Why doesn't mass of light equal infinity

In summary, mass is converted to energy in nuclear reactions, but it's not the same as matter being converted to light.
  • #1
Sting33
16
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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?
 
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  • #2
I suppose what I am trying to figure out is what physical process takes place at the instant mass is converted to energy?

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
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
Sting33 said:
In a nuclear reaction, it is my understanding that mass is converted to energy.

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.

Sting33 said:
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?

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.)

Sting33 said:
I suppose what I am trying to figure out is what physical process takes place at the instant mass is converted to 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
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?

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
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
Also, thanks for straightening me out on the definitions of mass.

Well, I'm glad your getting straight, Sting. Not that there's anything wrong with the alternative:redface:
 
  • #8
Sting33 said:
I suppose what I am trying to figure out is what physical process takes place at the instant mass is converted to energy?
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 happened is that fermions have been converted into bosons, which perhaps feels a little less confusing.
 
  • #9
Sting33 said:
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.

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.
 
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  • #10
DaleSpam said:
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.

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
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
LastOneStanding said:
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.
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:
[itex]m=|P|=|P_{e^-}+P_{e^+}|=|(1,0,0,0)+(1,0,0,0)|=|(2,0,0,0)|=2[/itex]

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

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 referring to, but it is not the same as the mass of the system.
 
  • #13
Sting33 said:
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. :)
Oh, very good point. My apologies, I was so unclear as to be worse than useless.

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

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.
 
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  • #14
DaleSpam said:
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 referring to, but it is not the same as the mass of the system.

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
Sting33 said:
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. :)

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

1. Why doesn't the mass of light equal infinity?

The mass of a particle is related to its energy, and light has a unique property of having no rest mass. This means that light has no mass when it is at rest, and therefore cannot have an infinite mass. This is a fundamental property of light and is explained by Einstein's theory of relativity.

2. Can the mass of light ever change?

No, the mass of light cannot change because it has no rest mass. It only has energy, which can change depending on the frequency and wavelength of the light.

3. How is the mass of light calculated?

The mass of a particle, including light, can be calculated using the famous equation E=mc², where E represents energy, m represents mass, and c represents the speed of light in a vacuum. Since light has no rest mass, its mass in this equation is always zero.

4. What does it mean for light to have no mass?

Having no mass means that light does not experience the effects of gravity and cannot be accelerated to a stop. It also means that light always travels at the speed of light and does not require a force to maintain its motion.

5. Is it possible to have a particle with both mass and light?

No, it is not possible for a particle to have both mass and light. As mentioned earlier, the mass of a particle is related to its energy, and light has no rest mass. Therefore, a particle cannot simultaneously have both properties.

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