SPF = x^2 + 2x – 3

Uncertain Principles: Algebra Is Like Sunscreen

My one-word piece of advice for students planning to study physics (or any other science, really, but mostly physics): Algebra.

Since we’re on the topic of math, let’s double the fun by visiting Cocktail PArty Physics: NEW VOICES: “math sucks”

“When I write, I can say whatever I want to say, but in math there’s just one right answer.”

She had a point there. I loved mathematics for its concreteness, its lack of ambiguity. It felt to me like a solid anchor in a hostile, subjective world. But the flip side of that is you can be definitely, unambiguously, totally wrong. You can’t plead “I was robbed,” like you can when the blind umpire calls you out or your sterling essay is marked with a D minus by a demented grader.

But … if the education is bland, and

[T]he core problem she faces, as she enters middle school “hating” math, is the math teaching itself, gender neutral, uninspiring for all.

There is the open question of why Austin (a boy) loves math.

I think an underlying issue is our desire to be able to point to a single problem to fix, when in reality there are multiple reasons why it’s tough to get kids to eat their vegetables learn their algebra.

No One Can Hear You Scream

Acoustic Black Hole Created in Bose-Einstein Condensate

The result is a region within the BEC in which the atoms move at supersonic speed. This is the black hole: any phonon unlucky enough to stray into this region cannot escape.

One reason why sonic black holes are so highly prized is that they ought to produce Hawking radiation. Quantum mechanics predicts that pairs of “virtual” phonons with equal and opposite momentum ought to be constantly springing in and out of existence in BECs.

Looking for Mr. DNAbar

The Electric Slide

The researchers used computer simulations and analytical calculations to show that a simplified model of a protein is attracted to DNA until it gets within a half-nanometer or so. At this short range, the protein is repelled, so it can slide freely until it finds its target sequence and binds more tightly. The results provide a more complete physical picture of this critical biological process.

Adding to the Confusion

Relativity is not an easy concept. Special relativity is hard enough, and General relativity really ups the ante; I am not well-versed in anything beyond the basics of the latter, but one of the notions of GR is that freefall in a uniform gravitational field is actually an inertial frame, i.e. non-accelerating, which is not a concept present in Special Relativity.

Which appears to be the linchpin behind the argument presented here: In Twin Paradox Twist, the Accelerated Twin is Older

In 1905, Einstein described the ideas behind the twin paradox to demonstrate the effects of time dilation according to special relativity. In 1911, physicist Paul Langevin turned the concept into a concrete story involving two hypothetical twins. Ever since then, scientists have offered various explanations for exactly why this aging paradox occurs, and whether it is even a true paradox at all.
As Abramowicz and Bajtlik note in their study, it is often claimed that the twin paradox can be explained by the acceleration of the traveling twin that occurs when he turns around to go back to Earth. Abramowicz and Bajtlik show, however, that it is not the acceleration that causes the age difference in most cases. By presenting a scenario in which the accelerated twin is older at the reunion, the scientists show that the final time difference between the twins often depends only on their velocities as measured with respect to an absolute standard of rest, and not on acceleration.

First of all, a note that “absolute standard of rest” is not something that is part of the original twins paradox. Which is because in 1905, there was only Special Relativity. The scenario presented is of the twins near a large mass, and one of them in a Keplerian obit, and thus not accelerating according to General Relativity. The notion of absolute rest is in contrast to accelerations and rotations, which can be distinguished, while motion in special relativity cannot. The mixing of the two frameworks isn’t even an instance of the reporter mucking things up — it’s presented in the ArXiv paper that way.

It is often claim that the resolution of the classical
twin paradox should be the acceleration of the “travel-
ing” twin: he must accelerate in order to turn around and
meet his never accelerating brother. The twin who accel-
erates is younger at the reunion. Here we challenge this
notion. We start with describing a situation in which,
like in the classical version of the paradox, one of the
twins accelerates, and the other one does not accelerate.
Quite contrary to what happens in the classical version,
the accelerated twin is older at the reunion.

That’s because you have changed the parameters, and are no longer describing the classical twin paradox.

I have no complaint about the physics. I just don’t think the authors should feign surprise at the result, as if it were somehow unforeseen that changing conditions could yield a different answer. The answer should not be surprising at all, because what they describe is one twin being at rest, and the other in an orbit. Which is exactly what would be described by an observer on a non-rotating planet, and another on a satellite. Maybe a satellite which is part of a navigation platform, able to communicate with a receiver and quadrangulate position and local time, with the modification that the satellite isn’t orbiting at a different distance from the planet.

All of this is pointed out in “Relativity in the Global Positioning System” by Neil Ashby. In section 5 there’s a graph of the results of differing orbital distances, and below some threshold we see that the satellite will age more slowly than someone on the planet surface. I’m not sure how old it is, but the update posted in June 2007 says

I have updated the text in quite a few places, such as eliminating the word “recently” which is no longer really recently.

So the notion is definitely not new, nor should have been surprising.

And Now a Word From Leonard Pinth-Garnell

Let’s take a look at some bad physics, demolished in A cornucopia of cluelessness

Amazing. We’re going to change a unit conversion factor using technology. Apparently, such a breakthrough will also enable us to develop overunity devices, overcome the Second Law of Thermodynamics, and achieve perpetual motion. I suggested in my comment on Michael’s blog that perhaps we should also be looking into the technological possibility of getting more gallons per liter and more miles per kilometer. In fact, why stop there? I will look into employing technology to change the number of centimeters per inch and make myself taller and lengthen my…. But I digress.

(FYI, Leonard Pinth-Garnell)

Honor thy Scientists?

why you should honor thy scientists

[I]t’s not just zealots who will equate scientific methodology with theistic dogmatism. In an attempt to appear completely objective and beyond any charge of bias, some writers will give equal importance to every opinion with seemingly no regard for whether it’s right or wrong. They think that by giving a biologist who’s life was spent researching evolution and a random televangelist the same weight in their articles will make them insightful reporters who diligently consider every side of a story. But the truth is that not everything you hear is accurate and if you’re reporting an incorrect assumption without actually doing your homework and noting that it’s wrong, you’re not an objective reporter or analyst. You’re a scribe afraid of being called biased.

Yes, We Think About Things Like This

ArXiv: Minimizing the footprint of your laptop (on your bedside table)

We are considering all placements of the laptop such that it will not topple o the table;
these are exactly the placements for which the midpoint of the laptop is also a point of the
table. We are then interested in determining for which of these placements the footprint of the laptop is of minimal area; here, the footprint is the common region of the laptop and the table.