Of course, everyone knows there are infinitely many primes. If you have not seen it before, here’s one easy way to prove that fact. We assume for a contradiction that there are only finitely many primes, let’s say k of them. Then we can make a list:

We now ask, what prime number divides N? It cannot be any of the primes on our list, since N leaves a remainder of 1 when divided by any of those primes. The only possible conclusion is that there must be a prime number that is not on the list. This contradicts our assumption that our list was complete. It follows that no finite list can possibly contain all the primes, and therefore there are infinitely many prime numbers.

There is also a clever trick for showing that there are arbitrarily long sequences of non-prime numbers. Recall that if n is a positive integer, then by n!, read “n factorial”, we mean the product of all the integers from 1 to n. For example, we have

So, there are infinitely prime numbers, but also arbitrarily long gaps between primes. There is also the prime number theorem, which tells us that for very large values of x, the number of primes smaller than x is closely approximated by

None of this really tells us much about twin primes, alas. But we do now know that there is some finite number with the property that there are infinitely many pairs of primes by differ by no more than that number:

On April 17, a paper arrived in the inbox of Annals of Mathematics, one of the discipline’s preeminent journals. Written by a mathematician virtually unknown to the experts in his field — a 50-something lecturer at the University of New Hampshire named Yitang Zhang — the paper claimed to have taken a huge step forward in understanding one of mathematics’ oldest problems, the twin primes conjecture.

Editors of prominent mathematics journals are used to fielding grandiose claims from obscure authors, but this paper was different. Written with crystalline clarity and a total command of the topic’s current state of the art, it was evidently a serious piece of work, and the Annals editors decided to put it on the fast track.

Just three weeks later — a blink of an eye compared to the usual pace of mathematics journals — Zhang received the referee report on his paper.

“The main results are of the first rank,” one of the referees wrote. The author had proved “a landmark theorem in the distribution of prime numbers.”

What is that finite number? According to the conjecture, that number should be two. Here’s what Zhang achieved:

His paper shows that there is some number N smaller than 70 million such that there are infinitely many pairs of primes that differ by N. No matter how far you go into the deserts of the truly gargantuan prime numbers — no matter how sparse the primes become — you will keep finding prime pairs that differ by less than 70 million.

70 million might seem pretty far from 2. What you have to remember, though, is that the difference between 2 and 70 million pales in comparison to the difference between 70 million and infinity. So Zhang’s theorem is definitely a big deal!

“Because dark energy makes up about 70 percent of the content of the universe, it dominates over the matter content. That means dark energy will govern expansion and, ultimately, determine the fate of the universe.” -Eric Linder

It’s been a while since we’ve spoken about dark energy, and we were just talking about Einstein’s greatest blunder, so let’s just dive right in.

Image credit: S. Beckwith & the HUDF Working Group (STScI), HST, ESA, NASA.

This is our observable Universe, as unveiled by the Hubble Space Telescope. With hundreds of billions of galaxies stretched out some 41 billion light years in all directions, finding out about what our Universe was like in the distant past, the recent past, and what it’s like today is limited only by our willingness to look. In particular, there are three great sets of observations that tell us ever so much about the Universe on the largest scales.

Image credit: Northern Galactic Cap from the SDSS-III release, via http://www.sdss3.org/.

1.) The way galaxies cluster together on the largest scales. By looking at huge, tremendous surveys of galaxies, we can see how the visible matter in the Universe has clustered, clumped, and grouped together, as well as where it hasn’t, and has left us great cosmic voids. By putting various ingredients into a model Universe governed by General Relativity, we can also simulate how structure should form in our Universe. Where the simulations and the observations match up, that tells us what’s in our Universe.

Image credit: ESA and the Planck Collaboration.

2.) The temperature fluctuations in the cosmic microwave background. By looking at the temperature fluctuations — the hot-and-cold spots — in the CMB, we can know what the Universe looked like in terms of overdensities, underdensities, and how they’re clustered with respect to one another all the way back at a time when the Universe was just some 380,000 years old! Because the light has had to travel for nearly the entire 13.8 billion years that the Universe has been around (it’s been traveling for 99.997% of the Universe’s history), we can find out information about what the Universe was like back then, but also how it’s expanded since then. This pattern of fluctuations also tells us what the various combinations of ingredients are in our Universe.

Image credit: Kowalski et al., Ap.J., 2008.

3.) Direct observations of well-understood objects at various distances/redshifts in the Universe. Everything from variable stars to properties of galaxies to distant supernovae help us get a handle on this, the cosmic distance ladder. This tells us how the Universe has been expanding since as far back as we can measure until the present day.

When these three data sets are combined — and we can combine others, too, but these three are the best data sets we have — they tell us that there’s matter in the Universe, about 31-32% of the Universe is matter (most of which is dark matter), and that there’s another type of energy, dark energy, that makes up the rest.

Image credit: Planck Collaboration: P. A. R. Ade et al., 2013, A&A Preprint; annotations by me.

So, you ask, just what is dark energy, and how do we know?

In principle — and by in principle, I mean in General Relativity — matter, energy, topological defects, and pretty much anything else that you throw into your Universe is going to affect how your Universe expands because of two properties inherent to it: it’s energy density and its pressure.

Image credit: Large Synoptic Survey Telescope, NSF, DOE, and AURA.

Because of the way the Universe is observed to expand, and because of the known way that matter (yes, even dark matter, according to General Relativity) behaves, we can infer something about the energy density and pressure of dark energy. In particular, we know that dark energy’s pressure is negative, and that it’s quite negative.

In General Relativity, we can relate the pressure of any component of the Universe to its energy density by the simple equation:

ρ = w P / c²,

where ρ is the energy density, P is the pressure, c is the speed of light, and w is just some number.

Image credit: A.V. Vikhlinin, R.A. Burenin, A.A. Voevodkin, M.N. Pavlinsky.

According to the best data we have right now, w is equal to -1. Now, as time goes on, we hope to constrain it better; we can say it’s probably about -1.00 ± 0.08 right now, which is pretty good.

Now, here’s the thing: in theory, the pressure of different things in cosmology goes in increments of 1/3. For example:

• Radiation has w = +1/3, like photons and ultra-relativistic matter.
• Matter, both normal and dark matter, has w = 0, or is virtually pressure-free.
• Cosmic strings, or 1-dimensional topological defects, have w = -1/3. This is the border between what would cause a Universe to accelerate (more negative than this) or not.
• Domain walls, or 2-dimensional topological defects, have w = -2/3.
• A cosmological constant (or textures, a 3-d defect) has w = -1.

Those are the easy possibilities.

Image credit: NASA / CXC, via http://chandra.harvard.edu/.

But dark energy could also be something weird. It could be a field, whose relationship between pressure and energy density changes over time. It could be coupled to something we don’t understand. It could be really, really weird, and our measurements of w = -1, to the best we can see, could only be what the Universe is so far.

So we’ve attempted to look for a change in w over time. We’ve attempted to look for departures from w = -1. We’ve attempted to look at different models and their signatures.

Know what we’ve found?

Image credit: Pearson / Addison-Wesley.

The farther back into the past we look, the more and more consistent everything appears to be with the cosmological constant option.

The cosmological constant option has the theoretical bonus of being:

• easily explained,
• inevitable (in that it must exist, even though its value could be 0),
• and requires no new physics beyond the standard model/GR to explain.

We’re going to keep exploring different variants of dark energy, quintessence, scalar field-driven dark energy, etc., of course. But theoretically, there’s no motivation unless we see some sort of evidence that tells us that dark energy is something more (or other) than a simple cosmological constant. And trust me, we’re looking.

Image credit: LSST and others, via http://www.lsst.org/lsst/science/scientist_dark_energy.

This doesn’t mean dark energy is a cosmological constant, it just means that this is the best working hypothesis until evidence suggesting otherwise comes along, and such evidence does not exist today. That’s the best we’ve got, so far.

Last week’s post was written very quickly, and thus ended up a little more jargon-y than I usually shoot for, so let me try to set the stage a little better for this one. the physical system I’m talking about is just a simple pendulum, a mass on the end of a string swinging back and forth. The idealized version of this is very simple mathematically, and gives a very regular oscillation at a frequency that just depends on the length (which is why old clocks contain pendulums). When you dig into the details, though, there’s some rich physics involved in terms of forces, because the force the string needs to exert varies over the course of the swing, getting bigger toward the bottom and smaller out at the ends (this is why, if you have small kids or are just a kid at heart and thus spend time on swingsets, you feel “heavier” at the bottom of the arc of a playground swing, and lighter out at the turning point).

What I did in the simulation was rather than using physics to figure out the force needed to make the bob swing back and forth in advance, I treated the “string” on the simulated pendulum as if it were a spring, with a force that increases as it gets “stretched.” There’s a nice simple mathematical form for this, characterized by a number called the “spring constant,” and the bigger that constant is, the bigger the force you get for a given stretch.

This is nice because it saves me having to code equations into VPython, and also because it is, in some ways, an accurate representation of what actually happens. If you make a pendulum out of a ball and a bit of string, the string doesn’t know how to solve physics equations. It supplies the appropriate force by stretching a small amount and exerting a force in response. The string you typically use to make a pendulum doesn’t stretch very much, so it looks very close to the “ideal” case where the equations are easy to solve, namely a string that doesn’t stretch at all. And, in fact, my toy computer model does exactly that when you make the spring constant big. Physics works, hooray.

Of course, having put together the code with an arbitrary spring constant, the fun part is sticking in parameters that aren’t very close to the “ideal” case, to see what happens. In this case, the spring stretches substantially as the pendulum swings, and the path it follows makes nifty patterns– kind of a braided look in the post from last week, or the cartoon mustache kind of thing on the left in the “featured image” at the top of this post (RSS readers, click through). That happens because I’m lazy, and didn’t want to work out the details of the starting conditions, so I just imagined that the spring-string was unstretched when it was released, because that’s easy to do.

When that happens, you get two things going on: a back-and-forth motion that’s the “normal” pendulum track, and an in-and-out motion characteristic of a spring. You can sort of see what’s going on in that left-hand image above, which is a spring with a small (25 N/m) spring constant released from an unstretched position. Right as it’s let go on the right side of the swing, it falls more or less straight down, with the spring stretching a lot. As the stretch gets big enough, it pulls the bob gets pulled back in, and the combination of the sideways pendulum motion and the inward spring motion flattens out the bottom of the arc, then makes the upturn at the left end, whereupon the whole thing reverses itself.

Of course, this isn’t the only possibility, and in fact, it happens only because I was lazy. If I started the spring with some stretch, though, the force it provided would be bigger sooner, and the oscillation would look more like a “normal” pendulum. This is what you see on the right above: I found a value of the stretch for which this looks much simpler, and the spring hardly stretches at all.

Now, there are two ways to do find this proper prestretch value: brute force trial and error, or using physics. What I did was a combination of the two, and that’s the baffling part. I tried to use physics to estimate the starting stretch, but ended up being way wrong, and finding the actual value by trial and error.

So, what’s the physics guess? Well, the simple treatment of a pendulum has the string not stretch at all, which means that the initial force along the string must be big enough to counter the portion of the pull of gravity that tends to stretch the string. This leaves just the sideways component, and drives the regular oscillation. The value of that radial component of gravity is easy to calculate, and turns out to be the weight of the bob multiplied by the cosine of the release angle.

Of course, for the simulated pendulum to work right, the string needs to stretch a little, so as to allow for the increasing force you need to make the thing work. So, I reasoned correctly that the appropriate stretch wouldn’t be exactly the stretch needed to cancel the stretching part of gravity, but something a little smaller. I had no idea what the exact value should be, though, and didn’t see an easy way to calculate it, so what I did was to stick in an arbitrary factor in front of that extra force when calculating the stretch. So, the pre-stretch of the spring in the simulation is given by the weight times the cosine of the angle times an arbitrary factor. I varied the arbitrary factor and looked for the value that gave the minimum amplitude of the oscillation– that is, the track that looked most like a “normal” pendulum.

So, I did this for a bunch of different factors and a bunch of different spring constants, and like a good physicist, I made a graph:

Radial oscillation amplitude vs. pre-stretch factor, for various simulated pendula.

This plots the amplitude of the in-and-out oscillation on the vertical axis, and the arbitrary factor on the horizontal axis. And it’s totally bizarre.

For one thing, my initial assumption had been that the factor should be a number less than one– the “ideal” value that would keep the spring from stretching in the first instant of the swing would leave it too short to provide the needed force in the next instant, leading to a big oscillation. I figured that the correct value would end up being a bit smaller than that– say, 75% of the “ideal”–allowing some spring stretch and keeping everything nice.

What you see from the graph, though, is that the correct value turns out to be substantially bigger than that– of the five spring constants I tested, the smallest value is around 2.4– that is, 240% of the “ideal” value. My initial thought was that this was just a numerical error on my part, but I don’t see where I made a mistake.

And there’s another reason to think that this isn’t just a coding screw-up in my definition of the starting point, which is that the value depends on the spring constant in a complicated way. If I had just managed to get the force wrong by a factor of 2.5, you would expect that factor to be the same for each different spring, but the five spring constants I tried give different values for the factor needed to get the smallest amplitude. I can graph that, too, and it looks like this:

Pre-stretch factor for minimum amplitude vs. spring constant.

The factor gets bigger as you increase the spring constant, though it seems to reach some maximum value a bit below 5. I have no idea what causes that, though. Which is why I didn’t bother to fit a function to those points, because I don’t even know what I should guess as the appropriate form.

The other weird thing about the first graph is an aesthetic point– all the data points fall on V-shaped curves. On either side of the minimum value, the points are beautifully linear– in fact, that’s how I got the data for the second graph: I fit straight lines to the data to either side of the minimum, and calculated the point where those lines crossed. (I could find the uncertainty in that value, but there’s a limit to how much math I’m willing to do for a blog post, and anyway, they’re close to the by-hand optimized values for the 100 N/m and 400 N/m cases, where I just plugged in factors until I found the minimum amplitude to four decimal places.) That’s kind of a weird shape, though, in terms of physics graphs. You don’t see a lot of natural phenomena that have that kind of pointy shape to them– a parabola, or some other kind of smooth curve would be more “normal.” You kind of need to be a physicist to be bothered by that, but it’s definitely a thing that jumped out at me.

So, anyway, I’m baffled by this. It’s very robust, in that I get the same basic behavior even if I make changes to the simulation code, but also very odd. I’m also not at all sure how to go about calculating the right answers. The easiest way to do it would probably involve a Lagrangian, but even there, I suspect you wouldn’t get an analytical solution, but would need to do some numerical solving of equations. Which might or might not be more reliable than my crude modeling of the situation.

If I were going to teach intermediate classical mechanics at any time in the near future, this might be a great way to re-learn all that Lagrangian stuff that I forgot from my undergrad classical mechanics courses. It’ll be at least six years before I do that, though, so I’m not likely to put in the effort (then again, I’ve spent umpteen hours screwing around with VPython, so…). I might also be able to dig up somebody else’s solution– the pendulum is, after all, a very important physical system, and I’m sure it’s been studied in detail by lots of people– but I have too much else to do to go in for a long literature search. Thus, this blog post, where I’ll just throw this out there for people to either recognize, or calculate themselves, or point out the embarrassing flaw in my whole approach to this question.

In the absence of a better conclusion, then, let me just say again that this is a nice demonstration of how rich the physics of even very simple and well-studied systems can be. And also, what an enormous dork I am, spending hours and hours playing around with this to no concrete purpose…

UPDATE: The ScienceBlogs uploader rejects the code “for security reasons,” but here’s a Dropbox link to the poorly documented VPython program I used to do these simulations.

“BSU appears to offer a class that preaches religion, yet gives students honors science credit,&rdqu; foundation attorney Andrew Seidel wrote to Gora. “BSU appears to have a class with a non-biologist undermining genuine science and scholarship of the Ball State biology department by teaching creationism, a religious belief … masquerading as science.&rdqu;

Hedin and department chair Tom Robertson declined to comment to The Star Press.

But Provost Terry King, a chemical engineer and the university’s chief academic officer, said, “Faculty own the curriculum. In large part, it’s a faculty matter. But we have to ensure that our teaching is appropriate. All I have so far is a complaint from an outside person. We have not had any internal complaints. But we do take this very seriously and will look into it.”

He added that the class is an elective course and not part of the core curriculum.

“All the books are by creationists, IDers (intelligent designers), or people who try to show that science gives evidence for God,” evolutionary biologist Jerry Coyne, a professor at the University of Chicago, told The Star Press, referring to the bibliography for Hedin’s course. “There are no straight science books.”

It appears Hedin “presents a non-view of science in a science class,” said Coyne, author of the book Why Evolution is True.

“The students are being duped. It’s straight theology with no alternatives. It’s a straight Christian intelligent design/creationist view of the world, which is wrong. It’s not science. It’s not that it’s not science, it’s science that has been discredited. It’s like saying the Holocaust didn’t happen.”

Especially interesting is the response of some of the other faculty, as quoted in the article:

He suspects Hedin is “asking people to think a little broader, outside the box, which causes controversy. It’s funny.”

Ruth Howes, a retired professor from the department who now lives in Santa Fe, said, “The people I know in the department are very straightforward thinkers. I don’t think they mean to preach to anybody, except possibly F = ma (one of Newton’s laws of motion).”

Hedin replaced Howes when she retired.

“It is the university’s job to help students understand viewpoints that differ from their own,” Howes said. “Students are not expected to totally agree with these viewpoints, but they are expected to understand them. I think that is probably what professor Hedin is trying to do, and I would expect the university to back this effort thoroughly. For example, if I were teaching a class on Islam, I would not expect students to convert to Islam, but I would expect them to understand the basic tenants that Muslims believe.”

These explanations are not credible in the face of the reading list for the course:

Behe, Michael, Darwin’s Black Box (1998).

Brush, Nigel, The Limitations of Scientific Truth. Why Science Can’t Answer Life’s Ultimate Questions, (2005).

Collins, Francis, The Language of God, A Scientist Presents Evidence for Belief, (2007).

Consolmagno, Guy, God’s Mechanics, (2008).

Davies, Paul, The Goldilocks Enigma: Why is the Universe Just Right for Life? (2006).

Davies, Paul, The Mind of God. The Scientific Basis for a Rational World, 1992.

Davies, Paul, The 5th Miracle (1999).

Dembski, William A. “Intelligent Design as a Theory of Information”

Dubay, Thomas, “The Evidential Power of Beauty. Science and Theology Meet”, 1999.

Flew, Antony, There is a God: How the World’s Most Notorious Atheist Changed His Mind, (2008).

Gange, Robert “Origins and Destiny” (1985). Online: http://www.ccel.us/gange.toc.html

Giberson, Karl W. and Collins, Francis S. The Language of Science and Faith: Straight Answers to Genuine Questions, (2011).

Gingerich, Owen, God’s Universe (2006).

Gonzalez, Guillermo The Privileged Planet (2004).

Lennox, John, God’s Undertaker: Has Science Buried God? (2007).

Lennox, John, God and Stephen Hawking: Whose Design is it Anyway? (2011).

Lewis, C. S., Miracles, (1947).

Malone, John, Unsolved Mysteries of Science, (2001).

Meyer, Stephen C., “The Origin of Biological Information and the Higher Taxonomic Categories”, Proc. of the Biological Society of Washington, 117, 213 (2004).

Meyer, Stephen C., Signature in the Cell: DNA and the Evidence for Intelligent Design (2010)

Penfield, Wilder, The Mystery of the Mind (1975).

Penrose, Roger, The Road to Reality: A Complete Guide to the Laws of the Universe, (2005).

Polkinghorne, John and Beale, Nicholas, Questions of Truth: Fifty-one Responses to Questions About God, Science, and Belief, (2009).

Quastler, Henry “The Emergence of Biological Organization” (1964).

Ross, Hugh The Creator and the Cosmos (2001).

Ross, Hugh Why the Universe is the Way it is (2008).

http://www.reasons.org (Extensive materials on reasons for faith and science).

Ross and Rana, “Origins of Life” (2004).

Schroeder, Gerald L., The Hidden Face of God. Science Reveals the Ultimate Truth, 2001.

Seeds, Michael A., Astronomy: The Solar System and Beyond, 3rd Ed. (2003).

Spetner, Lee, Not by Chance (1996).

Strobel, Lee, The Case for a Creator. A Journalist Investigates Scientific Evidence that Points Toward God, 2004.

Von Baeyer, Hans Christian, Information: The New Language of Science, (2003).

Sorry, but that reading list has nothing to do with expanding students’ horizons. That’s just straight up Christian evangelism. There’s no attempt at balance, and there’s very little in the way of straight science. Worse, several of the entries on that list are outright garbage. Lee Spetner’s book Not By Chance, for example, is just one of those sleazy creationist tomes that has no place in any serious science course, regardless of the religious viewpoint of the professor. If you know rudimentary probability theory and a smidgeon of biology, it should be obvious within a few pages that Spetner hasn’t the faintest idea what he’s talking about. Similar criticisms could be leveled at anything by Lee Strobel, Hugh Ross, or Gerald Schroeder. Including these books in any course related to science is the equivalent of reading books by Ann Coulter in a political science class.

For that matter, if a political science professor based his course reading list on Ann Coulter, Glenn Beck, Mark Levin, and Sean Hannity, that would be prima facie evidence that it was not a serious course at all. But Hedin’s reading list is little better.

To seal the deal, the article reports on some student comments about the course:

Some of the students who have taken Hedin’s class have reported on Rate My Professor that he is a very nice guy who “constantly talks religion,” has “an extremely Christian bias and does not believe in evolution,” and who is “constantly bringing religion into class,” Seidel complained to Gora.

The right is constantly going-on about left-wing indoctrination in college courses. You can be sure that they would go ballistic over a professor who constantly talks about atheism or who is constantly criticizing religion in class. Well, there’s plenty of right-wing indoctrination as well. There are unprofessional people on both sides who are willing to use their classrooms as their own personal soapboxes.

A professor can make clear his own viewpoint without being dogmatic and one-sided. If I were teaching a course about the religious implications of evolution, I would not try to hide my skepticism about the possibility of reconciling Christianity and evolution. But I would also be sure to include readings from the best writers on the other side, and I would treat their views respectfully in class discussions. I would consider it irresponsible to do anything else. The extremely one-sided nature of Hedin’s reading list is very troubling, as his inclusion of cranks and crackpots.

Jerry Coyne has been covering this extensively, and he has argued that, since Ball State is a public university, this course represents a first amendment violation. I’m pretty sure he’s wrong about that. Professors at public universities are not agents of the state in the same way that public high school teachers are. But I don’t really know this area of the law. Is there no point at which the first amendment comes into play? What if I conducted my class like a Pentecostal preacher and graded my students based on their ability to convince me they had come to Jesus? That would certainly be unprofessional, but it would specifically violate the first amendment? Would it matter if the course were required or not? If anyone knows of any court cases on this point I’d love to hear about them.

It also makes me queasy to have outsiders tell college professors what they can and cannot do in the classroom. As bad as this course appears to be, trying to shut him down would be even worse. When the creationists start arguing that it’s a first amendment violation for a biology department to teach about evolution, we want them to be laughed at. I think it’s better just to glare at him in faculty meetings, and let him teach his course.

But I do think it would be perfectly reasonable to take this seriously during annual reviews and tenure evaluations. If the course is as bad as it appears, then his behavior is at least arguably unethical. I would want to take a good hard look at what sort of assignments he assigns and how they are graded, for example. Academic freedom counts for a lot, but at some point your department gets to say that it does not approve of your activities.

I would feel the same way about any professor who was constantly pushing atheism in a science class. College professors are given quite a lot of latitude, and they have considerable power over their students. It is incumbent on us to be responsible in our use of that power. Our job is to educate, not indoctrinate. That doesn’t mean completely suppressing our own views and opinions, but it does often mean giving respectful treatment of views different from our own.

Frankly, I don’t understand professors who preach and indoctrinate on class. In my math courses it’s all I can do to get the students to do the problems right. Who has time to worry about anything else?

“Science literacy is a vaccine against the charlatans of the world that would exploit your ignorance.” -Neil deGrasse Tyson

Well, I guess it’s that season again. The charlatan who claims to have invented a cold fusion device — the same device whose flaws were exposed here two years ago — has just held an “independent test” of his device, and there’s now a physics paper out claiming that this device works, and must be powered by some type of nuclear reaction!

Image credit: G. Levi et al.; get the whole paper here: http://arxiv.org/pdf/1305.3913v2.pdf.

Well.

Look, let’s get a few things out into the open first. If there is a cold fusion device that actually works, that can harness the power of nuclear fusion to create energy, it would change the world. We would — as I’ve written recently — have a virtually limitless source of clean and cheap energy, and would not only be able to travel to Mars, but to any other world in our Solar System. We could even, literally, reach for the stars!

Image credit: OeWF (Katja Zanella-Kux), via http://www.wired.co.uk/.

But it’s not enough to just simply think about how wonderful it would be if it were true, especially because whether cold fusion can even physically happen in our Universe is currently an open scientific question. (The evidence so far says no, but that doesn’t mean it isn’t possible in principle!)

What we must do, when confronted with a claim that’s this extraordinary — that we have a device, at low-temperature, with neutral atoms, fusing atomic nuclei — is demand evidence that shows this is really true, and that we aren’t falling victim to some elaborate ruse.

Image credit: John Cooke, of “Piltdown Man”, one of history’s most elaborate scientific hoaxes.

What we need, if we want to take this claim seriously, is solid, incontrovertible evidence that what’s being claimed is what’s actually happening. Because one of the most important responsibilities that science has to society is to protect it from frauds, hucksters, shysters and con artists who would defraud you out of your money, time, and trust with their cheap trickery and chicanery.

Image credit: Rossi, Kullander, Essen and the e-Cat, retrieved from energydigital.com.

I’m taking it for granted that the vast majority of you don’t have the required expertise to tell whether this is legitimate, or whether this is an example of someone trying to swindle you (and all of us) into investing in something that’s meritless. But a lot of normally smart people are getting very excited about this, including:

• Sebastian Anthony over at ExtremeTech,
• Francie Diep over at Popular Science,
• Mark Gibbs over at Forbes, and shockingly,
• Tommaso Dorigo of Quantum Diaries.

So we’ve got to ask, is this test the real deal, or is it nothing more than crackpottery, as Lubos Motl says?

Image credit: from the Nov. 12, 2012 testing of the E-Cat, via G. Levi et al.

Let’s answer the following question: What would it take to convince a reasonable observer that you’ve got a controlled nuclear reaction going on here?

There are a few ways we could do it:

1. Allow a thorough examination of the reactants before the reaction takes place, and another of the products after the reaction, and show that nuclear transmutation has in fact taken place.
2. Start the device operating by whatever means you want, then disconnect all external power to it, and allow it to run, outputting energy for a sufficiently long time in a self-sustaining mode, until it’s put out a sufficient amount of energy to rule out any conventional (i.e., chemical) energy sources.
3. Place a gamma-ray detector around the device. Given the lack of shielding and the energies involved in nuclear reactions, gamma-rays should be copious and easy to detect.
4. Accurately monitor the power drawn from all sources to the device at all times, while also monitoring the energy output from the device at all times. If the total energy output is in sufficient excess to the total energy input to rule out any conventional (i.e., chemical) energy sources, that would also be sufficient.

Fair enough? These all sound reasonable to me, and I would accept any independent test of these three methods as enough evidence to pique my interest. Let’s see what the claims are.

Image credit: G. Levi et al.

So they’re again claiming that this is nickel + hydrogen fusion, which should result in copper. Now, it’s important to know, the last time this was claimed, the nickel that was analyzed was found to contain the isotopic ratios of normal nickel mined on Earth, while the copper (10% of the product) was found to contain the isotopic ratios of copper found naturally on Earth, not the ratio you’d expect to find copper in if nuclear fusion had occurred! (Since only Nickel-62 and Nickel-64 can fuse with hydrogen into copper, it’d be impossible to get a 10% copper product in any case!)

Image generated using the free graphing software at nces.ed.gov.

For this test, Rossi disallowed the examination of either the reactants or the products, claiming that it would reveal his secret catalyst. So option 1 wasn’t available.

Rossi also refused to unplug the machine while it was operating! Now, Peter Thieberger (who co-wrote this post with me, and who is a respected nuclear/particle physicist) has demonstrated just how easy it would be to keep power flowing to a device in such a way to fool an ammeter, which is a device for measuring electrical current. In other words, it would show that no current was flowing when one actually was!

Image credit: Peter Thieberger.

So option 2 wasn’t available, either; there could’ve been more power continuously supplied to this setup than was accounted for.

There was also no attempt made to measure gamma-rays, so option 3 didn’t happen. Reading the paper, Rossi left the machine plugged in at all times, and hid a great many details during this independent test. Such as:

“… the E-Cat HT was already running when the test began…”

“…it was not possible to inspect the inside of the control box…”

So, what did this team actually do?

Image credit: Figure 6, from G. Levi et al.

They measured the tube, from a distance, with an infrared camera, to determine its temperature over time. They claim to have set up radiation detectors at a distance to look for high energy photons, but do not include those results. (They say that the results are available upon request. If you get them, please post them in the comments!)

They claim that the input power is well-measured and comes out to an average of 360 Watts, over a timespan of around four days. They provide no data for this, they simply claim it. What can you do; are they telling the truth, are they telling the truth as best as they know it, or something else? Without the data, how can you know?

Image credit: Figure 14 from G. Levi et al.

Well, the short of it is, it got very hot and stayed very hot — about three-to-seven times hotter than you’d expect based on 360 W of continuous power — for the entire time that it ran.

And then, when you get all the way to page 20, you find this red flag:

During the coil ON states, the instantaneous power absorbed by the E-Cat HT2 and the control box together was visible on the PCE-830 LCD display. This value, with some fluctuations in time, remained in any case within a range of 910-930 W. By checking the video image relevant to the PCE-830 LCD display, we were also able to estimate the length of the ON/OFF intervals: with reference to the entire duration of the test, the resistor coils were on for about 35% of the time, and off for the remaining 65%.

So… it wasn’t a continuous 360 Watts, but rather there was a switching between on/off states, where it was drew over 900 W of power for about a third of the time, and then far less for the other two-thirds. They also only approximate, rather than measure (or provide data for) the amount of power drawn.

Then they claim the following:

Image credit: page 22 of G. Levi et al.

Okay, look.

I’m done pretending that this is science, or that the “data” presented here is scientifically valid. If this were an undergraduate science experiment, I’d give the kids an F, and have them see me. There’s no valid information contained here, just the assumption of success, the reliance on supplied data, and ballpark estimates that appear to be supplied “from the manufacturer.”

This is not a valid way to do science at all. And this is certainly not even close to meeting the criteria required for extraordinary evidence to back up such an extraordinary claim.

Image credit: Hemant Mehta of the Friendly Atheist blog.

I — for once — will also encourage you to read Lubos’ take on this, because he seems to be the only person other than me who recognizes what awful pretend-science this is.

I’m not trying to rain on your parade, I’m not trying to poo-poo things we don’t have a full understanding of, and I’m not even trying to convince you that cold fusion is impossible. I’m trying to get you to recognize that there are standards of evidence you must hold these claims to, and that this crappy, crackpot paper has failed to meet them, and has failed egregiously.

But if you test it scientifically, then we’ll talk. Not before. Until then, you’re just preying on people who don’t know enough physics to see through your ruse, and I’ll be here to speak up against it, and call shenanigans.

Image credit: from Ebaumsworld; bonus points if you recognize the source.

Shenanigans, bitches. Now you know.

I do, however, want to take issue with one thing in the post. When assessing the historical place of American physics, he writes:

Here’s my personal list for the title of greatest American physicist in history, in no particular order: Joseph Henry, J. Willard Gibbs, Albert Michelson, Robert Millikan, Robert Oppenheimer, Richard Feynman, Murray Gell-Mann, Julian Schwinger, Ernest Lawrence, Edward Witten, John Bardeen, John Slater, John Wheeler and Steven Weinberg. I am sure I am leaving someone out but I suspect other lists would be similar in length. It’s pretty obvious that this list pales in comparison with an equivalent list of European physicists which would include names like Einstein, Dirac, Rutherford, Bohr, Pauli and Heisenberg; and this is just if we include twentieth-century physicists. Not only are the European physicists greater in number but their ideas are also more foundational; as brilliant as the American physicists are, almost none of them made a contribution comparable in importance to the exclusion principle or general relativity. [...]

More importantly though, the sparse list of great homegrown American physicists makes two things clear. Firstly, that America is truly a land of immigrants; it’s only by including foreign-born physicists like Fermi, Bethe, Einstein, Chandrasekhar, Wigner, Yang and Ulam can the list of American physicists even start to compete with the European list. Secondly and even more importantly, the selection demonstrates that even in 2013, physics in America is a very young science compared to European physics. Consider that even into the 1920s or so, the Physical Review which is now regarded as the top physics journal in the world was considered a backwater publication, if not a joke in Europe (Rhodes, 1987). Until the 1930s American physicists had to go to Cambridge, Gottingen and Copenhagen to study at the frontiers of physics.

I would argue that there’s a word missing near the end of that last sentence, namely “theoretical.” It’s absolutely true that American theorists like Oppenheimer studied in Europe in order to learn from the quantum pioneers, but I would say that even by the 1930′s, American experimental physics was nearly equal to that in Europe. Michelson, Millikan, Lawrence are a trio to put up against anyone Europe has to offer in that same time period (Thomson and Rutherford are the big names on that side of the pond), and you can throw in people like Compton and Davisson and Germer as well. Depending on whether you count cosmology as part of physics, you could probably get Hubble into the mix on the American side, as well.

Now, it’s true that they didn’t contribute “foundational” ideas to physics, which tends to see them pushed somewhat down the list of “greats,” but I think that’s a mistake. Yeah, the exclusion principle and general relativity are great ideas, but big ideas are meaningless unless you can measure them, and Americans were essential to that process. Einstein famously proposed a revolutionary particle theory of light to explain the photoelectric effect, but it was Millikan’s measurements (which grudgingly confirmed the photon model) that forced people to take it seriously, and Compton’s gamma-ray scattering experiments helped seal the deal.

This is, of course, a personal obsession with me, but I think it’s essential to remember that theory and experiment go hand in hand. Revolutionary theories arise because they’re needed to explain experimental results, and they’re ultimately accepted because they’re found to agree with further measurement. Experiments get downplayed because they’re full of fiddly technical details and harder to explain and interpret, but they’re absolutely essential, and the US was pulling its weight in experimental physics even before top theorists started fleeing fascist regimes. (This is prompted in part by a bunch of recent reading on the history of 20th century physics, where even some big European names grudgingly admit that the Americans were good experimenters…)

So, while Europe is still ahead, I think it’s a somewhat closer thing than Jogalekar suggests, when you properly weight the two facets.

As for the general question of who was the greatest American physicist, I’d probably cast my vote for John Bardeen, who is, after all, the only person to share two Nobel Prizes in Physics. He’s the “B” in the “BCS” theory of superconductivity, but more importantly helped invent the transistor. It’s hard to think of anyone whose contributions to physics had a bigger influence on the way we live today, and if that’s not greatness, I’m not sure what is.

The second part of the scandal is the auditing of political activists who have opposed the administration. The Journal’s Kim Strassel reported an Idaho businessman named Frank VanderSloot, who’d donated more than a million dollars to groups supporting Mitt Romney. He found himself last June, for the first time in 30 years, the target of IRS auditors. His wife and his business were also soon audited. Hal Scherz, a Georgia physician, also came to the government’s attention. He told ABC News: “It is odd that nothing changed on my tax return and I was never audited until I publicly criticized ObamaCare.”

Franklin Graham, son of Billy, told Politico he believes his father was targeted. A conservative Catholic academic who has written for these pages faced questions about her meager freelance writing income. Many of these stories will come out, but not as many as there are. People are not only afraid of being audited, they’re afraid of saying they were audited.

Anecdotes. Powerful stuff. But Silver brings the bucket of cold water:

Ms. Noonan is surely correct that many conservative taxpayers were audited. In fact, based on some simple math that I’ll present in a moment, it’s likely that hundreds of thousands of Mitt Romney voters were selected for an audit in 2012.

However, it’s also likely that hundreds of thousands of Mr. Obama’s supporters were audited. Although the percentage of taxpayers who are audited is relatively low — about 1 percent — the number of taxpayers in the United States is so large that this still yields well more than a million audits every year, across the political spectrum.

That’s just the beginning. The details come later.

Go to Astrobiology Future to sign in to the live web chat. Questions and comments will be taken both from call-ins and from written questions.

The online discussion will be moderated by Dr Francis McCubbin from UNM, Dr Sean Raymond from Laboratoire d’Astrophysique de Bordeaux, and yours truly…

The live session will, as with the other Roadmap sessions, be followed by a week long opportunity to input questions, ideas and topics for discussion at The Astrobiology Future Forum.

The four questions identified to kick-off the discussion are:
• Is life a chemical consequence of thermodynamics or did it emerge in spite of thermodynamics?
• Will we ever be able to uniquely identify fossils of microorganisms in the rock record of another planet given the absence of biologically exclusive chemical and morphologic signatures?
• Organic molecules can be produced a wide variety of inorganic chemical processes, what geologic conditions are needed to promote the concentration and complexification of organics towards abiogenesis?



• What factors determine the amount of water delivered to planets in a star’s habitable zone and the availability of that water for participation in chemical reactions?


Water delivery to the inner planets for different planetary system configurations: Raymond, Mandell & Sigurdsson

As I have noted before, it is critically important that the community in general, and junior researchers in particular, provide input, questions and ideas.
If you don’t, I’ll decide your research priorities for you.
So there!

Giant Intelligent Squid!

The NASA online discussion session on the Astrobiology Roadmap continues this week.

This morning there was a web chat on “Early Evolution of Life and the Biosphere”, which is being followed up by an ongoing online discussion on the questions posed and soliciting ideas for priorities in research direction.

The questions being discussed are:

• How has the exponential growth in our discovery and understanding of exoplanets impacted the kinds of questions and information we extract from the early Earth record?
• Are there problems you think are vital to understanding the early evolution of life and the biosphere that have not yet been articulated by NASA?
• What types of approaches are needed to answer mechanistic questions about the early evolution of life and the biosphere, and which specific approaches are most helpful for particular types of questions?

It is critical that there be community input to these discussions.
The questions posed and ideas suggested will be factored into the current and immediate discussion on the future priorities for research in Astrobiology.
It is particularly important the junior researchers provide their perspective on what are the interesting and important questions do explore.

“The Milky Way is nothing else but a mass of innumerable stars planted together in clusters.” -Galileo Galilei

Welcome back to another Messier Monday here on Starts With a Bang! With 110 deep-sky objects making it up, the Messier Catalogue is the first comprehensive, accurate catalogue of faint (but not too faint) fixtures in the night sky. Each object tells its own unique tale, and is visible to amateur and professional skywatchers alike with even the simplest of equipment. Many of these objects were discovered by Charles Messier himself (or his assistant, Pierre Méchain), while others go all the way back to antiquity!

Image credit: SEDS compilation of all 110 Messier objects, via http://messier.seds.org/.

Today, we’re taking a look at just the fifth object in his catalogue, the globular cluster Messier 5. Discovered in 1702 by Gottfried Kirch and Maria Margarethe, it’s a collection of some 100,000 stars contained within a radius of around 100 light years, like all globular clusters. However, Messier 5 is unlike the majority of globulars for a number of reasons, which you can marvel at every time you take a look at it. Here’s how to easily find this wonder of the night sky.

Image credit: Me, using the free software Stellarium, via http://stellarium.org/.

The brightest star in the northern hemisphere, Arcturus, is one of the easiest to find: just follow the “arc” of the Big Dipper’s handle and you can’t miss this orange giant! You can “speed on” to Spica, a bright blue star, and find yellowish Saturn just a few degrees away for the rest of the year. But if you look to the left of Arcturus and Spica, you’ll find a fainter but still bright star called Unukalhai (or α Serpentis), the brightest star in the constellation of Serpens.

If you look back towards Spica a few degrees, you’ll see the faint, naked-eye star 5 Serpentis, and if you train your binoculars or telescope on that star, you can’t miss Messier 5, less than half-a-degree away.

Image credit: Me, using Stellarium.

Being a globular cluster, M5 looks like a dense, fuzzy ball that’s brighter towards the center and gradually fainter the farther you move away from the core. Like most globulars, it’s very old — more than 10 billion years for certain and possibly up to 13 billion, as dated from its Hertzsprung-Russell diagram — and metal-poor, with its stars containing less than 10% of the elements heavier than hydrogen and helium that the Sun has.

Image credit: Eduardo Mariño, via his flickr photostream.

But unlike most globulars, there are virtually no bright stars in M5; the brightest star in there is only of magnitude 12.2, meaning that (realistically) you need at least a 6″ (15 cm) telescope to actually tell that this fuzzball is made of stars! Messier himself wrote that it’s a round nebula that doesn’t contain any stars, which is exactly what I see with my own equipment.

But even many casual amateurs have far better equipment than Messier did in the latter-half of the 18^th Century.

Image credit: CN member 2020BC, via Charlie Hein of http://www.cloudynights.com/.

There are a number of features that make this globular cluster really stand out:

1. It’s very close (20′ to be precise) to a naked-eye star, something that’s true for only a small minority of deep-sky objects,
2. It’s got a very dense nucleus where individual stars become very difficult to resolve, and yet also is a very extended globular cluster, with a radius approaching 200 light-years,
3. And, as you may have already been able to tell (but it’s abundantly clear in the image below), this cluster is ellipsoidal, rather than spherical!

See for yourself!

Image credit: Robert (Bob) J. Vanderbei of Princeton University.

Because this globular cluster is — like most globulars — so old, the very bright blue stars you can see are blue stragglers, or stars that were created relatively recently from the merger of smaller stars, and the bright yellow/orange stars are Sun-like stars that have evolved into giant stars, something that will be our star’s fate when it’s as old as Messier 5 is now!

But what you might not realize is that this globular cluster is full of a special class of low-mass variable stars known as RR Lyrae stars. What you see actually depends slightly on when you look!

Image credit: Robert (Bob) J. Vanderbei of Princeton University, once again.

With at least 105 known variable stars in it, Messier 5 is one of the most prolific globular clusters in this sense! It’s also one of the larger ones, with some estimates of the total number of stars in M5 reaching 500,000! (This makes sense, since one out of every few thousand stars is known to be a variable-type star.) It’s located a distance of 25,000 light-years away, moving away from us at about 52 km/sec.

Image credit: © 2006 – 2012 by Siegfried Kohlert of http://www.astroimages.de/.

The closer you can look into the core, the higher the concentration of blue stars becomes. This is a relatively common feature in globular clusters, as mergers and mass-transfer becomes more common in the densest regions of a cluster. This beautiful image by Adam Block really showcases just what’s going on in terms of star color and how it changes with radius.

Image credit: Adam Block, Mt. Lemmon SkyCenter, University of Arizona.

As always, however, the best image of the core of this globular cluster comes from the Hubble Space Telescope, whose resolving power is really unparalleled when it comes to separating out individual stars in dense, distant regions. The central core here is only 6 light-years in diameter, or just 50 arc-seconds across as seen from our point-of-view.

Image credit: ESA / Hubble & NASA.

Because I’m a sucker for it, let’s take a full-resolution trip through the inner core of Messier 5, just to show you how spectacularly (and how quickly) the star density rises-and-falls as you pass through the very central region!

Image credit: ESA / Hubble & NASA.

Remember, there are 29 globular clusters in Messier’s catalogue and some 200 total in the halo of our galaxy, but each one is a unique collection of ancient stars with its own history, and I’m pleased to get to share this one with you today, on Messier Monday!

Including today’s entry, we’ve taken a look at the following Messier objects:

• M1, The Crab Nebula: October 22, 2012
• M5, A Hyper-Smooth Globular Cluster: May 20, 2013
• M8, The Lagoon Nebula: November 5, 2012
• M13, The Great Globular Cluster in Hercules: December 31, 2012
• M15, An Ancient Globular Cluster: November 12, 2012
• M20, The Youngest Star-Forming Region, The Trifid Nebula: May 6, 2013
• M25, A Dusty Open Cluster for Everyone: April 8, 2013
• M30, A Straggling Globular Cluster: November 26, 2012
• M33, The Triangulum Galaxy: February 25, 2013
• M37, A Rich Open Star Cluster: December 3, 2012
• M38, A Real-Life Pi-in-the-Sky Cluster: April 29, 2013
• M40, Messier’s Greatest Mistake: April 1, 2013
• M41, The Dog Star’s Secret Neighbor: January 7, 2013
• M44, The Beehive Cluster / Praesepe: December 24, 2012
• M45, The Pleiades: October 29, 2012
• M48, A Lost-and-Found Star Cluster: February 11, 2013
• M51, The Whirlpool Galaxy: April 15th, 2013
• M52, A Star Cluster on the Bubble: March 4, 2013
• M53, The Most Northern Galactic Globular: February 18, 2013
• M60, The Gateway Galaxy to Virgo: February 4, 2013
• M65, The First Messier Supernova of 2013: March 25, 2013
• M67, Messier’s Oldest Open Cluster: January 14, 2013
• M72, A Diffuse, Distant Globular at the End-of-the-Marathon: March 18, 2013
• M74, The Phantom Galaxy at the Beginning-of-the-Marathon: March 11, 2013
• M78, A Reflection Nebula: December 10, 2012
• M81, Bode’s Galaxy: November 19, 2012
• M82, The Cigar Galaxy: May 13, 2013
• M83, The Southern Pinwheel Galaxy, January 21, 2013
• M92, The Second Greatest Globular in Hercules, April 22, 2013
• M97, The Owl Nebula, January 28, 2013
• M102, A Great Galactic Controversy: December 17, 2012

Come back next week, where we’ll take a look at one of the rare “late additions” to Messier’s catalogue and explore another one of these deep-sky wonders, only here on Messier Monday!