It seems you are not thinking very logically. So what happens when the matter has released its energy? You can’t say that Mass = energy + that same quantity of mass we started with in the first place
Do you see what I mean? If it releases energy (by falling into a gravitational field), then the mass has to decrease.
When I stated that it was “exponential”, what I was trying to say is this:
That the gravitational forces between any two bodies of matter might seem minuscule, but when you consider the potential gravitational forces between all the matter in the universe it is tremendous!
And it is indeed exponential: The energy released from three earth-sized planetoids falling together is 3 times the amount of energy as would be released from only two earth-sized planetoids falling together. Again, nothing mysterious here, it is entirely intuitive. Just think about it.
That is why I previously gave the formula (1/2)(n)(n-1)
let n be the number of earth-sized planetoids
But the energy per amount of matter is not exponential, because (1/2)(n)(n-1) divided by n
It is linear in the sense that the greater n is, the more energy will be released per each unit of matter.
No, it won’t. What you might be missing here is that, with the increase of mass, the black hole’s event horizon also expands, so that the mass won’t be able to fall as far. This exactly compensates for the increased mass, such that the energy you can get out of dropping a mass into a black hole depends entirely on the mass of the dropped object and not at all on the mass of the hole.
Yes, it does. Your point?
You do not see the significance of this?
Would that not set an upper limit on the possible amount of mass in the universe?
Because only so much energy can be released from a particle before it no longer has any mass at all.
That is a very interesting point. The Schwazschild radius is directly proportional to the mass of the Black Hole.
I am wondering about the Schwarzschild radius of all the mass in the entire universe.
I am also wondering how far light can travel away from the center of the universe before gravitational forces eventually bends it back.
Of course, many theorists vehemently deny the universe is comparable to a Black Hole:
http://www.preposterousuniverse.com/blog/2010/04/28/the-universe-is-not-a-black-hole/
There must be something going on in the interior of a Black Hole because otherwise the Big Bang would never have been able to happen. Previously I had thought that if the inside of a Black Hole contained enough energy it could still explode outwards, but now Chronos’s point has me questioning this. If the matter, for all practical frames of reference, never actually reaches the interior of the Black Hole, then the entirety of its mass will never be converted to energy.
I have taken a look at the math and it looks like it is impossible to tell whether or not our observable universe constitutes a Black Hole. I suspect this may have to do with some fundamental property of the universe concerning frames of reference. It would not be possible for an observer inside a Black Hole to tell if they were inside a Black Hole or not either.
Except for the fact that over time (long periods of time) our observable universe will (presumably) become bigger and bigger. But then again this could just alternatively result from outside mass entering into the Black Hole. And we really do not know for sure whether our observable universe is actually going to grow in the future because of our limited temporal perspective.
So it looks like it is possible to tell whether or not we are inside a Black Hole, but not at any single instant in time.
But again, I pose the question: Will light eventually bend back towards the center of the universe? How long will it be able to endure the small but steady tug of gravitational attraction? (even though this attraction may become weaker as the photon travels farther away)
Sorry, but the more I “just think about it,” the more I’m sure you’re wrong.
Do you have a literature cite for this?
What do you mean by “the center of the universe?” Are you imagining some specific location? That would imply there are “edges” to the universe, for this center to be equidistant from. This is pretty much rejected these days. The universe doesn’t have a “center” – or edges – any more than the surface of a sphere does.
(Asimov covers this in at least one of his science fact essays…)
No, of course not. Or rather, if you think it does, why not show us that upper limit? Do you have any calculations?
Well, let’s see…
The Gravitational Constant is 6.67408 × 10^-11 m^3 / (kg^1)(s^2)
1 eV = 1.60217733 x 10^-19 (kg) (m^2)/s^2
It seems I have run into a problem because, according to my assertion, the amount of rest mass in the universe is proportional to the size of the universe. 
(the m^3 and m^2 factors do not fully cancel out)
Particles should have more mass the further they are away from “the center” of the universe (or rather the further away they are from all the other matter).
This could explain why the expansion of the universe will eventually have to slow down, because the energy of momentum of the expanding matter in the universe is very slowly being converted to rest mass.
This should even be true of photons, to some extent. Maybe a photon can gain angular momentum? This would have to be quantized, so the photon could only gain energy over long intervals of travel. If a photon gains angular momentum, it cannot have zero rest mass, by the way. Very interesting implications.
True, but it’s asymptotic, and almost all matter in the Universe is already so far from other matter that its mass is already almost at that asymptotic value.
When I stated “a photon with angular momentum cannot have zero rest mass”, that sort of gets into semantics, all I meant is that this needs to be included in the calculation as if it had rest mass. This is not an important part of my original idea, so we do not need to get sidetracked arguing over definitions of “rest mass”.
Which means there is a very large amount of gravitational potential energy residing within each particle. But I do not think it is fair to say the amount of this energy is literally infinite.
I am wondering, could the rest mass of matter match up to the amount of potential energy there is to be released, taking into account the great distances there presently is between matter in the universe? Or is this just obviously wrong because the theoretic gravitational potential energy that could be released is far higher than the rest mass.
If the latter, then the question naturally arises where all this energy is hiding. Because mass has to accompany energy. So where is all this hidden mass hiding out?
Gravitational potential energe does not “reside.” It is observed when an object is raised to a higher elevation with respect to a gravitational potential.
If you lift an anvil two feet above the table, it has more potential energy than it had when sitting on the table. On the other hand, it has much more potential energy with respect to the floor, and yet more with respect to the bottom of a deep well, and even yet more with respect to the center of the earth.
You might ask, how can a single anvil have four different values of gravitational potential energy? (Including “zero” when measured with respect to its current elevation.) The answer is that gravitational potential energy is not absolute, but only relative to a given frame of reference. The energy does not “reside” anywhere; it’s a measure of how much kinetic energy would be released if you dropped the anvil.)
(Animaniacs physics.)
Wherever there is energy, mass has to accompany it. That is why when the nucleus of a radioisotope emits a gamma ray it loses a small but measurable amount of mass.
We should indeed expect an anvil to have very slightly more mass high up on Mt. Everest than at sea level; though it would be far too small to actually measure.
But the change in mass would be entirely dependent on the reference frame. The speed of light and rate of time do change in a gravitational well, but only to an outside observer not constrained by the influence of these effects.
You may be confusing relativistic mass with rest mass. A photon does not have rest mass, only relativistic.
I’m not sure of this. I’d like a cite. The closest thing I can think of to this is when a photon moves to a higher place from a lower place (in a gravitational field.) This causes it to lose energy, by wavelength red-shift. It doesn’t gain energy, and it certainly doesn’t gain mass.
Actually you have it reversed; when a photon moves from a higher place to a lower place in a gravitational field it gains energy. And similarly when it moves from a lower place to a higher place it loses energy. This is why electromagnetic radiation emanating from an object in close proximity to a black hole would become so red-shifted to an outside observer.
As far as I can tell (but I may likely be wrong), I am the first person to propose this. The proposed phenomena is the basis for my whole idea expressed in this thread.
We know mass contains a tremendous amount of energy (theoretically), 1 gram of mass being equivalent to about 8.9876 x 10^13 Joules of energy. (That is is a number with 14 zeros on it, for any of you who are clueless about math :p)
So if an anvil gives up energy falling down through the earth’s atmosphere, the amount of mass it would lose would be pretty insignificant.