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Relativity + Electrostatics = Magnetism

Original article can be read at: Relativity + Electrostatics = Magnetism

There is another dramatic success of Special Relativity that is virtually unknown among laymen. Special Relativity is what causes magnetism.

First, what is the electrostatic force, and what is the magnetic force?

The electrostatic force is what causes opposite charges to attract, and like charges to repel. Electrons, negatively charged, tend to stick to protons, positively charged. Two protons would repel each other, as would two electrons. On a macroscopic scale, the electrostatic force is what causes static electricity, in which an object accumulates an excess or shortage of electrons. It also causes lightning, which is basically static electricity on an even larger scale.

The magnetic force acts upon moving charges. If I've got an electric current, where the electrons are moving forward in a wire, the current creates a magnetic field. If I place two of these wires next to each other with the currents going in the same direction, they will attract. If the currents go in opposite directions, the wires repel. What we call magnets are materials with permanent circular currents on an atomic scale. The north pole of a magnet has currents going counter-clockwise, and the south pole has currents going clockwise. The north and south poles attract because when they are placed together, the currents go in the same direction.

The magnetic and electric forces interact and effect each other, but it is not clear why. Why should currents in the same direction attract? The wires, after all, have no net charge. There are just as many electrons as protons in each wire. So it can't be that the electric force is somehow sneaking in, disguised, right?

There is, in fact, a paradox associated with magnetism. Magnetic forces only act upon moving charges. But if we consider a moving particle's reference frame, the particle always has zero speed relative to itself. Therefore, from the particle's reference frame, it cannot be affected by magnetic forces. These forces shouldn't be disappearing just because our reference frame is different!

Let's consider a specific case: two wires with current going in the same direction. Wires, along with most everyday objects, consist of equal numbers of protons and electrons. If a wire has electric current going through it, that means that the protons are remaining still while the electrons are moving in one direction along the wire. The electrons, in fact, are moving at a large range of speeds, but for simplicity's sake I will assume that they are all moving at one constant speed.

Let's consider the wires with Relativity in mind. Of course, from the protons' motionless frame of reference, the wire is electrically neutral. But what happens if we consider the frame of reference of a moving electron? From the electron's point of view, the other wire contains a bunch of motionless electrons and a bunch of backwards-moving protons. Since the electrons and protons are moving relative to each other, we must take into account Lorentz contraction. If you don't recall, Lorentz contraction makes all distances in the direction of motion smaller. Lorentz contraction causes the protons to be closer together, more densely packed. As a result, the other wire has an overall positive charge, creating an electrostatic force. The electron will be attracted by this force.

So from my point of view, standing still, the wires attract because of magnetic forces. From the electron's point of view, they attract because electric forces. Both of us are correct, much in the same way that we would both be correct in thinking the other's clock ticks slower than our own. The resolution to the paradox is that electrostatic and magnetic forces transform into each other as we change reference frames. It turns out that magnetism is necessary for Special Relativity and electrostatics to make any sense together.

What's interesting about this is that it occurs at extremely low velocities. I did a bit of math, and I found that if we have 10 amps (a quantity of current) going through a copper wire of diameter 1mm, then the average velocity of electrons is 9.4*10^-5 [edit: corrected math] 3.3*10^-5 meters per second. That doesn't even begin to approach the speed of light (3*10⁸ meters per second). And yet, if you place two of these wires next to each other, there will actually be a measurable magnetic force. Not a significant force (about the weight of a paperclip per foot of wire), but not negligible either. We rely on this force for electric motors, generators, and countless other applications.

Usually, when you learn Special Relativity, teachers are quick to say that it is entirely ignorable at everyday speeds. But it turns out that even at microscopic speeds, Relativity does no less than power the modern age.

Beetle Genitals

You want to put WHAT in my what??!?

Smallest Font

Stanford researchers have reclaimed bragging rights for creating the world's smallest writing, a distinction the university first gained in 1985 and lost in 1990.

How small is the writing? The letters in the words are assembled from subatomic sized bits as small as 0.3 nanometers, or roughly one third of a billionth of a meter.

The researchers encoded the letters "S" and "U" (as in Stanford University) within the interference patterns formed by quantum electron waves on the surface of a sliver of copper. The wave patterns even project a tiny hologram of the data, which can be viewed with a powerful microscope.

http://www.sciencecodex.com/stanford_writes_in_worlds_smallest_letters

Energy Scale - Orders of Magnitude

Relativity in Chemistry: The Color of Gold

A reader asks:

Why is gold yellow?

Metals exhibit their characteristic shininess as the delocalised electron sea in the metallic bonds are able to absorb and re-emit photons over a wide range of frequencies. Thus the reflectance spectra of most metals appears fairly flat and they appear silver in colour.

A few metals, such as copper and gold, have a reflectance spectrum where the red end (400--700nm) dominates. Why is this so?

I first thought that it may be something to do with the single unpaired electron in the outermost valence shell, but Silver also displays this but has a flatter reflectance curve.

Can anybody shed some light (groan) on this?

Chemists often consider the first sub-shell of a given angular momentum to be anomalous. The 3d, filled in copper, is less shielded by the s and p subshells than you might otherwise expect. Silver, with a filled 4d behaves more like you think it should. Now when you get to gold (5d) relativistic effects become important. Compared to non-relativistic results the s and p subshells are more contracted (the so-called relativistic stabilization) while d and f are destabilized and more diffuse. So gold also behaves somewhat differently. If you were to do a solid state calculation on gold without including relativistic effects you would predict it to be silvery. Including relativistic effects you get reasonably good agreement with reality.

http://math.ucr.edu/home/baez/physics/Relativity/SR/gold_color.html

Pekka Pyykko's Relativistic theory of atoms and molecules gives a nice overview of this and many other phenomena, as well as a huge bibliography of papers dealing with relativistic effects in chemistry. Oh, that mercury is a liquid is another one.

Hard Work

In the 1990's, psychologist K. Anders Ericsson conducted an experiment with the Berlin Academy of Music. He divided the school's violinists into three groups: the elite, the good, and those that were unlikely to ever play professionally.

All of the kids had started playing when they were 5 years old, but what divided them, aside from ability, was simply how many hours each had spent practicing. The really good ones had totaled 10,000 hours of practice, while the good ones had only managed to squeak away on the catgut for 8,000 hours or so.

The underachievers? Just 4,000 hours of practice.

The most surprising thing was that they really couldn't find any "naturals." Nor could they find any grinders, people who just worked harder than everybody else but just didn't have the talent to become elite.

The thing that distinguished one from another was simply hard work, nothing else.

But the weird thing is that 10,000 hours — roughly the amount of practice a truly committed devotee could accrue over 10 year — keeps popping up in different fields. Whether you're a writer, a concert pianist, a basketball player, computer programmer, or chess master, true greatness seems to pivot on that magic number.

http://www.t-nation.com/readArticle.do?id=2682770

Strongest Material Ever Tested

Graphene, praised for its electrical properties, has been proven the strongest known material.

http://www.technologyreview.com/Nanotech/21098/?a=f

Rich

"It's the rich who hire everyone else. As countless African dictators have discovered, the quickest way to destroy your economy is to crack down on your rich people."

Feynman on knowledge

"I can live with doubt and uncertainty and not knowing. I think it is much more interesting to live not knowing than to have answers that might be wrong."