# Why doesn't mass of light equal infinity

1. Jan 26, 2013

### Sting33

I'm trying to wrap my head around what happens as mass is converted to energy. In a nuclear reaction, it is my understanding that mass is converted to energy. It is also my understanding that as matter approaches the speed of light it's mass approaches infinity. If that is so, why is the mass of light itself zero? (In my mind, matter that has been converted to energy is going the speed of light). I apologize if this is a really elementary question, but could you set me straight on where the error in my thinking is?

I suppose what I am trying to figure out is what physical process takes place at the instant mass is converted to energy?

2. Jan 26, 2013

### DiracPool

Umm...I'll let you in on a little secret..yes, come closer and I'll whisper in your ear...the answer is..you just answered it yourself! The mass is converted to energy. What is mass and what is energy? Well, there's a Nobel prize awaiting your explanantion, Sting, get on it.

3. Jan 26, 2013

### Sting33

So the answer is... Nobody knows where the mass goes and suddenly the matter is going the speed of light without having its mass approach infinity? So what's all the talk about needing an infinite amount of energy to accelerate mass to the speed of light?

4. Jan 26, 2013

### Staff: Mentor

This is not the same as matter being converted to light. There are many nuclear reactions that have matter particles as both reactants and reaction products, but still convert mass to energy (the energy shows up as the kinetic energy of the reaction products). See further comments below.

You're confusing two different concepts that go by the name "mass".

One is "rest mass" or "invariant mass" (the latter is a better name for reasons which will appear in a moment). Ordinary objects, and matter particles like electrons, have nonzero invariant mass; light has zero invariant mass. (The case of light illustrates why "rest mass" is not a good name: light always moves at the speed of light, so it's never at rest, but it still has a well-defined invariant mass of zero.)

The other is "relativistic mass", which is really just total energy. This is the "mass" that increases without bound as an ordinary object, or a matter particle like an electron, approaches the speed of light. The term "relativistic mass" is out of favor now among physicists because, first, it causes confusion, and second, we don't need it because we already have a perfectly good word, "energy", for the same concept. (Note that light itself also has energy, but the concept of "relativistic mass" is never applied to light; we just talk about its energy.)

When people talk about this happening, as in the nuclear reactions you referred to, what they mean is that the sum of the invariant masses of the reactants is greater than the sum of the invariant masses of the reaction products. The difference shows up as energy in the reaction products; this energy can appear as kinetic energy of matter particles in the reaction products, or it can appear as electromagnetic radiation such as gamma rays, or both. The physical process involved is just whatever nuclear reaction is taking place: particles interact with each other to form other particles.

5. Jan 26, 2013

### DiracPool

That's a valid question. Your first query has been addressed in a recent thread here on PF, the putative conclusion of which is that the Lorentz mass gain at relativistic speeds was somehow not actually true and forced upon us by a media-hyped culture bent on exploiting the "Einstein factor." Your second query is more legitimate. The ugly truth is that E really does not equal MC^2. Sorry to burst your bubble. Just like the cosmological constant, there's a dirty fudge factor in the most famous equation of all time. That fudge factor is the +pc you don't see so often that relates to photons in particular (no pun intended). This is how they squeeze around the problem you mentioned...they invented this thing called "rest mass", to make E=MC^2 work. If you want light, then you have to eschew the MC^2 and pick up the +pc. That's just how it is.

6. Jan 26, 2013

### Sting33

Thank you both for your insightful comments. I do remember now the +pc, I had forgotten. Also, thanks for straightening me out on the definitions of mass.

7. Jan 26, 2013

### DiracPool

Well, I'm glad your getting straight, Sting. Not that there's anything wrong with the alternative

8. Jan 26, 2013

### Staff: Mentor

I know that it is common to speak of "converting" mass to energy, but I don't like that. Mass has energy and energy has mass. When a positron and an electron anhillate the energy and mass of the system is the same before and after. Mass has not been converted to energy, since the system has the same of both. What has happend is that fermions have been converted into bosons, which perhaps feels a little less confusing.

9. Jan 26, 2013

### ZapperZ

Staff Emeritus
You might also want to start by browsing the Relativity FAQ subforum. It might have answered your question.

https://www.physicsforums.com/forumdisplay.php?f=210 [Broken]

I'm posting this not just for your information, but also something we have to do regularly to make sure other new members are aware of such a source.

Zz.

Last edited by a moderator: May 6, 2017
10. Jan 26, 2013

### VantagePoint72

Huh? Mass is definitely not conserved in pair annihilation: an electron and a positron both have mass, and two photons do not. Only the total energy is conserved, which is rest energy + kinetic energy before the annihilation and purely kinetic after.

11. Jan 26, 2013

### Sting33

Dalespam, so if mass has energy and energy has mass, is light not energy? It has no mass. But perhaps I'm confusing the two different concepts of mass again.

I'm trying to reconcile everyone's replies now. So I think what you are saying is relativistic mass has energy and energy has relativistic mass. Or, in other words, the way peterdonis explained it, since relativistic mass is just total energy, we are saying that total energy has energy and energy has total energy. :)

12. Jan 26, 2013

### Staff: Mentor

Mass of the system is definitely conserved. Using units where c=1 and the mass of the electron = 1 before the anhillation the mass of the system is:
$m=|P|=|P_{e^-}+P_{e^+}|=|(1,0,0,0)+(1,0,0,0)|=|(2,0,0,0)|=2$

After the anhillation the mass of the system is:
$m=|P|=|P_{\gamma_1}+P_{\gamma_2}|=|(1,1,0,0)+(1,-1,0,0)|=|(2,0,0,0)|=2$

Note that the mass of a system of particles is different from the sum of the masses of the individual particles. The former is conserved, the latter is not. The latter is what you are refering to, but it is not the same as the mass of the system.

13. Jan 26, 2013

### Staff: Mentor

Oh, very good point. My apologies, I was so unclear as to be worse than useless.

The relationship between (invariant) mass and energy is:
$c^2 m^2=E^2/c^2-p^2$

Momentum is in there also. So light has as much energy as momentum (in units where c=1) and therefore has no (invariant) mass. For something at rest, p=0 and you get the familiar E=mc².

Last edited: Jan 26, 2013
14. Jan 26, 2013

### Staff: Mentor

Just to clarify for Sting33, "mass" here means "invariant mass", and the key point here is that the invariant mass of a system of particles is not necessarily equal to the sum of the invariant masses of the particles, because the particles may be in relative motion.

15. Jan 26, 2013

### Staff: Mentor

Relativistic mass *is* total energy; the two are just different words for the same thing.