Oh Dear, Have You Put On Some Mass?

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The topic comes up, as it sometimes does, of the mass-energy equivalence from relativity. There are different tangents to this — what does the equivalence really mean, can you really turn energy into mass, does a photon have rest mass, what is the difference between relativistic mass and rest mass, and is the use of relativistic mass grounds for justifiable homicide, or is one compelled to stop at maiming?

E = mc2 is the equation everyone knows, but what many don’t know is that the equation already assumes one is at rest. The actual equation is E2 = p2c2 + m2c4, which reduces to the more familiar form when the object is at rest. The implications of this are that photons have no mass, the mass term for massive particles doesn’t change when you move — that energy is in the kinetic term, (which renders relativistic mass moot) and also that the mass will increase if you add energy that does not appear in the kinetic term, i.e. extra energy in the center-of-momentum frame appears as mass.

The last concept showed up at Cosmic Variance recently, in the context of the mass of a spinning top

The spinning gyroscope has more energy than the non-spinning one. As a test, we can imagine extracting work from the spinning gyroscope — for example, by hooking it up to a generator — in ways that we couldn’t extract work from the stationary gyroscope. And since it has more energy, it has more mass. And the weight is just the acceleration due to gravity times the mass — so, as long as we weigh our spinning and non-spinning gyroscopes in the same gravitational field, the spinning one will indeed weigh more.

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Mini-Hoops

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Over at Popsci, the physics of tossing a ping-pong ball into a beer cup, with videos of, well, tossing a ping-pong ball into a beer cup, under various conditions you’d find in a dorm (starting with the unlikely presence of beer cups).

These guys are pretty amazing. And the nonchalance with which they accomplish each trick shot adds a certain understated humor to this entertaining video. But though the guys seem to be developing a seemingly useless (if highly impressive) skill in their spare time, there’s quite a bit of complex science at play.

I think being able to edit out the misses tempers that amazing/impressive just a little. Mostly it reminds me of how much free time I had in college, even though it didn’t seem that way at the time.

You Spin Me 'Round

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From arXiv, rotation of a thin film of water when subjected to perpendicular electric fields.

The question is: what’s causing the rotation? The team can easily control the direction and speed of rotation by varying the relative angle and direction of the electric fields, which rules out the possibility that convection is causing the rotation (something that is seen when a field is applied to some thin films of liquid crystals). Neither does adding salt to water change the effect, ruling out the possibility that ion movement directs the flow.

Movies

Random Thought

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Business section of the LOLcat Times-Gazette, headline about the pedestrian eating habits of a well-known an activist shareholder

Icahn Has Cheeseburger

(sometimes on the treadmill, all one can do is think silly thoughts)

Doomed to Fail

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A while back I posted some links to anti-relativity sites and gg suggested that it would be fun to debunk the claims. Sometimes that’s fun, but often — and especially after doing it a number of times — I find that it’s tedious. An error is present, and one has to find it in a morass of often awkwardly defined and unnecessarily complicated scenarios (hey, let’s use three trains, and multiple clocks which will be juggled by a clown on each train!) set up by the author. Sometimes with some horrific ASCII “art,” to boot, though some do have fancy animated gifs.

The reason one knows that an error is present in these thought experiments is because a contradiction has been found. One might think that this is a dogmatic BESS (Because Einstein Said So) argument, but it isn’t — the issue here is that the ultimate authority, and the only authority one is allowed to quote, is absent from the problem: nature. These are thought experiments, and it all boils down to doing coordinate transformations and calculations. Special relativity consists of Lorentz transformations, which are derived from the hypothesis that the speed of light is invariant; all inertial reference frames will measure the same value. This has the admittedly strange consequence (especially to the uninitiated) of time and length not being absolute quantities, which runs counter to most peoples’ everyday experience. We think in Galilean terms which serves us reasonably well in everyday experience, and the differences presented by Lorentz transformations are not apparent to us under these conditions.

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Classic Physics: Light is an EM Wave

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Classic Science Paper: Otto Wiener’s experiment (1890) at Skulls in the Stars.

By 1890, then, scientists were interested in seeing whether similar results held for light waves: it seems that a number of scientists remained unconvinced that light truly was just another manifestation of electromagnetic waves! One big obstacle stood in the path of such studies: the smallness of the wavelength of light. Hertz’s radio waves had a wavelength of meters, but visible light has a wavelength on the order of 500 nanometers, or 500 billionths of a meter! Such distances cannot be directly observed with the naked eye, so experimental ingenuity was required – and Otto Wiener provided it.

(My own summary of some “classic” physics is progressing)

Odd Odds

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I have an odd sense of humor, bordering on the macabre. OK, it’s pretty much an open border and I visit there often, because I don’t need a passport.

I read the results of the Kentucky Derby and the unfortunate news of Eight Belles. But because I don’t really follow horse racing much and when I hear about it always seems to be about an injury to a horse and how you deal with that, what flashed through my mind (along with Gary Larson’s cartoon about veterinary medicine, where the chapter on horse ailments was so easy) was along the lines of

The 3-1 favorite, Big Brown, won the 134th running of the Kentucky Derby Saturday in commanding fashion, paying $6.80. Eight Belles finished second and paid $10.60, and later buckled, collapsed and was euthanized, which went off at 26-1 and paid $52.50.