Q: How can wormholes be used for time travel?

Posted on December 7, 2011 by The Physicist

Physicist: A good way to think about a wormhole is as a single region of space.  That is, while the ends may be in two different locations, the wormhole itself is a single “piece of space”.

A wormhole, despite having ends in two very separated regions of space and/or time, is still a single chunk of spacetime. You can move the ends to any location or time you want; the inside stays the same.

So, even if you move the entrances far apart, the distance you travel from one side to the other always stays the same.  Similarly, even if you move the entrances far apart in time, the time it takes to get across them stays the same in very much the same way.

That shouldn’t make much sense (if it did, sober up), but here’s the idea:

The two ends of the wormhole will always be connected to each other such that they’re always connected at the “same age”.  So, if you enter one end 5 years after the creation of the wormhole, you’ll exit the other end 5 years after the creation of the wormhole, no matter where the ends are located.

Two clocks, separated by a little space, and ticking in sync as they move though time.

Two synced clocks on opposite sides of a room will stay synced up.  The nature of the space between them isn’t particularly important.  For example, if the space between them is, say, a wormhole instead of a sitting room, they’ll still stay synced up.

This has exciting potential for time-machine building.  If you can somehow get one side of the wormhole to experience more or less time, from an outside perspective, then, from that outside perspective, you’ll have a difference in ages between the ends of the wormhole.

If you can get the ends of the wormhole to move through time at different rates, then the ends will be different ages. Here, the clock and wormhole mouth on the left are allowed to move through time normally. The clock and wormhole mouth on the right are forced to experience less. Looking through the wormhole you find that the clocks are still synced, but from outside the wormhole, the left side is older, and the right side is younger.

Luckily, relativity (both special and general) gives us some tricks for slowing down the amount of time an object experiences.  Taking advantage of the twin paradox (special relativity), you can take one end of the wormhole and move it (never mind how) at very high speeds for a while.  When it’s brought back to rest, its clock will register less time than its stationary counterpart.  Alternatively, you can take advantage of gravitational time dilation (general relativity).  Time moves “slower the lower“.  So, if you park one end of the wormhole in orbit around a black hole or something else heavy, then it will also experience less time.

So, say you’ve created a wormhole.  Never mind how.  You take entrance B, attach it to a ship and fly it around at nearly the speed of light (doesn’t matter where), and then bring it back, while entrance A sits still.  While entrance B experiences 5 years (for example), entrance A experiences 5,000 years (for example).  Now you’ve got two entrances, but one is 5 years old and the other is 5,000.  Since they’re “connected at the same age”, stepping through the B entrance will take you back to the time when the A entrance was 5 years old, which was 4,995 years ago.  Similarly, stepping through the A entrance would take you to the time when the B entrance is 5,000 years old, 4,995 years in the future (assuming there’s no further wormhole moving).  In the picture above A is on the left and B is on the right.

As for how exactly the mechanics of time travel works, what with grandfather paradoxes and what not, I couldn’t say.  That’s more of an “ask a sci-fi writer” sort of thing.

The methods used to create, stabilize, and move wormholes generally involve some pretty abstract (“abstract” = “impossible”) math and physics.  General relativity, among other things, gives us a way of relating the curvature of space to the distribution of matter and energy in that space.  So, for example, you can figure out how the presence of a star’s worth of mass will affect the spacetime around that star.

Alternatively, you can back-solve.  You take the weird spacetime of a stable wormhole, do a mess of math to figure out how you’d need to arrange matter, and find that in general wormholes need a whole lot of negative energy and matter.  The drawbacks of negative matter, sometimes called “exotic matter”, are: 1) it’s very difficult to work with and 2) it doesn’t exist.

However, the tricks used to slow down time are legitimate science!  Here’s a fun home experiment: Find yourself a merry-go-round.  One of the big ones, with the horses and the brass band and whatnot.  The twin paradox applies to anything that makes a round trip.  So, every time you make a full turn you’ll have experienced about 0.4 femtoseconds (0.0000000000000004 seconds) less than everyone else.  That’s forward time travel!

Innocent fun, or nefarious time machine?

But be warned, you’ll be cursed to live in the future forever.  Never able to go back and warn people about the misfortunes of their extremely near futures.

Posted in -- By the Physicist, Physics, Relativity | 17 Comments

Q: If gravity suddenly increased would airplanes fall out of the sky, or would it compress the air in such a way that airplanes could keep flying?

Posted on December 3, 2011 by The Physicist

The original question was: “In Kurt Vonnegut’s “Slapstick” there is talk of Earth’s gravity randomly changing, causing planes to fall out of the sky. Since planes fly because of air pressure variance between the top and bottom of the wings, would an increase in gravity really make them fall? The weight of air would increase by the same relative amount as the weight of the plane.”

Most plausible-ish answer so far: If gravity suddenly increased, yes, planes would fall out of the sky. When a plane is maintaining a constant altitude, the force of gravity and the force of lift are equal. If gravity were suddenly increased, there would no longer be an equilibrium, and the plane would drop. The plane would have to pick up speed to increase the lift to match the new level of gravity. Although air pressure does affect lift (the less air pressure, the faster you have to go to get the same lift), in this case I think the increase in air pressure and the increase in the weight of the plane would cancel each other out.

Physicist: They kinda do cancel out!

So, once gravity has been turned up, and the atmosphere has had a chance to equilibrate at a higher pressure and density (and get squished shorter), planes will still be able to fly (in theory).  But if, for example, the gravity doubles, the planes will need to fly through double-density air to stay up (or fly about 41% faster).  But in so doing, they’d experience double the drag.

Unlike airplanes, dirigibles and hot air balloons would do just fine.

Lift, L, is given by \frac{1}{2} \rho v^2 A C_L, where \rho is the air density, v is the velocity, and A and CL are constants that depend on the air craft.  When a plane is flying it needs its Lift force to be greater than its weight.  You may notice that your computer (or phone, or tablet, or whatever) isn’t flying right now.  At best it’s falling.  That’s because its lift force is zero.

Drag, which affects planes, cars, sleighs, or anything else that moves through air is given by \frac{1}{2} \rho v^2 A C_D (this equation applies well to things that are faster than snails, but slower than sound).

That being said, clearly planes can fly in air of different densities.  The difference in densities between “cruising altitude” and sea level is about a factor of 4.

The problem is that, generally, the Drag and the Lift are proportional.  You may have already noticed that the equations for Lift and Drag are practically the same: L=\frac{1}{2}\rho v^2AC_L and D=\frac{1}{2}\rho v^2AC_D.  CL and CD change a bit for different scenarios, but aside from that, for any particular aircraft, the equations are proportional.

So, if the gravity doubles, then the lift needs to double (because the plane weighs twice as much).  The plane can do this by flying faster, or flying through denser air.  But whichever method is used to double the lift, will also double the drag.  The long and the short of it is: if gravity increases by some amount, then the amount of power required to keep the aircraft aloft will increase by the same amount.  For example, 5 times gravity would require 5 times the power.

So while airplanes can fly in higher gravity, it may take more power than their engines can output to keep them in the air.

Posted in -- By the Physicist, Physics | 30 Comments

Entanglement omnibus!

Posted on November 29, 2011 by The Physicist

We’ve recently gotten several short questions about entanglement.  In keeping with other, better, “ask” services: entanglement omnibus!

Q: What is entanglement? (nobody asked this, but it’s a good place to start)

A: If you understand what correlation is, then you’re 90% of the way to understanding what entanglement is.  Say Alice and Bob each have a marble in a box.  For reasons beyond contemplation, Alice and Bob have always been perfectly happy with one Blue marble and one Red marble.  Neither of them knows which marble they have, but they both know that they have different colored marbles.  The moment either of them looks at their marble, no matter how far apart they are, they’ll suddenly know what color the other marble is (correlation!).

For each of them the marble they have is completely random.  The only time they notice anything interesting is if/when they meet up to compare results, and find that their results are always opposites.  This “opposite color marble” thing is just one form that correlation (entanglement) can take.  You could also set up a “same color marble” thing.

Entanglement is nearly the same as simple correlation.  The difference is that while regular correlation involves states that are merely unknown (the marbles are each a particular color, it’s just that nobody knows which is which), entanglement involves particles in multiple states.  “Quantum marbles” can be both red and blue, at the same time (when things are in more than one state at a time they’re said to be in a “superposition“), and yet be correlated with each other. That shouldn’t make much sense, so don’t stress.

There’s an older post that may help you build intuition a little.  In very much the same way that a single particle can be in multiple states (like a single particle going through both slits in the double slit experiment), two entangled particles are in two states together.  In the marble example the two quantum marbles are in a superposition of the two states “marble 1 blue, marble 2 red” and “marble 1 red, marble 2 blue”.

Because notation will be useful in a minute, here’s how you would notate a couple situations:

\begin{array}{cl}|R\rangle_1 & \textrm{first marble red}\\|R\rangle_1|B\rangle_2\quad or\quad |RB\rangle&\textrm{first marble red, second marble blue}\\|R\rangle_1 +|B\rangle_1 & \textrm{first marble in a superposition of red and blue}\\|RB\rangle+|BR\rangle&\textrm{the entanglement in the example above}\\|RR\rangle+|BB\rangle&\textrm{superposition of both red / both blue}\\|RR\rangle+|RB\rangle+|BR\rangle+|BB\rangle&\textrm{superposition of every combination (not entangled!)}\\\end{array}

Also, there are several ways to write states, depending on what you’re trying to say.  For example, |RR\rangle+|RB\rangle=|R\rangle_1|R\rangle_2+|R\rangle_1|B\rangle_2=|R\rangle_1(|R\rangle_2+|B\rangle_2).  The first form is a little cleaner/standard, but the last form makes it clear that the first marble is always red, while the second marble is in a superposition of red and blue.

 

Q: How are entangled particles created?

A: There are a lot of ways that particles can be entangled.  Almost any piece of information you can have about a particle is something you can entangle.  For example, the directions a pair of particles are moving in.

When things bounce off of each other, they bounce in opposite directions.  While particles can be in many places, and move in many directions at the same time, in this case they need to do it in opposite directions.

If you bounce a couple of particles off of each other, you won’t be able to say which direction either one bounces in, but you will be able to say that they’re bouncing in opposite directions.  Generally speaking, when a quantum physicist says “you can’t know which of these things the particle did” what they really mean is “the particle did each of those things at the same time”.  The particles are bouncing apart in a superposition of directions, but in a correlated way.  Entanglement!

If you have a method of generating particles in pairs, but at random times, then the particles so created will be entangled in terms of their creation times.  That is: you have two particles flying around, you don’t know when they were created, but you don know that they were created at the same time.  Their ages are entangled!

Another classic example; if you create an electron/positron pair (“positron” = “anti-electron”) they must have opposite spins.  This is guaranteed by the conservation of angular momentum; if nothing is rotating then the angular momentum is zero and if the particles are spinning in opposite directions then the angular momentum stays zero.

When an electron/positron pair is created they’re always spinning in opposite directions.  So, even though they each spin in a “superposition” of directions simultaneously, they do it in such a way that they’re always opposites.

So, you can have clockwise/counterclockwise, counterclockwise/clockwise, or (since you can have things in multiple states) a combination of both.  Or, saying the exact same thing using the notation in the picture above: |01\rangle, |10\rangle, or |01\rangle+|10\rangle.  Notice that the states |00\rangle and |11\rangle never show up, because they would involve the particles spinning in the same direction.

Notice, by the way, that it isn’t enough to talk about the states of each particle one at a time.  In order to describe things accurately requires us to talk about the “state of the system”.  In both of the examples above (and in any example involving entanglement) the particles involved are in multiple states, but knowing the states of each particle individually doesn’t tell the whole story.  Entangled particles share states with each other.  In the last example, there’s no way to express |01\rangle+|10\rangle in terms of just one particle and then the other.

In practice, photons are the easiest particles to work with.  They’ve got nice, big, easy-to-work-with wavelengths, they’re incredibly easy to create (in fact, try not to make photons), and they’re easy to entangle.

The most common method (used in fancy labs and whatnot) is to use a “parametric down conversion crystal“.  You fire a photon at the crystal, and for reasons best described as “stupid-complicated”, two photons of half the original frequency are spit out the other side.  These new photons are entangled such that their polarizations are the same (type 1 crystal) or opposite (type 2 crystal).

A little more abstract, if you can get a “quantum controlled not gate”, then you can induce an entanglement.  There are slightly more ways to create a controlled not gate than there are ways to create a quantum computer (many), but the idea is always the same.  A controlled not gate involves two bits: a Control bit and a Target bit.  If the control bit is 1, then the target bit is flipped, and if the control bit is 0, then the target bit is left alone, and if the control bit is in a superposition, then the target bit will likewise be in a superposition of flipped and not flipped.

Starting with a control bit in the state |0\rangle_c + |1\rangle_c (technically, a superposition of zero and one is called a “qbit“) and a target bit that’s in the state |0\rangle_t, you have the overall state: |0\rangle_c|0\rangle_t+|1\rangle_c|0\rangle_t.  The effect of the c-not gate is:

|0\rangle_c|0\rangle_t+|1\rangle_c|0\rangle_t\rightarrow |0\rangle_c|0\rangle_t+|1\rangle_c|1\rangle_t

which is entangled!  Before the c-not gate is applied the state of one bit tells you nothing about the state of the other, but afterward the state of each tells you everything about the other.  Those mothers are hella entangled.

 

Q: Can more than two particles be entangled?

A: Hells yes!  So far, the record for the largest number of “maximally entangled” particles is 14 (“Maximally entangled” means “perfect correlation”).  Entanglement can take a lot of forms, but one example state of perfect 14 particle entanglement would be something like: |00000000000000\rangle + |11111111111111\rangle.

 

Q: Could a home scientist hope to create entangled particles?

A: It depends…  I don’t think a home scientist could keep track of a single particle, let alone an entangled pair.  That being said, most interactions create entanglements, but not interesting/useful ones.  When air molecules bounce off of each other their motion becomes entangled, but really; who cares?  There’s a lot of air, and a lot of molecules bouncing off of each other and getting entangled, but none of it is useful or controlled.

So, you are entangling yourself with everything around you all the time, but that’s clearly not the spirit of the question.  The spirit of this question is (probably) about perfectly entangled, two-state systems.

If you really wanted to, you could buy a down conversion crystal, some lasers, some photo-detectors, and all the rest of the equipment necessary to do entanglement experiments.  It’s expensive.  However, there are some examples of “clean” entanglement (not just stuff randomly interacting) that you can find around the house.  Specifically: carbon rings.

Benzine (shown) is the simplest carbon ring.  Carbon rings  have two ways for bonds to arrange themselves, and in fact exist in a superposition of those two states.  The bonds are each entangled with each other: if you know whether one is a double or single bond, you know what each of the others are.

Carbon likes to have 4 bonds.  It also likes to form rings that are six atoms around, and even chains of those rings.  Many organic molecules are put together with pieces like this.  But when so arranged, each carbon is only bonded to three other atoms.  It gets a fourth bond by doubling one of those bonds.  But (check the picture above), this establishes an arrangement of double and single bonds all the way around the ring, so the single/doubleness of each bond is correlated to each of the others.  And, rather than being in just one arrangement or the other, carbon rings exist in a superposition of both.  Superposition of states with correlation?  Entanglement!  It’s not terribly exciting, but many of the atoms and bonds in your body are involved in some very clean, two-state entanglements.

So, technically you create maximally entangled particles by being alive and eating food, because they’re a part of a lot of the chemicals that we naturally produce.  But, of course there’s no way to verify that entanglement using just the sorts of things you’d find around the house.  So… I suppose you can just take comfort in the knowledge?

By the way, if you know a biochemist, ask them if they’ve ever had dreams about the sort of picture that’s in the image above.  Spoiler: They totally have.

 

Q: What is the speed of entanglement?

A: Faster than the speed of thought, but slower than the speed of love.

Entanglement is sometimes described as a “superluminal effect” (an effect that travels faster than the speed of light).  In fact, nothing is traveling at all, which is good because superluminal stuff causes a whole mess of problems.  In the first example, way back at the beginning of this post, when Alice looks at her marble she’ll immediately know what Bob’s marble is.  But that’s just correlation.  No signal is sent, no information can be carried.

On the other hand, if the marbles are entangled, then they’re each in a (correlated) superposition of states.  So when Alice looks at her marble and sees, for example, “Blue” then Bob is guaranteed to see “Red”.  Bob’s marble is no longer in a superposition of states, it’s in just one.  This is the effect that seems to be traveling: Alice turns Bob’s two-state marble into a lonely-one-state marble.

But even that effect is illusory.  Like freaking everything weird in quantum mechanics, you can resolve this with the Many Worlds Interpretation.  Basically, not only are the marbles in multiple states, but the people are too.  By interacting with the marbles Alice and Bob become entangled with them.  Using fancy notation (where “\phi” means “hasn’t looked yet”) the state of the entangled marbles and Alice and Bob is:

\begin{array}{ll}|\phi\rangle_{Alice}\left(|R\rangle_1|B\rangle_2+|B\rangle_1|R\rangle_2\right) |\phi\rangle_{Bob}\\=|\phi\rangle_{Alice}|R\rangle_1|B\rangle_2|\phi\rangle_{Bob}+|\phi\rangle_{Alice}|B\rangle_1|R\rangle_2 |\phi\rangle_{Bob}\end{array}

When Alice looks at marble 1, she will suddenly be entangled with her marble.  For example, the “Red” state becomes coupled with Alice’s “saw Red” state.  Likewise, Bob will become entangled with his marble when he interacts with (observes) it.

\begin{array}{ll}|\phi\rangle_{Alice}|R\rangle_1|B\rangle_2|\phi\rangle_{Bob}+|\phi\rangle_{Alice}|B\rangle_1|R\rangle_2 |\phi\rangle_{Bob}\\\rightarrow |saw \,Red\rangle_{Alice}|R\rangle_1|B\rangle_2|saw \,Blue\rangle_{Bob}+|saw \,Blue\rangle_{Alice}|B\rangle_1|R\rangle_2 |saw \,Red\rangle_{Bob}\\\end{array}

So, it’s not that some effect magically moves from one marble to the other, it’s just that the people involved “get caught up in the correlation”.  The state of “Alice sees Red” always coincides with the state “Bob sees Blue”, but no actual communication is necessary.  This weird transference of entanglement (where the entanglement between two particles causes other things to become entangled) is essentially how quantum teleportation works.  Also, and this is a subtle point, Alice and Bob have no way of noticing that they got the same result until they’ve at least had a chance to compare notes.  “Note comparing”, it’s worth noting, is always slower than light.

By the way, in very much the same way that correlation is boring and underwhelming, quantum teleportation is also pretty disappointing.  Nothing ever really gets teleported.  Total rip off.

 

Q: Is entanglement useful for anything?

A: Psh!  Yes!

Quantum computers are a total pain to get working, but if/when they do work, they’ll be able to do all kinds of things, like break encryption keys and simulate complex quantum mechanical systems, like protein folding.  Also (and this is the point) they require lots of entanglement.  So far, one of the big accomplishments of quantum computation is factoring the number 15.

It’s 5 times 3.

Today the killer app for entanglement is “quantum cryptography”.  The name is a little misleading.  It should be “quantum shared random secret generation”…  Having written that, I can see why everyone uses the first name.

The idea is; Alice and Bob get a whole bunch of entangled photons, then they each measure pairs one at a time.  Since the photons are entangled, Alice and Bob will always get the same result from their measurement, and the results will always be perfectly random.  So, Alice and Bob end up with identical, but perfectly random strings of 1’s and 0’s.  These can then be used as one time pads (the only perfect form of encoding).

The beauty and the curse of entanglement is that it’s easy to mess up.  When you interact with a particle that’s in multiple states, it ends up being in one state (from your perspective).  So, if anyone intercepts either entangled photon before it gets to where it’s going, the entanglement is broken (remember: entanglement means correlation and multiple states).  Alice and Bob will no longer get exactly the same results, and so they’ll detect that there’s a spy in their midst.  There’s a little more to it, but that’s the general idea.  Normal information can be copied, but quantum information (which includes entangled stuff) can’t.  This is called the “no cloning theorem“.

Quantum cryptography: two streams of entangled photons are created such that when measured they always have the same result, either a 1 or 0.  These streams are sent to Alice and Bob. If some Shadowy Figure (known as “Eve” in crypto circles) were to intercept one of the streams, that Shadowy Figure wouldn’t be able to replicate the entanglement, and Alice and Bob would find their random numbers don’t line up.

Right now the longest “quantum channel” is about 150 km long.  But, with some fancy tricks, like quantum error correcting, quantum teleportation, and really clean fiber optic cables, we may be seeing “quantum networks” in the relatively near future.

If you’ve made it this far, firstly: congrats, these were supposed to be short answers.  Secondly, if there’s an obvious entanglement question that was missed, let me know.  It’s easy enough to make long posts longer.

Posted in -- By the Physicist, Particle Physics, Physics, Quantum Theory | 12 Comments

Q: How are imaginary exponents defined?

Posted on November 26, 2011 by The Physicist

The original question was: How do you do xi (x to the i power), and how on Earth was it developed?  There isn’t really anything to base xi on from previous rules of exponents as it is a completely new idea.

Physicist: Euler, the dude who originally came up with using the imaginary unit, i, as a placeholder for \sqrt{-1} (which, despite having no actual solution, is still something we can talk about), also came up with “Euler’s equation“: e^{i\theta} = \cos{(\theta)} + i \sin{(\theta)}, where “e” is equal to 2.718281828…

Leonhard "Lenny" Euler. A squinty genius.

Euler’s (surprising) equation provides a way to talk about complex exponents (“complex” = “involves i“).  So, Euler not only provided an idea that’s confusing as hell (i), but also a way to deal with it efficiently.

So, for example (using Euler’s equation and some log properties):

\begin{array}{ll}3^i\\=e^{\ln{(3^i)}}\\=e^{i\ln{(3)}}\\=\cos{(\ln{(3)})} + i\sin{(\ln{(3)})}\\\approx 0.455+0.891\,i\end{array}

So why is this formalism used, instead of some other set of rules?  Like everything else in mathematics, it’s a matter of convenience and self consistency.  You’d hope that the usual, old rules would apply in a natural, convenient way.  For example, you’d want x^i x^{-i} = 1.  And that’s exactly what happens:

\begin{array}{ll}x^i x^{-i}\\=\left[e^{\ln{(x^i)}}\right]\left[e^{\ln{(x^{-i})}}\right]\\=\left[e^{i\ln{(x)}}\right]\left[e^{-i\ln{(x)}}\right]\\=\left[\cos{(\ln{(x)})} + i\sin{(\ln{(x)})}\right]\left[\cos{(-\ln{(x)})} + i\sin{(-\ln{(x)})}\right]\\=\left[\cos{(\ln{(x)})} + i\sin{(\ln{(x)})}\right]\left[\cos{(\ln{(x)})} - i\sin{(\ln{(x)})}\right]\\=\left[\cos{(\ln{(x)})}\right]^2 - i\cos{(\ln{(x)})}\sin{(\ln{(x)})} + i\cos{(\ln{(x)})}\sin{(\ln{(x)})}-i^2\left[\sin{(\ln{(x)})}\right]^2\\=\left[\cos{(\ln{(x)})}\right]^2-i^2\left[\sin{(\ln{(x)})}\right]^2\\=\left[\cos{(\ln{(x)})}\right]^2 + \left[\sin{(\ln{(x)})}\right]^2\\=1\end{array}

(Here I’ve used: Cos(-x) = Cos(x), Sin(-x) = -Sin(x), i2=-1, and the Pythagorean identity.)

Even more important, this technique is used because it recovers the usual rules for real exponents (exponents that don’t involve i), or at the very least doesn’t mess them up.  It keeps arithmetic nice and self consistent.  After all, when you’re coming up with new math, you want to make sure that you don’t trash what you’ve already got.  Euler’s equation is an “analytic continuation” of the exponential function (e^x) from the real numbers, to the complex ones.  An analytic continuation takes a function defined on a fairly small set, like all the real numbers, and generalizes it to work on a larger set, like all complex numbers (which includes real numbers like “3”, but also includes numbers like “i” and “4-2i”).  It’s not obvious, but it turns out that Euler’s equation is the only “nice” way to define complex exponents.

You’ll find (at least, those people who are so inclined will find) that Euler’s equation, and in particular the method for finding imaginary exponents above, is consistent with all the rules of exponentiation.  Specifically, \left(x^A\right)^B = x^{AB}, x^Ax^B = x^{A+B}, x^Ay^A = (xy)^A, and x^0 = 1.

Posted in -- By the Physicist, Conventions, Equations, Math | 36 Comments

Q: Why do nuclear weapons cause EMPs (electromagnetic pulses)?

Posted on November 20, 2011 by The Physicist

Physicist: The weapon itself doesn’t cause the EMP (or not much of one).  The pulse is actually generated by the weapon’s effect on the Earth’s ionosphere.

Nukes: bad piece of business. The explosion itself expands in every direction, but the pillar of fire and the mushroom cloud are direct results of the convection currents (updraft) caused by the heat.

An EMP is just a sudden change in the electric and magnetic fields, which on its own isn’t too bad.  It doesn’t hurt people at least.  However, changing EM fields induce currents in anything capable of carrying a current.  This is especially true of power lines, where the current can really “build up some steam”.  The problem with current suddenly showing up where it’s not expected is that it can arc or overload circuits.  The kind of components and wiring you find in today’s electronics (and the last 30 some odd years) can be destroyed by the sort of sudden surge you get from regular old static electricity.

Of course because of that, sensitive electronics are generally grounded (with ground lines!) and/or shielded with Faraday cages.

Antistatic wrist strap. For use in case of nuclear attack or someone walking across a carpet.

The way you generate an EMP (or any interesting electromagnetic effect) is you get a bunch of charge and suddenly move it.  A nuclear weapon on its own doesn’t have a bunch of extra charges to move around, but luckily (unluckily?) the Earth abides!  Between about 40 and 300 miles above your head (about 39 and 299 miles for our Denver readers) there’s a layer of charged particles called the ionosphere.  It’s created by radiation from space (mostly the Sun) knocking electrons free of their host atoms.  A nuke releases enough heat, suddenly enough, that the resulting upward and outward “puff” of air literally moves the ionosphere overhead.  That moving charge is what causes the bulk of the EMP.  To a lesser extent, a nuclear device also ionizes the surrounding air, and then moves that.

The Soviets and Americans, being good at this sort of thing, have done a number of tests that involved setting off nuclear devices in and just above the ionosphere.  The best known are America’s “Starfish Prime” (you’d think the black ops people would hire better namers-of-things) and the USSR’s “test 184” (classy name).

According to a review for the US Energy Research and Development Administration, EMP damage was recorded almost a thousand miles away:

“Starfish produced the largest fields of the high-altitude detonations; they caused outages of the series-connected street-lighting systems of Oahu (Hawaii), probable failure of a microwave repeating station on Kauai, failure of the input stages of ionospheric sounders and damage to rectifiers in communication receivers. Other than the failure of the microwave link, no problem was noted in the telephone system.”

The Soviet tests sound even more fun, but the relevant details are a little harder to track down:

“…it knocked out a major 1000-kilometer (600-mile) underground power line running from Astana to the city of Almaty. Several fires were reported. In the city of Karagandy, the EMP started a fire in the city’s electrical power plant, which was connected to the long underground power line.” (ref.)

It’s worth mentioning that nuclear bombs aren’t the only thing that cause these sorts of large-scale electronic nastiness.  Any bomb big enough will have a similar effect (if there were other bombs big enough).  Also, every now and again, the Sun belches out a cloud of ionized gas that pushes the Earth’s magnetic field around.  The results are the similar to a nuclear EMP, but global and toned way down.  These “geomagnetic storms” mostly just mess with communication channels, which are often already bumping up against their signal-to-noise limit.

Posted in -- By the Physicist, Physics | 24 Comments

Q: How does the expansion of space affect the things that inhabit that space? Are atoms, people, stars, and everything else getting bigger too?

Posted on November 16, 2011 by The Physicist

Physicist: Way back in the day Edwin Hubble (of telescope fame) noticed that the farther away a galaxy is, the faster it’s moving away from us.  From this he figured out that the universe is expanding, but in a very specific, weird way.  Rather than things just flying apart (like debris from an explosion), the space between things is actually increasing on its own.

There’s some detail on what the difference is over here.

You’d think that, what with space itself expanding, everything else would expand with it.  After all, the expansion of space is roughly analogous to a stretching rubber sheet.  If you stretch the sheet anything drawn on it will stretch just as much.

The expansion of space doesn’t cause the things in space to expand, just move apart.

But in fact, while the space between and inside everything increases, the things themselves don’t.  Or at least, they snap back faster than they can be stretched.  The size of atoms, their chemical bonds, and by extension everything that’s composed of them, is determined by physical laws and constants.  For example, the size of electron orbitals is scaled by the Bohr radius, a0,which is just fit to pop with physical constants.  a_0 = \frac{4\pi\epsilon_0\hbar^2}{m_e e^2}, where \underline{\pi}, \underline{\epsilon_0}, \underline{\hbar}, \underline{m_e}, and \underline{e} are all constants, etched indelibly into the fabric of the universe, and none of them are terribly concerned with the amount of space around.

So everything around is the size it’s “supposed to be”.  At least, everything solid.  Fluffier things, like stars, gas clouds, and whatnot tend to have a particular stable size.  As space expands a star in that space will expand as well.  However, with a drop in density comes a drop in the fusion rate, the core cools a little, and the star is free to collapse back into its preferred equilibrium size.  The same idea applies to chemical bonds: atoms in any given molecule like to be a set distance from each other, and while the expansion of space may move them slightly farther apart then they’d like, they have no trouble at all returning to their original distance.

It’s worth noting that this isn’t the sort of thing that anyone would need to worry about / include in any calculations / talk about publicly.  Right now the universe is expanding at the rate of approximately 72 (km/s)/Mpc (“kilometers per second per megaparsec”).  This rate is called the “Hubble Constant“, which is a weird name, considering that over the history of the universe it hasn’t been constant.  Unlike other physical constants, which are constant.  This expansion rate means that distances increase in size by about 0.0000000074% every year.  On the scale of the universe (45 billion of light years, give or take) that expansion is important.  On the scale of our galaxy (100,000 light years), and especially on the scale of people (2\times 10^{-16} light years), that expansion doesn’t mean anything.  Your hair grows about 1 billion times faster than the universe “expands you”, and your atoms don’t naturally compensate for hair growth.

That all being said, the Hubble constant doesn’t seem to be constant.  In fact it’s increasing.  So, in the future the expansion may be noticeable on a smaller scale.  At some point, in the inconceivably distant future, the expansion of space may be fast enough to overcome the forces that return matter to equilibrium.  Once the gravitational force of a star is overcome it’ll fly apart.  Once the electrical forces that maintain chemical bonds is overcome, there goes everything else.  This unfortunate occasion, is known as the “Big Rip” to juxtapose it with the “Big Bang”.  The jury’s still out on when and if the Big Rip will happen, but it’s a very long way off if it does happen.

Posted in -- By the Physicist, Astronomy, Physics | 31 Comments