heh. “What has it got in its rocketses?”
I’m puzzled by this too. The total mass-energy of a system is constant, but the proportion that is mass and the proportion that is energy can easily change. Fusion takes a certain amount of mass and replaces it with a smaller amount of mass plus the missing part in energy. Particle collisions create large numbers of new particles out of the energy created in the collision. That’s how colliders find new and heavier particles.
Ring is one of the physics people, though, so I assume that some nitpicky technical definition is being used. For purposes of all popular science exposition, mass can be converted into energy and vice versa as long as the total mass-energy is conserved. Or else Ring needs to get busy and start rewriting a billion words of print. 
It is not a nitpicky technical definition, it’s a correction of a common misperception (that I shared too, until I dug out my freshman physics notes).
Mass and energy cannot be converted into each other. Rather, E=mc^2 implies that all mass has a certain amount of energy, and all energy has a certain amount of mass. They are essentially two ways of measuring the same thing.
Theoretically, if you could measure just the mass of a system, you would know how much energy it has - and vice-versa (I don’t know of any way to measure the energy content directly, though). They are not independent quantities, they are two different measurements of the same parameter, always linked by E=mc^2.
When a particle accelerator creates more particles by colliding two other particles at high speed, the kinetic energy of the two particles itself has mass, exactly equivalent to the mass of the new particles that are created.
Some of the rest mass in an atomic nucleus comes from the binding energy that keeps neutrons bound to protons. In fusion and fission reactions, some of this binding energy is given off as kinetic energy of the reaction products. If one were to look at the rest mass of the reaction products, you would find that a small amount of mass has gone. But it hasn’t been “converted” into energy - it was already energy, the binding energy of the fusing nuclei. The kinetic energy of the reaction products had the “missing” mass.
If one could construct a truly closed system, no matter how many fusion or fission reactions occurred, you would find that it always had the same mass. Before any reactions occurred, most of that mass would be in binding energy in the nuclei. After many reactions have occurred, some of that mass would in thermal energy of the nuclei.
Of course, if you could not keep the system truly closed, some energy would escape, and you would find that the mass of the system had in fact decreased. But the mass was not “converted” into energy. The energy that escaped had mass itself.
Mass and energy cannot be “converted” into each other. They are the same thing.
The key is in looking at a truly closed system. Let’s take the simplest example where it might be said that “mass is converted to energy”: A positron and an electron annihilate with each other to produce two gamma rays. The way people usually look at this is to first look at the initial system of a positron and an electron, and say “Yup, there’s mass here”, and then after the annihilation, look at one of the photons and say “Nope, the photon’s massless”, and then look at the other photon and say “This one’s massless, too”. But really, you should be looking at both photons at once after the reaction. And while it’s true that any single photon does not have mass, a system of two or more photons can and usually does. In fact, the mass of the system of two photons after the annihilation will be exactly the same as the mass of the system of electron and positron before the annihilation (which will, in turn, be at least twice the mass of an electron, but probably a little more).
I’m having difficulty reconciling these two statements. Is it a quantum thing?
Here’s another example:
The electromagnetic and kinetic energy generated by a fission reaction comes from the reduction of the potential energy of the nucleus. In other words potential energy is converted to electromagnetic and kinetic energy—one form of energy is just converted to another form.
The mass of the system remains the same, and the local mass defect is caused by the reduction of its potential energy.
As Absolute and Chronos say a completely sealed vault would weigh the same both before and after an internal nuclear explosion.
Sorry, about this affair, but I just feel the need to point this stuff out every now and then.
Ok, so where is the mass if both photons look massless individually? Is there more ‘stuff’ than the two photons produced in the annihilation?
Well, they are not the same thing in the sense the mass and energy are different properties, measured in different ways, that describe different behaviors.
They are the same thing in that you can’t have one without the other, in the exact proportion given by E=mc^2.
Ice and water cannot be “converted” into each other. They are the same thing.
Ice and water are indeed the same thing. Mass and energy are the same thing. And yet we can quite correctly say that we can convert water into ice as well as mass into energy.
Why? You’re using a different meaning of “converted” than the one that is used in popular science discussions. They are both correct in the proper context.
Is one meaning superior to the other? Not necessarily. It’s important to understand that ice and water are both collections of hydrogen atoms bound to oxygen atoms, but in some contexts the macro structural differences in the bonds are more important to emphasize and isolate than the micro makeup of the individual atoms. Same with mass and energy.
This is not a physics issue. It is a language issue. And you’re not understanding the nuances.
It’s so much fun to be able to say “you’re not understanding the nuances” to the physics guy in one of these threads instead of the usual reverse. 
Your analogy is wrong. When you have energy, you always have a certain amount of mass (m=E/c^2). And when you have mass, you always have a certain amount of energy (E=mc^2). There is no such relationship between ice and water. You can have ice without water and water without ice.
Popular science discussions are simply wrong and inaccurate. The explanation that energy is “converted” into mass is wrong, and not any simpler or easier to understand than the truth.
Energy has mass. Sometimes that energy is tied up inside a nucleus and contributes to the mass of the nucleus, and sometimes that energy is released and that mass disappears from the nucleus, to reappear somewhere else. Saying that mass is “converted” into energy, in fusion for example, is misleading. What happens is that some of the nuclear binding energy is released.
A better analogy would be the weight of a quantity of water, and it’s volume at 1 atmosphere. A certain volume of water will have a certain weight, and vice-versa. But you cannot “convert” volume into weight, or weight into volume. They are both independent measurements that nevertheless are always exactly correlated. If some volume leaves the system, it’s weight will decrease, and vice-versa.
Obviously not a perfect analogy, since it falls apart if you change the pressure, but mass-energy equivalence of course does not.
To elaborate a bit more: this is not a language issue or an issue of context.
Ice and liquid water are different states of the same substance, water. When we say you convert “ice” to “water”, we mean you convert water in the solid state to water in the liquid state.
No such thing occurs between matter and energy. A closed system will always have a certain amount of energy, and a certain amount of mass, in proportions given exactly by E=mc^2. Matter and energy are not states of anything.
Even if we gave a name to some substance that gives rise to both mass and energy - let’s call it Exapnomium - you could not “convert” Exapnomium in the “mass state” to Exapnomium in the “energy state”. Rather, a certain amount of Exapnomium would always have a certain amount of mass and a certain amount of energy.
Mass and energy are not states of anything, they are properties.
Now - what they are properties of? That’s a difficult question. What “is” kinetic energy?
The mass is in the photons. Note the plural there; that’s essential. The first photon, looked at in isolation, has no mass, and the second photon, looked at in isolation, has no mass, but the system of two photons, looked at together, does have mass. This does not mean that there’s some other particle or field or something in between the photons that has the mass; ultimately what it means is that mass is not additive like we usually think of it as being. The mass of a system is not equal to the sum of the masses of its component subsystems.
Thanks. I’ll be needing a new head now.
You can’t, because in ordinary language ice is always water ice. If you mean any other type of ice you have to specify or use it in a context which allows for other types of ice.
So context is most certainly the heart of the matter. All language is always context. It is no more possible to have language without context than it is to have mass without space-time.
Einstein’s relativistic equation that relates mass (m), energy (E) and momentum § is a pretty simple thing when c is set equal to 1.
m[sup]2[/sup] = E[sup]2[/sup] - p [sup]2[/sup]
So, when the net momentum § of a system is zero; m [sup]2[/sup]= E [sup]2[/sup]
or m = E or E =mc[sup]2[/sup] (c not equal to 1)
If a particle and its antiparticle are heading toward each other one has a positive momentum and the other has a negative momentum, and the net momentum of the system is 0, and again m = E
Since momentum is conserved it must still equal zero after the particles interact and annihilate, and of course the mass of the system must still equal E. So extra particles aren’t necessary, mass is just a property of the system of photons in their center of momentum frame.
Or more technically mass is the magnitude of the energy-momentum four vector, and you might find it interesting to look that term up.
For Exapno’s edification it might be beneficial for him to wonder how, if mass and energy are the same thing, a system can have energy but no mass.
As I understand it, both mass and energy are made of information. I think there are about 10^65 bits per kilogram. There is also a fundamental rule that says the number of bits you can fit into a sphere is equal to 3/4 of its area, measured in square Planck length units, or something like that - was it 3/4 time pi, maybe? I forget. This sphere fills according to the second power of its diameter, rather than the third power, because of Einsteinian relativistic warping of the space inside the sphere by the mass of the information. There was a fascinating if dense article about this in Scientific American a few years back. I think figuring this out was one of the things the world of physics was working on during the 1980s.
I thought we were talking about ice (solid water) vs. liquid water.
You’re right, context matters. But context does not change an inaccurate, misleading description of mass-energy equivalence into an accurate one.
Ok, I sort of get it. The measurement of mass of system will include its components and interactiong forces. Anyway, at least the idea that mass as measured as a property of a system will not be the sum of the masses of the particles within it.
The four vector stuff is interesting. I wish I understood the math, but I can see how it relates to conservation of momentum.
Is the measurement of a particle within a system in a different reference frame than the whole system?
There’s a shorter, and maybe more comprehensible, description at Holographic principle - Wikipedia if you’re interested.
Recently, some people have claimed that the holographic principle is a testable theory, in that it would cause the gravitational background noise caused by random fluctuations in position to show up differently, at a scale that we can just barely test today. I don’t know what the current status of that idea is.