[quote[Saying E= mc^2 is saying that mass and energy can be interchanged, not that one is the other.[/quote]
Do you have some more convincing argument or reference for that statement? The Relativity FAQY says, in Does Light have Mass?:
“What is the meaning of the equation E=mc2? You can interpret it to mean that energy is the same thing as mass (emphasis added - jrf) except for a conversion factor equal to the square of the speed of light. Then wherever there is mass there is energy and wherever there is energy there is mass.”
I seem to recalla Feynman reference for that, too, but I can’t seem to dig it up.
Er, shouldn’t you hav attached a “in Relativity” to that statemnt? And a defintition of “straight line” would be useful …
AFAIK, in Quatum Electrodynamics photons are not defined to travel in straight lines, but caclulations can be made to show that they usually appear to. There are situations (e.g. the old chestnut double slit experiment with a single-photon-at-a-time source) in which they do not appear to travel in straight lines.
The source for the gravitional field is energy and momentum (which are conserved), not mass, so the gravitional field will not disappear. E = MC^2 tells you how much energy you have bound up in a mass M, but the total energy also includes kinetic energy, e.g.
When I say mass above, I’m referring to rest mass. Relativistic mass is an old-fashioned concept. I don’t think it is taught much any more.
JohnF Thanks for the link. I wanted to link to that page, but I couldn’t find it.
It seems to me to say that the problem is in how we define mass – that currently physics uses mass to mean invariant mass (or the deprecated term rest mass) or whether we mean relativistic mass.
In my thought experiment (matter and antimatter annihilation in an insulating box) the energy increases, but (In a frame of reference tied to the box) the momentum will remain zero. Mass-energy is conserved and momentum is conserved, but energy and momentum are not conserved. From outside the box, there should be no observable change before and after annihilation (except that after, the box might be warm to the touch). In particular, there would be no change in the inertial or gravitational mass of the box and its contents. Whether you say “The mass-energy of the photons contributes to the gravitational field.” or say “[T]he light contributes to the total mass of the box.” is (apparently to me) semantics, not a disagreement about the theory.
You’ve lost me here. If by “mass-energy” you mean total energy in the box, including energy due to mass using E = mc^2, yes that’s conserved. The total momentum of a closed system is also always conserved.
Yes. When you treat the box and contents as a single object, you can describe it as a particle having mass = energy/c^2.
The same situation occurs for any bound system. e.g. the rest masses of the quarks which make up the proton are each about 10 or 20 times the electron rest mass, and do not sum up to the mass of the proton (over 1800 times the electron mass). You have to include the binding energy of the quarks to get the mass of the proton. If you start talking about quarks as separate particles and ask what the gravitational force due to 10^N protons is, and just use the rest mass of the 10^3N quarks, you get the wrong answer.
And whether you say “the binding energy of the quarks contributes to the gravitational field” or “the binding energy contributes to the mass of the proton” is essentially the same difference.* As long as you understand what’s going on when you say this, I won’t argue with it.
*Do people still say “same difference” anymore? I’ve always wanted to say it and have it be plausibly correct.
Great questions! They deserve great answers. Your best bet is to scour the Net for a guy who calls himself ‘PMB’. He’s a physicist and a mathematician and will surely be able to give clarifying responses.
