Topic by Warp

Posted: 8/28/2015 4:35 PM

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Warp

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When hydrogen fuses to form helium, this process releases energy. Wikipedia explains the reason: "Comparing the mass of the final helium-4 atom with the masses of the four protons reveals that 0.007 or 0.7% of the mass of the original protons has been lost. This mass has been converted into energy, in the form of gamma rays and neutrinos released during each of the individual reactions. The total energy yield of one whole chain is 26.73 MeV." That made me think: "Ah, so neutrons are lighter than protons (because in the fusion process two protons become neutrons, losing stuff along the way). How else could it lose mass?" But then I go and check the mass of a proton, and it's approximately 1.6726×10⁻²⁷ kg, while the mass or a neutron is approximately 1.6749×10⁻²⁷ kg. What gives? How can neutrons be more massive than protons, yet Helium-4 be lighter than the four original protons?

Posted: 8/28/2015 7:20 PM

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AdituV

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Warp: it's called the mass defect. The strong nuclear force, which holds the nucleus together, has an effect curve that looks roughly like this:

At this typical distance between nucleons (i.e. neutrons and protons), the attraction of the strong force outweighs the repulsion of the electrostatic force between the two protons, leaving the nucleons in a lower energy state compared to being a bit further apart. If you were to move the four nucleons much further apart, they would gain potential energy due to moving against the field, in a similar way to gravitational potential energy gained by something when you lift it up. Now imagine two systems: one with the four nucleons in the ⁴He nucleus, and one with the four nucleons "infinitely far" apart (that is, negligible force exerted on each other). There is a difference in energy between the two systems: the nuclear binding energy, or the energy required to split a nucleus into its components. Because mass and energy are equivalent (E=mc²), the systems have different masses, with the difference in mass (Δm) proportional to the difference in energy (ΔE): Δm = ΔE / c² This happens to be a great enough quantity for ⁴He that it is greater than the difference in mass between two protons and two neutrons.

Posted: 8/28/2015 7:46 PM

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marzojr

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While the explanation is correct, I just want to point out that nothing here is unique to the nuclear force, or quantum physics: any bound system has a total lower energy than an unbound system, and the more tightly bound the system is, the lower the total energy will be. And since total energy is related to mass by relativity, the mass deficit in the helium atom is actually a relativistic effect. A helium nucleus has less mass than the sum of its nucleons' masses because they are bound together. But so does the Solar system have a lower total mass than the sums of its component masses, as they are gravitationally bound together.

Marzo Junior

Posted: 8/28/2015 7:49 PM

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AdituV

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marzojr wrote:

And since total energy is related to mass by relativity, the mass deficit in the helium atom is actually a relativistic effect.

I was unaware of this; could you expand on how mass-energy equivalence is a relativistic effect please?

Posted: 8/29/2015 5:08 AM

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marzojr

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AdituV wrote:

I was unaware of this; could you expand on how mass-energy equivalence is a relativistic effect please?

As I said in IRC, here are some links: First, the Wikipedia article; it is very comprehensive, with some history of the principle. Then this article from one of the physicists involved in finding the Higgs boson, which is more in-depth in some aspects, and is more conceptual. I can't seem to find a good derivation of the equation that is (1) simple enough to be easily understandable without a heavy math background; and (2) correct enough to satisfy me. So here is a flawed one that skips a lot of important steps (particularly between the first 3 equations), but has the general correct idea. If you have any questions about those, fire away.

Marzo Junior

Posted: 8/29/2015 8:57 AM

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endrift

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It's also worth noting that the difference in mass between a neutron and a proton is close to the mass on an electron. An unbound neutron will naturally decay (via the weak nuclear force) into a proton and an electron (also an electron anti-neutrino, but most of the energy in the neutrino is kinetic).

Posted: 8/29/2015 1:06 PM

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marzojr

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Kinetic energy also carries away mass; it has to come from somewhere.

Marzo Junior

Posted: 8/29/2015 5:04 PM

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Warp

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So, if I understood correctly, and extremely roughly speaking and simplifying, the state in which the particles are unbounded (ie. far apart from each other) has more energy in it than the state where they are bound to form a single nucleus, and it's this extra energy that causes the system to have more mass. Btw, I have two additional, somewhat related questions: 1) If I understand correctly, nuclear fusion happens, essentially, because of the heat. The enormous heat causes the atoms to move very rapidly, so rapidly in fact, that they start colliding with enough force to fuse. The heat, in turn, is caused in stars because gravity compresses the hydrogen gas with an enormous amount of force, and this compression heats the gas up. My question is: Why does compressing gas heat it up? (This may be a trivial and fundamental question, but I actually don't know why it happens.) 2) The proton-proton chain reaction, where hydrogen fuses into helium, consists of three distinct steps. (First two hydrogen atoms fuse into deuterium. Then a deuterium and a hydrogen atom fuse into Helium-3. Then two such Helium-3 atoms fuse to form a "normal" Helium-4 atom (and two protons.)) But what happens in a hydrogen bomb? Does it involve only some of those steps, or all of them? Is actual Helium-4 produced in a hydrogen thermonuclear explosion?

Posted: 8/29/2015 5:24 PM

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Ferret_Warlord

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Warp wrote:

My question is: Why does compressing gas heat it up?

As an A/C service tech, this sort of thing is very important in my line of work; however, I'm not a physicist, and I don't know the exact mathematics, but I do have a very simple way of thinking about it that may or may not be entirely accurate. It should get things started, though. Heat and temperature are related concepts, but are not the same thing. Heat is the kinetic energy of molecules moving around, while temperature is the intensity of that heat. In other words, temperature can be thought of as the density of heat. So, when you take a volume of gas and compress it into a smaller volume, its temperature goes up from the gas's heat being forced closer together. Mathematically, this can be seen in the Ideal Gas Law - pressure and temperature are directly proportional. Likewise, the same happens in reverse: relieve the pressure, and the temperature goes down. For something that's more in depth, this page looks useful.

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Posted: 8/29/2015 11:20 PM

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OmnipotentEntity

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I have a rather specific and dumb question about physics. I'm currently taking Physics II which is mostly just Electromagnitism. We're currently going over the electric field due to uniformly charged rods. Are uniformly charged rods made from conductors realistic? As in, I would intuitively imagine the charge density to be greater near the edges than the center, due to the potential required to bring a charge to that point from infinity.

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Posted: 8/30/2015 12:15 AM

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Bobo_the_King

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OmnipotentEntity wrote:

I have a rather specific and dumb question about physics. I'm currently taking Physics II which is mostly just Electromagnitism. We're currently going over the electric field due to uniformly charged rods. Are uniformly charged rods made from conductors realistic? As in, I would intuitively imagine the charge density to be greater near the edges than the center, due to the potential required to bring a charge to that point from infinity.

Boy do I have just the video for you: Link to video For the TL;DW version, the charge distribution within an object tends to uniformity as it approaches a 1-D configuration. It's actually a pretty surprising result because symmetry arguments suggest that the system should not be in equilibrium with a uniform charge distribution.

Posted: 8/30/2015 12:23 AM

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RGamma

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This also seems somewhat related (but pertaining to AC): https://en.wikipedia.org/wiki/Skin_effect

All syllogisms have three parts, therefore this is not a syllogism.

Posted: 8/30/2015 8:34 AM

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thatguy

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When you charge a conductor, to a very good approximation the charge is uniformly distributed throughout the volume. It's the lowest-energy configuration (because clumping charges together raises the potential energy associated with their mutual electrostatic repulsion) and, because it's a conductor, there's nothing to stop the charges moving about freely to find the lowest-energy state.

Posted: 11/8/2015 12:29 AM

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Warp

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The newest What If? states that if 10⁵² electrons (ie. about 9.2*10²¹ kg of them) would be put into a sphere of the size of the Moon, they would collapse into a black hole. And not only into just any black hole, but one with the mass of the entire observable universe. Because potential energy and stuff. I don't get it.

Posted: 11/8/2015 5:48 AM

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Amaraticando

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The potential energy of a moon made only of electrons is the potential energy necessary to move every electron from infinite to their position. As this is a huge system and we don't really know the best arrangement to place those electrons (in order to know every pair of distance between them), then we must make an approximation. Consider it a homogeneous sphere of radius R and charge e*10^52. The total energy, at least in order of magnitude, is similar to the gravitational binding energy(but gravitation is attractive), changing the fundamental constants (G to K_e) and mass to charge. So: U = 3*K*(e*10^52)²/(5*R) U = 3*8.98755e9*(1.6e-19*1e52)²/(5*1.737e6) U =~ 7,9475e69 J Converting to mass, using E = mc²: m = U/c² =~ 8.83e52 Kg The mass of the observable universe is around 1e53 Kg.

Posted: 11/10/2015 12:23 AM

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thatguy

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So I had a really detailed answer written up... and then out of curiosity I read the article and realised they'd explained everything a thousand times better than I had. My advice is to console yourself with the thought that this will never actually happen. Actually, thinking about it, this is pretty much the reverse of the mass defect you were asking about a while ago in the thread. In an atomic nucleus, the particles attract each other*. so there is a negative binding energy, and this means that the total mass/energy is less than the sum of its parts. In this weird electron moon, the particles repel each other and so the total mass/energy is greater than the sum of its parts. *(even though they have similar charges, there's another, attractive force called the strong interaction which dominates the system at nuclear length scales)

Posted: 11/11/2015 10:38 PM

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Warp

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I suppose that my problem is that I still don't understand "potential energy". I still can't grasp the concept that it's not just an abstract mathematical tool invented to make calculations easier, but it's actually a real, physical thing, with actual mass (according to GR). It's also hard to grasp the concept that the total mass of a system can be more (or sometimes even less) than the sum of the masses of its individual particles.

Posted: 11/12/2015 12:34 AM

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Amaraticando

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Electrons repel each other. So, to bring an electron 1 cm to another takes work, because of this repulsive force that follows Coulomb's inverse-square law. The more electrons you have in the bunch, the stronger the force. With 10^52 electrons, in a sphere with radius of 1700 km, those electrons would be really close to their neighbors; and remember that there're no protons to overcome the electric repulsion. Therefore, the total work to bring together all those charges is really huge, so huge that its mass-energy is about the same of the observable universe. A sphere of pure protons would have the same mass (slightly more, because they are naturally heavier). That's why there can be neutron stars, but no electron/proton stars.

Posted: 11/12/2015 4:34 PM

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thatguy

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Warp wrote:

I suppose that my problem is that I still don't understand "potential energy". I still can't grasp the concept that it's not just an abstract mathematical tool invented to make calculations easier, but it's actually a real, physical thing, with actual mass (according to GR). It's also hard to grasp the concept that the total mass of a system can be more (or sometimes even less) than the sum of the masses of its individual particles.

Whether energy exists or is merely a mathematical construct is really more of a philosophical question than a scientific one. In classical physics it generally acts as a book-keeping device to simplify calculations. However, at the beginning of the twentieth century special relativity was formulated, explaining how "abstract" energy could be converted into "real" matter and vice-versa. Then quantum mechanics explained how energy was discrete, and systems changed their "abstract" energy by emitting or absorbing "real" particles. So I doubt there are many physicists still around who view energy as merely a mathematical construct. In any case, this philosophical question doesn't affect any of the mathematics, so in a sense it doesn't matter (though personally I find the philosophy of science, and particularly physics, very interesting). As for the sum-of-masses thing, it's a special relativistic effect because it comes out of mass-energy equivalence (because forces and relative motions between particles add additional energy terms to the system, and this energy can be thought of as mass). You wouldn't get any such term in classical physics; and for most systems it tends to be pretty small anyway. For example the Earth has a mass of around 6*10^24 kg. Its effective mass would be changed very slightly because the gravitational binding energy holding its particles together has an effective negative contribution to the mass, but this correction is only about 2.5*10^15 kg, less than a billionth of the total mass.

Posted: 1/6/2016 3:30 PM

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Tub

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hi, I know we have a few actual physicists in here, so let me ask this to an audience smarter than google: By interpolating the formulas of relativity in certain situations, we arrive at a mathematical singularity. This has lead many popular physicists to postulate that there must be a physical representation of that mathematical singularity, a physical singularity, which is worth researching. To this day, singularities and black holes seem to be one of the most popular topics in physics forums and blogs. People just love to talk about them, about possibilities, hypothesises, interpretations and the stance on nudity of a yet unobserved object. Any wikipedia article on the subject talks about the singularity at the center of the black hole as if it was a scientific fact. What I don't see is anyone acknowledging that an infinitely-dense object is in fact very very small, and it's been known for over a century that you don't trust relativity at those scales. Meanwhile, QM continues to shrug its shoulders and asks: "Uhhm, what's gravity?". So my two questions.. * Am I wrong to be sceptical about any work on physical singularities until and unless we have a theory that both predicts singularities and is valid at the relevant scales? Why is the answer about the center of a black hole still "a scary singularity" instead of "we don't know, but there's no reason to panic yet"? Is it just because it makes for interesting discussion and sci-fi, or is there a good scientific reason for that? * Have there been actual results from applying QM to situations where relativity predicts a singularity? Every now and then I catch an article claiming some breakthrough, but I lack the background to even understand the papers the articles are referencing, much less to figure out if they're valid or not.

m00

Posted: 1/6/2016 4:28 PM

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Warp

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This is complete and absolute layman's guessing, but I'm guessing that the existence of singularities is taken more or less for granted because any claim that singularities don't exist would contradict general relativity at a very fundamental level, and that's not something that can be done lightly. Any model that predicts there not being singularities would need to agree on everything else that has been observed as factual in general relativity but explain away the singularities, which GR predicts. It would need to be a rather drastic revision of GR (in the same way as GR is this to Newtonian mechanics.) GR predicts that it's just not possible to maintain a shape of non-zero volume within the event horizon of a black hole. No matter what you do, you cannot avoid approaching the central singularity. (I don't even know if traversing back in time, if that's even possible, would avoid it. Would it?) Any model that forbids singularities would need to explain how exactly the matter within the event horizon is able to maintain a shape of non-zero size. Quantum mechanics might provide a feasible answer, but the problem is that QM and GR are incompatible at a very fundamental level (a subject that I have basically zero knowledge and understanding of, so I can't give even a layman's version of it.)

Posted: 1/6/2016 5:24 PM

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Tub

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Except is has already been contradicted, by this other well proven theory called QM. We know both GR and QM to be mostly true in their domains, but we also know both to be inaccurate in corner cases, and at least one of them must be wrong about the center of black holes. GR says that everything inside the event horizon must fall towards the singularity, hawking radiation says that it eventually manages to escape anyway. GR says that there's a point of infinite density at the center, while heisenberg objects to particles existing at a precisely defined location (inside the point-like singularity) with a precisely defined momentum (zero). Now two well-respected and well-proven theories disagree. Since this is a corner case for both GR (small scale) and QM (lots of gravity), I wouldn't trust either. If I had to pick a side, I'd notice that neither singularities nor hawking radiation have been observed, but the uncertainty principle has, so my money is on "no singularity". However, everyone else seems to disagree.

m00

Posted: 1/6/2016 9:29 PM

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thatguy

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It's somewhat of a misconception that the singularity is this infinitesimal point with infinite density. In mathematics, the term "singularity" is really synonymous with "undefined" - ie we don't know what happens at the singularity. Most physicists believe that there is some underlying Planck-scale theory which reproduces both QM and GR and would be able to tell us what goes on at the singularity. And if you find it you'd better start drafting your Nobel Prize acceptance speech.

Posted: 1/6/2016 9:33 PM

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thatguy

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Also Hawking radiation is not as inconsistent as you might expect: it comes out a weak-field approximation of GR, where QM is perfectly well-defined (otherwise how would it ever have been theorised considering it is a fundamentally quantum phenomenon). It does give rise to the black hole information paradox though: there is no information in Hawking radiation, so if information-laden matter collapses into a black hole and then that black hole evaporates away to nothing via Hawking radiation, where did the information go? (Another Nobel Prize on offer there).

Posted: 1/6/2016 9:38 PM

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Warp

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thatguy wrote:

It's somewhat of a misconception that the singularity is this infinitesimal point with infinite density.

"Infinitesimal" would imply that it has non-zero size (the very definition of "infinitesimal" is a quantity that is explicitly non-zero). However, GR does not allow it to have a non-zero size. It just collapses to zero size. If it has a finite mass but zero volume, then the density is, technically speaking, infinite. (OTOH, does it make any sense to talk about the density of an object of zero volume? Density is defined as a function of volume, and there is no volume in a singularity...)