Superluminal claims require super evidence

Neutrinos, those mercurial smidgens of the particle world, travel faster than the speed of light. That's the claim the OPERA collaboration makes in a paper subtly titled: Measurement of the neutrino velocity with the OPERA detector in the CNGS beam. This is a big claim that could have implications for particle physics and time travel. It has made the news, news, news, news, but what does it all mean? Lets talk about neutrinos.

First, let me say that if neutrinos do travel faster than the speed of light then physicists have a lot of explaining to do. The repercussions of faster that light travel for any particle (also known as superluminal travel) would be revolutionary. So revolutionary that most physicists I spoke to this past week at a conference did not take the news too seriously: it was too extraordinary to comment on without further thought and details. The OPERA collaboration is actually very brave for putting this paper out there (i.e. on the ArXiV) and asking for outside analysis. They don't even pretend to begin to consider the ramifications. The last line of the paper sums up their position:

We deliberately do not attempt any theoretical or phenomenological interpretation of the results.

So let me ignore the wild theoretical implications and discussions of tachyons and just talk about the experiment and an astrophysical constraint on the velocity of neutrinos.

Why are physicists so confident that neutrinos travel at the speed of light? Well, start with the fact that every piece of credible data ever taken has never seen anything—be it particle or information—travel faster than the speed of light. Given previous observations it is hard to understand how neutrinos could be any different. Of course neutrinos are very difficult to measure because they interact very weakly with regular matter. Consider that 60 billion neutrinos generated from the core of the sun pass through your pinky each second and none of them interact with you (nor do they interact with the Earth, they are passing through you day and night).

The creation and detection of neutrinos is complicated. The process begins for the OPERA experiment over at CERN where the Super Proton Synchrotron (SPS) creates high energy (400 GeV/c) protons that collide with a graphite target producing pions and kaons which decay into muons and muon neutrinos. The neutrinos coming out of SPS are almost pure muon type neutrinos with an average energy of 17 GeV. The neutrinos travel through the solid Earth in a straight path unimpeded into a cavern below a mountain, Gran Sasso, in Italy. The OPERA neutrino experiment was designed to look for the direct appearance of muon to tau neutrinos (ν_μ → ν_τ), but their anomalous findings on the velocity of neutrinos is much more interesting.

The OPERA experiment found that the velocity of neutrinos was about 0.00248% faster than the speed of light. This measurement was made by precisely measuring the distance traveled by neutrinos and the time of travel. The OPERA collaboration did a lot of work to measure both parameters precisely. They found this velocity by measuring that the time of arrival of neutrinos at their detector by using atomic clocks. Their measurement was precise to a few nanoseconds. Wow, that is quick. Light only travels about a foot in a single nanosecond.

In order to measure the distance between CERN and Gran Sasso the OPERA team used very precise GPS systems. For example, they noticed a 2009 earthquake in that area produced a sudden displacement of 7 centimeters. So the exact distance the neutrinos traveled was 730534.61±.20 meters (or about 2.44 light milliseconds), however some have suggested that the GPS based positioning they used has errors introduced by atmospheric refraction. Intriguing possibility.

In order to measure the time, what OPERA calls the time of flight measurement, they used atomic cesium clocks. But the 'time' cannot be precisely measured at the single interaction level since the protons from the SPS source have a 10.5 microsecond extraction window. They had to look at time distributions where the most likely time for a burst of neutrinos to be created was inferred to higher precision. Additionally, the actual moment where the meson produces a neutrino in the decay tunnel is unknown, but it introduces negligible inaccuracy in the time of flight measurement. So, these distance and time measurements are really important, but really subtle. I recommend reading the paper if you are a glutton for punishment.

There is a very interesting constraint on the speed of neutrinos that comes from astronomy. It was the neutrinos and photons released from the death of a star. Supernova 1987A (SN 1987A) exploded 168,000 years ago when fusion in the core of an old star ceased and the weight of the outer layers of the stars caused the core to collapse. The protons in the atoms of the core of the star merged with the electrons present and converted themselves into neutrinos and electron neutrinos. A mega amount of electron neutrinos, about 10⁵⁸, were generated and they began their epic journey to Earth. Some of these neutrinos arrived on Earth one morning in February of 1987 in a burst lasting less than 13 seconds. Of those many neutrinos two dozen interacted with detectors on Earth.

Astronomers observed light from SN 1987A just three hours after the neutrinos arrived. Just such a delay is expected as the fireball of the supernova had to have some time to expand and become transparent to photons, whereas neutrinos could escape much sooner. The explosion occurred at a known distant out in the Large Magellenic Cloud. This distant explosion created photons and neutrinos in a timed race to the Earth. With the these measurements in hand (the distance to the supernova and the time of arrival of the photons compared to neutrinos) we can determine the speed of neutrinos from SN1987A.

The accuracy and precision of measurements from SN 1987A are actually much greater than measurements taken at Gran Sasso despite the three hour time window difference between neutrino and photon travel. It comes down to the fact that the relative distance between Earth and SN 1987A is about 10¹⁶ times larger than the distance between CERN and Gran Sasso. This means that time measurements from SN 1987A can be extremely imprecise and still be much more precise than the OPERA measurements.

If the neutrinos from supernova 1987A had been traveling as fast as the neutrinos detected at Gran Sasso they would have arrived about four years sooner than the light from SN 1987A.

This supernova constraint on the velocity of neutrinos is very nice, but it doesn't answer every question because the comparison may not be apples to apples. The OPERA neutrinos are tau type, not electron type. And they are traveling through the Earth, not empty space. And they were much higher energy. The neutrinos from SN 1987A were only about 10 MeV, about one hundred times lower energy than the neutrinos in this study. Some may argue that higher energy neutrinos travel faster than lower energy neutrinos. However, a velocity-energy dependence should have stretched out the 13 second arrival time of neutrinos. Further, part of the OPERA collaborations analysis involved splitting the data into two bins with mean energies of 13.9 and 42.9 GeV; a comparison between the two bins indicated no energy dependence on velocity. Thus, while it may still be true that GeV neutrinos move faster than MeV neutrinos, the theoretical wiggle room is shrinking.

This experiment may be a signal of new physics or a case of systematic errors. Yet, even physicists who have developed theories that allow for superluminal velocities are doubtful so I would not bet on proof of hidden extra dimensions or time travel to come from this experiment. Much more extraordinary evidence is necessary to confirm such an extraordinary claim as breaking the speed limit of our Universe.

Turtles all the way down

The beginning was heralded by an elephant's trumpet.

The universe is carried on the back of an ancient turtle.

There were once ten suns embodied by crows. All but one crow was shot by an archer.

The moon is a decapitated head. Her face is painted with bells.

The stars are your ancestors eyes worth remembering.

In time you too will have nine tails and be older and wiser.

All the things which you do not know are vague. Drift clouds.

Having come so far is a matter of vagueness.

I wrote this poem because even modern cosmology faces infinite regression paradoxes with respect to the initial impetus of the Universe. The various creation stories independently formed in different cultures create some stunning mental images for me. The funniest idea for me is that the Universe is resting on the back of a giant turtle. What is the turtle resting on? Why it is turtles all the way down. Oh, and I almost forgot the best blog posts always have a picture; here is a picture of a turtle.

You've been Westinghoused Mr. Edison

Recently while glancing through an old physics text I found a line I had underlined, Westinghouse Electirc Corporation, and I remembered a little phrase that I used to use with other physics students. The phrase was, you've been Westinghoused. Let me explain. There is a curious episode in history know as the the war of the currents wherein the early pioneers of electricity were trying to commercialize the transmission of electricity. Nikola Tesla with the financing of George Westinghouse supported alternating current (AC) against Thomas Edison who supported direct current (DC). Edison tried to discredit the idea of AC transmission by showing how dangerous it was. Edison attempted shenanigans like electrocuting an elephant in public, but in the end practicality and economics prevailed. AC transmission is much more viable than DC transmission because of the pure physics: with DC transmission in order to get adequate power transmitted either the wires would have to be copper as thick as your arm or you would have to have power stations every block or so. It was probably a combination of physics and the shrewd business sense of Westinghouse that it came to pass that Edison lost the war of the currents. This history, like the story of Bohr and Heisenberg, has interesting characters and a certain mystique that lends itself to historical plays and documentaries.

Tesla was a modern Prometheus. Some say that history overlooked Tesla, however, there is a current (pun intended) revival in interest for Nikola Tesla, if not always for his science, for his eccentric personality. This documentary about Tesla talks about his life and work. The part about the war of the currents begins at 18:35.

Now, as Edison fought against AC current he tried to be really clever and he wanted to brand death by electrocution as being Westinghoused. However, Edison's electric empire faded and history summarily shows that he was bested by Tesla and Westinghouse. Scientists are a competitive bunch, so I propose that when one colleague bests another colleague in an academic pursuit, we proclaim that the the defeated has been Westinghoused. It isn't the worst thing to be Westinghoused, it just means you were bested in that pursuit. Edison was a great inventor and is still famous to this day, but he surely got Westinghoused.

Sailing

There was an amazing article up on Wired today about the America's Cup. It reminded of just how cool competitive sailing is. I wrote about sailing upwind in 2009 before the last America's Cup race and I mentioned a revolutionary solid wing multihull boat created by team Oracle. That boat was in fact as fast as promised and it won the race and by doing so team Oracle won the right to dictate the rules of the next America's cup. What they did was create the America's Cup World Series of standarized fixed wing catamaran sailing boats (you can read more about the entire thing in the Wired article). These boats are super fast and super intense. The America's Cup World Series is the water equivalent of Formula 1, but instead of crashes there are capsizes. Well, actually there are crashes too. Here is a hectic highlight real of these boats racing in the first ever event a few days ago in Cascais, Portugal.

Modern sailing is a paradoxical mix of elements. The boats are designed with advanced knowledge of physics and constructed of carbon fiber, yet they are powered by the simplicity of the wind. I think there is an appeal to working with nature to accomplish work rather than fighting against it. Working with nature always seems to be the most graceful option. In space travel rather than firing rockets to propel ships it is advantages to use gravitational assists by swinging by planets. And then of course there are solar sails in space too. The Japanese IKAROS satellite recently successfully unfurled itself in space and is now being pushed by photons on a unique journey. If you think about it astronomy and sailing go together.

A Cubic Millimeter of Your Brain

Are there more connections in a cubic millimeter of your brain than there are stars in the Milky Way? We are going to answer that question in a moment, but first take a look at this image of hippocampal neurons in a mouse's brain. It is an actual color image from a transgenic mouse in which fluorescent protein variations are expressed quasi-randomly in different neurons. This kind of image is known as a brainbow and is aesthetically awesome further it may be one way to empirically examine a cubic millimeter of the brain (neuron tomography).

In reality mapping even an entire cubic millimeter of the brain is an extremely daunting task, but we can still answer my original question. First, I know that there are different kinds of neurons that vary in size and that some neurons can have a soma (the big part that has the nucleus from which the dendrites extend) spanning a millimeter in size. Thus if you picked a random cubic millimeter of brain you could run right into the heart of a neuron and you would find very few connections. Given this fact, we can very easily answer this question with a resounding no, however, this seems like an unsatisfactory trite approach. So I looked up some numbers on how many neurons are in the brain, how many connections are in the brain, and how many stars are in the Milky Way. Lets answer the question using the 'average' number of connections per cubic millimeter.

How many neurons and connections there are in the brain? This is kind of a tricky question and I am not a nuerobiologist so I have gone to several resources for the answer. Professor of Computational Neuroscience at MIT Sebastung Seung says in a TED talk

your brain contains 100 billion neurons and 10,000 times as many connections

Professor of Molecular Cellular Physiology at Stanford Stephen Smith says in a press release on brain imaging that

In a human, there are more than 125 trillion synapses just in the cerebral cortex alone

René Marois from the Center for Integrative and Cognitive Neurosciences at Vanderbilt Vision Research Center states in a recent paper ^[1]

The human brain is heralded for its staggering complexity and processing capacity: its hundred billion neurons and several hundred trillion synaptic connections can process and exchange prodigious amounts of information over a distributed neural network in the matter of milliseconds.

I have enough expert sources now to confidently say these experiments agree that the human brain has some 100 billion neurons (10¹¹). The number of connections seems less precise, but it is at least several 100 trillion connections (10¹⁴) as judged by Marios and Smith and as much as 10¹⁵ as judged by Seung.

The number of connections in the brain is tricky to define. We may define a synaptic connection as each place the neuron touches another neuron and a synapse is present. It doesn't seem to make sense to simply count incidental contact. Further, there is the question of whether we should count redundant contacts between neurons. We can obtain an upper bound on the number of connections in the brain by considering the case in which every neuron is connected to every other neuron. Coincidentally the operation of connecting every node in a network with every other node is a process I am familiar with from cross correlating radio signals. Anyways, the equation we are looking for is N(N-1)/2 where N is the number of nodes in the network. Thus, for our N=10¹¹ neurons the maximum number of non-redundant connections is about 10²². This maximum bound is huge! But how huge is it really? Hilariously, while searching for an answer to my original question I found a message board pondering the grand statement

There are more connections in the brain than atoms in the Universe.

A really clever person pointed out that

Theoretically, if we took all the atoms in the universe; wouldn't that include the atoms within the brain?

People have this feeling that the number of connections between items can be much larger than the number of actual items in the collection and while this intuition is true the idea that there are more connections in the brain than there are atoms in the universe is absurd. Lets put it in perspective that a few grams of any substance, like water, is measured units of moles. A mole is standard unit of measurement corresponding to the absolute 6.02 x 10²³. Thus even a drop of water contains more atoms than there are connections in the brain.

Now we need to know how many neurons and connections are in an average cubic millimeter of the brain. How big is the brain? John S. Allen of the Department of Neurology at University of Iowa stated in a recent paper that^[2]

The mean total brain volumes found here (1,273.6 cc for men, and 1,131.1 cc for women) are very comparable to the results from other high-resolution MRI-volumetric studies.

We can take the volume of the brain as 1000cc as a low estimate (which will only over estimate the density of connections).

The final thing we need to know to answer the question at hand is the number of stars in the Milky Way. Like every other number we have been working with it is rather uncertain. Even if we define a star as only those spheres of gas which are large enough to fuse hydrogen at some point in their lifetime we don't know the answer because we can't see the multitudes of dim stars. There are probably at least 500 billion star like objects in the Milky Way. Lets take 100 billion as the number to be conservative.

Finally, lets bring all the numbers together. One cubic millimeter is 1/1000 of a cubic centimeter and 1/1000000 (10^-6) of the entire volume of the brain. We can scale the total number of connections in the brain (using the high estimate of 10¹⁵ connections in the brain) then we find that there are 10⁹ connections in a cubic millimeter of the brain. The 10⁹ connections in a cubic millimeter of the brain is two orders of magnitude smaller than a low estimate of the number of stars in the Milky Way. No, on average there are not more connections in a cubic millimeter of your brain than there are stars in the Milky Way. 

My first response to this question was bullshit! This question (or rather statement) is made by David Eagleman here at a TEDx talk and here on the Colbert Report. Colbert also called out Eagleman when he dropped this factoid, but it didn't stop the interview. I have also contacted some actual neuroscientists to see what they thought of this statement and they agree with me that it is not true. Maybe there is special part of the brain particularly more dense in connections than the brain on average, but that would be misleading like saying the density of the Milky Way is that of water because, you know, certain parts of the Milky Way are water. The better statement would be to say that there are are more connections in the brain than there are stars in the Milky Way. As Colbert would say, I am putting you on notice Eagleman.

While we are on the subject I want to mention my favorite talk about the brain which mixes just the right amount of wonder and fact. It is the TED talk I mentioned earlier by Sebastian Seung on what he calls the connectome - the network of connections in your brain between neurons which physically dictates how you think. In the video he discusses another volume tomography technique in the brain using a cube of mouse brain tissue just 6 microns on a side. It is another great visualization for what is actually in a cubic millimeter of your brain.

References

[1] Marois, R., & Ivanoff, J. (2005). Capacity limits of information processing in the brain Trends in Cognitive Sciences, 9 (6), 296-305 DOI: 10.1016/j.tics.2005.04.010

[2] Allen, J., Damasio, H., & Grabowski, T. (2002). Normal neuroanatomical variation in the human brain: An MRI-volumetric study American Journal of Physical Anthropology, 118 (4), 341-358 DOI: 10.1002/ajpa.10092

On Replications

Repetition is ubiquitous and has many different meanings in education, art, literature, science, and life Ideas replicate and mutate; cultural memes spread through culture seamlessly. Manufactured goods are produced as nearly identical as possible. Deviations from the mold are discarded and parts are interchangeable. Digital data is almost limitlessly replicable. Any data or idea committed to the digital world is perfectly copied (sparing the occurrence of a flipped bit) until it is intentionally modified. This characteristic of digital ideas presents a unique challenge for creators of content, distributors, and bored people on the internet. And of course animals and plants on Earth have the ability to self replicate themselves with minor variations. What do we make of all of this?

I am keen on the intersection of art and science on this matter. I like making collages and have highlighted repeated images before with 35 images of space helmet reflections and 100 images of macchiatos. Through repetition and distortion images may be amplified or diminished. It depends on perspective. Generally in artistic endeavors, as in life, the slight variations of a repeated theme are aesthetically pleasing. On the other hand technical work such as engineering, data analysis, or manufacturing requires precise replication. I work in radio astronomy where each radio telescope in the array is nearly identical and the need for precision trumps all other considerations. I find that randomness is never particularly interesting, but neither is absolute order. Somewhere in between these extremes we have something really beautiful.

Looking back and looking forward

This photo was taken on the last US manned space flight in 1975 before the first shuttle launch in 1981. Portrayed is the historic handshake between Tom Stafford and Alexey Leonov through the open hatch between the American Apollo and Russian Soyuz ships. Today the Atlantis shuttle lifted off for the the last shuttle mission. It is the end of an era. Alas, all good things must end.

Mars Rover Curiosity

This animation depicts what will happen in August 2012 if all goes as planned for Curiosity, NASA's next Mars rover. This rover is much larger and and more competent than the previous rovers. It is about the size of a small car and has an entire suite of experiments on board. During entry it uses a series of thrusters to maneuver to the designated landing area. Once the ship has slowed down to Mach two (keep in mind that the atmospheric pressure on the surface of Mar's is of the order .05% that of Earth's) a parachute is deployed. As the vehicle slows the heat shield comes off and a radar detects how close the surface is approaching in order to slow for a smooth landing. The last daring step is a so called 'sky crane' which lowers the rover with a long cable from the rocket thrusted ship above. Eventually Curiosity will begin roving, but it won't be limited to roving only during the day by solar panels as the previous rovers were. The large tilted box on the back of the rover contains 4.8 kg of plutonium dioxide which emits heat serving as the power source of the rover. The power should keep flowing for much longer than the minimum specked science mission of two Earth years. The rover will seek out rough rocks such as ancient Martian riverbeds or canyons where evidence of early environments on Mars can be found. The ability to navigate to these areas is an important science requirement for the rover and is one of the reasons for the rover's large size and nuclear battery which should allow it to travel at least 20 kilometers during its lifetime. Geologists and astrobiologists also want to know if certain conditions such as those necessary for organic molecules are present. In the video a laser and a drill are shown performing experiments. The laser is ChemCam which will project onto hard to reach rocks and detect the reflected light in order to discern the chemical composition of rocks. The drill is about a centimeter in diameter and will extract the dust from the holes it creates to run experiments in mineralogy (the laser device inside the rover shown in the video) or detecting organic molecules. All of these experiments aim to answer the question, could Mars have had an environment capable of supporting life at one time?

If the sky crane works we may soon know the answer to this question. Curiosity has a launch window from November 25 to December 18, 2011 from Kennedy Space Center in Florida. And in other news NASA's James Webb Space Telescope is being threatened with the axe in budget bill in the U.S. House of Representatives today. NASA will never run out of adversaries pulling it down: Gravity and the budget.