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Quantumaniac is where it’s at - and by ‘it’ I mean awesome.

Over here I post a ton of physics / math / general interesting posts in an attempt to make your brain feel good. My aim is to be as informative as possible, all while posting fascinating things that hopefully enlighten us both a little to the mysteries of our truly wondrous universe(s?). Plus, how would you know if the blog exists or not unless you observe it? Boom, just pulled the Schrödinger’s cat card. Now you have to check it out - trust me, it said so in an equation somewhere.

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Possibly the Greatest Mathematician You’ve Never Heard Of

So I was recently reading The Universe in the Rearview Mirror by Dave Goldberg (which I really recommend), and a little less than halfway through I read the name Emmy Noether for the first time. In retrospect, I’m embarrassed that I had never heard of her before; as Goldberg writes, “few people in the twentieth century did more to explain how the universe ultimately works.” 

The New York Times wrote:

Albert Einstein called her the most “significant” and “creative” female mathematician of all time, and others of her contemporaries were inclined to drop the modification by sex.

Noether (pronounced NER-ter) was born in Erlangen, Germany, in 1882. Despite her father being a prominent mathematician of the time, she had a number of things working against her - not only was she a female in Germany at a time when most German universities didn’t even accept female students, but she was also a Jewish pacifist in the midst of the Nazis’ rise to power. 

Due to her brilliance, she managed to achieve the equivalent of a “guest-lecturer” position at Göttingen, where she began to study the mathematical topic of invariance, numbers (variables) that can be transformed and manipulated in various ways and still remain constant in certain ways. “In the relationship between a star and its planet, for example, the shape and radius of the planetary orbit may change, but the gravitational attraction conjoining one to the other remains the same — and there’s your invariance.”

In 1915, once Einstein published his general theory of relativity, Noether began working her invariance work with it, and eventually derived Noether’s theorem, a remarkably deep expression that combines symmetry with conservation - it effectively states that every symmetry corresponds to a conserved quantity. 

What the revolutionary theorem says, in cartoon essence, is the following: Wherever you find some sort of symmetry in nature, some predictability or homogeneity of parts, you’ll find lurking in the background a corresponding conservation — of momentum, electric charge, energy or the like. If a bicycle wheel is radially symmetric, if you can spin it on its axis and it still looks the same in all directions, well, then, that symmetric translation must yield a corresponding conservation. By applying the principles and calculations embodied in Noether’s theorem, you’ll see that it is angular momentum, the Newtonian impulse that keeps bicyclists upright and on the move.

Some of the relationships to pop out of the theorem are startling, the most profound one linking time and energy. Noether’s theorem shows that a symmetry of time — like the fact that whether you throw a ball in the air tomorrow or make the same toss next week will have no effect on the ball’s trajectory — is directly related to the conservation of energy, our old homily that energy can be neither created nor destroyed but merely changes form.

With this in mind, it’s quite surprising that Noether has been largely forgotten outside of especially nerdy circles. Nonetheless, she was one of the most remarkable theoreticians of all time, and her work has resounding applications that still fascinate and push our greatest minds forward today. 

Sources: NYTimes, Goldberg

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So I just started doing research in a new lab, and one of the professors puts these phenomenal labels everywhere.

Study reveals potential treatments for Ebola and other deadly viruses

Illnesses caused by many of the world’s most deadly viruses cannot be effectively treated with existing drugs or vaccines. A study published by Cell Press in the March 21 issue of the journal Chemistry & Biology has revealed several compounds that can inhibit multiple viruses, such as highly lethal Ebola virus, as well as pathogens responsible for rabies, mumps, and measles, opening up new therapeutic avenues for combating highly pathogenic viruses.

"The medical field currently does not have ideal antiviral therapies, often no therapeutics at all, and the development of broad-spectrum antivirals is a great way to provide treatment in the future," says study author Claire Marie Filone of Boston University School of Medicine. "Toward that end, we have identified a drug that targets multiple viruses- and may be developed into an antiviral treatment for known and emerging viruses."

Many viruses that cause human diseases are nonsegmented, negative-strand (NNS) RNA viruses, which include the highly lethal Ebola virus and other pathogens mentioned above. In contrast to the many antibiotics that work against a wide range of bacteria, there are currently no highly effective or safe broad-spectrum drug treatments for viral diseases.

To address this need, John Connor and John Snyder of Boston University and their team screened thousands of diverse compounds for small molecules that showed strong antiviral activity against multiple NNS viruses. They identified several molecules that inhibited infection in cells exposed to either Ebola or another NNS virus called vesicular stomatitis virus. These molecules, which are related to a class of plant-derived compounds called indoline alkaloids, share a common chemical structure that can be modified to enhance antiviral activity.

The most potent of these compounds turned off NNS viral genes by blocking transcription. “Because our antiviral targets such a critical step in virus replication, we may be able to develop it into a therapeutic that could be used against many different types of viral infections,” Filone says.

Source

9 Year Old Discovers New Dinosaur And Has It Named After Her

One little girl’s odd hobby has led to an extraordinary find for British paleontologists.

At the age of 9, Daisy Morris has discovered a new dinosaur species, which scientists have since named after her. The new creature has been dubbed Vectidraco daisymorrisae, the “Dragon from the Isle of Wight.”

Daisy was just 4 when she stumbled upon the fossilized remains of an unknown animal during a family walk on the beach in 2009. The family lives near the coast of England’s Isle of Wight — also known as the "dinosaur capital of Great Britain."

"She has a very good eye for tiny little fossils," her mother Sian Morris told BBC. Daisy apparently first began fossil hunting at age 3. “She found these tiny little black bones sticking out of the mud and decided to dig a bit further and scoop them all out,” her mother said.

Realizing that Daisy had possibly uncovered an ancient specimen, her family took the findings to Southampton University’s fossil expert Martin Simpson.

Over the past several years, the bones Daisy discovered have been thoroughly analyzed by paleontologists. The findings were finally published this Monday. The fossilized remains belong to a previously unknown genus and species of a small flying reptile called the pterosaur.

The remains date back to the Lower Cretaceous period and may be up to 115 million years old.

The family has donated the fossils to the Natural History Museum while Daisy’s personal collection continues to grow. Sian Morris told the Daily Mail, “She’s fascinated and we’re very proud of her.”

Source: The Huffington Post

How Fast Would the Earth Have to Spin to Fling People Off?

Neil deGrasse Tyson is the man. As a semi-regular guest on The Daily Show, he might have some special status. On a previous episode, he point out to Jon Stewart that their spinning Earth logo was spinning the wrong way. Well, they fixed their logo. Check it out here. That’s much better, isn’t it?

Although the Earth rotates the correct direction, Neil still wasn’t happy. He commented that it was spinning the right way but it was way too fast. I think his actual quote was “if it was spinning any faster people would just fly off the Earth”. For me, this is like a bat signal in the sky. It begs the question: would people really fly off the Earth at this speed?

Oh yes. Here comes the physics.

How Fast Is It?

Yes, there seems to be three concentric Earths. Why did Neil point out an error in the rotation speed but not an error in the Earth-in-Earth problem? Maybe these are showing Middle Earth and Middle-Middle Earth. Fine there are multiple Earths. Let me just look at the last one that looks the most like the Earth (has the best colors).

As just a rough approximation, it looks like the final Earth rotates around once in about 0.4 seconds. This would give it an angular speed of about 15.7 rad/s2. Let’s just go with this value. Oh, just a quick note. In this case, I looked at the time it took for one Earth based feature to go half way around the Earth. Many video players just show the video time rounded to the nearest second. So, I use Tracker Video. I can just mark two points the video and it will give me a more exact time difference.

And just for reference, the Daily Show’s normal spinning Earth has an angular velocity of about 2.5 radians per second.

What Would This Feel Like?

First, it depends on WHERE on the Earth you are. If you were at the north or south pole, you would just be spinning around in place. So, at the poles you would feel cold and dizzy. This video seems to suggest that the world record spinning rate for a skater is around 32 rad/s – so it is possible for humans to spin this fast.

Let me skip down to look at a person at the equator. Here is a view of the Earth from the North pole.

Screenshot 3 9 13 9 31 am

There are really only two forces on this person. There is the gravitational force of the Earth pulling on the person and the ground pushing up. The combination of these two forces result in the person moving in a circle around the center of the Earth. However, in this case we want to consider what the person feels like, not how the person moves. Here is will use a fake force.

Fake forces get a bad reputation from introductory physics. Actually, it is probably justified. Why? Because people like fake forces and they like to use them incorrectly. Fake forces are like a light saber. In the hands of the untrained, you are probably going to cut off your leg at the knee. Well, unless you just want to use it to cut open a tauntaun – you know for warmth.

What are fake forces? Well, what are real forces? Real forces are interactions between two objects. When you have a net force on an object, it changes the momentum of this object (I refer to this as the momentum principle – but most other people call it Newton’s second law). Here is the catch. The momentum principle only works if the momentum is determined from a non-accelerating reference frame. If you are using the surface of the Earth as your reference frame, it is spinning in a circle and thus accelerating. The momentum principle doesn’t work in this case. There is one way to fix this accelerating reference frame (also called a non-inertial reference frame) problem – add fake forces.

The fake force is a force added to an object such that the momentum principle works again. In simple cases, the fake force can be found as:

Screenshot 3 9 13 9 49 am

So, in this case, the frame (surface of the Earth) is accelerating towards the center of the Earth since it is moving in a circle. This means that the fake force is pushing away from ground. And yes, many people call this the centrifugal force – which literally means “center fleeing force”. Since I know the magnitude of the acceleration of an object moving in a circle, I can get the magnitude of the fake force.

Screenshot 3 9 13 9 52 am

Here, m is the mass of the object (or person) and not the Earth. The R is the radius of the circle that the frame is moving in. At the equator, R is the radius of the Earth – but at other locations these two things are different. Finally, ω is the angular velocity of the Earth.

What about at other locations on the Earth? Here is another diagram.

Screenshot 3 9 13 10 13 am

If I add in the angle θ (which would be the latitude of the person), then the fake force would be:

Screenshot 3 9 13 3 16 pm

Before I get to the “what would it feel like” question, let me address another question. When you “fly off” the face of the Earth? From the viewpoint of this accelerating frame, if the fake force is greater than gravity, you will accelerate away from the ground. Of course, you wouldn’t really fly away. Instead, the gravitational force would not be strong enough to keep you moving in a circle so you would move in a straight-ish line. As seen from the ground this would look like you are shooting away from the surface. Anyway, there is your fly-away condition. The fake force must be greater than the gravitational force.

Screenshot 3 9 13 3 23 pm

If I put in an angle corresponding to the equator, I get an minimum angular velocity of 1.24 x 10-3 rad/s (0.012 rpm). Yes. I know what you are thinking. That’s not very fast. Of course, this is still much faster than the Earth’s rotation rate now which is around 7.27 x 10-5 rad/s.

Well, I guess that puts an end to the first question. If you spin the globe faster, would people fall off? Yes and no. People would fall off even at the speed shown. You don’t have to spin it faster. So, spinning it faster will STILL make people fall off – so it is kind of true.

Where would people stop falling off the Earth? Not everyone would fall off. Santa Claus wouldn’t fall off since he is at the North pole. Let me draw a diagram for some undisclosed location on Earth.

Screenshot 3 9 13 5 08 pm

For this person, these forces (in this frame with the fake force) adds up to the zero vector. Why is the force from the ground not perpendicular to the ground? Try this. Redraw that diagram with the ground force in the opposite direction as the gravitational force. What do you see that is “odd”? Yes, there is no force parallel to the ground except for a component of the fake force. This would make the person accelerate towards the equator. The ground can push parallel to the ground – we call this friction.

Ok, but I looking for the latitude where the y-component (which I am calling up and down as the person sees it) forces add up to zero. At the most extreme case, this would be just due to the fake force and gravity. In the y-direction, I can write.

Screenshot 3 9 13 5 20 pm

If I put in my Daily Show value for the angular speed, I get a θ (latitude) of 89.95°. That’s pretty close to the North pole. I was going to draw this on the map, but it is a crazy small area near the poles. Crazy small.

Source: Dot Physics

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How Did We Not See the Russian Asteroid Coming? 

Over a hundred people are injured after a meteor or meteors reportedly exploded over Chelyabinsk, Russia this morning. Although there are no confirmed deaths, the full extent of the situation is still being assessed.

Chelyabinsk is a city of about a million people, located just to the east of the Ural Mountains. This morning, several people captured video of a bright trail streaking across the sky, followed by a saturatingly bright light. Although some people say that the lights were caused by a meteor shower, others believe that it was a single meteor that cut across the sky and exploded in the atmosphere.

Accounts of injuries vary, but it appears that anywhere between one hundred and four hundred people were injured, most of them by glass from shattering windows. (Reuters is saying 400.) The explosion shook the buildings, and it seems as though the 6000-square-foot roof of a Zinc Plant collapsed. Some people say that fragments of the meteor rained down on the town. Given that it was one of the biggest meteors to hit Earth in possibly a century, why didn’t we see it coming?

For answers, we turned to NASA’s Amy Mainzer, a scientist who works with the space agency’s Near Earth Objects (NEO) program, and one of the main researchers on the NEOWISE satellite project to map NEOs in the sky.

We are quickly learning a lot about the Russian fireball. It was pretty small - only about 15 m and about 7000 tonnes - and that’s why it wasn’t detected. This object wasn’t seen earlier because it was really faint, and it might not have been visible to observers in the night sky. Most of the survey efforts have been very successful in finding the largest asteroids (about 90% of the near-Earth objects larger than 1 km in diameter have been found), but there is still a lot of work to be done with finding and tracking the smaller objects.

Though it seemed enormous, the meteorite that struck Russia was relatively small. It’s likely that objects like this could hit again without warning, simply because right now our satellite systems are combing the skies for truly deadly objects that could wipe out a country or even a continent.

Still, added, Mainzer:

NASA is studying ways to improve the survey capabilities; an example of a prototype new system is the NEOWISE project that I worked on, which used an infrared telescope to discover and characterize NEOs. But the program has been expanded in budget by about a factor of 3 in the last couple of years, so that’s good.

One way that NEOWISE was helpful was that it could measure objects that appear dark to other telescopes. Often we judge the size of asteroids and meteors by measuring how bright and reflective they are. The problem is that some large objects are actually quite dark and very little light bounces off them. Using an infrared telescope like the one on NEOWISE helps us identify even these cloaked objects that might be invisible to other devices.

Images via AP

Source: io9

Happy Birthday Charles Darwin

Born 204 years ago today, Charles Darwin was a British scientist who laid the foundations of the theory of evolution and transformed the way we think about the natural world.

Charles Robert Darwin was born on 12 February 1809 in Shrewsbury, Shropshire into a wealthy and well-connected family. Darwin himself initially planned to follow a medical career, and studied at Edinburgh University but later switched to divinity at Cambridge. In 1831, he joined a five year scientific expedition on the survey ship HMS Beagle.

At this time, most Europeans believed that the world was created by God in seven days as described in the bible. On the voyage, Darwin read Lyell’s ‘Principles of Geology’ which suggested that the fossils found in rocks were actually evidence of animals that had lived many thousands or millions of years ago. Lyell’s argument was reinforced in Darwin’s own mind by the rich variety of animal life and the geological features he saw during his voyage. The breakthrough in his ideas came in the Galapagos Islands, 500 miles west of South America. Darwin noticed that each island supported its own form of finch which were closely related but differed in important ways.

On his return to England in 1836, Darwin tried to solve the riddles of these observations and the puzzle of how species evolve. Influenced by the ideas of Malthus, he proposed a theory of evolution occurring by the process of natural selection. The animals (or plants) best suited to their environment are more likely to survive and reproduce, passing on the characteristics which helped them survive to their offspring. Gradually, the species changes over time.

Darwin worked on his theory for 20 years. After learning that another naturalist, Alfred Russel Wallace, had developed similar ideas, the two made a joint announcement of their discovery in 1858. In 1859 Darwin published ‘On the Origin of Species by Means of Natural Selection’.

The book was extremely controversial, because the logical extension of Darwin’s theory was that homo sapiens was simply another form of animal. It made it seem possible that even people might just have evolved - quite possibly from apes - and destroyed the prevailing orthodoxy on how the world was created. Darwin was vehemently attacked, particularly by the Church. However, his ideas quickly gained currency and have become the new orthodoxy.

Darwin died on 19 April 1882 and was buried in Westminster Abbey.

Ignorance more frequently begets confidence than does knowledge: it is those who know little, and not those who know much, who so positively assert that this or that problem will never be solved by science. 

Sources: BBC

Image Sources: HistorySmithsonian 

The Brontosaurus Never Existed

Think of dinosaurs, and a few specific creatures inevitably come to mind -a T. Rex, maybe a Velociraptor, and probably a Brontosaurus as well. The Brontosauruses, due to their daunting size and impressive likeness, have been portrayed on TV and in films for decades. However, scientifically speaking - they don’t exist. While these long-necked dinosaurs exist in our culture, science abandoned them long ago, as the name is considered a junior (albeit redundant) synonym of the Apatosaurus. 

According to Matt Lamanna, curator of the Carnegie Museum of Natural History in Pittsburgh, the scientific community has known that the Brontosaurus was a fictitious dinosaur for more than a hundred years. But as with some popular trends, the Brontosaurus remained a cultural fixture until this very day. 

Lamanna said the story of Brontosaurus dates back over a century, to a period known as the Bone Wars. This early period of paleontology in the US saw a wealth of new dinosaur fossils being discovered, with Othniel Charles Marsh and Edward Drinker Cope at the forefront of most discoveries. The feud between them was called the Bone Wars, as they were frequently trying to outdo one another. 

“There are stories of either Cope or Marsh telling their fossil collectors to smash skeletons that were still in the ground, just so the other guy couldn’t get them,” Lamanna said in a detailed interview with Guy Raz of NPR’s All Things Considered. “It was definitely a bitter, bitter rivalry.”

It was this heated race to get dinosaurs published that led to the unwarranted naming of the Brontosaurus. In 1877, Marsh, who had discovered numerous dinosaur fossils, discovered the partial skeleton of a long-necked, long-tailed, herbivorous dinosaur he dubbed Apatosaurus. Since the fossil was missing a skull, in 1883 when he published a reconstruction of his Apatosaurus, he borrowed a skull from another dinosaur — possibly a Camarasaurus — to complete the skeleton.

A few years later his fossil collectors had sent Marsh a second skeleton he believed to belong to a completely new dinosaur, which he named Brontosaurus, according to Lamanna.

However, this new dinosaur was actually a more complete Apatosaurus. And in Marsh’s rush to outdo Cope, he carelessly mistook the dinosaur for something new, Lamanna added.

The dinosaur mistake was eventually spotted by scientists in 1903, but for some reason, the Brontosaurus named lived on in popular culture and children’s imaginations everywhere. It was not until another 67 years, in 1970, when two Carnegie researchers took a second look at the controversy and determined, once and for all, the Brontosaurus was a fictional-only dinosaur.

This conclusion was met due to a dinosaur skull discovered in Utah in 1910 that was correctly attributed to the Apatosaurus rather than Marsh’s defunct Brontosaurus.

“Brontosaurus means ‘thunder lizard,’” he said. “It’s a big, evocative name, whereas Apatosaurus means ‘deceptive lizard.’ It’s quite a bit more boring.”

Sources: RedOrbitNPR

Image Sources: 1, 2

What is an IP Address?

In one way or another, we’re all vaguely familiar with the term IP address. Hardly any of us, however, are actually familiar with how it works. In essence, an IP address is nothing more than a series of numbers that allows a digital device to communicate with the internet. Each individual IP address allows each of the billions of digital devices across the globe to be located and differentiated from one another. In this sense, an IP address is comparable to a standard mailing address.  “IP” stands for Internet Protocol, which is just a set of rules that govern and legitimize Internet activity and allow for the completion of various tasks on the Internet. While that sounds vague, an IP address is one part of a precise grid that facilitates online communication by locating and connecting devices and locations. 

The address itself consists of four sets of numbers separated by single dots, each of which may contain one to three digits. Each of the series of numbers can range from 0 to 255. For example, an IP address could look like 82.243.1.119. There are two types of IP addresses: 

  • Static: A static IP address will never change, they serve as a permanent address. They are based on location, so the numbers represent such information as the city, country, continent etc. that the computer is in - and the Internet Service Provider (ISP) that serves that computer. Generally preferable for online gaming and other communication and location-heavy acts. However, they are generally considered to be less secure because they can be tracked for data-mining purposes. 
  • Dynamic: These IP addresses are, unsurprisingly - ‘un-static,’ or changing. These are temporary, and one is assigned each and every time a computer accesses the internet. Essentially, these addresses are borrowed from a set of shared addresses. Only a limited number of static IP addresses can be assigned, so many ISPs share addresses among their customers in this way.

Image Sources: 1, 2 

Are there physical limits in the universe other than the speed of light?

Hells yeah.

Fastest fast: This is worth commenting on since you often hear “nothing can travel faster then light”, but the justification is almost always missing. The universe seems to be pretty happy thinking of the speed of light as being the same to everybody first (Maxwell’s Laws give you the speed of light, but Maxwell’s laws are the same to everybody so the speed of light is the same to everybody), and as a speed limit second. Since you always see light moving at the same speed, then no matter how much you speed up, it will always pass you by. So catching up to it isn’t an option, and everyone will always see you traveling slower than the speed of light.

Densest dense: The harder you compress something, the denser it becomes. Normally this is reflected in the distance between atoms shrinking. However, if the pressure is great enough, the atoms will find that it’s easier to have their electrons merge with their protons which then turn into neutrons (and also spit out neutrinos, but whatever). Without battling electron shells, the once mostly-empty atoms can be packed nucleus-to-nucleus.  Pressures and densities this high only seem to show up in neutron stars (guess where the name comes from). You can also cheat a little.  If a neutron star has a mass of more than about 5 Suns it will collapse into a blackhole, which is technically more dense.

Coldest cold: You might have guessed: zero. Specifically 0K = -273°C = -460°F. However, this is more of an “asymptotic limit” and can never quite be reached. An object with a temperature of absolute zero will have no atomic movement (heat) whatsoever, but that’s not possible. One way of thinking about it is in terms of the Heisenberg uncertainty principle which, in a paraphrased nutshell, states: “You can’t have both a perfectly certain position and a perfectly certain momentum,” and a temperature of 0 K would effectively have both. Most people who have heard of Heisenberg’s uncertainty principle are under the impression that it’s a limit on how well we can know about an object. In fact, it’s far better to think of it as a description of how well the universe can know about an object. Despite the difficulties imposed by the uncertainty principle, we can still get things crazy cold. The world record for lowest temperature now stands at 0.0000000001K = 0.1 nK.

Smallest small: Again, for “uncertainty principle type reasons” it doesn’t make sense to talk about objects or events smaller than the Planck scale, which is about 10-35m. So far, nobody can think of anything in the universe, at any scale, that would really care, or be able to tell the difference between two points separated by 10-35m.

Emptiest empty: One version of the Heisenberg uncertainty principle can be written: 

\Delta E \Delta t \ge \frac{\hbar}{2}

which means that the time and energy of something can’t both be perfectly well known (not even by the universe, the quantities themselves are uncertain). If you apply this principle to empty space you’ll notice that over short enough time scales there will be measurable, non-zero energy, and over really short time scales you’ll find particles popping in and out of existence. These particles are called “virtual particles”, and this phenomena is sometimes described as a “particle foam”.

So even with a perfect vacuum, you’ll still have crap around.  This crap is often called the “vacuum energy” or “zero point energy”.

Sadly, harvesting the vacuum energy is physically impossible (it would violate the uncertainty principle).  The vacuum energy amounts to about 10-13J/m3, or about “the energy a baseball has falling off a table per volume of Lake Superior“.
 
Images: 1, 2