Q: What would the consequenses for our universe be if the speed of light was only about one hundred miles per hour?

Posted on June 10, 2010 by The Physicist

Physicist: In terms of things like space travel, the difference between 100mph and light speed is academic.  Everything out there is really far apart.  The speed of light, “C”, is woven into the laws of the universe from top to bottom, mostly in the context of electro-magnetism.  Changing the speed of light would have profound effects on chemistry and the fundamental forces.

But those changes are boring.  What’s more interesting is the effects that special relativity would have on every day life.

For what follows, the speed of light is now C = 100 mph (161 km/h for our Canadian or otherwise foreign readers).

"Gamma" is a measure of how much velocity dilates time and shrinks distances. Most of the action happens beyond 90% of C.

Movement? Nopers: If you’ve taken intro physics you may have learned that the kinetic energy of an object is E=\frac{1}{2}mv^2.  But this is just a low-velocity approximation of the true equation (found by Einstein), which is E=\frac{mc^2}{\sqrt{1-\frac{v^2}{c^2}}}\approx mc^2+\frac{1}{2}mv^2+\frac{3}{8}m\frac{v^4}{c^2}+\cdots.

The first term is the famous rest mass energy (E=mc2), the second term is the regular kinetic energy, and the third, fourth, fifth (and so on) terms are only important when the velocity is a substantial fraction of light speed (so Newton can be forgiven for getting this one wrong).  But if C=100mph, then suddenly those later terms become important even at low speeds, and you’ll find that moving as fast as 0.01mph would require something like a rocket or a nuclear-powered car.

But that’s boring, so let’s pretend that it isn’t the case.

No long range communication: 100mph is about 45m/s, so having a conversation with someone who isn’t close at hand will result in really annoying delays.  It would be like those satellite interviews, only in person.  To send a message to someone on the other side of the world would take at least 5 days and 4 hours at the speed of light.

I’m ignoring the effects, by the way, of the Earth rotating at about 1,000 mph (at the equator).

Leave your watch at home: The act of walking around would cause you to lose about half a second for every mile you walk, which isn’t to bad.  But if you started moving around in a car at highway speeds (65 mph), then you could expect to lose about 17 seconds for every mile you travel.

“Super Speed”: One of the slick things about traveling at relativistic speeds is that, although you can only pass things at up to 100mph, you can actually cover more distance than the 100mph speed limit might imply.  There are two ways to look at this.

From your point of view the world around you undergoes length-contraction.  So, for example, at about 87mph you would see the world contracted by a factor of 2.  So while you’d see things pass by at 87mph, you’d be eating up distance as though you were traveling at 174mph (2 x 87mph).

From everyone else’s point of view, you’re traveling through time slower.  At 87mph they’d see your watch ticking at half the usual rate, so the trip will only take half the time it should.

Pretty colors: Even at running speed there would be enough relativistic doppler shift to change the colors around you.  If you were driving past a yellow field of grain, it would appear blue in front of you and fade to deep red as it passed behind you.

There are just a hell of a lot of other effects, so if you’re wondering about any of them, just ask in the comments.

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

Q: Do virtual particles violate the laws that energy can be created or destroyed? Have virtual particles ever been observed? In any other instance can energy ever be destroyed or created?

Posted on June 7, 2010 by The Physicist

Physicist: Almost. There’s a version of the uncertainty principle that says that the amount of energy and the amount of time involved in an event can’t both be certain.  You can think of this version of the uncertainty principle as the universe making clerical errors.
Generally a virtual particle will pop into existence, do whatever it does, and then pop out before the universe catches it.
For example: the gluon (pronounced “glue on”) is the virtual particle that holds the nucleus together. But the time that it can exist is so short that it can’t even get from one side of the nucleus to the other. This is a big part of why big atoms fall apart (uranium, plutonium,…).
Unfortunately, only “real” particles can be measured. Virtual particles have to be inferred. We can observe gluons by introducing enough energy that they don’t have to rely on clerical errors to exist (I’m talking about particle accelerators here).  But virtual particles can only be detected in terms of the effects they have on other particles (like holding an atom together).
Aside from the uncertainty principle, everything obeys conservation of energy. And even with the uncertainty principle the extra energy gets ironed out faster than you can blink.

Posted in -- By the Physicist, Particle Physics, Physics, Quantum Theory | 6 Comments

Video: How do we know that 1+1=2? A journey into the foundations of math.

Posted on June 6, 2010 by The Mathematician

AskAMathematician.com presents a lecture on the foundations of math and whether we really can know that one plus one equals two. How was math invented? Where does mathematics come from? Are the axioms of math provable? Is math true? Can it be proven on purely logical grounds? Can it be demonstrated empirically? Can it only be justified from a pragmatic perspective? These are some of the questions discussed in the three videos below.

Part 1 of 3:

Part 2 of 3:

Part 3 of 3:

Posted in -- By the Mathematician, Videos | Tagged , , , , , , , , , , , | 18 Comments

Q: Would it be possible to generate power from artificial lightning?

Posted on May 31, 2010 by The Physicist

The original question was: Would it be possible to create a very dense cloud cover inside a laboratory under controlled conditions and generate “artificial lightning”?  the Power output would be Amazing!!  it would really help solve our energy crisis.

The Chaitén volcano in Chile. Holy shit.

Physicist: Lightning is generated in the same way that static electricity is generated when you drag your feet on a carpet.  A storm cloud or an ash cloud is just a whole mess of feet and carpet.  As ash explodes out of a volcano it rubs together.  Almost all of that kinetic energy becomes more heat, but a very, very small fraction becomes electrical energy.

It is entirely possible to create static electricity, and even lightning using this method.  Van de Graaf generators, for example, use rubbing to generate voltages in excess of a 1,000,000V.  However, it’s a very inefficient method for generating power.  Dynamo generators (the standard generator) are surprisingly efficient.

Essentially, it would take a lot of energy to throw all that dust into the air and get it moving and, because you can’t get more energy out than you put in, it wouldn’t be worth it.  In fact the electrical power you would get out would be tiny compared to the power it took to make it work in the first place.  That being said, it would look pretty cool, so why not?

Artificial lightning (in miniature) is regularly created in places like NEETRAC at Georgia Tech.

The last thing on my bucket list is "pee on an artificial lightning generator".

An artificial lightning bolt.

This lightning is generated using capacitor banks (not rubbing stuff together, the way natural lightning is created) and is feeble by comparison to the real thing.  Also, it isn’t used to generate power.  It’s used to test the ability of new equipment and machines to survive lightning strikes.

Posted in -- By the Physicist, Engineering, Physics | 28 Comments

Q: What is the optimum spectrum to visualize things with? Theoretically, which type of vision would be the best to see things with?

Posted on May 30, 2010 by The Physicist

Physicist: At the risk of being a smart-ass; it really depends on what you want to see.

Andromeda, the nearest galaxy to the Milky Way, as seen in the infrared, radio, visible, and x-ray parts of the spectrum.

Different wavelengths are good for seeing different things.  Infrared is good for seeing dust, x-rays are good for finding blackholes, novas, and bones.  You want to see stars and pretty much nothing else?  Radio waves.

So the short answer is that there’s no best spectrum for seeing stuff.  But given the choice, I personally would go with x-ray vision.

Posted in -- By the Physicist, Physics | 5 Comments

Q: What causes iron, nickel, and cobalt to be attracted to magnets, but not other metals?

Posted on May 29, 2010 by The Physicist

Physicist: The magnetic properties of a material are governed entirely by the configuration of the electrons in that material.  In metals there are two types of electrons: bound electrons and free electrons.  The free electrons are free to move between atoms, and are the cause of conductivity in metals.  The bound electrons are stuck to the individual atoms.

Each electron, in addition to having charge, also has a “magnetic moment” which is a fancy way of saying that it’s a tiny bar magnet.  Generally the bound electrons will be paired off in opposite spin pairs.  This is like putting a North-South magnet next to a South-North magnet.  They almost completely cancel each other out.  However, sometimes (in iron, nickel, and cobalt for example) you’ll have one or more un-paired electrons.  The magnetic fields of these electrons aren’t canceled out by another, oppositely-oriented, electron.  As such they lend an overall magnetic field to the atom they inhabit.

So, some metals are attracted to magnets because they are full of tinier magnets.  Those tinier magnets twist about so that they align with the field of the larger magnet.  However, that just pushes the question back to “Why do magnets attract each other?”.

Those free electrons aren’t completely useless.  If they’re exposed to a changing magnetic field (wave your magnet around) they’ll start moving around in “eddy currents”.  Those eddy currents always try to resist the changing field (“Lenz’s law” or “the universe is a stubborn jerk law”).  So all conductive metals interact with magnetic fields (otherwise generators wouldn’t work), but not in the “attracted to” kind of way.

Answer gravy: “Why do magnets attract each other?”  Magnetic fields, like high school students, don’t really want to exist.  A magnetic field of strength B that fills up a volume V has an associated energy E=\frac{B^2}{8\pi}V.  So creating magnetic fields takes energy, and getting rid of them frees up energy.

It turns out that processes that release energy are usually forces.  For example; when you drop an object energy is released, and it so happens that gravity is a force.  Similarly, magnets will try to line up in such a way that they will cancel out each other’s fields.  Less fields = less energy.  So, the process of lining up to cancel out their fields decreases the energy tied up in those fields, and as such there’s a force that tries to line up the magnets.

Also: The physics behind the magnetic properties is really nasty.  Nasty enough that the math can’t be done, and computer simulations can’t be trusted (generally).  Here’s a map of the (experimentally found) magnetic properties on the periodic table:

Some patterns, but lots of exceptions as well. The magnetic properties of the heavier elements are difficult to study, since they generally have half-lives of substantially less than a second.

Posted in -- By the Physicist, Physics | 29 Comments