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

[keithl]

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 rounding error in Randall's work. According to Wikipedia, the moon's mass is 7.3477e22 kg, and the electron's mass is 9.10938215[45]e-32 kg, so the ratio is 8.066e52 electrons per moon. That makes an unimaginable result eight times as unimaginable.

An interesting aspect of this is that we (or at least, Wikipedia) know the mass of the electron 200 times more accurately than we know the mass of the Earth or the Moon. Presumably, that is because to estimate the masses more accurately we need to measure the gravitational constant more accurately, and that is difficult.

I wonder if we could send a known test mass far out into the solar system (where the tidal forces from Sun and Jupiter are small), and orbit a small object around it, measuring positions and shapes with laser interferometers and computing the gravitational constant from that. This would be very important if we subsequently replace the moon with electrons - an experiment we can only perform once, hence we should do it accurately.

[Diadem]

An interesting aspect of this is that we (or at least, Wikipedia) know the mass of the electron 200 times more accurately than we know the mass of the Earth or the Moon. Presumably, that is because to estimate the masses more accurately we need to measure the gravitational constant more accurately, and that is difficult.

Pretty much. We know the product of G * M_earth to about 10 decimal places, roughly the same as the accuracy with which we know the electron mass. But measuring G is hard.

The accuracy of the measured value of G has increased only modestly since the original Cavendish experiment. G is quite difficult to measure, as gravity is much weaker than other fundamental forces, and an experimental apparatus cannot be separated from the gravitational influence of other bodies. Furthermore, gravity has no established relation to other fundamental forces, so it does not appear possible to calculate it indirectly from other constants that can be measured more accurately, as is done in some other areas of physics. Published values of G have varied rather broadly, and some recent measurements of high precision are, in fact, mutually exclusive.[3][6] This led to the 2010 CODATA value by NIST having 20% increased uncertainty than in 2006.[7]

Apparently our uncertainty over G has only been going up.

[stayaway]

Everybody is providing information on their own way.

[gmalivuk]

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

It's not outdated, it's just potentially confusing.

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.

Importantly, this is explicitly the interpretation Randall made in the What-If, which is why it's the one everyone else is talking about in the thread.

[kytau]

I am really starting to think that there is a connection between the comic from a couple weeks back "The Source" and the lack of What if? updates. While I realize that What if? updates have been sporadic for a while now, it has now been a particularly long time since an update, and "The Source" would serve as a pretty clean metaphor for this project. Randall might have gotten annoyed at all the noise generated by What If? and pulled the plug. The timing of that comic certainly seems right to support this.

I guess we will see if this is the last What If? forever.

[GrumpyCatFace]

When exactly would we find out? We might check the website a few seconds before the end of Time, but we'd have to hypothesize that we were correct, and it wasn't updated in the last few microseconds...
Truth is, that we will never know until Randall updates us or dies. Therefore, to break the suspense, we must kill him. WHO'S WITH ME?

[The Moomin]

When exactly would we find out? We might check the website a few seconds before the end of Time, but we'd have to hypothesize that we were correct, and it wasn't updated in the last few microseconds...
Truth is, that we will never know until Randall updates us or dies. Therefore, to break the suspense, we must kill him. WHO'S WITH ME?

What if . . . we killed Randall to definitively answer whether there would or would not be further What If? posts?

[Keyman]

Seems drastic to me. I note the publication and book tour associated with his Thing Explainer. A book which he only got to do because of the success of the "WhatIf?" book.

Seems to me, all we need to do is kill the publisher.

[Flumble]

When exactly would we find out? We might check the website a few seconds before the end of Time, but we'd have to hypothesize that we were correct, and it wasn't updated in the last few microseconds...
Truth is, that we will never know until Randall updates us or dies. Therefore, to break the suspense, we must kill him. WHO'S WITH ME?

What if . . . we killed Randall to definitively answer whether there would or would not be further What If? posts?

I would fire Randall at a black hole just to spite those who want that question answered.
Too bad I don't have enough firepower, so you'll only have to wait 0.5 (adjusted for inflation) lifetime for the definitive answer.

[ijuin]

Killing him would ensure that the answer to "Will there be more What Ifs?" is "no". Therefore, if we want there to continue to be any remaining chance of a "yes", then we will have to keep him alive.

[KittenKaboodle]

Killing him would ensure that the answer to "Will there be more What Ifs?" is "no". Therefore, if we want there to continue to be any remaining chance of a "yes", then we will have to keep him alive.

The first part of that is not true at all, lots of things have been published posthumously. Anyway, the original idea was to remove uncertainty, I think that for practical purposes that could be accomplished by simply wiping out all life on earth. Well, sure, since Randal knows people at NASA there could hypothetically be a "What If" in the memory of one of the probes headed out of the solar system, but really, anything that may happen across such data sometime in the future is not likely to be currently concerned about there being another "What If".

Fortunately, Randal has given us several methods by which we can end this state of uncertainty