“Someone, somewhere went to sleep and dreamed us all alive. Dreams get pushed around a lot, and I doubt if we’ll survive. We won’t get to wake up; dreams were born to disappear, And I’m sure that none of us is here.” - Jim Stafford
I’m not a physicist. But from reading these threads over the years it is my understating that:
- Mass is not energy.
- Energy is not mass.
- Mass cannot be converted into energy.
- Energy cannot be converted into mass.
- Mass is conserved.
- Energy is conserved.
- Mass has energy.
- Energy has mass.
The hypothetical in the subject in your OP is false.
Mass is Energy.
Everything is Energy.
Mass is a different form of Energy.
Energy is some kind of *Energy itself, some kind of existence that we’ve yet to identify.
I have the sinking feeling that that is the most salient answer I will ever receive to that question, here or anywhere else. 
Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo.
Assuming there is no conceptual misunderstanding, this is a semantics issue. The four letters M-A-S-S form a word with multiple meanings. I have no problem with the phrase “mass is converted into energy”, as long as the speaker and listener both understand the context. But, I am solidly a linguistic descriptivist, and a prescriptivist may take issue with my position.
Part I
Consider an neutral pion. It has mass. (135 MeV/c[sup]2[/sup], for what it’s worth.) It decays to two photons. Photon A has no mass. Photon B has no mass. The sum of the masses of the two photons is zero. The two photons have no mass. This paragraph has used mass in a consistent and valid way.
Part II
Energy (E) and momentum (p) are both conserved quantities in this decay. Together, they form a Lorentz four-vector, which means that
E[sup]2[/sup]-p[sup]2[/sup]
is a constant that does not depend on one’s frame of reference. In the initial pion’s rest frame, this constant is the square of its mass. It is useful, then, to generalize this definition: a system’s mass is the magnitude of the system’s energy-momentum four-vector (given by the square root of the expression above).
Here, mass isn’t a property of a particle; it’s a property of any arbitrary system. So, the two photons that leave the decay will have the same total energy and same total momentum as the initial pion, and so they (as a system) must have a mass equal to the pion rest mass.
Part III
The latter definition is what Ring, et al., are championing. To be sure, there are many subfields of science where this definition is assumed at all times. But sometimes – and certainly in lay language – “mass” is used as in Part I. (In contexts where different uses may co-exist, one often sees “invariant mass” when the latter, relativistic definition is intended.)
As an analogy, consider the sentence: “An electron stuck a proton.” There are any number of nitpicks you might make. “It struck a quark, not a proton.” Or, “It never even touched the proton; photons did.” But this is all silly if the intended information is communicated by “an electron struck a proton.”
So too with “mass”. An excited carbon-12 nucleus has some amount of mass. If it de-excites by emitting a gamma ray, that gamma ray will do its gamma thing, and we’ll still be looking at a nucleus that is the bound state of six protons and six neutrons, just like before. It was a carbon nucleus before and it is still a carbon nucleus – a well-defined object under scrutiny. But, it’s mass is now different. It has lost mass. The nucleus has lost mass. Where did it go? Into energy.
In this case, the loss is wrapped up in the fact that the system definition changed (as in: it wasn’t a closed system). But that’s the reality of many experimental situations. Thus, the idea that the scalar sum of constituent masses might be interesting to talk about isn’t crazy. Is it unfortunately that the word “mass” is used for this? Perhaps.
But, as long as everyone understands the concepts and contexts, using “mass” in different ways shouldn’t buffalo anyone.
So just to be sure I’m clear on the concept, you’re saying that the same amount of mass and the same amount of energy, considering each as a separate amount. Not the same amount of mass and the same amount of energy because mass and energy are the same thing.
AAUUGHH You people are driving me nuts!
- True
- True
- FALSE
- FALSE
- FALSE
- True
- True
- FALSE
So, if mass cannot be converted into energy what happens in a matter/antimatter reaction?
If energy cannot become mass what was going on in the instant post Big Bang (which I thought at this point was far, far too hot for matter to form…matter came later as the universe cooled)?
Your answers to 3 and 7 are inconsistent. If a mass m already has energy mc^2, how are you then converting it into energy? Unless you’re using the word “mass” in two different ways, but then you really need to be explicit about that (in this thread, at least).
In the thread that led to this one, Exapno Mapcase linked to an earlier thread. In it, MikeS made the following post, which I think is worth reposting here (bolding added).
The bold sentence is important to understand, and why it’s important to be explicit what is being referred to when the word “mass” is used when there’s the possibility of confusion.
Thinking about this some more, “energy” can also have multiple meanings. You might talk about the energy of a system being the sum of potential energy and kinetic energy, and maybe heat, and the total energy being the sum of all three, always neglecting the mc^2 term.
Used that way, it is reasonable to talk about “converting mass to energy”, even though the total energy doesn’t really change when you include the mc^2 contributions.
I think that the use of different meanings for “mass” and “energy”, or not understanding that there are different meanings, is the major source of confusion here.
Slightly off. I’m the one trying to understand this well enough to explain it to others who have no grounding or foundation in physics whatsoever. This is not the crowd who comes into threads and protests that quantum mechanics must be wrong because it doesn’t conform to common sense. They do need to be told that the universe operates under different rules. But people who just want that glimmer of understanding, that “aha” moment, are sincere despite their lacking of the technical terminology.
There’s nothing special about physics in this sense. I guarantee that you - and Ring and all the others - operate this way when it comes to law, medicine, politics, economics, and every other body of knowledge under the sun. You don’t want the technical education, you don’t want terms you can’t define, you don’t want gobbledygook, you want enough to get you through that peripheral section of your life.
Your real issue? You’re a classicist and I’m an Einsteinian. You argue that physics is a privileged body of knowledge and I’m insisting that no privileged viewpoints can exist. 
Pasta wrote:
Pasta you know more physics than I ever will, but surely you’re not saying that a system of two photons, that have a center of momentum frame, has no mass?
I think my biggest problem with “arbitrary systems” and “closed systems” and the specific use of the words mass and energy as not really being produced by the distruction (or conversion) of mass or energy is that there ain’t no setch beastie as a closed system, and arbitrary systems are entirely imaginary.
So, let’s consider the only closed system I can imagine, the Universe. Now unless the Universe started with the same exact amount of mass that it has now, and the same exact amount of energy it has now, neither mass or energy is entirely conserved, although it might be true that the total amount remains in either one form or another according to the E = mC[sup]2[/sup] proportion.
So, did the singularity have the exact same mass as the current universe?
Tris
Isn’t the common explanation for this that there is equal amount of anti-matter in the universe as matter?
I’m saying that it is a semantics question. In Part II, I note:
If you use “mass” to mean the magnitude of the system’s energy-momentum four-vector (as in Part II), then the (system of) photons has mass. The theme of my post, though, is that this is but one use of that four-letter word, and that I personally don’t mind other uses, as they are useful in certain circumstances.
I don’t think we differ in our take on the physics. I think I just take a slightly more forgiving approach with its translation into language, and I further think that this is in-line with common usage outside of certain subfields.
If you want to discuss the kinematics of muon decay:
m –> e + [symbol]n[/symbol][sub][symbol]m[/symbol][/sub] + [symbol]n[/symbol][sub]e[/sub]
one might want to simply the math by assuming the neutrinos are massless. So, one might declare: “Assume the two neutrinos are massless.” That doesn’t mean that the system of two neutrinos has zero invariant mass. It means that the scalar sum of their individual masses is taken to be zero. And, this doesn’t cause confusion because context makes it clear what is meant. Other terms appear in fields where multiple uses co-exist, and in some situations, the naked word “mass” is never used to mean the relativistic mass of an unbound, multi-particle system.
I’m afraid I just don’t see it. I can’t think of any situation where you could correctly just add the zero masses of two photons and say that the system has a mass of zero. (Unless,of course, they don’t have a zero momentum frame.)
Could you give me an example of which you speak?
You are implying a particular definition of mass. I’m not saying that the system has no (invariant) mass. I’m proposing that one should admit into the language other definitions of the word “mass”.
As for an example, let’s ignore the photon case and focus solely on the statement in this quote:
“Assume the two neutrinos are massless.” Do you agree that this a valid thing to say?
The thread started with the OP wondering why…
I am arguing that it is not incorrect. I am arguing that these are valid uses of the words involved, and issues arise only when one tries to prescribe particular definitions to these multi-use words. I have no doubt that you have no doubt that I understand that a system of two photons can have a non-zero invariant mass. You should take my posts as containing linguistic points, not physical ones. Indeed, I read the OP as a linguistic question, not a physics one.
I think you mean e = mc² where c is the speed of light. If you assume the speed of light to be 1, which I believe is an important idea in physics maybe, then you get:
E = M1²
which simplifies to
E = M1 because 1² is 1
which further simplifies to
E = M because 1 times anything is that anything.
Is there a cite available for the “local mass defect” concept? So far nearly all hits on this phrase I’ve found via google are on message boards by a poster named Ring. Do you mean “local mass deficit” perhaps? Thank you!