# proposed explanation for the phenomena of mass

It is known that mass is equivalent with energy, and that if a piece of matter loses energy it loses a small degree of mass (such as the nuclei of atoms). But scientists have never really been able to determine what energy it is exactly that all this mass represents. It is known that mass can be completely transformed into energy if a particle annihilates with its antiparticle, but there is not enough antimatter in the universe for all the matter that exists, so why should matter still have so much mass? What form of potential energy does all this mass embody?

Here is my thought: What if all this mass represents the potential energy of gravitational attraction? Scientists believe that when a piece of matter falls into a Black Hole, over 10 to 40 percent of its mass can be converted to energy. So if all the mass in the universe were to fall together, could not all this potential energy of rest mass be released?

And if so, should it not be possible to calculate exactly how much mass exists in the universe (or at least set an upper limit) using precise measurements of exactly how much energy is released when two known quantities of matter are allowed to gravitationally attract together? (and combining that with the known rest masses of particles, for example scientists know that the rest mass of a proton is equivalent to 938.257 million electron-volts of energy)

To summarize, rest mass of each particle individually is equivalent to gravitational potential energy of all the matter in the universe within the system.
I am thinking this could have very profound implications.

What do you mean, we don’t know what kind of energy it is? Mostly, it’s binding energy from the Strong Force.

That would just tell you the masses and sizes of the objects you used in the experiment (which you presumably already knew). It wouldn’t tell you anything at all about the rest of the Universe.

If there is a strong force holding particles together, that means they have LESS energy.
(i.e. it takes a lot of energy to pull them apart)

Binding energy is really a “negative” form of energy, if you want to look at it that way.

Or did you mean that matter (i.e. hydrogen nuclei) has mass because it could be bound by the strong force, forming heavier nuclei, and release that energy?

When a positron and electron are allowed to bind together, they annihilate, and the binding energy is released as photons (energy).
(typically 2 photons, but I won’t get into all the details here, as it is not relevant)

Actually, what’s fun is that it works both ways. For very light atoms, like Hydrogen, you get energy when two of them get stuck together, to make Helium. But with very heavy atoms, like Uranium, you get energy when you split them apart. So (in our universe) it depends on exactly where along this “binding curve of nuclear energy” the atom happens to sit.

Alas, no, your idea that it is related to gravity is not going to work. Gravity is incredibly weak, at the nuclear scale. Yes, two protons have a gravitational attraction, but the electrical repulsion between them is far stronger…by a factor of around 10^36.

Inside atoms, gravity might just as well not even bother.

Yes, but when you start clumping a lot of matter together, the gravitational forces can release a lot of energy. It is exponential, when you have just two particles, very little energy is released. When you have three particles, 3 times as much energy is released than when you only have 2 particles. When you have 4 particles, 6 times as much energy is released, and so on. Basically the equation is ½n(n-1), where n is the number of particles (or units of mass).

In Isaac Asimov’s book (yes, he wrote non-fiction too), “The Neutrino” he mentioned an interesting thing. Before scientists had any idea about nuclear fusion they were trying to figure out where all the energy came from in the sun. Scientists calculated that gravitational compression from all the matter in the sun could release enough energy to power the sun for 400 years. That is, if all the contents of the sun were in a gas cloud and they merged together, the force of all the matter being pulled together by gravity would make core very hot, even in the absence of nuclear fusion.

Letting two huge chunks of mass fall together releases exponentially more energy than letting two small pieces of mass attract together.

Think of it this way. Imagine two planets with the mass of the moon falling together. They would both accelerate at about 1.6 m/s. Now imagine two planets the size of earth falling together, they would both accelerate at about 9.8 m/s
(I know this is a terrible example but it does illustrate what the point I am trying to make)

But even if we keep the acceleration the same, increasing the mass increases the energy released to a proportional degree. A small object that weighs twice as much as a smaller object will release twice as much energy when it falls towards the earth.

So two planets that have twice the mass of the earth, if they were allowed to fall together, would release roughly FOUR times the energy compared to two planets with the same mass as the earth.

When you start adding up all the matter in the universe, that is a lot of potential energy of gravitational attraction. In fact, you start wondering where all the mass is, because if there is potential energy, there has to be mass too, and it is hard to believe particles have enough rest mass to account for all that energy. So the situation is really just the opposite of what you were contending. There is a HUGE amount of gravitational binding energy, if we examine the entire system of the universe as a whole.

Binding energy only applies to things that are bound.

And a proton or neutron is made up of three quarks, but its mass is much greater than three times the mass of a quark. The remainder is all strong-force binding energy. Or more precisely, color-force binding energy: The strong force is just a residual manifestation of the even stronger color force.

Gravitation is linear with mass, not exponential. Newton’s Law applies inside atoms and inside galaxies equally.

You are describing the number of lines between objects in a graph or network, but gravity doesn’t work that way. Gravity doesn’t increase on the basis of the number of objects mutually attracting. If it did, Jupiter’s Moons would have different orbital relationships than Earth’s Moon (twenty-some objects as opposed to two.)

Asimov’s non-fiction books are GREAT! The berries! They’re fun, educational, entertaining, and a very, very good introduction to science.

And, yes, definitely, before nuclear energy was known, people figured that the sun might be hot and glowing solely on the basis of gravitational compression. After all (or “before all!”) that’s how the sun got so hot as to trigger nuclear fusion at its core. A cloud of gas compressed, got hot, compressed further, got hotter, and, even without fusion, it would have been a big hot glowing thingie.

As you note (and Asimov noted) this wouldn’t have kept the sun “sun-hot” for five billion years. That took fusion.

I love Asimov’s science-fact collections! Recommended highly for anyone reading this thread!

Yeah, I read a ton of his essays as a boy. This lead me down a few wrong paths in adulthood (I’m thinking of you, Uncertainty!), but overall, a huge net plus for me. (I find myself thinking about his essay on global warming, written God knows when, read by me in the 70’s, a lot in the past few years.)

I wish I could find something equivalent for my son to latch onto. I finally got my son to try Neil DeGrasse Tyson’s “Death by Black Hole”; he’s reading it for school, so he has to get through it. My fingers are crossed. (I’ve had trouble liking him myself, I don’t know why- maybe I’m just stuck on Asimov and Sagan.)

BTW- I’ve seen this figure before, and I’ve wondered where it comes from. I’ve read that the heat comes from friction in the accretion disk. I guess the number comes from an estimate of gravitational potential energy difference between far away and close to the event horizon. But won’t a particle take most of it’s kinetic energy with it into the black hole? What if a particle just falls straight in (say at one of the poles) and doesn’t bump into anything else?

The upper bound would be 50%, and that’s fairly easy to calculate. But of course, nothing is ever as efficient as possible, and figuring out in practice how much actually is released, versus how much is wasted, is going to depend on some sort of modeling of the stuff falling in. A particle that falls straight in without bumping anything will release almost no energy, but just how typical is that situation actually?

It isn’t quite the same, but Stephen Jay Gould is a lot of fun, and David Quammen is my favorite living science writer. “Song of the Dodo” is unbelievably depressing…but hugely informative, and, in a sad way, very much worth reading. “Flight of the Iguana” is a lot more fun!

I have about 50 of his nonfiction books. I subscribed to the Magazine of Fantasy and Science Fiction from the age of 13, partly to get his monthly science column. Sadly, many of them are very, very dated.

Gravitational compression could power the sun for 400 years. Its actual expected lifetime is 10 billion years. Shouldn’t that give you a clue that basing your energy calculations on gravity will lead to poor results?

It’s more complicated than that. Actually most of a Protons mass comes from the sea of quarks transiently coming into and out of existence from the quantum vacuum within the proximity of the field from the strong force (that is what particle physicists currently believe). That is not really the same thing you said.

When you try to pry quarks apart, it just ends up adding an incredible amount of energy and mass, and new particles are formed.

If you look at Enthalpies of formation in chemistry, there is a reason why the energy values for most compounds (like sodium chloride) are negative. It takes energy to break those bonds. Similarly, in particle physics, in takes energy to overcome binding energy. The binding energy of an electron in the first orbit of a hydrogen nuclei is negative, because energy has to be added to move it the next orbit further away. Binding energy does not add mass or energy to particles, it takes it away!

The situation inside a proton is much different and unfortunately we do not have the time or space to fully discuss the mechanics here. But just think: when two light nuclei are added together, they release energy.

Maybe we can more phrase it this way: “As more particles are bound together the binding energy decreases”. But it depends exactly what you mean by “binding energy”, you have to be careful how you use that term.

Gases will typically become ionized if they come anywhere into the proximity of a Black hole. The gravitational acceleration is such that the charged particles gain a huge level of velocity and tend to fall into orbit. The particles in the accretion disc are moving so fast that they radiate much of their momentum in the form of electromagnetic radiation.

It is more complicated than that, but going into further details would be beyond the scope of this thread.

Hypothetically, if we assumed that matter fall straight into a black hole, without emitting any energy, then all that energy of momentum would be trapped within the surface of the Black Hole. The temperature inside a Black Hole is very hot. For the biggest of the supermassive Black Holes, it is likely that a substantial portion of its mass actually exists in the form of energy. When you drop one gram of matter into a Black Hole, that matter has less mass inside the Black Hole. But you have also added a lot of energy to the Black Hole too, so the combined mass + energy still equals one gram of mass. It is just that that mass does not exist entirely in the form of matter at this point.

(I’m also just going to point out before anyone makes any objections that rest mass is not the same thing as mass)

Hypothetically, if you were to carefully add matter to a Black Hole while somehow extracting most of the energy of that matter falling in, adding 1 gram of matter will add significantly less than 1 gram of mass to the Black Hole, because you have converted matter into energy. The mass of any large planetoid is very slightly less than the total mass of all the matter that fell together to create it (theoretically, the effect is so tiny as to be completely negligible when we’re not talking about black Hole physics).

Think of it this way: The more matter you dump into a black hole, the more energy will be released when additional matter is dumped into the black hole. It’s not a linear relationship.

If a Black Hole keeps sucking up mass, eventually its gravitational force will grow.

Now question:
We know mass is equivalent to energy, even if we do not fully understand exactly how. Energy cannot disappear, it has to go somewhere. So when we look at all the energy being released when a piece of matter begins falling into a gravitational field, where did that energy exist in the first place? Presumably it existed in the form of matter, right, or what do you think? Then the potential energy of gravitational attraction is tied up in the form of mass. It’s like an electric battery. If electricity is going to come out later, we know the battery must be charged, the energy is inside that battery. And if potential energy resides within a particle, that means the particle must have more mass, correct?

If I dump a 1 kg mass into a black hole that is as big as one solar mass, it will have a certain specific effect. If I dump the same mass into a black hole that is as big as two solar masses, you are claiming it would have a greater specific effect.

I don’t know if this is true or not, but I believe it is not. Please verify and validate your claim.

In ordinary circumstances – objects in orbit – all gravitational attraction is linear. The equations describing Newton’s laws do not have exponential terms.

Well of course it’s more complicated: It’s quantum field theory. But that sea of quarks would have exactly zero mass, absent the chromodynamic binding energy. The mass is due to the binding energy.

This is not true. No matter what the mass of a black hole is, you’ll recover at most half of the mass of whatever you’re dropping in as energy.

We understand exactly how. Mass is that portion of energy which cannot be transformed away in any reference frame. The energy released when a piece of matter is dropped into a gravitational field previously existed in the piece of matter. There’s no mystery here, and there will continue to be no mystery no matter how many times you say there is.

I’m not claiming anything extraordinary. All I’m saying is that if you have a Black Hole with a mass of 2 x 10^33 metric tons and you dump in 1 x 10^33 tons of matter into that Black Hole, the gravitational force of that Black Hole will then increase by 50 percent. There’s nothing incredulous about that, it’s perfectly intuitive.

But then when you drop the next batch of 1 x 10^33 tons of matter into the Black Hole, this time more energy will be released than the first time, simply because the Black Hole has more matter. If you drop something into a massive Black Hole it will release more energy than a less massive Black Hole would. I think there’s nothing controversial about that.

The gravitational force is so strong that tremendous amounts of energy can be released when even a small amount of matter falls into a Black Hole.

What you are describing is linear.

ETA: I think what you are describing is correct. It’s just linear, and not exponential.