There is/was a thread (can’t remember which one)where it was said that mass could be coverted into energy. Just to set the record straight, Special Relativity says this can’t be done.
What really happens is that binding energy is converted into kinetic energy, heat and radiation. The local mass defect is a result of the energy release not the cause, and the system mass remains invarient.
I’m not a scientist but I think this is wrong. Take some antimatter and put it together with an equal amount of matter and I think you will have nothing but energy on your hands and no physical matter left.
Energy however can behave like mass IIRC. The energy released by the matter/antimatter annihilation will still bend spacetime the same as just the mass did previously (assuming the energy is contained in the same volume of space as the mass was).
And just for the record antimatter does exist. Fermi Lab near Chicago is one of several laboratories that has some on hand. It is VERY hard to make and hold (the more you have the harder i tis to hold) but they have a teeny bit nontheless.
Mass is the magnitude of the energy momentum four vector and energy is its time component. Mass like energy is a property of a system and not a thing in its own right. When annihilation occurs matter is converted to radiation (photons) and this system of photons has mass.
The curving of spacetime is governed by Einstein’s stress energy tensor and does not necessarily require mass.
Photons have no mass. They have a zero rest mass (if you could ever get one to sit still which I think is impossible). They have a mass equivalent since their movement counts as energy and energy is equivalent to mass. This is not to say however that they have mass. Nothing with mass can travel at the speed of light which photons quite happily do. If a photon had actual mass then it would have to have infinite mass when moving light speed.
Well, I never said that a photon has mass. What I said is that a system of photons can have mass as long as the net momentum of the system is zero. Think of it this way: If a nuclear weapon is exploded in a vault which completely contains all the blast products (particles, heat, radiation) then the vault weighs the same after the explosion as it did prior to the detonation.
There’s somethin’ wrong here. In all my classes they taught that mass and energy were interconvertible, and all the nuclear reaction equations had more mass on the left, and an excess of kCal on the right. If you go by the reactions (as written), then there would certainly be a difference in mass inbside that vault of yours.
You’re wrong, Ring.
Relativity shows that mass and energy are the same thing, essentially, and you can convert one to the other.
For example, take a proton colliding with a deuteron:
p + D -> [sup]3[/sup]He + photon
The rest mass of the [sup]3[/sup]He is less than the rest mass of the proton + deuteron by about 5.5 MeV/c[sup]2[/sup]. Photons have zero rest mass, so some of the system’s total rest mass was converted into energy.
As for your “nuclear blast in a vault” example, look at the sun (which is basically exactly that). The sun is losing rest mass at a rate of 4.5E6 tons/sec, due to nuclear fusion of hydrogen into helium.
No, Ring is correct. The Sun is losing mass through radiation (and also through the solar wind). If the Sun were in an insulated box, cutting off the radiation and solar wind, its mass wouldn’t decrease.
The same is true of your reaction:
p + D -> [sup]3[/sup]He + photon
If this occurred in a massless, perfectly insulated box, the mass of the box would be the mass of p + D, not of [sup]3[/sup]He.
Isn’t this one of those standard homework assignments? Calculate the difference in radiation pressure at the top and bottom of a perfectly reflective box in a gravitational field, and show that the excess pressure on the bottom is exactly equal to the weight of a mass equivalent to the energy in the radiation.
Except that pressure ain’t mass. It’s not even mass per unit area. It’s Force per unit area, and it pushes up as well as down.
That’s why I wrote “Calculate the difference in radiation pressure.”
You are correct that you have to integrate over the top and bottom areas to get a force. Mea culpa. Apart from that, I stand by the example.
ZenBeam, radiation pressure is different than mass. Photons can have momentum, and hence exert an impulse by reflecting off a surface. This doesn’t mean that they have any mass.
Ring was using this example to show that a system of photons can somehow have mass, even though individual photons can not. I think his statements are inaccurate and misleading. Rest mass and energy are well-defined quantities, which are not individually conserved, unless you include rest mass as a form of energy.
Matter can be converted to energy…not mass. Matter just happens to have mass as one of its attributes so the two words are used interchangeably in loose conversation even though it’s not strictly correct to equate the two.
Both matter and energy bend spacetime in such a way as to be indistinguishable from each other so the explosion in a box works. It’s weight will remain the same whether it’s holding energy or an equivalent amount of matter.
All of that said I’ve never seen mass used as an attribute of energy and I don’t know if scientists do either. Photons have a zero rest mass (i.e. mass cannot be attributed to a photon) even though a photon can bend space the same way that matter can via mass. Does an Amp or Volt have a mass value associated with it?
From “Spacetime Physics” by Taylor and Wheeler.
Page 232
“A system consisting entirely of zero mass photons can itself have a nonzero mass”
Page 248
Question: “Does the explosion in space of a 20 megaton hydrogen bomb convert mass into energy?”
Answer: “Yes and no! The question needs to be stated more carefully. Mass of the system of expanding gases, fragments, and radiation has the same value immediately after explosion as before; mass M of the system has not changed.”
Giraffe, are you sure you have an advanced degree in physics?
There is rest mass AKA invariant mass and there is relativistic mass. When you say: “As you approach the speed of light, your mass increases”, you are refering to relativistic mass. When you say photons have no mass, you are refering to invariant mass. (It seems kind of strange to say rest mass of a photon when a photon cannot be at rest.) It seems that physicists today usually mean invariant mass when they say mass and don’t talk about relativistic mass much any more. Anyways, the relativistic mass is the mass-energy that affects gravity. And the (invariant) mass together with the energy make up the relativistic mass.
Mass is a form of energy, and pretty much the only thing that distinguishes it from other forms is that it’s very concentrated. Gravity does not care about mass per se, but total energy, so if you had a box with perfectly mirrored walls, and put it on a scale with a positron and an electron inside, it would weigh exactly the same before and after they annihilated.
DrMatrix, I don’t think anyone here is confusing relativistic mass and invariant mass.
Actually, ZenBeam, that is exactly what Ring is doing. “Spacetime Physics”, by Taylor and Wheeler (the worst book on relativity I’ve ever seen, btw), uses relativistic mass throughout.
On p.232, the problem is to calculate the relativistic invariant quantity E[sup]2[/sup]-(pc)[sup]2[/sup] for different systems of photons and particles. They call this the “system mass”, probably as a way of making the invariance seem more natural.
I should be clear that the idea of relativistic mass is not wrong. It’s just different language. If you redefine the mass, then momentum is still p=mv, which some people find more natural. But a lot of physicists find it unnecessary – rest mass, energy and momentum are more than sufficient, and more natural, IMO, since a particle’s mass is not well-defined outside of its rest frame.
To be clear, I don’t yet have a PhD in physics. (I have a masters, I guess, but no one really cares about that in physics.) I’ll be finishing my PhD this summer, assuming I don’t spend all my time posting to the SDMB.
But, Ring, about physics graduate school: no one cares if you have a degree, or can quote a book. (Some advanced physics texts by well-respected physicists are partially or completely wrong.) You make your point by explaining what you mean clearly, with well-defined terms, and backing it up with evidence. And even then, people may believe different interpretations, until proven wrong.
Ring states “Mass is the magnitude of the energy momentum four vector and energy is its time component.” Sounds to me like he’s using “mass” to mean invariant mass, regardless of what Taylor and Wheeler are using.
I have to ask, does the “mass” of the Sun mean only the mass of the particles which make up the Sun, not including the kinetic energy of those particles, or the radiation inside the Sun? Does the “mass” of a proton only include the free quark masses, perhaps some binding energy, but not any kinetic energy the component quarks have? How do you decide which forms of energy count as “mass” of a system, and which don’t?
Well, I’d use whatever mass I’d need to compute my trajectory if I planned on whizzing past the sun in my spaceship, but hey- I’m an engineer, not a physicist 
Arjuna34