# T or F: Mass can only be created or destroyed in a nuclear reaction

T or F: "Mass can only be created or destroyed in a nuclear reaction"

"Mass can only be created or destroyed in a nuclear reaction", quote anonymous authority figure.

Someone, perhaps an educator at my university, repeatedly makes the above statement and states its because of the relationship E=mc2. Every time I hear this person say this, I cry [email protected]#$% as I do not believe this to be true. It is my understanding that the above equation merely states a mass-energy equivalence in which the mass of the body has an energy equivalence. Some simple examples: -A charged battery has more equivalent mass than an identical discharged battery. -A pen sitting on a shelf has more equivalent mass than an identical pen sitting on the floor. -1kg of water at 100'C has more equivalent mass than 1kg of water at 25'C. Am I wrong about this? Every time this argument comes up, people, perhaps other educators, tell me that my above examples are completely wrong. Am I missing something here or am I just surrounded by incompetence? Last edited: ## Answers and Replies Drakkith Staff Emeritus Science Advisor What exactly do they mean by their satement? Other than in particle colliders I am unaware where we can create any matter. And nuclear reactions don't destroy matter either as far as I know, but merely convert them into different elements. tiny-tim Science Advisor Homework Helper Hi Topher925! "Mass can only be created or destroyed in a nuclear reaction", quote anonymous authority figure. They mean rest-mass. Energy is mass, and mass is energy, so obviously for example a hot spring has more mass than an identical cold spring, and so does a compressed spring. But they all have the same rest-mass … no rest-mass has been created or destroyed. Someone, perhaps an educator at my university, repeatedly makes the above statement and states its because of the relationship E=mc2. Every time I hear this person say I cry [email protected]#$% as I do not believe this to be true. It is my understanding that the above equation merely states a mass-energy equivalence in which the mass of the body has an energy equivalence.

e=mc² can either mean what you describe, or it can simply refer to rest-mass.

Talking about rest-mass is far more convenient … for a particular body, it doesn't change.

Hi Topher925! They mean rest-mass.

Energy is mass, and mass is energy, so obviously for example a hot spring has more mass than an identical cold spring, and so does a compressed spring.

But they all have the same rest-mass … no rest-mass has been created or destroyed.

e=mc² can either mean what you describe, or it can simply refer to rest-mass.

Talking about rest-mass is far more convenient … for a particular body, it doesn't change.

You just confused me Tim. If you mean to say that they meant rest-mass, then that refers to rest-mass being created or destroyed. But then you later say that rest-mass doesn't change for a particular body. Is that true for all processes or just nuclear processes?

tiny-tim
Science Advisor
Homework Helper
But then you later say that rest-mass doesn't change for a particular body. Is that true for all processes or just nuclear processes?

I was envisaging that if the body took part in a nuclear reaction, we wouldn't call it the same body afterwards. russ_watters
Mentor

Some simple examples:
-A charged battery has more equivalent mass than an identical discharged battery.
-A pen sitting on a shelf has more equivalent mass than an identical pen sitting on the floor.
-1kg of water at 100'C has more equivalent mass than 1kg of water at 25'C.
It's my understanding that if you had a sensitive enough scale (probably not possible with current technology), you'd be able to detect the weight (and hence mass) difference of the first and third. For the second, the mass is in the earth-pen system.

"Mass can only be created or destroyed in a nuclear reaction", quote anonymous authority figure.

Someone, perhaps an educator at my university, repeatedly makes the above statement and states its because of the relationship E=mc2. Every time I hear this person say I cry [email protected]#$% as I do not believe this to be true. It is my understanding that the above equation merely states a mass-energy equivalence in which the mass of the body has an energy equivalence. Some simple examples: -A charged battery has more equivalent mass than an identical discharged battery. -A pen sitting on a shelf has more equivalent mass than an identical pen sitting on the floor. -1kg of water at 100'C has more equivalent mass than 1kg of water at 25'C. Am I wrong about this? Every time this argument comes up, people, perhaps other educators, tell me that my above examples are completely wrong. Am I missing something here or am I just surrounded by incompetence? In any interaction the total inertial mass is fixed. You are correct in your second paragraph as indeed the famous Einstein mass-energy equation merely states an equivalence. in your simple examples the first and third are correct. The second needs a slight re-interpretation in that it is the system comprising the Earth plus the pen that has to be considered as a whole. In getting from being at rest on the shelf to being at rest on the floor the loss of potential energy has resulted in that potential energy being converted into some other form, and the inertial mass of the Earth now includes the mass equivalent of that lost potential energy. (But where that mass equivalent now resides is less clear and depends on the details of the process.) So your final question comes about because the answers you had received were based on unstated assumptions on the part of those answering. Dale Mentor 2020 Award "Mass can only be created or destroyed in a nuclear reaction", quote anonymous authority figure. False, but nuclear reactions are so energetic that the mass deficit is significant and easily measurable. The mass lost in a chemical reaction is so small that it would be very difficult to detect. OmCheeto Gold Member Does pair production count as a "nuclear reaction"? K^2 Science Advisor Rest mass is lost/gained by molecules in ordinary chemical reactions. The statement is absolutely false. Everyones comments are good and true but miss the authority's point. They mean that chemical reactions do not alter the atomic numbers of the constituent atoms but nuclear reactions would. "Mass can only be created or destroyed in a nuclear reaction", quote anonymous authority figure. Someone, perhaps an educator at my university, repeatedly makes the above statement and states its because of the relationship E=mc2. Every time I hear this person say this, I cry [email protected]#$% as I do not believe this to be true. It is my understanding that the above equation merely states a mass-energy equivalence in which the mass of the body has an energy equivalence.

Yeah, everytime I hear it too, I find that the two extremes on the issue gear up for war. Perhaps I can shed some light on the issue.

The formula E=mc2 comes from a more basic formula in SR, which is
E^2=p2c2+m2c4

When p=momentum=0 then we get E=mc2. Thus the formula tells us the energy that can be accounted for due to an object's mass. Mass is defined as the amount of matter in an object. - Note that this also means that E=mc2 does not apply for moving objects since if m/=0 and v/=0 then p/=0.

Another thing to realize is that not all energy is equivalent. The prominent example is the difference between kinetic energy, defined as the energy due to motion, and potential energy, defined as the energy due to the force applied on the object. There is a propensity for some people to simply declare all energy the same and then conclude all kinds of nonsense.

Some simple examples:
-A charged battery has more equivalent mass than an identical discharged battery.
-A pen sitting on a shelf has more equivalent mass than an identical pen sitting on the floor.
-1kg of water at 100'C has more equivalent mass than 1kg of water at 25'C.

All of these examples are a result of confusing different kinds of energy with the energy that is just due to mass. However there are examples where E=mc2 can be correctly applied:

-Main sequence stars burn hydrogen to helium in a nuclear reaction called the proton-proton chain. As a result for every atom of helium produced about 0.7% of the mass of four hydrogen atoms disappears and gets converted to electromagnetic radiation that has energy given by E=mc2.
-In PET-scans, electrons and positrons (anti-matter of electrons) collide and produce two 511 keV X-ray photons. A calculation shows that this follows E=mc2 exaclty, since photons have no mass.

Am I wrong about this? Every time this argument comes up, people, perhaps other educators, tell me that my above examples are completely wrong. Am I missing something here or am I just surrounded by incompetence?

No, you're not *completely* wrong on this. The essense is that even though different forms of energy can be converted to one another, they are not exaclty equivalent.

PS= Apologies for not using TeX, but it seems to be screwing up on this machine. I'll figure it out.

The formula E=mc2 comes from a more basic formula in SR, which is
E^2=p2c2+m2c4

When p=momentum=0 then we get E=mc2. Thus the formula tells us the energy that can be accounted for due to an object's mass. Mass is defined as the amount of matter in an object. - Note that this also means that E=mc2 does not apply for moving objects since if m/=0 and v/=0 then p/=0.

Really, I think this only rekindles the fires of confusion.

E2=p2c2+m2c4 is the Lorentz invariant equation for a closed system. It tells us nothing about the distribution of
energy and momentum.

Without a Lorentz boost it reduces to E2=m2c4 in the center of mass frame.

Another thing to realize is that not all energy is equivalent. The prominent example is the difference between kinetic energy, defined as the energy due to motion, and potential energy, defined as the energy due to the force applied on the object. There is a propensity for some people to simply declare all energy the same and then conclude all kinds of nonsense.

All of these examples are a result of confusing different kinds of energy with the energy that is just due to mass. However there are examples where E=mc2 can be correctly applied:

-Main sequence stars burn hydrogen to helium in a nuclear reaction called the proton-proton chain. As a result for every atom of helium produced about 0.7% of the mass of four hydrogen atoms disappears and gets converted to electromagnetic radiation that has energy given by E=mc2.

Now this is what I'm talking about. The energy does not "disappear" and get converted to radiation. The electromagnetic radiation had better have nonzero mass and zero momentum or the conservation of both energy and momentum have been violated.

Last edited:
K^2
Science Advisor

kg4pae said:
Some simple examples:
-A charged battery has more equivalent mass than an identical discharged battery.
-A pen sitting on a shelf has more equivalent mass than an identical pen sitting on the floor.
-1kg of water at 100'C has more equivalent mass than 1kg of water at 25'C.
All of these examples are a result of confusing different kinds of energy with the energy that is just due to mass.
Absolutely wrong. Charged battery has greater chemical potential energy than uncharged. Chemical potential energy contributes to rest mass. Pen at the shelf has more gravitational potential energy. Gravitational potential energy contributes to rest mass. A hot glass of water has more thermal energy. Thermal energy contributes to rest mass of an object.

All of these can be converted to kinetic energy which does not contribute to rest mass, "destroying" mass in the process.
Everyones comments are good and true but miss the authority's point.

They mean that chemical reactions do not alter the atomic numbers of the constituent atoms but nuclear reactions would.
Change in mass and change in quantum numbers of a nucleus are two entirely different subjects. The authority figure is wrong. No further discussion is necessary on that.