Although I’ve taught kids to calculate the energy released in an atom bomb, I hadn’t really thought of energy itself having mass. I know that’s clearly an implication of the famous equation, but, really? Having energy increases mass? Wow.
Is that related to the idea that something moving near the speed of light increases significantly in mass? I thought that had to do with relativity, but is this also included? Is it automatic because of the idea that energy is mass?
You said it yourself. It is right in the equation.
E=MC[sup]2[/sup]
Mass and energy are interchangeable. One can convert into the other and back again. Thus having energy increases your mass. While moving you have more energy (running into a wall while moving will illustrate that abundantly) thus your mass increases. If you are adding to one side of that equation the other side must adjust to keep up and the speed of light is fixed. Therefore mass gets bumped up when energy increases.
For instance assume in the following equation the number “5” is fixed and cannot change:
8 = 3+5
9 = X+5
Obviously X has to go from 3 to 4 to make the equation work.
A friend of mine in high school made a custom T-shirt that read M=E/C2. It was interesting to see people’s reactions because many of them had never thought about how the equation can be read both ways.
Part of the problem is that we’re just too used to thinking of both planets and atoms as styrofoam balls hung from the ceilings of classrooms. It works for planets, but atoms would probably be better represented as a bunch of intertwined springs all vibrating away at their own wavelengths.
Obviously too young to have experienced a night club with Barry White playing . . . 
I sometimes read atomic bombs described as converting mass to energy. This is true, but it implies that this is peculiar to atomic reactions. Your wristwatch decreases in mass as its spring winds down or its battery drains.
E = mc[sup]2[/sup] (really it’s E[sup]2[/sup] = m[sup]2[/sup]c[sup]4[/sup] + p[sup]2[/sup]c[sup]2[/sup]) is an equality not an identity. The mass of a system is equal to the energy of a system that cannot be transformed away. Thus relativistic mass is an outmoded concept.
Mass and energy are not things they’re attributes of a system. And therefore they are related, but mass is not energy and mass cannot be converted to energy. As long as you’re consistent in defining the system both its mass and its energy are conserved.
Just imagine, when you first felt up a girl, all you did was have your fields gets resisted by her fields.
You were still rejected, even if she let you go for it.
That was chemistry not phyics.
not really. you’re not turning mass into energy. Energy derived from fission comes from taking a lump of unstable mass and hitting it with neutrons until it splits apart. The energy comes from the protons in the nucleus since all those like charges are being unleashed.
a FUSION reaction (H bombs) is when you take a fission reaction to squeeze 2 nuclei together and when the nuclear bonds in the nucleus are rearranged in that fashion, energy is released as well. the energy is the “strong force” holding that atom’s nucleus together. (nucleus is jam packed with protons and neutrons. all that positive charge and it not repelling? something’s holding it together. strong force.) So when you break a bond in the nucleus you release that force and the result is a nuclear reaction.
naturally the strong force is a greater force than the EM force of protons so more energy is released in fusion than fission.
the misconception comes when you weigh the products and reactants. the masses won’t match up so people make the leap that mass has been converted to energy. E=mc2 states that there is no real difference in mass and energy. if the products and reactants included initial and final energy then the equation would balance out. the point of special relativity isn’t to say that we’ve figured out an alchemestic process to turn mass into energy but rather the two are interchangeable.
loose analogy: we’re not turning gold into lead, but rather gold and lead are no different than ice and steam.
There is probably some subtlety I am missing here because I do not understand that.
Take our sun. It fuses hydrogen into helium. Four hydrogen atoms fuse to make one helium atom. When comparing the mass of the two the helium atom has a bit less mass than the four hydrogen atoms that went in to it. The difference in mass, as I understood it, is released as energy thus balancing the system.
Conservation of mass/energy tells us we cannot create or destroy mass/energy. All the bits can be accounted for. Where’d the energy come from if not the mass? Where did that bit of mass go?
Actually what occurs in a fission reaction is that the nucleus rearranges itself into configurations that have less potential energy. It’s the conversion of this potential energy into kinetic and electromagnetic energy that accounts for the local mass defect.
So, no mass is converted to energy, instead one form of energy is just converted to another form. The local mass defect is the result of this loss of energy, not the cause.
they’re is no conversion of mass to energy, and for the system both properties are conserved.
That’s exactly correct. But I think what you’re missing is that the system after the reaction includes the released energy and since m[sup]2[/sup] = E[sup]2[/sup] - p[sup]2[/sup] (c =1) both the energy and mass of system remain the same.
A vault capable of completely containing a nuclear explosion weighs the same both before and after the explosion.
Another couple of examples to illustrate just how much empty space there is in an atom:
In The Quantum Zoo, physicist Marcus Chown writes, “If the empty space in atoms were removed, the entire human race would fit in the volume of a sugar cube.”
Also in that book he quotes from Tom Stoppard’s play Hapgood, “Now make a fist, and if your fist is as big as the nucleus of an atom then the atom is as big as St. Paul’s, and if it happens to be a hydrogen atom then it has a single electron flitting about like a moth in an empty cathedral, now by the dome, now by the altar.”
Although it’s harder than you’d think, even, to construct a vault that does completely contain a nuclear explosion, since eventually, heat will trickle out through the walls. And once all the heat has trickled out, it will indeed be lighter.
Not to mention containing the nutrinos, which can pass through a lightyear of lead…
It’s not accurate to say that an atom is mostly empty space, since there are electrons in that volume. If you’re going to claim that an atom is mostly empty space, you might as well claim that an atoms nucleus is mostly empty space, since the quarks are point particles in the same sense as electrons.
So you guys don’t think this would be an off the shelf item?
Well in that case, neglecting the damn neutrinos, please submit your designs, and for extra credit show your work. For even more credit, what percent of the total weight of the bomb would be lost via the neutrino flux?
I’m not going to do the math, but for those who want to - a surprising amount of the energy in a fission bomb is lost by neutrinos. According to Wikipedia it’s:
Wow. I agree that’s much higher than I would’ve expected. That’s one hell of a lot of totally useless energy.
That’s nothing. A black hole merger could be expected to release several times the mass of the Sun in radiant energy, and yet be nearly completely undetectable to anyone even a few hundred kilometers away, since all of the energy is in gravitational waves.