Einstein! Nukes!

Just a quick question: why is E = mc^2 always invoked when discussing nukes?

I understand that energy is equivalent to mass, in the sense that if something has a large amount of potential energy, it'll weigh more.

For example, if two chemicals react in an exothermic reaction, they loose a small amount mass (each atom weighs less), and the energy released by the chemicals is equivalent to the mass they loose.

I also understand that you get energy from a nuclear reaction because of the interplay of the electric and strong forces; for example, in a fusion reaction (say, firing a proton at a larger particle), you get energy because once you overcome the electric force, the strong force does a large amount of work on the proton giving the particle kinetic energy, until the strong force also becomes repulsive. In this case, again, the total weight of the (subatomic) particles has decreased, although no particles are actually destroyed.

What I don't understand is how this situation is any different from the chemical one. Why is E = mc^2 required to explain this at all? Why can't we just use Newtonian physics, in the same way that we understand chemical energy (which is released because of the interplay of electric forces only, rather than electric and strong forces), that is to say in terms of forces and potentials? Yes, the stuff after weighs a bit less, but that seems rather inconsequential, and indeed in the chemical case it's totally ignored (it's a smaller mass loss, but so is the energy gain, so relatively it's just as 'important'). I've also always been told that physicists realised the potential of nuclear energy when Einstein discovered his formula and the consequence that particles contain large amounts of energy, yet the formula doesn't seem to predict any such thing; no particles are destroyed. Rather, the large amount of energy is by virtue of the large magnitudes of the electric and strong forces, especially at close range.

In other news, why don't we see large blobs of neutrons floating round? If there were a load of them floating around in space, wouldn't they come together to form some kind of huge atomic nucleus, considering they're all pulled together by the strong force but repelled by no electric force?

Ooh, and are there any chargeless massive particles? If so, do they all exist as many particles in the same place, considering there's no repulsion at all, but there is gravitational attraction? On second thoughts, as there is nothing to retard the motion, I guess they'd just... orbit each other?

http://cdn.mikeabundo.com/wp-content.../01/lolwut.jpg

Most chemical reactions involve the exchange or sharing or electrons, while nuclear reactions deal with alterations in an atom's neucleus. Thought I'd clar that.
In most nuclear reactions, calculations have to be precise. A sub-atomic particle, during a typical nuclear reaction, can lose up to 0.01% of it's mass. Newton didn't know that energy could be converted to mass, and vice versa. v = u + at (or any other Newtonian theory, for that matter) can not explain what's going on here, and that's why e = mc^2 is invoked here. With particles travelling near the speed of light, you cannot just 'ignore' the energy (and therefore, the mass) loss that occurs, however minute it may be. Yes, the electric and the 'strong' forces, as you say, are the reason why particles have so much energy, but E = mc^2, in my humble opinion, does not explain that particles contain a load of potential energy and that it can be used by fission or fusion. How physicists came to realize that, I hae no idea.
Err, large blobs of neutrons floating around? Look up neutron stars. They ARE, in theory, large blobs of neutrons, err, not floating around, but packed together very tightly in a bunch. Yes, they do not result from gravitational attraction between seperate neutrons, rather, they are left at the death of massie stars. If there were singular neutrons floating here and there, I doubt that they would be numerous enough to conques the vast expansion of space. Four MILLION light years is the distance between the sun and the closest star to it, Proxima Centauri. (Correct me if I am mistaken) I don't expect a micrometer wide bunch of particles to EVER cluster in a bunch. Even if, IF, a bunch of wanderign neutrons happened to come across, and cluster with each other, there would be trillions of neutrons needed to make a noticeable thing. And when you look at our chances of finding a small cluster of non-charged, neutral, and basically undetectable mass of neutrons, well.............you get the idea.

Does this help?

http://en.wikipedia.org/wiki/E%3Dmc2...uclear_physics


I know that the mass-energy equivalence equation was published about 30 years before any real work on the atomic bomb started, so it's not like like it was the catalyst for the nuclear age. They didn't even know about subatomic particles (or atomic nuclei) when Einstein published his equation.

Quote:

---

Most chemical reactions involve the exchange or sharing or electrons, while nuclear reactions deal with alterations in an atom's neucleus. Thought I'd clar that.

---

Thanks but that's exactly what I said.

Quote:

---

v = u + at can not explain what's going on here, and that's why e = mc^2 is invoked here.

---

What does v = u + at have to do with anything? I'm talking about the definition of energy (I believe pretty much all of thermodynamics was developed long after Newton, but still far before Einstein), which is force multiplied by distance moved in the direction of the force. This is fundamentally what explains chemical reactions, as electrons essentially loose potential energy by 'falling down' electric fields, settling in a lower energy state. It also explains nuclear reactions. You need E = mc^2 for neither.

Quote:

---

With particles travelling near the speed of light, you cannot just 'ignore' the energy (and therefore, the mass) loss that occurs, however minute it may be.

---

...particles in chemical or nuclear reactions are travelling at near light speed? No? That has nothing to do with the mechanics of reaction and energy gain.

Quote:

---

Err, large blobs of neutrons floating around? Look up neutron stars. They ARE, in theory, large blobs of neutrons, err, not floating around, but packed together very tightly in a bunch. Yes, they do not result from gravitational attraction between seperate neutrons, rather, they are left at the death of massie stars. If there were singular neutrons floating here and there, I doubt that they would be numerous enough to conques the vast expansion of space. Four MILLION light years is the distance between the sun and the closest star to it, Proxima Centauri. (Correct me if I am mistaken) I don't expect a micrometer wide bunch of particles to EVER cluster in a bunch. Even if, IF, a bunch of wanderign neutrons happened to come across, and cluster with each other, there would be trillions of neutrons needed to make a noticeable thing. And when you look at our chances of finding a small cluster of non-charged, neutral, and basically undetectable mass of neutrons, well.............you get the idea.

---

I know about neutron stars, but my understanding is that it isn't the strong force stopping them collapsing; rather, quantum physics. You're forgetting that all the matter we see around us is the result of gravity pulling together separate particles.

Quote:

---

Does this help?

http://en.wikipedia.org/wiki/E%3Dmc2...uclear_physics

---

Ahh, interesting. What that essentially says was that nuclear reactions were thought of potential proof of E = mc^2, and not vice versa. E = mc^2 applies to chemical reactions just as much but the energy loss is not enough to detect a mass gain. It's unsourced, though...

Quote:

---

Originally Posted by Xei

What does v = u + at have to do with anything? I'm talking about the definition of energy (I believe pretty much all of thermodynamics was developed long after Newton, but still far before Einstein), which is force multiplied by distance moved in the direction of the force. This is fundamentally what explains chemical reactions, as electrons essentially loose potential energy by 'falling down' electric fields, settling in a lower energy state. It also explains nuclear reactions. You need E = mc^2 for neither.

---

I was merely stating that Newtonian physics isn't sufficient to be of much use in precise, and advanced nuclear operations. E = mc^2 is not essential for nuclear reactions where the main objective is to harness the enery inside the nucleus. And even in that case, I don't see how you could NOT use E = mc^2 to calculate how much kilograms of nuclear fuel are needed, how much energy will be released, etc. etc. In particle accelerators and collision chambers, however, E = mc^2 becomes absolutely necessary. I don't need to explain that.

Quote:

---

Originally Posted by Xei

Ahh, interesting. What that essentially says was that nuclear reactions were thought of potential proof of E = mc^2, and not vice versa. E = mc^2 applies to chemical reactions just as much but the energy loss is not enough to detect a mass gain. It's unsourced, though...

---

That's what I thought, too. I don't see why mass loss as a result of energy loss should be of much importance in chemical reactions, do you? But if it's simply a matter of whether E = mc^2 is applicable or not, it DOES apply to chemical reactions as well.

Quote:

---

And even in that case, I don't see how you could NOT use E = mc^2 to calculate how much kilograms of nuclear fuel are needed, how much energy will be released, etc. etc.

---

Why? How, even?

All you need to do is calculate, or obtain by experiment, the amount of energy released per kilo of fuel.

You don't know what proportion of the mass of fuel will be converted. You'd have to weigh a sample before and then after reaction, hence calculating mass lost per kilo, and hence energy per kilo. That seems very convoluted; why not just find the energy released in the reaction?

Quote:

---

In particle accelerators and collision chambers, however, E = mc^2 becomes absolutely necessary. I don't need to explain that.

---

Sure, because massive particles are actually created.

Quote:

---

That's what I thought, too. I don't see why mass loss as a result of energy loss should be of much importance in chemical reactions, do you? But if it's simply a matter of whether E = mc^2 is applicable or not, it DOES apply to chemical reactions as well.

---

Yeah, I'm just confused why The Bomb is intrinsically linked to Einstein and E = mc^2. People always seem to say 'Einstein showed that there is a huge amount of energy even in the tiny masses of particles', but as I see it, that has nothing to do with it, because the masses of the particles isn't what's being converted. E = mc^2 can no more be used to explain the energy released in nuclear reactions than it can be used to explain the energy released in chemical reactions, or indeed any other kind of thermodynamic process (heating liquid, lifting a brick, etc.).

Quote:

---

Originally Posted by Xei

Just a quick question: why is E = mc^2 always invoked when discussing nukes?

---

the whole point of fission is that a heavy nucleus fissions into two smaller nuclei and converts some of its mass to energy in the process. E = mc^2 is what makes this possible.

Quote:

---

Originally Posted by Xei

I understand that energy is equivalent to mass, in the sense that if something has a large amount of potential energy, it'll weigh more.

---

this is slightly confusing. even if it weighs more, it doesn't 'mass' more. potential energy is always a function of the form f(x) + u where u is an arbitrary constant (or function in a lot of cases) and x is position. You can set the potential energy of something to be anything you want by manipulating the u. You just need to keep u constant (or account for it changing) through a calculation. but you surely know all this.

Is this even true? Can you give an example? if you were to lift a bowling ball to the edge of the atmosphere it would weigh less correct? However it would have way more potential than when at rest on the surface. Weight is confusing. Just stick to mass if you're trying to think clearly about this stuff.

Quote:

---

Originally Posted by Xei

What I don't understand is how this situation is any different from the chemical one. Why is E = mc^2 required to explain this at all? Why can't we just use Newtonian physics, in the same way that we understand chemical energy (which is released because of the interplay of electric forces only, rather than electric and strong forces), that is to say in terms of forces and potentials? Yes, the stuff after weighs a bit less, but that seems rather inconsequential, and indeed in the chemical case it's totally ignored (it's a smaller mass loss, but so is the energy gain, so relatively it's just as 'important').

---

Newtonian physics doesn't really explain anything - it only describes it. Positivism aside, Einstein explained stuff. Newton left gravity as some force. Einstein dispelled the notion of a force at work and left it as the curvature of spacetime. I don't know enough chemistry to say for sure but I highly doubt that chemistry based on newtonian physics explains anything: it just describes it.
It is debatable if it is possible to do anything else but relativity 'feels' much more like an explanation once you grok it.

Quote:

---

Originally Posted by Xei

In other news, why don't we see large blobs of neutrons floating round? If there were a load of them floating around in space, wouldn't they come together to form some kind of huge atomic nucleus, considering they're all pulled together by the strong force but repelled by no electric force?

---

I never really got to the strong force (I currently crap out after basic quantum mechanics and haven't been doing any math or physics in close to a year). I do know that it's essentially of the form 1/(x^n) for some n > 5, so it gets pretty weak pretty quick. I would imagine that at a meters distance, two protons are being pulled apart faster by an expanding spacetime than they are being attracted by the strong force. That's just a guess though.

Quote:

---

the whole point of fission is that a heavy nucleus fissions into two smaller nuclei and converts some of its mass to energy in the process. E = mc^2 is what makes this possible.

---

This kind of ignores everything I've asked in the thread.

Why is this any different from a chemical reaction, in which mass is also converted to energy?

Both can be explained perfectly well by the interplay of forces.

Quote:

---

this is slightly confusing. even if it weighs more, it doesn't 'mass' more. potential energy is always a function of the form f(x) + u where u is an arbitrary constant (or function in a lot of cases) and x is position. You can set the potential energy of something to be anything you want by manipulating the u. You just need to keep u constant (or account for it changing) through a calculation. but you surely know all this.

Is this even true? Can you give an example? if you were to lift a bowling ball to the edge of the atmosphere it would weigh less correct? However it would have way more potential than when at rest on the surface. Weight is confusing. Just stick to mass if you're trying to think clearly about this stuff.

---

Yeah I was speaking informally, when I equate an increase in mass to an increase in weight it's implicit that you don't move in the gravitational field.

The bowling ball weighs less, but has a greater mass, as the mass increase is tiny whilst weight for a constant mass decreases pretty quickly with height.

Although potential is arbitrary, I think you can talk about absolute total potential energy if you set 0 as the minimum. For example, a bunch of particles have minimum gravitational potential energy when they form a singularity.

Quote:

---

Newtonian physics doesn't really explain anything - it only describes it. Positivism aside, Einstein explained stuff. Newton left gravity as some force. Einstein dispelled the notion of a force at work and left it as the curvature of spacetime. I don't know enough chemistry to say for sure but I highly doubt that chemistry based on newtonian physics explains anything: it just describes it.
It is debatable if it is possible to do anything else but relativity 'feels' much more like an explanation once you grok it.

---

I'm not sure why Einstein isn't subject to positivism either, but anyway; as I explained to someone else, I'm just using 'Newtonian' to mean 'pre-Einstein'. No matter how obscure your field, energy is still defined by classical concepts like force. When I talk about chemistry in this way, I mean that the energy gained can only meaningfully be explained via the definition of energy, i.e. energy is gained because electrons are closer to more protons and hence potential energy has been converted to kinetic energy by virtue of electric forces doing work on the particles. Yes, chemistry really requires a quantum description, but classical concepts are still at the heart of it.

Quote:

---

I never really got to the strong force (I currently crap out after basic quantum mechanics and haven't been doing any math or physics in close to a year). I do know that it's essentially of the form 1/(x^n) for some n > 5, so it gets pretty weak pretty quick. I would imagine that at a meters distance, two protons are being pulled apart faster by an expanding spacetime than they are being attracted by the strong force. That's just a guess though.

---

I'm not sure where you got the power law from, I'm pretty sure the strong force is modelled by an exponetial-type decay, although there is no simple function to describe it. As I explained to somebody else, the strong force would indeed be negligible, but the initial attraction would be caused by gravitation (which is how all matter in the universe came together in the first place, after all).

Quote:

---

Originally Posted by Xei

This kind of ignores everything I've asked in the thread.

---

Sorry but I think you're having a fundamental misunderstanding that's leading you to ask an illformed question.

Potential energy has no effect on mass in classical mechanics. (that I know of - can you bring some documentation?) Potential energy would not be nearly so easy to derive if you had to account for a feedback loop between mass and potential energy.

The increase in mass that you are referring to is a relativistic effect and is not predicted or accounted for by newtonian physics. (using newton in the same sense as you and pretty much everyone else)

So what you are essentially doing is ascribing an attribute of relativistic mechanics to classical mechanics and then asking why we need relativistic mechanics.

Quote:

---

Originally Posted by Xei

I'm not sure why Einstein isn't subject to positivism either, but anyway;

---

He certainly is if you want to play that game. I'm honestly ambivalent towards it though. It's a very good frame of thought for scientists to be aware of but takes some of the satisfaction out of things. Newton left 'spooky action at a distance'. Einstein removed that and said that mass moves in straight lines - period. Einstein still didn't provide an explanation for inertia which causes this but he did move the explanation forward significantly IMO.

Quote:

---

Originally Posted by Xei

I'm not sure where you got the power law from, I'm pretty sure the strong force is modelled by an exponetial-type decay, although there is no simple function to describe it. As I explained to somebody else, the strong force would indeed be negligible, but the initial attraction would be caused by gravitation (which is how all matter in the universe came together in the first place, after all).

---

I remember seeing it somewhere as a rough approximation. I think n is 11. At any rate gravity is so weak that I doubt that it would do much either.

Quote:

---

Sorry but I think you're having a fundamental misunderstanding that's leading you to ask an illformed question.

Potential energy has no effect on mass in classical mechanics. (that I know of - can you bring some documentation?) Potential energy would not be nearly so easy to derive if you had to account for a feedback loop between mass and potential energy.

---

You're misunderstanding my question somehow, I've never said anything of the sort... Einstein was the one who discovered this (technically everything before quantum including Einstein was classical, but I understand you're using classical to mean pre-Einstein).

Quote:

---

So what you are essentially doing is ascribing an attribute of relativistic mechanics to classical mechanics and then asking why we need relativistic mechanics.

---

I really don't know how you've gotten this impression; I can only suggest that you read my posts again, I thought I was being quite clear.

What I'm asking is why relativistic mechanics is required to explain nuclear energy when actually the reason for nuclear energy is the interplay of nuclear forces (classical mechanics) and the loss of mass is a product of this, not the cause, which is exactly analogous to chemical energy (I only mention this to clarify further), which is also explained by the interplay of forces, and again E = mc^2 is not an explanation for this phenomenon in any sense but rather a by-product.

To take a very simple example: raise a .1 kilo brick by a metre. Let it fall. It gains 1J of kinetic energy. Clearly this is because of the gravitational force doing work on the brick. Due to E = mc^2 the brick has slightly more mass when it's raised, but it obviously doesn't make sense to say the kinetic energy is a result of the brick losing mass. That is a consequence, not a cause.

Quote:

---

He certainly is if you want to play that game. I'm honestly ambivalent towards it though. It's a very good frame of thought for scientists to be aware of but takes some of the satisfaction out of things. Newton left 'spooky action at a distance'. Einstein removed that and said that mass moves in straight lines - period. Einstein still didn't provide an explanation for inertia which causes this but he did move the explanation forward significantly IMO.

---

Yeah well, you're always going to have some kind of spookiness in any scientific framework, because science is not a priori but rather relies on some observed but unreducible axioms.

Quote:

---

I remember seeing it somewhere as a rough approximation. I think n is 11. At any rate gravity is so weak that I doubt that it would do much either.

---

Like I say, gravity pulled together neutral hydrogen atoms to form stars.

Quote:

---

Originally Posted by Xei

Yeah, I'm just confused why The Bomb is intrinsically linked to Einstein and E = mc^2. People always seem to say 'Einstein showed that there is a huge amount of energy even in the tiny masses of particles', but as I see it, that has nothing to do with it, because the masses of the particles isn't what's being converted. E = mc^2 can no more be used to explain the energy released in nuclear reactions than it can be used to explain the energy released in chemical reactions, or indeed any other kind of thermodynamic process (heating liquid, lifting a brick, etc.).

---

Physicists must have seen something we normal folk can't. Or they are WAY too deep in love with Einstein and his theories.

Both nuclear and chemical reactions end up with something called mass defect. This mass defect is (or should be, don't remember) the equivalent of the energy released if you use E=mc^2. Now, mass defect is a couple of orders of magnitude larger for nuclear reactions. For chemical reactions it's so small that it's safe to ignore it, but it still exists.
Ok, so what does mass defect have to do with energy? Well, energy that's released in fission is the energy that kept the original nucleus together, its binding energy. The theory is that this binding energy has mass, and that mass is equivalent to the mass defect.

Again, take this with a grain of salt, I was too lazy to review it.

SnakeCharmer gave you a good answer, sorry for the misunderstanding. It's what I get for trying to think about this stuff too late at night.

Quote:

---

Originally Posted by Xei

Like I say, gravity pulled together neutral hydrogen atoms to form stars.

---

In that case however the mass was much more concentrated which leads to a more powerful gravitational field. Such is not the case for loose protons in general

Quote:

---

Originally Posted by SnakeCharmer

Both nuclear and chemical reactions end up with something called mass defect. This mass defect is (or should be, don't remember) the equivalent of the energy released if you use E=mc^2. Now, mass defect is a couple of orders of magnitude larger for nuclear reactions. For chemical reactions it's so small that it's safe to ignore it, but it still exists.
Ok, so what does mass defect have to do with energy? Well, energy that's released in fission is the energy that kept the original nucleus together, its binding energy. The theory is that this binding energy has mass, and that mass is equivalent to the mass defect.

Again, take this with a grain of salt, I was too lazy to review it.

---

Yes I understand the physics, that's not my question. My question is why E = mc^2 is always talked about in relation to nuclear physics when it doesn't seem to have any more consequence or practical use particular to that field than any other kind of energy change (chemical, physical, whatever).

Back at school when I had to do these kind of questions, we had to calculate the mass deficit, and hence the energy changes.

This seems to me completely pointless; why don't they just give you the energy data?

I mean, you could do the same thing for chemistry; have the mass of the reactants before and after reaction of a mol of reactant, and hence calculate energy changes in reactions. But that'd be stupid because you might as well just give the data as energy per reaction (per mol); which of course is done in practice.

Quote:

---

Originally Posted by PhilosopherStoned

In that case however the mass was much more concentrated which leads to a more powerful gravitational field. Such is not the case for loose protons in general

---

Hm, well, I was only really talking about hypothetical circumstances anyway. Though my understanding was that stellar formation happened with matter with very low density; gravitation falls off with distance slowly enough to pull large volumes of gas together.

Quote:

---

Originally Posted by Xei

I mean, you could do the same thing for chemistry; have the mass of the reactants before and after reaction of a mol of reactant, and hence calculate energy changes in reactions. But that'd be stupid because you might as well just give the data as energy per reaction (per mol); which of course is done in practice.

---

Mass deficit in chemical reactions is about 10^-12 grams. Using E=mc^2 for chemical reactions is certainly nothing more than an academic exercise, it has no practical meaning.
With nuclear reactions it should be possible to actually measure the mass deficit, making this calculation a practical matter.

The mass difference is still pretty small, I remember figures of the initial and final masses had to be accurate to a large number of figures to have any use.

But still, why not just measure energy / use energy per mol in calculations?

This is all incidental though, I still just want somebody to answer my original question: why do talk about mass conversion when talking about nukes as if it's the causal factor? People talk about the tiny amount of mass converted in the bomb as if this is what causes the bomb to have so much power, but really it is no more of an explanation than the mass lost in chemical reactions explains chemical energy.

Why is Einstein and E = mc^2 linked to nukes? Is it just a common misunderstanding?

Quote:

---

Originally Posted by Xei

Why is Einstein and E = mc^2 linked to nukes? Is it just a common misunderstanding?

---

That's what I'm thinking. It's definitely not the cornerstone of nuclear weapons development (as far as I know it's used to calculate yields).

Quote:

---

Originally Posted by Xei

why do talk about mass conversion when talking about nukes as if it's the causal factor?

---

I really think you're splitting hairs here. their are all sorts of causal factors involved. Suppose a prank gets out of control and I accidentally end up dropping a nuke on your house. If someone asks you why you don't have a house anymore, it would be perfectly reasonable for you to reply that one gram of uranium was converted to one gram of electromagnetic radiation and heat on top of your house and so now you don't have a house. How I got that conversion to occur may or may not be of interest.

without e=mc^2, (hence forth to be referred to as da kine) it would not have been understood that this was even possible.

Hmm no, I'd say the causal factor is subatomic particles falling into a lower energy state via their interactions with the strong and electromagnetic force.

The fact remains that E = mc^2 is no more an explanation for nukes that for any other thermodynamic process, so why the association?