I had a good laugh when I read on Quora this brilliant answer by Jay Cashen, and just had to share! The question, of course, being what happens to all our missing socks…
What happens to all our missing socks?
Washers spin clothes at high revs. That generates high centripetal acceleration which an instrument in the washer would experience as indistinguishable from a very strong gravitational field (Principle of Equivalence).
Einstein’s General Relativity (GR) tells us that spacetime is warped or curved in such a region.
Now the radial field in the washer has unusual properties vs a normal gravitational field due to a large mass like the sun or white dwarf, neutron star, etc:
Although it is causally connected to ‘asymptotically flat spacetime’, and thereby satisfies an important requirement of the Singularity Theorem (Hawking and Penrose), for black hole formation, the real reason you don’t disappear down a massive gravitational well, along with the house, neighborhood, and ultimately, the Earth, is the actual geometry of the field produced:
When we have a collapsing stellar core or similar, and we move away from it (if our velocity is great enough to do so), gravity decreases as the square of the distance from the barycenter. As we move away from R to 10R from the center, gravity would be reduced by a factor of 100.
But the radial field in a washer is increased by a factor of 10 for the same motion from R to 10R away from the center. That field is a thousand times stronger than we would expect for a normal gravitational field produced by a compact mass at the center if we move out to 10R, though they produce the same acceleration at R.
Luckily, the field stops abruptly beyond the actual drum. Otherwise, housework would be even more dangerous than supposed. As Phyllis Diller warned, housework might not kill you, but why take the chance? Most people I know, apart from teenagers, are a bit blase about this and think that washers are completely harmless. If socks can disappear, and not big stuff like duvet covers, surely we are safe, they say, no matter how hard I try to explain the math of generating a stronger field than the Sun (which has a mass of 2 x 10^30kg) in a hundred-kilo machine (about my mass).
About traversable wormholes
I am sure you have read about traversable wormholes and how they would revolutionize space travel, and even visiting granny if she is more than a short walk away. One vital ingredient of a traversable wormhole is that it must be held open by a negative gravitational gradient, otherwise, the wormhole would collapse upon itself, and kill anyone traversing it at the time.
Most scientists conclude that negative energy is required to do this, because the stress-energy tensor associated with any positive energy will always result in an attractive force, which will collapse the wormhole upon itself, like a runaway collapse inside the Schwarzschild radius of a black hole.
Negative energy would produce a radial repulsive field, that still decreases as the square of the distance, like all such gravitational fields. And G, the Universal Gravitational Constant, is very small, so it takes a huge mass to create a small distortion in spacetime that we experience as the acceleration due to gravity.
But spinning a drum creates a radial repulsive field as required, and it increases as the distance until the max radius, that of the drum itself, is reached. If ever there was a better candidate for holding open a traversable wormhole, it hasn’t been found yet. All others require humongous masses/negative energy. Regarding the latter, the Casimir effect, with forces and energy so tiny they are hard to measure, just won’t do.
How practical is that wormhole?
One thing nobody tells you about traversable wormholes is that, for them to be practical, the ends must be at the same gravitational potential. Otherwise, if you stepped into a 10-meter wormhole opening on the Moon, you’d arrive a tiny fraction of a second out of the end of the wormhole on Earth, having been accelerated by the gradient(dV/dR, where R is in the order of 10 meters, so the equivalent acceleration is approx 1,374.000 g to a velocity of 11 kilometers per second. This is the equivalent of stepping off a 13740km cliff(2R for the Earth) and accelerating downward at a constant 1 g. The explosion at this end, releasing (mv^2)/2 = 6 x 10^9 Jules for a hundred-kilo astronaut (+gear) would be approx 15 times bigger than if the astronaut was replaced by a hundred kilos of TNT(4 x 10^8 Joules). The equivalent of 1.5 tons of TNT would really get your attention. And what if a really fat person with a pile of luggage arrived?
And trying to go up to the Moon through this end of the wormhole, would be pushing against this 1.37 million G plus repulsion. You would have to fire a shell from a railgun at 11km/sec(approx Earth escape velocity), into this end of the wormhole, for it to just about arrive and plop harmlessly out of the wormhole onto the floor on the Moon. If you miscalculated, and it didn’t have enough energy to reach the Moon, it would fall back down (Conservation of energy, PE back to KE) and cause a 6 x 10^7 Joule explosion for a one-kilo projectile arriving back at this end. Of course, if there was any air in the room where the Moon end of the wormhole was open, it would be sucked into the wormhole by the massive gradient, and exhaust at super high velocity at this end.
How to safely traverse a wormhole
Some obvious conditions for safely traversable wormholes we might accidentally make here on Earth:
- They have the same gravitational potential for two-way travel. One way from higher to lower, but the difference in potential energy which turns into kinetic energy, can’t be too great. So the entrance and exit couldn’t give you an easy way to climb Everest, or even visit Granny in Kansas if you lived near the coast. Socks will migrate from washers on higher floors to washers on lower floors in skyscrapers. You might think that going from the equator to the north pole would be like falling off a 20km cliff, due to the difference in the equatorial and polar radii. Not true. Issac Newton correctly predicted in the sixteen hundreds that the material of the Earth would try to form what we now call an equipotential surface. So that wouldn’t be the trouble at all, just deviations because of local topography and the wickedness of high rise construction. Angular momentum is where it is at.
- They have the same angular velocity, so you conserve angular momentum. This would mean you’d have to visit people near the same line of latitude, or near the corresponding line of latitude south of the equator.
- And then we have to match the spin angular velocity of the washer drum(to conserve angular momentum), taking into account the axis of spin which must be aligned for a match.
- And then we have to approximately match the actual linear velocity at the instant of leaving one washer drum and entering the other to avoid dangerous sock impacts.
So traversable washer wormholes that are not actually dangerous as a soggy sock appears from the Himalayas, or a pair of gold shorts from Trump’s penthouse, have to obey rules… namely the laws of physics.
Any washers out there?
So are there any washers that obey these conditions vis a vis your washer? Quite a lot actually. Haven’t you ever noticed an extra sock that you never saw before? One that you or your loved ones would never buy in a million years (Justin Bieber smile or something like that)? Just look around. The culprit could be nearby, at the same level or somewhat higher (but not high enough to be catastrophic), and with a similar spin machine that is aligned with yours. And, if exactly the same level, they could have one or more of your socks(which they might think are bad taste, and might be looking for the culprit. Notice the beautiful symmetry that we often find in laws of physics).
Q: Explain how duvet covers or other large stuff never gets transported, only socks and undies.
A: Simple: the field is maximum at max radius. It requires an equipotential surface inside the drum. It must match up with a properly aligned drum in another washer that fulfills the conditions above. This precludes anything bulky enough to have a non-negligible variation in R.
PS. For an alternative theory, read Beetley Pete’s blog: socks are alive!