) the Upsilon "4S" resonance is exploited to do just this very thing. I've added this photon article to my watchlist. I have experience in this and it has always been an interest of mine. I look forward to contributing to this article thus. Astrobayes 21:57, 26 June 2006 (UTC)

## Photons at rest mass

According to the article, photons have a rest mass of zero but have a small relativistic mass while they are moving. There's just one thing I don't understand about that. Hypothetically, if I were to somehow travel at the speed of light and then fly next to a photon, then relative to me, the photon would be at rest. However, as stated earlier, photons have a rest mass of zero. So, if I were to fly next to a photon, wouldn't it then blink out of existence?

In a sense. If you fly in the same direction as a photon sufficiently fast, then you can redshift its energy down to the point where no reasonable detector in your frame can detect it. Melchoir 02:59, 29 July 2006 (UTC)
It might be more correct to say that single photons in free flight have an undefined energy, since you can make their energy (or relativistic mass) anything you like, by choosing your inertial frame (you do that for particles, too-- for single particle the kinetic energy is anything you like, but zero only in ONE frame). But such a photon has no rest mass because it's never at rest. Only when you get two or more photons going in two or more different directions, do you get "stuck" with a minimal energy for the system, which will occur in just one of all possible frames, as with the single massive particle. This frame happens to be the frame in which the photons have no net momentum (it all cancels out). In that frame, they all have minimal energy, when you add it up. And THAT energy is their invariant mass, as a system. It's the energy in the system which is available to make massive particles with rest mass. But note that unless you have two or more photons, that energy doesn't appear. There is no way for nature to "decide" how much energy a single photon has available to make rest mass, unless it has a reference point frame (a second particle) to do it. And as soon as you choose that frame by introducing a second particle with rest mass at rest in that frame, you define the photon's energy FOR that frame, and thus define how much energy you have to work with, if it interacts with the second particle. For a system of two photons (where neither photon can be at rest, but both can be flying off in exactly opposite directions), it's the zero momentum frame (the center of momentum frame) which defines the minimal (rest) energy. I'm not sure that's clearSBHarris 03:25, 29 July 2006 (UTC)