Saturday, 30 April 2016

Strange moments in science: The theft of the EBEX telescope

In early 2013, a balloon-born telescope, EBEX, was launched from Antarctica and circled the South Pole over the course of two weeks, attempting to observe the Cosmic Microwave Background and its polarization. A number of things went wrong with this mission, but it almost didn't happen because  the truck containing the telescope was stolen from a motel in Texas.

EBEX before and during launch. Images from the Ebex in Flight blog via and NewScientist.

The EBEX (E and B EXperiment) telescope was assembled in Minnesota with input from an international team of collaborators. One group was at McGill where I was doing my PhD, and I played on a hockey team with a few people involved in the mission, including my friend Kevin who was the one of the main McGill guys on the collaboration. The telescope had a large number of bolometers (measuring incident radiation through a change in temperature) which, when floated above the lower atmosphere with a balloon would attempt to measure the polarization of the cosmic microwave background and look for B modes as a signature either of cosmic dust or primordial gravitational waves, something that was later somewhat controversially discovered by the BICEP2 telescope, also in Antarctica.

In May 2012, it was on its way from Minnesota to NASA's balloon centre in Palestine, Texas, being transported in the back of a truck. However, the truck failed to arrive, so the trucking company looked into it. According to its GPS, it was last seen at a truck stop Hutchins, Texas, and the trucking company attempted to contact the driver, but could not reach him. Several days later, he was found sleeping in the cab of his truck, but the trailer and the 8 million dollar cargo were still missing. The driver claimed the truck was stolen from the motel he was staying at. Eventually the trailer was found at a carwash in Dallas, with the telescope still inside and undamaged.
Artist's rendition.
According to a 2012 article, the driver had been fired, and the head of the trucking company commented "Why didn't he decide to do this on a load of potato chips?"

After it was recovered, the telescope was configured to the balloon and shipped to Antarctica, where it was launched. A number of things went wrong with EBEX: one of the orientation controllers overheated in the sun, causing the telescope to lose control of where it was pointing (I recall Kevin calling it "a dance party in space"), meaning it only imaged a donut-shaped swath of sky. It eventually landed out on the ice, and without sufficient time and resources to launch an immediate recovery the scientists had to wait until the next season to go access it. Not much has been heard from the collaboration since, although there may be plans to build and launch a new and improved version, hopefully one that will maintain orientation. To read more about EBEX and its launch and recovery (including the truck disappearance), I recommend this blog.

The flight of EBEX, from the EBEX in Flight blog.

As an experimental scientist I'm accustomed to things going wrong, but I can't imagine showing up to work one day to find my microscope missing.

Wednesday, 20 April 2016

Visit to the Roger Babson Anti-Gravity monument at Tufts

In the early 20th century lived an eccentric businessman named Roger Babson. He was a sort of Donald Trump of his time, writing books, founding a college, and running for president. Instead of hating Muslims and Mexicans, what Babson really hated was gravity, and declared it to be mankind's foremost enemy. 

He founded an organization devoted to defeating gravity's grip on humanity, part of which involved organizing the yearly Gravity Research Foundation essay contest, which has been won by the likes of Stephen Hawking and entered by the likes of me. He left a series of monuments around New England dedicated to his crusade. The closest one to me is at Tufts (yes, Tufts), and I visited it this evening. There used to be a yearly tradition of digging up the monument and carrying it to see if gravity had been defeated yet, but that was discontinued.

I plan to write a longer article about this history of his contest and his foundation, and for now you can find other articles about it online. I wrote an article about the history of the contest on PhysicsForums!

The text of the monument reads:
"This monument has been erected by the Gravity Research Foundation, Roger W. Babson founder. It is to remind students of the blessings forthcoming when a semi-insulator is discovered in order to harness gravity as a free power and reduce airplane accidents. 1961"

Saturday, 16 April 2016

Tiglath-Pileser's Hunting Omission

This post is on a different topic than usual post-doc ergo propter hoc content.

In the discussions or conclusions of academic papers, you will often find a description of work that the author had done but chose not to include in the paper. The reason is often because it would make the paper too long without adding much interest, or is a bit too tangential to keep the paper on topic. These are slightly different than the "future work will involve..." statements that often come at the end of papers. Including these references to omitted work can inform the reader that due-diligence was performed by the investigator, and also makes the author sound smarter and more impressive.

I was reading an account of the conquests of Tiglath-Pileser I, king of Assyria around 1100 BC. These accounts were inscribed on clay tablets in cuneiform script in the Akkadian language, and were found in the ruins of Assur, in what is now Iraq.
This is actually the equally ferocious Tiglath-Pileser III, who has a better picture than Tiglath-Pileser I.

Assyria was a dominant military power in the Middle East in the late Bronze Age and early Iron Age, before being supplanted by the Babylonians. They are known for their use of chariots in battle, their ferocious descriptions of their conquests, and the scattering of the ten "lost tribes" of Israel after conquering the Northern Kingdom. Tiglath-Pileser I ruled at the end of the Bronze Age, before a period of tumult involving the invasion of the Sea Peoples and the collapse of the Mediterranean Bronze age. Tiglath-Pileser I went on a rampage Eastwards, conquering literally dozens of kingdoms in several pitched battles, looting the region and defiling the temples of the defeated. He writes, in typical Assyrian fashion:

The city of Khunutsa, their stronghold, I overthrew like a heap of stubble. With their mighty troops in the city and on the hills I fought fiercely. I defeated them; their fighting men in the middle of the forests I scattered like chaff. I cut off their heads as if they were carrion; their carcasses filled the valleys and (covered) the heights of the mountains. I captured this city; their gods, their wealth, and their valuables I carried off, and burnt with fire. Three of their great castles, which were built of brick, and the entire city I destroyed and overthrew, and converted into heaps and mounds, and upon the site I laid down large stones; and I made tablets of copper, and I wrote on them an account of the countries which I had taken by the help of my Lord Ashur, and about the taking of this city, and the building of its castle; and upon it I built a house of brick, and I set up within it these copper tablets.

There are many such descriptions. However, after he finished his descriptions of all the armies he defeated and cities he destroyed, he left the following note:

I have omitted many hunting expeditions which were not connected with my warlike achievements. In pursuing after the game I traversed the easy tracts in my chariots, and the difficult tracts on foot. I demolished the wild animals throughout my territories.
In mentioning these omitted hunting achievements, he saves the reader the time that would have gone into taking in all this out-of-scope extraneous information, but uses the stated omission to bolster his credibility as a martial conqueror. I believe that this is one of the first published omissions to other relevant work, setting the stage for scholarly literature for the next three millennia.

This may not be the first reference to a deliberate omission; I haven't thoroughly scoured the Egyptian and Akkadian records.

Sunday, 10 April 2016

Physics Shower Thoughts Part II: Cosmic Radiation Pressure and Relativistic Spacecraft

This is the second instalment of "Physics Shower Thoughts," an exploration of an idea that I found interesting that ultimately may not have monumental consequences in the grand scheme of our understanding of the universe. In this case I was inspired by a question on reddit that was answered by another physics blogger, VeryLittle of Quarks and Coffee. The question was about the limits of acceleration given special relativity, and my shower thought was about the role of blue-shifted radiation pressure in limiting that acceleration.

The setup is thus: an object (let's call it a spaceship) under the influence of a constant force in its reference frame will accelerate. The acceleration will seem uniform but as it gets very fast relative to its initial rest frame, its velocity will plateau asymptotically towards light speed. In our universe, however, there is a cosmic microwave background that will be blueshifted in front of us as we move in one direction, and redshifted behind us. The radiation pressure from this background will become stronger and counter the force that our spaceship is producing. This may limit the ability of our spaceship to accelerate. So, to what extent does this matter?

It's a good picture, ok.

To figure this out, we need to work out two things: the blue-shifted blackbody radiation pressure, and the relativistic acceleration under special relativity. The shifting of the blackbody spectrum can be considered with varying degrees of complexity, including a Lorentz transformation of the entire spectrum and a mixing of polarizations. However, I am interested in a simple solution and an order-of-magnitude estimate, so I will be using a simpler method: I will consider the Stefan-Boltzmann law given a relativistic Doppler shift of the peak frequency of the blackbody distribution.

Incident electromagnetic power can be converted to a radiation force by dividing by the speed of light. The Stefan-Boltzmann law gives us areal power density, so we can multiply by the cross-sectional area as well to from power density to pressure to force:

$F_{r}=\frac{A}{c}\sigma T^4$

The Stefan-Boltzmann constant $\sigma$ is a product of several powers of Boltzmann and Planck's constants as well as the speed of light, but its value in SI units is easy to remember: 5-6-7-8, or 5.67x10$^-8$ Watts per meter squared per kelvin fourthed.

According to Wien's displacement law, the temperature is proportional to the peak frequency of the distribution, which I'll call f. In our universe at this time, f is about 160 GHz. The proportionality constant is based on numerically minimizing the Planck spectrum, and in terms of frequency Wien's law can be simply expressed:

$T=\alpha f$

The proportionality constant for frequency is actually very close to two times the constants of Pythagoras* and Boltzmann divided by that of Planck, or in SI units about 5.9x10$^{10}$ Hertz per kelvin.

Moving toward a source, the frequency experiences a Doppler shift and is transformed into f', and if the motion is fast enough we should take into account the full relativistic Doppler shift:


The radiation hitting us from behind is redshifted, and I will deem it small enough to ignore. Plugging this all together, the transformed cosmic radiative force on our spaceship is:

Now we consider the relativistic acceleration of this spacecraft. The way to incorporate special relativity into Newton's law of motion is to remember that the change in momentum is the product of force and time. Momentum is the product of mass, velocity, and the Lorentz factor. If we just have a constant force then we can find the acceleration as a function of time:

If you plot this vs time for some values of F and m you will find that it increases and asymptotically approaches light speed. Somewhat coincidentally, if you set F/m to be Earth's gravity, it will take about a year to get close to light speed.

Accelerating under Earth-gravity-equivalent for three years. To convert seconds to years, remember that pi seconds is a nanocentury.

If we then incorporate our radiation pressure into the force side of the equation, it gets a bit more complicated.

This does not have a closed form expression for the velocity, but if I solve it numerically I find.... that it increases and asymptotically approaches light speed. For the values I use, it is essentially indistinguishable from the radiation-free solution. However, if I calculate values for long enough times with high enough numerical precision, the radiation solution does converge on a sliiiiiightly subluminal value (99 point a bunch of 9's percent light speed). So, what's going on?
This is going on.
Basically when the spaceship is going fast enough, the radiation force becomes strong enough to counter the accelerating force, and the net force is zero. This velocity is easier to calculate, we just solve the transformed radiation pressure equal to constant F, and solve for v. To simplify notation, I have introduced the variable pressure P=F/A:

Just the general form of this expression is $(1+x-2\sqrt{x})/(1-x)$, which is monotone decreasing, passing zero when x=1. In our scenario, that corresponds to $f^{4}/P=\alpha^{4}c/\sigma$, which I guess is the frequency and pressure required to have zero acceleration from the rest frame.

So, let's plug in some realistic values for this critical velocity and see what happens. Using the space shuttle as a framework for a spaceship, it has a mass of two million kg, a thrust of 12.5 meganewtons, a cross-sectional area of roughly 200 square meters. This puts its maximum velocity at 99.99999992% the speed of light, given constant thrust.

Now there are many other factors I didn't take into account. I could use a more rigorous transformation of the blackbody radiation. The length-contraction of the spaceship might change the incidence of the radiation, compounding the effect (it's kind of funny that shape becomes important again, not for aerodynamics but for electrodynamics). The mass could decreases as fuel is ejected from the rocket (maintain fuel supply for this journey could perhaps be attained with a Bussard ramjet, but that's beyond the scope of this article), which increases the acceleration. And it would take so long to accelerate to these high speeds that the cosmic background radiation could become more significantly redshifted due to the intervening cosmic expansion.

As VeryLittle pointed out in his reddit post, such a cosmic speed limit already exists for protons: the GZK limit is the speed at which cosmic ray protons see the CMB blueshifted to the point that it interacts with the now-gamma rays. This corresponds to an energy of 8 joules, but the speed is close enough to light that the number of 9's in the percentage doesn't really matter (whereas for the space shuttle it's only 7 decimal 9's). I guess protons are more electroaerodynamic than spaceships.

So, to summarize, the blueshifting of the cosmic microwave background may have an extremely tiny effect on the limiting speed of relativistic spacecraft. However, if I were a relativistic spacecraft engineering, I wouldn't worry about it.

*also known as the square root of two.