From this thread, splitting it off to a new discussion.
OK, then. The original complaint is that I used the equality of mass and energy incorrectly. And the popular notion of mass being convertible to energy, as in a fusion reaction, is also incorrect. Granting that, how can I better express this concept without assuming any technical knowledge beyond the normal popular science vocabulary of mass, matter, and energy?
I’m game for a slightly more technical explanation: as far as I can tell, mass, matter, and energy are not easily grasped concepts anyway - if there’s a way of really connecting them by introducing a few more concepts, then I’m all for it.
I don’t see what the problem is of saying one form of energy is just converted to another form. Although, I don’t think people have a feel for how immense electromagnetic forces can be.
from the Feynman Lectures on Physics:
And, of course the nuclear force is many times the EM force, so the potential energy available for conversion is also truly immense.
Okay, I’m obviously way behind on this subject. I thought that part of the nuclear fission reaction was a conversion of matter into energy. I thought you fired a particle into a big atom. This particle caused the big atom to split into two smaller atoms and emit more particles, which would in turn hit other big atoms and repeat the cycle. And I thought that at some point in this process, some particles were converted into energy.
But if I’m understanding what Ring is saying, the energy was there all along. All the fission process is doing is releasing existing energy.
I’m sure at this point, those of you who know physics are shaking your heads and saying “where do I even begin?”
This.
I’m not nearly a person who “know[s] physics”. But it seams logical to me that if you can convert mass into energy and vice versa, they really are the same thing. And if you accept that, “the energy was there all along” is just an obvious statement.
And I may be completely wrong - I certainly can’t back any of this up to a sufficient degree.
A U235 nucleus is very large, and the strong force operates over a very short distance. Plus a nucleus with a single nuclei in its outermost shell is less stable then one with two. So it’s very close to being unstable.
When it absorbs a slow neutron it begins oscillating like a water drop and has a high probability of coming apart. When it comes apart it reorganizes itself into a configuration that has a much lower potential energy and thus a much higher binding energy.
This large reduction in potential energy is converted to other forms of energy, and because of this loss of energy the remnants of the nucleus has what is called a local mass defect. This is where the term “mass is converted to energy” comes from.
As I’m sure you can see the mass defect isn’t the source of the released energy it’s the result of this loss, and the mass of the entire system is conserved.
You could also say the energy release is equal to (not is) mc^2 where m is the local mass defect.
They’re not the same thing. In fact they’re not things at all. They’re properties of a system.
I’m going to have to get a little technical here and say that energy is the time component of the momentum four-vector, and mass is the magnitude. Look up energy momentum four vector.
Not really clear on what a local mass defect is.
But to simplify things to my level, let’s assume you have a nuclear fission reaction in a sealed container (I’m pictured a really well-built tupperware bowl). Your container has a certain amount of mass and a certain amount of energy at the start of the reaction. At the end of the reaction does it still have the same amount of mass and the same amount of energy? Or is there less mass and more energy than when you started?
I’m not seeing that. I can convert ice into steam and steam into ice but that doesn’t mean steam and ice are the same thing.
To stretch this metaphor if mass is the equivalent of steam and energy is the equivalent of ice, what is the equivalent of water? And by that I don’t mean the liquid state of water. I’m talking about its chemical state. What are mass and energy two different aspects of?
No, I (and I bet a large “we”) can’t, because you didn’t tell us what a “local mass defect” is.
A vault that is capable of completely containing a nuclear explosion will weigh the same both before and after detonation. This, by the way, is a fairly commonly used example of the conservation of mass.
Sorry I forgot this part of your question. The mass of the entire system, including the radiation and everything else is absolutely conserved. But the remnants of the nucleus alone, because of its loss of energy, has less mass. This is called a local mass defect.
See, the thing is, that mass and energy are directly related by Einstein’s relativistic equation:
E[sup]2[/sup] = m[sup]2[/sup]c[sup]4[/sup] + p[sup]2[/sup]c[sup]2[/sup]
But, just from looking at the equation, you can see that they can’t be the same.
Mass is equal to (not is) the energy of a system that cannot be transformed away.
The OP didn’t ask whether mass and energy are the same thing, he questioned whether they are the same. I assume he meant conceptually the same.
In non-relativistic theories, mass and energy are governed by separate conservation laws, whereas in relativistic theories they are two parts of a single underlying quantity conserved according to a single law. Therefore, if you accept relativity, mass and energy are the same, which is why the masses of subatomic particles can be given in energy units such as electron volts.
One has to be aware of the difference between phenomena and physical quantities. Mass, the phenomenon, is something we all have experiences with and opinions about. We can argue about these much as philosophers used to. Or, we can view mass and energy as quantities appearing in equations. The equations state exactly what mass and energy are, no more and no less. You can’t even measure them without tentatively accepting a theory in which they are defined. People measured different kinds of energy in the days when things like heat energy and kinetic energy were thought to be fundamentally different, and their measurements didn’t make sense. Only after someone posited a theory in which heat energy is really just kinetic energy, did the measurements make sense.
Fortunately physicists do not spend all their time arguing over phenomena, or what things “are”. If they did, progress would have stopped in about 1920. Are electrons particles or waves? Physics doesn’t care. Everything about electrons is in the equations. In this sense it is impossible to talk about mass, the physical quantity, without discussing the equations it appears in. If we say something about mass that the equations don’t say, then we are talking about mass the phenomenon and not mass the physical quantity.
Why would a nucleus have less mass because of a loss of energy?
Over the course of years a story has been pieced together to tell people. Atoms weighing a certain amount fuse together. When they do so they weigh a tiny bit less, with the missing mass being converted to energy. That explains fusion, and the way the sun works. (Yes, I deliberately used both weight and mass. Hey, so did you.)
This is simplified, but is extremely useful as a way of understanding a complex process. You can tell people to give it up, but if you do you have to substitute another story in its place that yields understanding.
Stories have rules, just as much as physics does. You can’t introduce terms at will. A few terms have been around for a long time and will be accepted. Every other one has to be explained. Explanations take space, of which there is always too little.
Mass defect is a term that is not used in popular science. Potential energy is barely within the rules, and probably needs flagging. You don’t get to say that these rules are wrong.
If people do hear “mass defect” they will naturally ask where the mass went. If its all energy to start, some of it in the form of mass, and all energy at the end, some of it in the form of mass, then you’re saying that mass is convertible to energy whether you intend to or not. Even talking about conservation of mass isn’t sufficient, since the story of relativity includes a tale about having to give up the separate rules of conservation of mass and conservation of energy and substituting conservation of mass-energy.
It took many years to get from the story of electrons orbiting the nucleus like planets to a story of electrons forming a probability cloud with no definite position. That may be equally technically wrong, but it’s a quantum story that people will accept, and it shows that stories can change over time.
What’s the new story?
If mass and energy were the same thing, wouldn’t E = m instead of E = mc2?
It’s not the universe’s job to be understandable by you, and it’s not the fault of physicists if you’ve been listening to oversimplified “popular science” stories of how the universe works for too long. The physics consensus in this area has not changed for about 100 years. This isn’t like diet recommendations, where every five years “scientists” change their opinion on what foods are bad for you. You’re the one who’s trying to understand this, don’t get all arrogant and huffy when you don’t like the explanation.
That said: energy and mass are properties of a system. They are independently conserved, and in any system they are always related by the formula E=mc^2. They’re not the same thing - they are two distinct properties that are always related.
A barbell that is 85 degrees Fahrenheit has more mass than one that is 84 degrees, all else being equal (the mass difference is given by m = dE/c^2, where dE is the difference in energy between the two). This is not the result of energy being “converted” into mass as the barbell is heated - rather, systems with more energy simply have more mass, at the same time as they have more energy.
Most of the mass of ordinary objects comes not from their thermal energy, but from the binding energy that holds the components of the nucleus together. When energetic fusion or fission occurs, some of that binding energy is released and converted into a different form of energy (like gamma radiation, or thermal energy). The rest mass of the particles left after the reaction is therefore slightly less, as the mass corresponding to the energy released is “gone”.
But this mass has not been “converted” into energy. Whatever other particles have been heated or otherwise energized by the energy released have had their mass increased.
As someone said upthread, if you detonated a nuclear bomb inside a completely sealed container, the mass of the container would not change. Some of the binding energy previously held inside the plutonium nuclei in the warhead would be converted into thermal energy and radiation, but the thermal energy and radiation would still contribute to the container mass just like the binding energy did.
To give a concrete example - in deuterium-tritium fusion, a deuterium nucleus (hydrogen with an extra neutron) fuses with a tritium nucleus (hydrogen with two extra neutrons).
The reaction releases an alpha particle (helium-4 nucleus), and a neutron, along with approximately 18 MeV of enerhy. Approximately 14 MeV of this is in the kinetic energy (velocity) of the neutron, and 4 MeV in the kinetic energy of the alpha particle.
If you were to measure the rest mass of the deuterium and tritium nuclei (meaning the mass of the particles with zero kinetic energy), and compare that to the rest mass of the alpha particle and neutron, you would find a “mass defect” missing from the alpha and neutron corresponding exactly to m = <18 MeV>/c^2.
However, if you were to measure the mass of the neutron and alpha particle together, immediately after the reaction (before they have a chance to lose energy), you would find that they have exactly the same mass as the deuterium and tritium nucleii did prior to the reaction. No energy has been created, and no mass has been lost. The binding energy in the deuterium and tritium nuclei (which previously contributed to the rest mass of those particles) has simply been converted into kinetic energy. But that kinetic energy still “has” a certain amount of mass.
So (and I mean this in all seriousness—I’m not trying to be funny or histrionic) is there anything really here?