Q: Can planes (sheets) be tied in knots in higher dimensions the way lines (strings) can be tied in knots in 3 dimensions?

Physicist: Yes!

And just to be clear, we're not talking about this. This is cheating.

Just to be clear, we’re not talking about this. This is cheating.

Mathematicians are pretty good at talking about things in spaces with any number of dimensions.  Sometimes that math is fairly easy and even intuitive.  For example, a line has 2 sides (ends), a square has 4 sides, a cube has 6 sides, and a hypercube has __* sides.

Ordinary knots (that you can tie with string) can only exist in exactly 3 dimensions.  It’s impossible to create a knot in 2D since every knot involves some amount of “over-and-under-ing” and in 2D space there’s none of that.  Because it makes the math more robust, mathematicians always talk about knots being tied in closed loops rather than on a bight.  In part because once you’ve connected the ends of your string the knot you’ve got is the knot you’ve got, and that invariance is very attractive to math folk.

In order to tie even the simplest knot (left) you need to

Left: In two dimensions, no matter how complicated and convoluted your string is it can never be tied in a knot.   Right: Even the simplest knot requires at least three over-under excursions into three dimensional space to get around self-intersections.

In 2D, if you have a dot inside of a circle, it’s stuck.  But if you have access to another dimension (“dimension” basically means “direction”), then you can get the dot out.  In exactly the same way, if you can “lift” part of a regular knot into a fourth dimension it’s like opening the loop and you’re free to untie your knot in the same way you’d untangle/untie anything.  Afterwards you just “lower” the segment of the string back so that it all sits in 3D and now you’ve just got a loop of unknotted string (very creatively, this is called an “unknot”).  So, you’ve managed to untied your knot without worrying about self-intersections and all it took was an extra dimension.

In 2D a dot can be stuck inside of a circle, but if we have the option to "lift"

In 2D a dot can be stuck inside of a circle, but if we have the option to “lift” part of the circle in a new direction then the dot can get out.  From the perspective of the flat denizens of 2D space, this looks like part of the circle being removed.

All that was just to say: be excited, the way you tie your shoes is only possible in universes similar to (with the same number of dimensions as) our own.  You can’t tie a knot in a string in two dimensions and a knotted string in four (or more) isn’t really knotted at all.

The way we talk about ordinary knots is in the context of a loop (tie your knot and then splice the loose ends of the string).  The generalization of a loop (a 1-sphere) to higher dimensions is first the surface of a regular sphere (a 2-sphere), then the surface of a hyper-sphere (a 3-sphere) and so on.  An N-sphere can be tied in a knot in N+2 dimensional space.

An N-sphere can be tied in knots in N+2 dimensions. 1-spheres can be tied in knots in three dimensions (they're call)

An N-sphere can be tied in knots in N+2 dimensions. 1-spheres can be tied in knots in three dimensions (these are known colloquially as “knots”), which means that they can actually be created.  2-spheres (the surface of a ball) can be tied in knots in four dimensions.  The image here is only a cross-section of such a knot.

It turns out that if you have an ordinary knot, you can use it to create a higher dimensional knot.  There are a several ways to do this.  There’s “suspension“, which usually doesn’t work (the created knot is often not a “manifold“, which is kinda cheating), and there’s also “spinning” which always works.

The basic idea behind spun knots. As the line moves it sweeps out a surface.

The basic idea behind spun knots.

To create a “spun knot” you rotate it in a higher dimensional space and collect all of the points that it sweeps through.  The picture above is more symbolic than applicable.  In this picture a knot in 3D is spun to create a sphere that’s still in 3D space, but with a funky-shaped tube running around its equator.  That’s not a knot (knot at all).  This process needs to be done in four dimensions, where the added direction allows you to get around the self-intersection problem, but the basic idea is the same.  So for every knot that you can tie with a loop of rope in 3D, there’s a knot you can tie with a hollow sphere in 4D.

And yes: you can keep going into higher and higher dimensions using the same idea.

While you can’t directly picture a four dimensional knot, you can create cross-sections (the same way a 2-dimensional being might picture 3-dimensional objects using cross-sections).  This video (~0.4MB) shows 3D cross-sections of a rotating 4D knot.  But be warned: that video is, for lack of a better word, groovy.

Sometimes a group of scientists will get really involved with a particular subject and kinda disappear up their collective butts for a while (especially mathematicians).  Eventually one of them will emerge like a prairie dog and bark “fellow dudes and dudesses, we should really send a message to the world so they don’t worry about us” at which point a summarizing paper such as this or this is written (about higher dimensional knots in this case), in an attempt to convey to a slightly broader audience what they’ve been doing.

And now to justify our existence!

Mathematicians after a long think.

The tied sheets painting is by Teun Hocks and is from here.

The 4D knot picture and the video are from here.

The spun knot picture was lifted remorselessly from the second paper mentioned earlier.


Posted in -- By the Physicist, Geometry, Math | 8 Comments

Gravity Waves!

Physicist: A few days ago we managed to detect gravity waves for the first time.  Gravity waves were predicted a century ago by Einstein as a consequence of his general theory of relativity.  This success isn’t too surprising from a theoretical stand point; if
your theories are already batting a thousand, then when they bowl yet another field
goal for a check mate no one is shocked.

What is amazing is not that gravity waves exist, but that we’ve managed to detect
them.  The effect is so unimaginably small that it can be overwhelmed by someone
stubbing their toe a mile away or filing their taxes wrong.  Gravity is literally
the geometry of spacetime: very particular, tiny increases and decreases in
distances and durations.  There’s a fairly standard technique for doing this: light
is bounced back and forth along two separate paths between mirrors (in this case the
length of those two paths are each 4km) dozens of times.  The light from these two
paths is then brought together and allowed to interfere.  If the difference in the
length of the two paths changes by half a wave length, then instead of destructive
interference we see constructive interference.  The actual path difference is
substantially less than half a wave length, but it’s still detectable.

LIGO is b

A gravity wave detector is a device that very, very carefully measures the difference between the lengths of two long paths.  (Left) The tiny difference is detected by looking at the interference between lasers that travel along each path.  (Right) What the detector in Livingston, LA looks like from above.

When a gravity wave ripples through the Earth, the lengths of the two paths change
by about one part in 1021 which is a tiny fraction of the width of a proton over 4 km.  Keep in mind that the light that’s doing the measuring is bouncing off of mirrors that are made of atoms (each of which is much bigger than a proton) and that those atoms are constantly jiggling, because that’s what any level of heat does to matter.  This level of precision is the most impressive part of this whole accomplishment.  Your heart beat is currently throwing around the building you’re in by a lot more than a proton’s width.  And yet, despite the fact that the literally everything in the world is a source of experiment-ruining noise, LIGO is able to filter all of it out and then go on to detect the ridiculously faint signal of a couple of black holes a fair fraction of the universe away and even sort out details of the event.

The signal that we’re hearing about now was actually detected in September.  The cause appears to be the merging of two black holes about 1.3 billion lightyears away (which puts the source well outside of our backyard).  These black holes started with masses of around 36 and 29 times the mass of the Sun and after combining left a black hole with a combined mass of about 62 Sun-masses.  Astute second graders will observe that 36+29>62.  This is because gravity waves carry energy.  In this case the final event turned about 3 Sun’s worth of energy into ripples in spacetime that are “loud” enough to literally (albeit very, very slightly) rattle everything in the universe.  So, if we ever contact aliens from the other side of the universe and they also have nerds, then we’ll have something to talk about.  By the way, this signal (unlike so many in physics) has a frequency well within the range of human hearing.  Properly cleaned up, it sounds like this.

(Top) The signal as detected at the two observatories. The noise is bad enough that without at least two observatories it would be much more difficult to see it. (Middle) The signal as predicted by our understanding of general relativity. (Bottom) The remaining noise after the signal has been subtracted. Notice that it is now fairly constant. (Picture on the bottom) This is a plot of the strength of the signal using color vs. frequency on the vertical axis and time on the horizontal axis.

(Top) The signal as detected at the two observatories. The noise is bad enough that without at least two observatories it would be much more difficult to see it.
(Middle) The signal as predicted by our understanding of general relativity. (Bottom) The remaining noise after the signal has been subtracted. Notice that it is now fairly constant.
(Picture on the bottom) This is a plot of the strength of the signal using color vs. frequency on the vertical axis and time on the horizontal axis.

This is the first direct measurement of gravity waves, but it isn’t the first evidence we’ve seen.  If you have two really heavy masses in orbit around each other, you’ll find that they’ll slowly spiral together.  This is strange because it implies that the masses are losing energy.  But to what?  We first measured this effect with pulsars, which are a kind of neutron star (the next densest things after black holes).  Pulsars are so named because they produce radio pulses that are extremely regular.  You can think of them as giant space clocks.  They’re precise enough that they allow us to figure out exactly how they’re moving using doppler shifts, and they’ve shown that closely orbiting pairs lose energy in exactly the way we’d expect based on our theoretical understanding of gravity waves.

So what can we use this for?  So far we’ve been able to “hear” black holes merging (several more times since September).  We’re not only detecting the spiraling in, but also the process of the black holes coalescing.  Once they come in contact they briefly form an unshelled-peanut-shaped black hole before assuming a spherical shape.  This process is called the “ring down” and it also creates audible gravity waves that give us information about the behavior of black holes.  But beyond heavy things in tight orbits and ringing black holes, what will we hear?  Short answer: who knows.  If you go out in the woods you’ll hear trees falling over when no one is around and lots of bears shitting, but there’s no telling what else you’ll hear.  The only way to find out is to go out and listen.  As our gravity wave detectors get better and more plentiful we’ll be able to hear fainter and fainter signals.  We can expect to hear lots of black holes merging; not because it’s common, but because it’s loud and the universe is big.  Soon we’ll start hearing things we don’t expect and that’s when the science happens.  It’s nice to have our theories regarding gravity waves proven right, but being right isn’t the point of science.  As long as you’re right, you’re not learning.  It’s all the things we don’t expect that will be the most exciting.

Gravity wave astronomy is only the third way we have of observing the distant universe: light, neutrinos, and now gravity waves.  We didn’t know what we’d find with the first two and it’s fair to say we don’t know what we’ll learn now.  Exciting times.

You can read the paper that announced the achievement here.  And check out the author list: there was more collaboration on this than a Wu Tang album.

Update (6/20/2016): And again!

Posted in -- By the Physicist, Experiments, Physics | 10 Comments

Q: Is it possible to parachute to Earth from orbit?

Physicist: Yes and no, but mostly no.

It’s certainly possible to parachute safely to Earth from the top (or nearly the top) of the atmosphere, but this question isn’t about parachuting from space it’s about parachuting from orbit.  An orbit isn’t just a matter of being very high, it’s mostly a matter of being very, very fast.

Newton tried to explain orbits in terms of a progressively more and more powerful cannon.

Newton tried to explain orbits in terms of a progressively more and more powerful cannon.

When you throw something it follows a curved path that eventually intersects the surface of the Earth (technically this is already an orbit, it just gets interrupted by stuff in the way).  If you use a cannon, then the curve straightens out a bit but it still intersects the surface of the Earth, just farther away.  With a really, really powerful cannon (or more likely: a rocket) you can get something moving so fast that the curve of its fall matches the curve of the Earth.  When this happens the object is in orbit; a closed loop around the Earth that repeats forever.

You may have noticed that the Earth isn’t terribly curved, so it may seem that you’d need to be moving impossibly fast to follow it.  That’s exactly the case: above the air but near the surface of the Earth you’d need to be moving sideways at about 8km/s.  This is more than 23 times faster than the speed of sound.  Not slow.

A) An astronaut in low Earth orbit, who will stay there.
B) A stationary astronaut at the same height, who will be on the ground (impact on the ground) in half an hour or so.

This 8 km/s speed corresponds to the slowest, lowest orbit.  Any other orbit either won’t bring you close to the atmosphere or will do so faster (at up to about 11 km/s).  Being the slowest and lowest, these roughly circular “near Earth orbits” are very popular (that is to say: cheap).  Near Earth orbit is probably what you’re imagining when you think of parachuting to the Earth.

Orbits at different heights. In low Earth orbit are the International Space Station, the Hubble space telescope, and most communication satellites.

Orbits at different heights. In low Earth orbit are the International Space Station, the Hubble space telescope, and most communication satellites.

So here comes the point.  You can go as fast as you want if you’re doing it in space, but when you’re measuring your speed in km per second, air starts to feel like concrete (hot concrete).

The effects of air on something designed to handle it. A bag of meat (a person) would fare worse.

The effect of air on a “heat shield” designed to handle it (the bottom of the Apollo 11 crew capsule).  A bag of meat (like a person in a spacesuit) would fare worse.

When an object plows through air at very high speeds it tends to burn, shatter, and shred.  Parachutes are used for most entries and reentries, but not initially; most of the deceleration from orbit is handled by heat shields, which are a cross between parachutes and bricks (or a brick and another kind of brick).  Once enough of a falling object’s speed has been shed by a heat shield (typically slower than sound, but up to a few times faster), it is then safe to deploy an actual parachute.

If you were to jump (fast) out of the International Space Station with the aim of entering the atmosphere and deploying your chute, you’d find it filled in short order then torn to ribbons shortly after.  Like any falling star, you’d find yourself hot, dead, and profoundly luminous.  Like icy meteors, you’d probably flash into steam and air burst before reaching the ground.

The reason you can’t parachute from orbit is simply a matter of engineering.  We haven’t yet created parachutes that can survive being deployed, and then work properly, at speeds above around mach 2.  At reentry speeds, which are in excess of mach 23, parachutes just can’t hold up.  However, someday it may be possible.  We know that the accelerations involved are survivable, and there don’t seem to be any fundamental limitations, we just need better materials and techniques.  Also, for at least a little while, a spacesuit capable of reentry on its own (before the parachute has had a change to slow it) would be nice.

Merely falling from space is probably pretty easy.  The highest jump so far was from 24 miles up.  A jump from space is a mere four times higher.  You’d need a rocket instead of a balloon, but aside from being a silly thing to do, there’s nothing stopping someone from doing it.

Posted in -- By the Physicist, Engineering, Physics | 8 Comments

Q: Why can’t we see the lunar landers from the Apollo missions with the Hubble (or any other) telescope?

Physicist: About why you’d expect: they’re just too damn small and too damn far away.  Nothing fancy.  That’s not to say that we can never get images, just that you need to be a lot closer.  The lunar landers are each about 4 meters across and about 384,400,000 meters away, which makes them about as hard to see as a single coin from a thousand miles away.  You gotta squint.

A picture of the Apollo 17 landing site taken by the Lunar Reconnaissance Orbiter which, as the name implies, was in orbit around the Moon when it took these rec

A picture of the Apollo 17 landing site taken by the Lunar Reconnaissance Orbiter which, as the name implies, was in orbit around the Moon when it took this presumably reconnaissance-related picture.  Those meandering lines are tracks left by a lunar rover.  Click to enlarge.

In fact, a big part of why we (humans) bother to go to the Moon, other planets, and space in general is that photographs from Earth leave a lot to be desired.  In addition to being far from everything else, here on the surface of Earth we’re stuck at the bottom of an ever-moving sea of air.  In exactly the same way that the surface of water scatters light, air makes it difficult for astronomers to practice their dread craft.

Also, not for nothing, telescopes are terrible at retrieving material samples.

The Apollo 17 landing site from even closer.

The Apollo 17 landing site from even closer.

You and every telescope on Earth (and the Hubble Telescope in low Earth orbit) are all about a quarter million miles from the Moon and the landing sites thereon.  If we ever get around to building something bigger on the Moon, like mines or cities or president’s heads, then we shouldn’t have nearly as much trouble seeing it from Earth.

Answer Gravy: It turns out that the best/biggest telescopes we use today on Earth are can’t detect things the size and distance of the lunar landers using visible light.  This isn’t due to poor design; the devices we’re using now are, in a word, perfect.  They literally cannot be made appreciably better (at detecting visible light).  The roadblock is more fundamental.

The “resolving power” of a telescope, is described in terms of whether or not you can tell the difference between a pair of adjacent points.  If the two points are too close together, then you’ll see them blurred together as one point and they are “not resolved”.  If they’re far enough apart, then you see both points independently.

Whether it uses mirrors or lenses, the resolving power of every telescope is limited by some fundamental constraints determined by the wavelength of the light that’s being observed and by the size of the aperture.

Every point in every image is surrounded by a rapidly diminishing Airy disk.

Every point in every image is surrounded by a rapidly diminishing “Airy disk” which are a symptom of light being wave-like.  This is only a problem really close to the diffraction limit.  You don’t see these when you take a picture on a regular camera because these rings are smaller than the individual pixels in the camera’s CCD (by design).

Because light is a wave it experiences “diffraction” which makes it “ooze around corners” and generally end up going in the wrong directions.  But the larger a telescope’s opening, the more the light waves have a chance to interfere in such a way that they propagate in straight lines, which makes for cleaner images where the light ends up more-or-less where it’s supposed to be when it gets to the film or CCD or your retina or whatever.

It turns out that the relationship between the smallest resolvable angle, θ, the wavelength, λ, and the diameter, D, of the aperture is remarkably simple:

\theta \approx 1.2\frac{\lambda}{D}

Visible light has a wavelength of around 0.5 micrometers (about 2,000,000 per meter) and the largest visible-spectrum telescopes on Earth are about 10 meters across (Hubble is a more humble 2.4m across).  That means that the absolute best resolution that any of our telescopes can hope to achieve, under absolutely ideal circumstances, is about \theta \approx 1.22\frac{0.5\times10^{-6}}{10} \approx 0.00000006 rad.  Or, for the angle buffs out there, about 0.01 arcseconds.  This doesn’t take into account the scattering due to the atmosphere; we can do a little to combat that from the ground, but our techniques aren’t perfect.

By carefully looking at how the atmosphere distorts a beam shot upwards from the telescope, we can take into account how the atmosphere affects light coming into the telescope from above.

By carefully looking at how the atmosphere distorts a laser beam shot upwards from a telescope on the ground, we can take into account how the atmosphere affects light coming into the telescope from space.

The lunar landers are a little over 4 meters across (seen from above) and are about 384,403,000 meters away.  That means that the landers subtend an angle of about 0.002 arcseconds.  In order to see this from Earth, we’d need a telescope that is, at absolute minimum, about 200 meters across.  If we wanted the image to be a more than a single pixel, then we’d need a mirror that’s a few miles across.

So, don’t expect that anytime soon.

Posted in -- By the Physicist, Physics | 9 Comments

Q: How bad would it be if we accidentally made a black hole?

Physicist: Not too bad!  Any black hole that humanity might ever create is very unlikely to harm anyone who doesn’t try to eat it.

Black holes do two things that make them (potentially) dangerous: they eat and they pop.  For the black holes we might reasonably create on Earth, neither of these is a problem.

Home-grown black holes: not a serious concern.

Home-grown black holes: not a serious concern.

The recipe for black holes is literally the simplest recipe possible; it’s “get a bunch of stuff and put it somewhere”.  In practice, you need at least 3.8 Sun’s worth of stuff and the somewhere is anywhere smaller than a few dozen km across.  That last bit is important: the defining characteristic of black holes isn’t their mass, it’s their density.

The gravity through the outer Gaussian surface stays the same, since both contain the same amount of matter. The gravity through the inner Gaussian surface increases dramatically after the star collapses, because it contains all of the star's mass, instead of just a small part of it.

For a given amount of mass the same amount of gravity “flows” through every containing surface.  In this picture, the same total gravity points through both outer surfaces if they contain the same total mass.  But if all of the mass is concentrated in a tiny place (as it is on the right), then the gravity through the smaller surface must be stronger in order to equal the weaker gravity through the larger surface.  Fun fact: this can be used to derive the inverse square law of gravitation and/or is a consequence of it.

If you’re any given distance away from a conglomeration of matter, it doesn’t make much difference how that matter is arranged.  For example, if the Sun were to collapse into a black hole (it won’t), all of the planets would continue to orbit around it in exactly the same way (just colder).  The gravitational pull doesn’t start getting “black-hole-ish” until you’re well beyond where the surface of the Sun used to be.  Conversely, if the Sun were to swell up and become huge (it probably will), then all of the planets will continue to orbit it in exactly the same way (just hotter).

To create a new black hole here on Earth, we’d probably use a particle accelerator to slam particles together and (fingers crossed) get the density of energy and matter in one extremely small region high enough to collapse.  This is wildly unreasonable.  But even if we managed to pull it off, the resulting black hole wouldn’t suddenly start pulling things in any more than the original matter and energy did.

For comparison, if you were to collapse Mt. Everest into a black hole it would be no more than a few atoms across.  It’s gravity would be as strong as the gravity on Earth’s surface within around 10 meters.  If you stood right next to it you’d be in trouble, but you wouldn’t fall in if you gave it a wide berth.  In fact, that’s why mountain climbers aren’t particularly bothered by Everest’s mass; even if you’re literally standing on it, you can’t get within more than a few km of most of its mass (fundamentally, Mt. Everest is a big, spread out, pile of stuff).

But the amount of material used in particle accelerators (or any laboratory for that matter) is substantially less than the mass of Everest.  They’re “particle accelerators” after all, not “really-big-piles-of-stuff accelerators”.  The proton beams at the LHC have a mass of about 0.5 nanograms and when moving at full speed have a “relativistic mass” of about 4 micrograms (because they carry about 7500 times as much kinetic energy as mass).  4 micrograms doesn’t have a scary amount of gravity, and if you turn that into a black hole, it still doesn’t.  A black hole that small probably wouldn’t even be able to eat individual atoms.  “Probably” because we’ve never seen a black hole anywhere near that small.

The other thing that black holes do is “pop”.  Black holes emit Hawking radiation.  We haven’t measured it directly, but there a some good theoretical reasons to think that it’s a thing.  Paradoxically, the smaller a black hole is, the more it radiates.  “Natural” black holes in space (that are as massive as stars) radiate so little that they’re completely undetectable (hence the name: black hole).  The itty-bitty black holes we might create would radiate so fast that they’d be exploding (explosion = energy released fast).  The absolute worst case scenario at CERN (where all of the 115 billion protons in each of the at-most 2,808 groups moving at full speed are all piled up in the same tiny black hole) would be a “pop” with the energy of a few hundred sticks of dynamite.

That’s a good sized boom, but not world ending.  More to the point; this is exactly the same amount of energy that was put into the beams in the first place.  This boom isn’t the worst case scenario for black holes, it’s the worst case scenario for the LHC in general (cave-ins and eldritch horrors notwithstanding).  It is this “pop” that would make a tiny black hole a hazard.  The gravitational pull of a few micrograms of matter, regardless of how it is arranged, is never dangerous; you wouldn’t get pulled inside out if you ate it.  However, you wouldn’t get the chance, since any black hole that we could reasonably create would already be mid-explosion.

A black hole with a mass of a few million tons would blaze with Hawking radiation so brightly that you wouldn’t want it on the ground or even in low orbit.  It would be “stable” in that it wouldn’t just explode and disappear.  This is one method that science fiction authors use for powering their amazing fictional scientific devices.

The kind of black holes that we might imagine, that are cold (colder than the Sun at least), stable, and happily absorbing material, have a mass comparable to a continent at minimum.  Even then, it would be no more than a couple millimeters across.  These wouldn’t be popping or burning things with Hawking radiation.  The real danger of a black hole of this size isn’t the black hole itself, so much as the process of creating them (listen, I’m making a black hole, so I need to crush all of Australia into a singularity real quick).

We have no way, even in theory, to compress a mountain of material into a volume the size of a virus.  Nature compresses matter into black holes by parking a star on it.  That seems to be far and away the best option, so if we want to create black holes the “easiest” way may be to collect some stars and throw them in a pile.  But by the time you’re running around grabbing stars, you may as well just find an unclaimed black hole in space and take credit for it.

Posted in -- By the Physicist, Physics | 21 Comments

Q: What if gravity acted like magnetism?

Physicist: The problem with magnetism and the electric force is that they tend to cancel themselves out.  For example, if you have a positive charge the first thing it does is repel all the other positive charges around it and attract all the negative charges.  In short order you end up with a positive and negative charge right next to each other, pulling and pushing on every other charge with the same force (however much the positive charge pulls, the negative charge next to it pushes and vice versa).

(Top) Like charges repel and unlike charges attract. (Middle) A pair of opposite charges will tend to grab onto each other, but this pair pulls as much as it pushes on other nearby charges. (Bottom) The result is that effect of the charges cancels out and we're left with "electrically neutral" matter.

(Top) Like charges repel and unlike charges attract. (Middle) A pair of opposite charges will tend to grab onto each other, but this pair pulls as much as it pushes on other nearby charges. (Bottom) The result is that the effect of the charges cancels out and we’re left with “electrically neutral” matter.

Same thing with magnets, if you have two bar magnets floating around, they’ll try to line up with their north side next to the other magnet’s south side.

As a result these “positive/negative” forces tend to balance out really fast.  There are “dipole forces” (one charge might be a little closer, so it pulls just a skosh harder), but dipole forces are tiny and decrease much faster with distance (technically, all magnets are dipole).  In your body right now you have somewhere in the neighborhood of 1028 or 1029 (between ten and a hundred thousand trillion trillion) charged particles in the form of protons and electrons.  The number of extra, unbalanced charges on a good Van de Graff generator that’s dangerous to approach is less than a billionth of a billionth of that.


A slight imbalance of charge.  The ratio of positive to negative charges here is on the order of 1 to 1.0000000000000000001.

Point is; with magnets and charges you always have a problem with things canceling themselves out almost perfectly.  The strength of the electric force between (for example) two protons is just a hell of a lot stronger than the gravitational force (about 1,000,000,000,000,000,000,000,000,000,000,000,000 times bigger), but you’d never know it since those huge forces are all balanced and cancelled out by all of the negative charges around.

Gravity, on the other hand, has only one kind of “charge”: matter.  All matter attracts all matter, so despite being far and away the weakest force, gravity is basically the last man standing on large scales.  You might imagine that if gravity acted like magnetism there would be planets and stars pushing and pulling each other every which way, but in all likelihood we just wouldn’t have large structures in the universe like planets in the first place.

Posted in -- By the Physicist, Physics | 13 Comments