On Gravity, Charge And Geese

A beautiful April day, far too nice to be inside working.  I’m on a brisk walk toward the lake when I hear puffing behind me.  “Hey, Moire, I got questions!”

“Of course you do, Mr Feder.  Ask away while we hike over to watch the geese.”

“Sure, but slow down , will ya?  I been reading this guy’s blog and he says some things I wanna check on.”

I know better but I ask anyhow.  “Like what?”

“Like maybe the planets have different electrical charges  so if we sent an astronaut they’d get killed by a ginormous lightning flash.”

“That’s unlikely for so many reasons, Mr Feder.  First, it’d be almost impossible for the Solar System to get built that way.  Next, it couldn’t stay that way if it had been.  Third, we know it’s not that way now.”

“One at a time.”

“OK.  We’re pretty sure that the Solar System started as a kink in a whirling cloud of galactic dust.  Gravity spanning the kink pulled that cloud into a swirling disk, then the swirls condensed to form planets.  Suppose dust particles in one of those swirls, for whatever reason, all had the same unbalanced electrical charge.”

“Right, and they came together because of gravity like you say.”

I pull Old Reliable from its holster.  “Think about just two particles, attracted to each other by gravity but repelled by their static charge.  Let’s see which force would win.  Typical interstellar dust particles run about 100 nanometers across.  We’re thinking planets so our particles are silicate.  Old Reliable says they’d weigh about 2×1018 kg each, so the force of gravity pulling them together would be …  oh, wait, that’d depend on how far apart they are.  But so would the electrostatic force, so let’s keep going.  How much charge do you want to put on each particle?”

“The minimum, one electron’s worth.”

“Loading the dice for gravity, aren’t you?  Only one extra electron per, umm, 22 million silicon atoms.    OK, one electron it is …  Take a look at Old Reliable’s calculation. Those two electrons push their dust grains apart almost a quintillion times more strongly than gravity pulls them together.  And the distance makes no difference — close together or far apart, push wins.  You can’t use gravity to build a planet from charged particles.”

“Wait, Moire, couldn’t something else push those guys together — magnetic fields, say, or a shock wave?”

“Sure, which is why I said almost impossible.  Now for the second reason the astronaut won’t get lightning-shocked — the solar wind.  It’s been with us since the Sun lit up and it’s loaded with both positive- and negative-charged particles.  Suppose Venus, for instance, had been dealt more than its share of electrons back in the day.  Its net-negative charge would attract the wind’s protons and alpha particles to neutralize the charge imbalance.  By the same physics, a net-positive planet would attract electrons.  After a billion years of that, no problem.”

“All right, what’s the third reason?”

“Simple.  We’ve already sent out orbiters to all the planets.  Descent vehicles have made physical contact with many of them.  No lightning flashes, no fried electronics.  Blows my mind that our Cassini mission to Saturn did seven years of science there after a six-year flight, and everything worked perfectly with no side-trips to the shop.  Our astronauts can skip worrying about high-voltage landings.”

“Hey, I just noticed something.  Those F formulas look the same.”  He picks up a stick and starts scribbling on the dirt in front of us.  “You could add them up like F=(Gm1m2+k0q1q2)/r2.  See how the two pieces can trade off if you take away some mass but add back some charge?  How do we know we’ve got the mass-mass pull right and not mixed in with some charge-charge push?”

“Good question.  If protons were more positive than electrons, electrostatic repulsion would always be proportional to mass.  We couldn’t separate that force from gravity.  Physicists have separately measured electron and proton charge.  They’re equal (except for sign) to 10 decimal places.  Unfortunately, we’d need another 25 digits of accuracy before we could test your hypothesis.”

“Aw, look, the geese got babies.”

“The small ones are ducks, Mr Feder.”

~~ Rich Olcott

Sir Isaac, The Atom And The Whirlpool

Newton definitely didn’t see that one coming.  He has an excuse, though.  No-one in in the 17th Century even realized that electricity is a thing, much less that the electrostatic force follows the same inverse-square law that gravity does. So there’s no way poor Isaac would have come up with quantum mechanics.

Lemme ‘splain.  Suppose you have a mathematical model that’s good at predicting some things, like exactly where Jupiter will be next week.  But if the model predicts an infinite value under some circumstances, that tells you it’s time to look for a new model for those particular circumstances.

For example, Newton’s Law of Gravity says that the force between two objects is proportional to 1/r2, where r is the distance between their centers of mass.  The Law does a marvelous job with stars and satellites but does the infinity thing when r approaches zero.  In prior posts I’ve described some physics models that supercede Newton’s gravity law at close distances.

Electrical forces are same song second verse with a coda.  They follow the 1/r2 law, so they also have those infinity singularities.  According to the force law, an electron (the ultimate “particle” of negative charge) that approaches another electron would feel a repulsion that rises to infinity.  The coda is that as an electron approaches a positive atomic nucleus it would feel an attraction that rises to infinity.  Nature abhors infinities, so something else, some new physics, must come into play.

I put that word “particle” in quotes because common as the electron-is-a-particle notion is, it leads us astray.  We tend to think of the electron as this teeny little billiard-ballish thing, but it’s not like that at all.  It’s also not a wave, although it sometimes acts like one.  “Wavicle” is just  a weasel-word.  It’s far better to think of the electron as just a little traveling parcel of energy.  Photons, too, and all those other denizens of the sub-atomic zoo.

An electron can’t crumble or leak mass or deform to merge the way that sizable objects can.  What it does is smear. Quantum mechanics is all about the smear.  Much more about that in later posts.

If Newton loved anything (and that question has been discussed at length), he loved an argument.  His battle with Liebniz is legendary.  He even fought with Descartes, who was a decade dead when Newton entered Cambridge.

Descartes had grabbed “Nature abhors a vacuum” from Aristotle and never let it go.  He insisted that the Universe must be filled with some sort of water-like fluid.  He know the planets went round the Sun despite the fluid getting in the way, so he reasoned they moved as they did because of the fluid.

Surely you once played with toy boats in the bathtub.  You may have noticed that when you pulled your arm quickly through the water little whirlpools followed your arm.  If a whirlpool encountered a very small boat, the boat might get caught in it and move in the same direction.  Descartes held that the Solar System worked like that, with the Sun as your arm and the planets caught in Sun-stirred vortices within that watery fluid.

Newton knew that couldn’t be right.  The planets don’t run behind the Sun, they share the same plane.  Furthermore, comets orbit in from all directions.  Crucially, Descartes’ theory conflicted with his own and that settled the matter for Newton.  Much of Principia‘s “Book II” is about motions of and through fluid media.  He laid out there what a trajectory would look like under a variety of conditions.  As you’d expect, none of the paths do what planets, moons and comets do.

From Newton’s point of view, the only use for Book II was to demolish Descartes.  For us in later generations, though, he’d invented the science of hydrodynamics.

Which was a good thing so long as you don’t go too far upstream towards the center of the whirlpool.  As you might expect (or I wouldn’t even be writing this section), Book II is littered with 1/rn formulas that go BLOOIE when the distances get short.  What happens near the center?  That’s where the new physics of turbulence kicks in.

~~ Rich Olcott