What-If 0140: "Proton Earth, Electron Moon"

[zero10]

Proton Earth, Electron Moon




In this comic it is mentioned:

At least, "normal" in some sense; it would be a black hole as massive as the observable universe.

How does he arrive at this conclusion?

Is he assuming a sphere the size of our moon composed completely of degenerate electrons? I don't think even that would be dense and large enough to account for the mass of our observable universe.

[Lawsome]

Electrons are positively charged

Uh

[SDK]

Is he assuming a sphere the size of our moon composed completely of degenerate electrons? I don't think even that would be dense and large enough to account for the mass of our observable universe.

It's not the mass of the electrons themselves, it's the potential energy they have being so close together.

"There's a huge amount of potential energy in this scenario—the energy that we imagined would blast all these electrons apart. That energy warps space and time just like mass does. The amount of energy in our electron Moon, it turns out, is about equal to the total mass and energy of the entire visible universe."

Once that's all packed into a black hole, it's all just mass. Or.. all energy? Hard to say... Either way, it's massive.

[zero10]

Is he assuming a sphere the size of our moon composed completely of degenerate electrons? I don't think even that would be dense and large enough to account for the mass of our observable universe.

It's not the mass of the electrons themselves, it's the potential energy they have being so close together.

"There's a huge amount of potential energy in this scenario—the energy that we imagined would blast all these electrons apart. That energy warps space and time just like mass does. The amount of energy in our electron Moon, it turns out, is about equal to the total mass and energy of the entire visible universe."

Once that's all packed into a black hole, it's all just mass. Or.. all energy? Hard to say... Either way, it's massive.

I had forgotten about mass energy equivalence. You're probably right and that makes a lot more sense than my bizarre assumption. Thanks!

[SciFi]

Electrons are positively charged

Uh

That's what I was just thinking. Now, to read the rest.

[cryptoengineer]

I notice that he totally ignores the 'proton earth' part of the question. I'm sure he's right in regard to an isolated electron moon, but together?

Presumably the earth becomes another black hole, but positively charged.

We already know of galactic core BHs larger than out solar system, so the two masses would share a common event horizon, and their
electrostatic attraction to each other, and self-repulsion, would presumably cause them to merge, very very quickly.
...and energetically, and inside the event horizon.

ce

[Pfhorrest]

I notice that he totally ignores the 'proton earth' part of the question. I'm sure he's right in regard to an isolated electron moon, but together?

Presumably the earth becomes another black hole, but positively charged.

We already know of galactic core BHs larger than out solar system, so the two masses would share a common event horizon, and their
electrostatic attraction to each other, and self-repulsion, would presumably cause them to merge, very very quickly.
...and energetically, and inside the event horizon.

ce

He did imply that that was what happened, when he talked about the charge of the resultant black hole being slightly less than the electron-moon part of it, because of the charge of the proton-earth canceling some of it out, but not much less because the electron-moon would have so much greater charge than the proton-earth. (Because protons are so much more massive than electrons, it takes way fewer of the former to make an Earth-mass than it does of the latter to make a Moon-mass, so you have way more electrons in a Moon-mass and so a much more highly charged electron-moon).

Since the total protonEarth-electronMoon system collectively has a sufficiently high density, it's all one black hole and there's no merging to go on. The whole thing just collapses instantly.

[MythSearcher]

If you put two electrons together, they try to fly apart. Electrons are positively charged, and the force of repulsion from this charge is about 20 orders of magnitude stronger than the force of gravity pulling them together.

Emmm...
Electrons are negatively charged...

[speising]

If i understand this right, the energy comes from the force needed to push the electrons together. But if they magically appear close to each other, there shouldn't really be any energy, should there? I mean, it's called "potential" for a reason.

[MythSearcher]

If i understand this right, the energy comes from the force needed to push the electrons together. But if they magically appear close to each other, there shouldn't really be any energy, should there? I mean, it's called "potential" for a reason.

The potential energy of the electrons repelling each other will also magically appear because they are now so close to each other.

[Pfhorrest]

Yeah. Basically, if you have the power to magically create a number of electrons, magically creating the energy necessary for their existence as you do so, then you must magically create more energy if you want to magically create your electrons closer together.

Interestingly, I guess that probably means it would take more energy to magically create an object somewhere far out in one of the intergalactic voids rather than, say, right next to a galactic supermassive black hole? Because the former, being "higher", has much more potential energy than the latter.

I wonder if there might be any actual physical implication of this, given the possibility of things happening, if not magically, then at least randomly, since the vacuum is never truly empty and you can make it do weird things with virtual particles becoming temporarily real, like the casimir effect. Is it less likely for particles to briefly spring into existence far out in the galactic voids, where they have more potential energy and so take more energy to be created (and so exist for less time and are less likely to have any effect on anything)? This immediately makes me think of something like dark matter or dark energy, where it seems to make a big difference whether you're in a dense matter-filled galaxy or somewhere out in the voids between them; could the shorter existence of spontaneously-emerging particles in the voids (if that is the case) have any impact on things like that?

[Flumble]

Electrons are positively charged

Uh

That's what I was just thinking. Now, to read the rest.

This, and I believe we're nerd-sniped. Now, to read the rest.

Where's the figure of 10⁵² electrons coming from? As 10⁵² rest masses it's an order of magnitude away from the Moon's mass. And taking all the electrons of the Moon and discarding the rest, your multiple orders of magnitude away.

[DanD]

Electrons are positively charged

Uh

https://xkcd.com/567/

[Copper Bezel]

Yeah. Basically, if you have the power to magically create a number of electrons, magically creating the energy necessary for their existence as you do so, then you must magically create more energy if you want to magically create your electrons closer together.

Strangely, this didn't make sense to me until I learned about color confinement, and how the amount of space separating the parts of an individual meson rather directly determines how many mesons you have. Then it kinda clicked.

[ijuin]

My understanding of the situation is that once particles that are packed densely enough exceed the Planck energy, it is impossible for them to achieve escape velocity even if they are outside of the event horizon, because adding extra kinetic energy to allow them to escape will increase their mass (and therefore the force pulling them back) by more than the energy would add to their escape.

For a not-quite-exact comparison, let's imagine a train on an uphill slope. A rail engine's adhesion (and therefore traction) increases in direct proportion to its weight, but increasing its weight too much prevents it from being able to climb no matter how much traction it has. Once the slope becomes too steep, adding weight in order to increase traction will hinder you more than helping you because the difficulty of moving the additional weight will increase faster than the traction will increase.

[rmsgrey]

Interestingly, I guess that probably means it would take more energy to magically create an object somewhere far out in one of the intergalactic voids rather than, say, right next to a galactic supermassive black hole? Because the former, being "higher", has much more potential energy than the latter.

I wonder if there might be any actual physical implication of this

Hawking radiation.

[mfb]

Relativistic mass in comment 4, really? That model is nearly as outdated as the Bohr model of the atom.

I don't think it is valid to use classical electrodynamics to calculate the total energy of the moon and then apply GR to find a black hole that has the same energy.
To contain 10^52 elementary charges, a black hole just needs a Schwarzschild radius of at least 1.5 light years, or about 4 trillion solar masses ([url=http://www.wolframalpha.com/input/?i=sqrt%28%2810^52+*+electron+charge%29^2*%28gravitational+constant%29%2F%284pi+eps_0*%28speed+of+light%29^4%29%29]calculation[/url]. That's a small fraction of the available energy in the observable universe.

[Zassounotsukushi]

I notice that he totally ignores the 'proton earth' part of the question. I'm sure he's right in regard to an isolated electron moon, but together?

Presumably the earth becomes another black hole, but positively charged.

We already know of galactic core BHs larger than out solar system, so the two masses would share a common event horizon, and their
electrostatic attraction to each other, and self-repulsion, would presumably cause them to merge, very very quickly.
...and energetically, and inside the event horizon.

ce

He did imply that that was what happened, when he talked about the charge of the resultant black hole being slightly less than the electron-moon part of it, because of the charge of the proton-earth canceling some of it out, but not much less because the electron-moon would have so much greater charge than the proton-earth. (Because protons are so much more massive than electrons, it takes way fewer of the former to make an Earth-mass than it does of the latter to make a Moon-mass, so you have way more electrons in a Moon-mass and so a much more highly charged electron-moon).

Since the total protonEarth-electronMoon system collectively has a sufficiently high density, it's all one black hole and there's no merging to go on. The whole thing just collapses instantly.

If the system became a neutral black hole, this point would kind of make sense. We would be discussing the merging of 2 things inside of the event horizon. By rule, an observer outside the event horizon couldn't detect any specifics of these events. If we temporarily discard that fact, it's clear that the objects go straight toward the singularity and quickly become a single singularity.

But the point made in the what-if is that this can't happen. There is such a thing as a "maximally charged" black hole. Beyond that amount of charge, it is physically impossible to add any more charge. In this system, both the moon and the Earth are substantially more charged than the maximum allowed by physics. If we temporarily accept that these two impossible objects exist, it is obvious that the electrostatic repulsion greatly overwhelms gravity. The objects move away from each other - exactly what general relativity dictates can't happen.

Likewise, the event horizon would cover the observable universe (from the moon alone! the Earth would cover... several universes? this is nonsense) if these objects were neutrally charged. But they are charged beyond the physical limit in blatant disregard for the laws of our universe. Because of this, we can't clearly say that there is any event horizon. The circumstance is just a big jumble of contradictions.

Any position you take is negated by evidence in the other direction. Just like we have paradoxical sentences, this is a paradoxical physical system. The more likely truth is that this is a violation of some fundamental holographic geometry axiom. The described system breaks rules, and these are not "soft" rules, these are rules required to fundamental consistency of our universe. It would be like a 2D being from flatland describing self-contradictory rules for a fictional 3D shape, which is totally possible to say in words, or write in a blog post. But not in the real world.

[Neil_Boekend]

Likewise, the event horizon would cover the observable universe (from the moon alone! the Earth would cover... several universes? this is nonsense)

TL:DR version: The proton-earth event horizon is smaller.

(I am not quite sure how Randall calculated the amount of electrons in our universe-destroying moon. I am taking a guess and assume that he took the rest mass of an electron and divided the mass of the moon through that since that approximately lines up.)
The electron moon:
An electron weighs approximately 10^-30kg (rest mass)
The moon weighs approximately 10²³kg
-> Total: 10⁵³ electrons (article said 10⁵² which is likely to be a rounding error either in my work or Randall's. I don't care which, it's close enough.)

A proton weighs approximately 10⁻²⁷kg (rest mass)
The earth weighs approximately 10²⁵ kg
-> Total: 10⁵² protons

The rest mass is NOT your problem. You see, to get electrons or protons together costs energy^Φ. Energy is mass. The mass-energy you pumped into the system to get the particles that close despite the massive repulsion they have totally eclipses the rest mass. And not by a silly factor of a trillion or so. It's more. So much more.
This means that the mass equivalence is relatively close to each other. The earth has less mass-energy both to having about a tenth of the particles and having a bigger diameter (the protons aren't as close to each other so they need less energy to get that close)
The additional mass-energy means the black hole event horizon is also bigger.

^ΦThink of it as magnets. If you have a box of imaginary magnets with only south poles and you try to push two of them together with their that takes energy, since the south poles are pushing away from each other. If you have managed to put two of them together and bind them with a tyrap and push another south pole towards those two south poles the energy you need gets bigger, since the two south poles repel the third one with twice the force. A fourth one needs even more energy.
Now the protons or electrons do the same, but with 10⁵² of them. The energy required is astounding.

(edited to clear up some use of force and energy. It was needlessly confusing.)

[Pfhorrest]

Maybe a better interpretation of the question would be one where the rest-mass of the Earth and Moon was each converted into an equivalent energy of protons or electrons -- that is, if it's going to take extra energy to pack two electrons close to each other like that, then you have less energy to spend on making more electrons out of the mass-energy of the original Moon. That way the total relativistic mass of both stays the same. We haven't magically created any new energy, we've just magically transformed it. You'd still get both of them exploding immediately from electrostatic repulsion, and a bunch of those protons and neutrons sticking to each other making hydrogen maybe if the resulting hot mess isn't too hot to just keep it all a plasma, but you wouldn't get self-contradictory physics or naked singularities or universe-swallowing black holes, at least.

[flymousechiu]

But electrons and protons ARE naked singularities!

[flymousechiu]

moon mass = 7.34767309 × 10^22 kg
electron rest mass = 9.10956 × 10^-31 kg
number of electrons = 8.06589 × 10^52
average moon radius = 1.7371 × 10^6 m
e = 1.602177 × 10^-19 C
mass-energy for a single electron = k_e × Q_1 × Q_2 / r / c^2 = 8.98755 × 10^9 kg·m^3·s^-2·C^-2 × 8.06589 × 10^52 × (1.602177 × 10^-19 C)^2 / (1.7371 × 10^6 m) / (299792458 m/s)^2 = 119.2kg ~~ 1.7 × typical standard adult human male mass (~~ 70 kg) (plus the mass of an electron at rest)
(assuming all electrons on the surface of the moon, I know every bits of mass on the originally "uniform" moon has been magically transformed before more volatile things could happen, but I love the shell theorem)
Those electrons are obese.

[paddyfool]

Maybe a better interpretation of the question would be one where the rest-mass of the Earth and Moon was each converted into an equivalent energy of protons or electrons -- that is, if it's going to take extra energy to pack two electrons close to each other like that, then you have less energy to spend on making more electrons out of the mass-energy of the original Moon. That way the total relativistic mass of both stays the same. We haven't magically created any new energy, we've just magically transformed it. You'd still get both of them exploding immediately from electrostatic repulsion, and a bunch of those protons and neutrons sticking to each other making hydrogen maybe if the resulting hot mess isn't too hot to just keep it all a plasma, but you wouldn't get self-contradictory physics or naked singularities or universe-swallowing black holes, at least.

Immediately after the standard what-if-induced chortling at destruction, I had a similar thought

[Zassounotsukushi]

This means that the mass equivalence is relatively close to each other. The earth has less mass-energy both to having about a tenth of the particles and having a bigger diameter (the protons aren't as close to each other so they need less energy to get that close)
The additional mass-energy means the black hole event horizon is also bigger.

I see what you were trying to do here, but it's not correct. The absurd energies come from the long-range nature of the electrostatic repulsion. The Earth has the same number of protons as electrons (almost). So when electrons are stripped away, it has many more positive charges than the moon has negative charges. Binding energy goes with M^2/R. If you assumed a constant density, it would be more like a R^5 term, because M is proportional to R^3. Earth has more energy by a factor of like 670 (not exact due to density differences).

But electrons and protons ARE naked singularities!

Electrons do have some controversy about them, but for protons at least, this statement is flagrantly incorrect.

[Neil_Boekend]

This means that the mass equivalence is relatively close to each other. The earth has less mass-energy both to having about a tenth of the particles and having a bigger diameter (the protons aren't as close to each other so they need less energy to get that close)
The additional mass-energy means the black hole event horizon is also bigger.

I see what you were trying to do here, but it's not correct. The absurd energies come from the long-range nature of the electrostatic repulsion. The Earth has the same number of protons as electrons (almost). So when electrons are stripped away, it has many more positive charges than the moon has negative charges. Binding energy goes with M^2/R. If you assumed a constant density, it would be more like a R^5 term, because M is proportional to R^3. Earth has more energy by a factor of like 670 (not exact due to density differences).

I think you are calculating the amount of protons and electrons differently than I and Randall do. The way we calculate it the moon has approximately 10 times the amount of electrons the earth has protons and they are in a smaller volume. Thus the proton earth has less energy.

I just took the mass of the moon and divided it by the rest mass of an electron. Same with the earth and protons. As a proton is far heavier, even more than the mass-ratio of the moon and the earth the earth gets less protons.
You appear to take the moon and remove all non-electron particles. This gives far less particles, especially in the moon. If you calculate the number of particles in a different way you logically get vastly different results. The end result would not be as devastating as the end results in the What-If, so I think that is why Randall chose that calculation method.

[Rombobjörn]

Wow, the repulsive force is so great that the potential energy causes an even greater attractive force that overpowers the repulsive force! The electric repulsion sort of prevents itself from working. Weird, but interesting.

So the proton Earth isn't charged enough to neutralize the electron Moon, but I was wondering what would happen if the electron Moon black hole would encounter another black hole with an equally great but positive charge, made from either protons or positrons. The two charged black holes would of course attract each other, both electrically and gravitationally, and would sooner or later merge. Then the electric charges would cancel each other out. One might then naively assume that both black holes would just evaporate because the enormous potential energy that the electric repulsion caused would be gone, but no, all of that energy can't just disappear. There is still a concentration of energy equal to twice the mass of the electron Moon inside its own Schwarzschild radius. I suppose it just becomes a regular, neutral supermassive black hole.

Electrons are positively charged

Uh

https://xkcd.com/567/

Either that, or Randall is really really sure that electrons definitely are charged.

[flymousechiu]

Electrons do have some controversy about them, but for protons at least, this statement is flagrantly incorrect.

oopsy, silly me. mark my quacks.

[Zassounotsukushi]

I think you are calculating the amount of protons and electrons differently than I and Randall do. The way we calculate it the moon has approximately 10 times the amount of electrons the earth has protons and they are in a smaller volume. Thus the proton earth has less energy.

I just took the mass of the moon and divided it by the rest mass of an electron. Same with the earth and protons. As a proton is far heavier, even more than the mass-ratio of the moon and the earth the earth gets less protons.
You appear to take the moon and remove all non-electron particles. This gives far less particles, especially in the moon. If you calculate the number of particles in a different way you logically get vastly different results. The end result would not be as devastating as the end results in the What-If, so I think that is why Randall chose that calculation method.

Maybe it would help to elaborate your thinking on that a little bit better. I also realized an error in my previous claims, I'll get into that here. Consider just an arbitrary Hydrogen atom where there's 1 electron and 1 proton. The conclusions won't be changed by considering other atoms. M>Q is the condition for a maximally charged black hole, but this is in "God units" that only theoretical physicists understand. In SI units, the statement is M>sqrt(4 Pi epsilon0) Q. For the Hydrogen atom, plug this into Google to calculate the maximum charge:

sqrt(4*Pi*G*(8.854*10^(-12) Farad/meter))*(1 amu)

That gives

= 1.43093361 × 10-37 coulombs

Charge of an electron/proton:

1.60217662 × 10-19 coulombs

So you could imagine either the proton or the electron as intrinsically naked singularities, although I'm pretty sure this is wrong. There's no reason to imagine these particles as black holes in the first place. There is a part of their rest energy attributed to their self-interaction in the first place, and this places some length scale on the "size" of the particle. It's that size which makes the electron seem like a black hole. It's not really relevant here anyway. I was wrong assuming that the Earth would not be maximally charged. It would be orders of magnitude over this charge, but the moon (with a lower mass both due to the lower mass of the moon and lower mass of electrons) would be even more over its own limit. In the end, the Earth dominates and the moon can mostly be ignored.

I will offer one more revision to my position. It is important to remain loyal to the specifics of the problem specification. The question stipulates that the electrons are removed from Earth. This is the detail we may not change. If removing those electrons imparts more energy to the Earth, and thus increases its rest mass, we must take that statement as-is. This means that Earth is not a naked singularity. It is simply a maximally charged black hole. Its new mass will be:

M = Q / sqrt(4*Pi*G*(8.854*10^(-12) Farad/meter))

((1.33 * (10^50)) * elementary charge) / sqrt(4 * Pi * G * (8.85400 * (10^(-12)) * (farad / meter))) = 2.47281506 × 10^41 kilograms

This is the most correct conclusion, and it's consistent with the What-If. This is an absurd mass, but it avoids the unknown physics. There really is no disagreement. Since we add mass as we separate the charges, there is no contradiction. This is the mechanism by which the universe avoids the contradiction.

[Copper Bezel]

It is important to remain loyal to the specifics of the problem specification. The question stipulates that the electrons are removed from Earth. This is the detail we may not change.

What if the Earth were made entirely of protons, and the Moon were made entirely of electrons?

If you remove the electrons from Earth, you have a lot of protons, but also neutrons as well, in a particular configuration (that won't last very long.) RM's interpretation was to replace the Earth and Moon with an equal quantity in rest mass of the respective particles at the same density. It's a perfectly valid interpretation of the question. There are obviously others. On the face of it, it seems most literal, so that's probably why he ran with it; it also presents the opportunity to peek into some really weird stuff that a lot of readers haven't heard of before and might do some reading on now, even if it doesn't ultimately add up to anything as an answer.

Had he gone with just removing the particles of opposite charge, it obviously changes nothing for the Earth, but quite a lot for the Moon. I'd personally have found an explanation interesting that was based on, like, let's say we have these two massively charged but otherwise ordinary objects, how does it affect their orbits, etc. But I really think that with a question as open to interpretation as this one, it made sense for RM to take it in a direction that just sort of sent a bunch of readers on personal Wikipedia trips.

[Zassounotsukushi]

How does destroying the known universe "obviously changes nothing for the Earth"? Where did anyone get this idea that the moon had more deleterious effects than the Earth? RM started off talking about the moon, but he states that the moon is less destructive.

The scientific question about how to go about the problem deals with 3 possibilities: 1) accept an invariant number of protons/electrons, 2) accept an invariant mass for the earth/moon, or 3) accept both and presume there are naked singularities. Only #1 closely matches the tone of "remove the electrons from Earth"

[Whizbang]

What if....png (5.13 KiB) Viewed 28267 times

[Diadem]

Why does this sound suspiciously familiar? Ah! We've discussed such a scenario before.

In that thread the question was about a kilogram of electrons in a 1 cm sphere. That was not quite enough to form a black hole, but plenty to destroy the earth. Taking the rest mass of the moon as electrons... I don't feel like doing the math, but "Equal to the entire energy content of the universe" sounds plausible.

Of course both the Schwarzschild equations and the Reissner–Nordström ones are for static black holes. They don't quite apply to our situation. Even a black hole like this needs time to form (nothing can beat the speed of light), and during its formation all kinds of fun and exciting things can happen. I won't begin to speculate on what, but my guess is it involves a truly titanic release of gravity waves.

I wonder how this is going to affect our galaxy, or even distant galaxies. Being swallowed by a billion light year radius black hole isn't immediately fatal. It just means that from that point on you're doomed to fall towards the singularity, but that'll s still take at least a billion years, so it's not an urgent concern. The gravitational waves from the black hole's formation though may be another matter. Plus there's still the huge electromagnetic force to account for. I wonder how many light years away the electric field will be able to pull atoms apart.

Honestly all in all I think Randall didn't go into enough detail on this one!

[flymousechiu]

I've redone my calculations today and interestingly the evenly distributed electron model of the moon returns a lesser value than that of electron shell moon model. Can somebody verify my findings or point out where i made a mistake?
Shared values:
moon mass = 7.34767309 × 10^22 kg
electron rest mass = 9.10956 × 10^-31 kg
number of electrons = 8.06589 × 10^52
average moon radius = 1.7371 × 10^6 m
e = 1.602177 × 10^-19 C
number of coulumbs of our peaceful moon: 1.29230 × 10^34 C

Electron shell:
U_e = kQq/r = k(1.602177 × 10^-19 C)(1.29230 × 10^34 C)/(1.7371 × 10^6 m) = 1.071 × 10^19 J
M_e = U_e/c^2 = 119.2 kg
M_moon = 119.2 kg × 8.06589 × 10^52 = 9.615 × 10^54 kg = 2.9 observable universes

Even distribution:
U_moon = ∫(r from 0 to moon's radius) k (4πr^2ρ) (4/3πr^3ρ)/r dr, where ρ is the charge density and is equal to the Q_moon/V_moon (value isn't relevant)
U_moon = 16/3kπ^2ρ^2∫(r from 0 to moon's radius) r^4 dr
U_moon = 16/15kπ^2ρ^2r^5 = 3/5k(4/3πr^3ρ)^2/r = (3k)/(5r)(Q_moon)^2 = 5.184 × 10^71 J
M_moon = U_moon/c^2 = 5.768 × 10^54 kg = 1.7 observable universes

[Copper Bezel]

How does destroying the known universe "obviously changes nothing for the Earth"?

The universe is destroyed in the same way regardless of whether you convert its mass into packed protons or just remove the electrons. "Convert the rest mass of all constituent particles into protons" differs from "remove the electrons from Earth" by about an order of two, so they're indistinguishable in this context.

Where did anyone get this idea that the moon had more deleterious effects than the Earth? RM started off talking about the moon, but he states that the moon is less destructive.

The scientific question about how to go about the problem deals with 3 possibilities: 1) accept an invariant number of protons/electrons, 2) accept an invariant mass for the earth/moon, or 3) accept both and presume there are naked singularities. Only #1 closely matches the tone of "remove the electrons from Earth"

So it's #2 I'm talking about. Well, unless you mean "invariant mass" very differently from the commonsense interpretation. "Accept an invariant [rest] mass for the [particles constituting] the earth/moon" is both the assumption I would have taken from the question and the one Randall seems to have. A Moon mass of electrons packed into a moon-sized ball is unquestionably more nasty than an Earth-ball of protons, and that is why the What-If focused on the Moon to the point of ignoring the Earth.

It would be another equally valid approach to consider the potential energy in the converted mass in the first place, but it would make for an even less interesting What-If.

[keithl]

First: I enjoyed this what-if immensely, and the resulting forum conversation as much. Thanks, people!

Second: I am curious what would happen to the universe if these electrons and protons in their differing numbers were not magically created in the tiny spheres of the earth and the moon, but more spread out, over the size of the solar system or the galaxy? After the excess protons found themselves an excess electron, and combined into a hydrogen atom in a flash of UV, there would still be an excess of electrons, repelling each other and scattering into the universe. So, the first question is - how far apart would the electrons have to be to not create a black hole? Second: how far apart would the electrons have to be to not (say) slowly rip apart the the galaxy - would a sufficiently negatively charged galaxy exceed the gravitational energy holding it together? Or would most of the widely spread electrons just scatter into the universe?

I would compute that myself, but that would be a distraction from a distraction - I'm currently calculating the detectability of 100 AU diameter, 60 Kelvin statite Dyson shells, and what natural astronomical infrared objects they might resemble, rather than designing satellites. I work on weird stuff.

[Jeff_UK]

Did anyone else notice the top result for "Infinitely Dense Objects" on the link is "The Big Book of Christian Apologetics: An A to Z Guide (A to Z Guides)?"


(see definition #2 https://www.google.be/search?q=dense#q=define:+dense)

[cryptoengineer]

Did anyone else notice the top result for "Infinitely Dense Objects" on the link is "The Big Book of Christian Apologetics: An A to Z Guide (A to Z Guides)?"

(see definition #2 https://www.google.be/search?q=dense#q=define:+dense)

No, I don't. Google is notorious for showing different results for the same search to different
people, based on what it *thinks* you want to see.

I do see a few pages critiquing William Craig Lane's (lame) attempts
to reconcile Christianity with Big Bang Cosmology, but that's about it.

The book you mention is on Amazon, and I agree; many of us would find TBBOCA pretty dense.

ce

[Copper Bezel]

Yeah, I thought the joke was that the search failed in all departments (and then defaulted to book titles) because infinitely dense objects are really hard to find, what with not existing and things.

[Zassounotsukushi]

How does destroying the known universe "obviously changes nothing for the Earth"?

The universe is destroyed in the same way regardless of whether you convert its mass into packed protons or just remove the electrons. "Convert the rest mass of all constituent particles into protons" differs from "remove the electrons from Earth" by about an order of two, so they're indistinguishable in this context.

Where did anyone get this idea that the moon had more deleterious effects than the Earth? RM started off talking about the moon, but he states that the moon is less destructive.

The scientific question about how to go about the problem deals with 3 possibilities: 1) accept an invariant number of protons/electrons, 2) accept an invariant mass for the earth/moon, or 3) accept both and presume there are naked singularities. Only #1 closely matches the tone of "remove the electrons from Earth"

So it's #2 I'm talking about. Well, unless you mean "invariant mass" very differently from the commonsense interpretation. "Accept an invariant [rest] mass for the [particles constituting] the earth/moon" is both the assumption I would have taken from the question and the one Randall seems to have. A Moon mass of electrons packed into a moon-sized ball is unquestionably more nasty than an Earth-ball of protons, and that is why the What-If focused on the Moon to the point of ignoring the Earth.

It would be another equally valid approach to consider the potential energy in the converted mass in the first place, but it would make for an even less interesting What-If.

So you are considering rest mass to be the particle's rest mass. Additionally, you are considering that the moon must have several orders of magnitude of electrons added in order to maintain that mass value. Obviously any approach to the problem is valid and this is consistent enough with the wording. You would be taking the charge to mass value as invariant, and to come from the electron's value. That would give a larger value, which could be computed and compared.

First: I enjoyed this what-if immensely, and the resulting forum conversation as much. Thanks, people!

Second: I am curious what would happen to the universe if these electrons and protons in their differing numbers were not magically created in the tiny spheres of the earth and the moon, but more spread out, over the size of the solar system or the galaxy? After the excess protons found themselves an excess electron, and combined into a hydrogen atom in a flash of UV, there would still be an excess of electrons, repelling each other and scattering into the universe. So, the first question is - how far apart would the electrons have to be to not create a black hole? Second: how far apart would the electrons have to be to not (say) slowly rip apart the the galaxy - would a sufficiently negatively charged galaxy exceed the gravitational energy holding it together? Or would most of the widely spread electrons just scatter into the universe?

I would compute that myself, but that would be a distraction from a distraction - I'm currently calculating the detectability of 100 AU diameter, 60 Kelvin statite Dyson shells, and what natural astronomical infrared objects they might resemble, rather than designing satellites. I work on weird stuff.

If the universe had a surplus of electrons, then it would cause galaxies to accelerate from each other. On the large scale, this means that essentially more space is added between them uniformly. This is describing dark energy. I'm pretty sure they ruled this out somehow as a valid candidate, but I don't know how.

Accumulation of matter, however, would favor a neutral charge. Go calculate the capacitance of the moon or the Earth. You will be surprised. Objects like these have very low capacitance values, and they have a way of removing extra charge. The electric field just causes it to push ions away. Going deeper... consider a stellar nursery of a low-density gas that is contracting to form stars and planets. As an initial condition, this gas has a uniform charge density, and there is approximately no field. Any accumulation of matter will maintain the same ratio of negative to positive charges, but this means that the electric potential will increase in the accumulation.

By this method, excess charge will prefer to exist in the space between stars and galaxies. The stars and galaxies will then remain relatively neutral. In general, star and planet formation is discouraged in this space because the matter repels itself possibly to a greater degree than what it attracts. This is a very tantalizing idea. Neutral matter can still attract more matter, and it can dispel extra charge it builds up in the process.

[Neil_Boekend]

@Zassounotsukushi: Most of what you say is complex enough to warrant a more detailed evaluation. However, the interpretation of the question is not.

I will offer one more revision to my position. It is important to remain loyal to the specifics of the problem specification. The question stipulates that the electrons are removed from Earth. This is the detail we may not change.

Wrong. The question is open to interpretation:

What if the Earth were made entirely of protons, and the Moon were made entirely of electrons?

Randall choose to interpret this as an object made of a moon mass of electrons (counting rest mass). I verified that in this post. This is the calculation that gets the 10⁵² electrons in the What If. Your calculation gets you far less, I estimate about 10^-5 times as many. Your interpretation differs from both Randall's and my interpretation. That does not mean your interpretation is wrong, it simply means that we'll get vastly different results.