Archive for: October, 2010

How not to promote science, American Physical Society style

The mission statement of the American Physical Society includes in their mission statement, among other things, the intention to be "an authoritative source of physics information for the advancement of physics and the benefit of humanity".

To this end, they seem to have locked papers from Physical Review from 1948 behind a paywall, for subscribers only, or for those who are ready to pay $25 for access. Thank you, APS. Yes, I know you have expenses, but I also know that I pay more than $100 a year to be a member of your society. Is this really advancing physics and benefiting humanity?

We seem to be locked into our notion that scientific journals belong to the same closed, proprietary publishing model as grocery-store checkout-line magazines. Our blindness to how this utterly contradicts the nature of the scientific endeavor is very similar to what I was just reading in commentary by Eddington from 1920 about how the astronomical community seemed to be clinging to the gravitational contraction model for powering stars, despite the fact that it no longer made sense across a wide range of science.

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"The End of Time" : somebody explain to me why this paper isn't all crap

One of my students this morning mentioned he'd seen a news article about scientists who suggested that time had a 50% chance of ending in the next 3.7 billion years, and that we have to accept this result if we accept the way we do our calculations.

The paper is arXiv:1009.4968, by Bousso et al. I have to admit that I am not in in the field, and so don't really know how people really do calculations for the probabilities of events in eternal inflation. But, as best I can tell, what this paper has done is taken a calculational tool that theorists use in order to make calculations tractable, and have interpreted it as reality.

Here's an analogy to what I think is going on. When you do "aperture photometry", you take a digital image of a star, and add up the number of counts in all the pixels that are less than a certain distance away from the center of that star. In reality, the probability distribution for photons from that star extend all the way out to the edge of the field, but it's not practical to try to add things up that way. So, if you care about the total light in the star (say because you're calculating your aperture correction, if you know what that means), you draw an aperture that's "big enough" that you know you're including 99.99% of the light from the star, and don't worry about the fact that you've thrown out the other 0.01% of the light of the star, as your other uncertainties and systematics are bigger than that anyway. The radius of your aperture is a cutoff you use in the calculation for purposes of making the calculation practical and tractable. It does not mean that you're interpreting your data to say that absolutely no light from the star can exist outside of that line. Yes, you're implicitly assuming that, but you don't really believe it. What's more, your calculation shouldn't be taken to mean that you require there to be no light outside your aperture for your measurement to have meaning, and to be useful.

As best I can tell, Bousso et al. are taking a similar cutoff that theorists use when doing calculations in an inflationary universe, and are interpreting that calculational cutoff as The End Of Time (dramatic chord).

Can somebody explain to me why this isn't just overinterpretation of an approximation made for the sake of finding numbers? Why this is any different from saying that "if you use Kepler's Laws to calculate the orbit of Mars, you will float away because the validity of your calculations depend on Earth having zero mass"?

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The Second Law Is...

I will sometimes see science blog posts refer to "The Second Law" as if we all knew exactly what they meant.

As far as I can tell, "The Second Law" could refer to any of:

  • F = ma
  • A line joining the planet to the Sun sweeps out equal areas in equal times
  • ΔS≥0
  • A robot must obey any orders given to it by human beings, except where such orders would conflict with the First Law.
  • The only way of discovering the limits of the possible is to venture a little way past them into the impossible.

(And probably a number of other things.)

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Why P=nkT is better than PV=NRT

If you've ever taken a Chemistry course, you've run across PV=NRT. That is, of course, the ideal gas law. Real gasses approximate ideal gasses; the noble gasses (Helium, Neon, Argon, Krypton, Xenon) probably approximate it best. It tells you that the pressure times the volume of a gas is equal to the number of moles of that gas, times the ideal gas constant, times the temperature in Kelvins.

So, fine. It's useful, and I've used it a lot. My problem is that as a physicist, I think that moles are an extremely gratuitous unit. Sure, I recognize that you're more likely to be dealing with 32 grams of O2 than 32 individual molecules, but still, it's yet one more concept that doesn't do much for me. What's more, the ideal gas constant is a constant that, at least as its name suggests, is of limited utility.

I much prefer this formulation:

P = n k T

All of the same information is there. However, instead of the ideal gas constant, we've got Boltzmann's Constant, which is a much more fundamental constant. Yes, all the same information is there— except that it doesn't come in units containing moles, so you don't need to know the definition of moles to use it— and Boltzmann's constant shows up as is in a lot of other equations.

On the left, we have pressure, the same as before. On the right, we have the number density of the gas. The variable n, instead of being just a number, is the number of particles per volume. OK, I will admit, that's going to tend to be a huge number. If I did my calculations right, for a gas at room temperature it's going to be something like 3×1025 m-3. So, I will admit that that is one advantage of the chemist's way of formulating it: the numbers are easier to deal with.

The rest of the right is kT. What's neat about that is that if you do physics (and probably chemistry as well, and probably many other natural sciences), you're used to seeing kT all the time. Boltzmann's constant times the temperature times a number of order 1 is the average kinetic energy of a particle in a gas that's at temperature T. This (other than aethetically preferring k to R) is the primary reason I prefer this formulation of the ideal gas law. It's got a piece in it that lets you directly connect this to other physics. "Aha", you say, "this law is somehow related to the average energy of individual particles!" And, sure enough, if you realize that pressure is the rate at which particles are crossing an imaginary wall, times the amount of momentum that each particle carries with it across that imaginary wall, you realize that it should be related to the kinetic energy of that particle.

There's another thing here. If you look at "nkT", you'll realize that that is just a number of order 1 times the kinetic energy density of the gas. kT is (close to) the kinetic energy of each particle, and n is the number of particles per cubic meter (or per cubic centimeter, if you like cgs units better). This leads immediately to the realization that the units of pressure are exactly the same as the units of energy density— something that seemed perverse to me the first time I came across the stress-energy tensor of relativity, as I'd been brainwashed into thinking they were entirely different things by the obscuration inherent in PV=NRT. To be sure, pressure and energy density aren't the same thing, but they are related. (One could say that energy density is momentum flux in a temporal direction, and pressure is mometum flux in a spatial direction, but you need an appreciation of spacetime for that to be illuminating.)

It may be just me as a curmudgeonly physicist talking back to chemists who've figured out a more convenient way to deal with it. I've certainly come across curmudgeonly physicists who express disbelief and either horror or amused condescension that astronomers would use a unit so silly as the "Astronomical Unit"... and their reaction is simply the result of them not being used to it, and not realizing that that unit is extremely convenient for star systems, just like their fermi is extremely useful for atomic nuclei. However, I do really think that from a clarity of concept point of view, P=nkT is a much better way to state the ideal gas law than PV=NRT.

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Off to VCON this weekend, talking about Newton's Laws in TV and movies

This weekend I'm going to be off hanging out at VCON 35, a science fiction convention in Vancouver. As has been the case with science fiction conventions I've gone to in the past, I'll be giving a talk about something science-related. (Yes, I wasted no time finding a geek convention to talk at after arriving up here in Canada! In fact, truth to tell, it was during the afterglow of Hypericon last year that I searched around to see what might be going on where I was about to move to, found VCON, and volunteered to give a talk.)

The talk I'll be giving is a slightly modified version of one I gave at Hypericon a couple of years ago: Newton's Laws in Science Fiction Movies and TV: the Good, the Bad, and the Ugly. I'm also going to be on a couple of other panels (presumably with other people).

Monday, it's back to the Energy & Matter course I'm teaching this block— and grading, since there's an assignment due Monday! (So if you're a student in the class, get to work! There's a wiki page to write....)

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