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How is geometry entangled in the fabric of the Universe?

Geometry can be seen in action in all scales of the Universe, be it astronomical – in the orbital resonance of the planets for example, be it at molecular levels, in how crystals take their perfect structures. But going deeper and deeper into the fabric of the material world, we find that at quantum scale, geometry is a catalyst for many of the laws of quantum-physics and even definitions of reality.

Take for example the research made by Duncan Haldane, John Michael Kosterlitz and David Thouless, the winners of the 2016 Nobel prize in physics. By using geometry and topology they understood how exotic forms of matter take shape based on the effects of the quantum mechanics. Using techniques borrowed from geometry and topology, they studied the changes between states of matter (from plasma to gas, from gas to liquid and from liquid to solid) being able to generate a set of rules that explain different types of properties and behaviors of matter. Furthermore, by coming across a new type of symmetry patterns in quantum states that can influence those behaviors or even create new exotic types of matter, they provided new meaning and chance in using geometry as a study of “the real”.

If the Nobel Prize winners used abstract features of geometry to define physical aspects of matter, more tangible properties of geometry can be used to define other less tangible aspects of reality, like time or causality. In relativity, 3d space and 1d time become a single 4d entity called “space-time”, a dimension perceived through the eye of a space-time traveler. When an infinite number of travelers are brought into the equation, the numbers are adding up fast and, to see how for example, a space-time of a traveler looks for another traveler,  we can use geometric diagrams of these equations. By tracing what a traveler “sees” in the space-time dimension  and assuming that we all see the same speed of light, the intersection points of view between a stationary traveler and a moving one give a hyperbola that represents specific locations of space-time events seen by both travelers, no matter of their reference frame. These intersections represent a single value for the space-time interval, proving that the space-time dimension is dependent of the geometry given by the causality hyperbola.

If the abstract influence of geometry on the dimensions of reality isn’t enough,  take for example one of the most interesting experiments of quantum-physics, the double-split experiment, were wave and particle functions are simultaneously proven to be active in light or matter. When a stream of photons is sent through a slit against a wall, the main expectation is that each photon will strike the wall in a straight line. Instead, the photons are rearranged by a specific type of patterns, called diffraction patterns, a behavior mostly visible for small particles like electrons, neutrons, atoms and small molecules, because of their short wavelength.

Two slits diffraction pattern by a plane wave. Animation by Fu-Kwun Hwang 

The wave-particle duality is a handful, since it is a theory that has worked well in physics but with its meaning or representation never been satisfactorily resolved. Perhaps future experiments that will involve more abstract roles of geometry in quantum fields, like in the case of the Nobel prize winners, will develop new answers to how everything functions at these small scales of matter.

In this direction, Garret Lissi tries to explain how everything works, especially at quantum levels, by uniting all the forces of the Universe, its fibers and particles, into a 8 dimensions geometric structure. He suggests that each dot, or reference, in space-time has a shape, called fibre, attributed to each type of particle. Thus, a separate layer of space is created, parallel to the one we can perceive, given by these shapes and their interactions. Although the theory received also good reviews but also a widespread skepticism, its attempt to describe all known fundamental aspects of physics into one possible theory of everything is laudable. And proving that with laws and theories of geometry is one step closer to a Universal Geometry theory.

When 25,000 little dice are agitated in a cylinder, they form into neat concentric circles

Behold the magic of compaction dynamics. Scientists from Mexico and Spain dumped 25,000 tiny dice (0.2 inches) into a large clear plastic cylinder and rotated the cylinder back and forth once a second. The dice arranged themselves into rows of concentric circles. See the paper and the videos here.

https://boingboing.net/2017/12/05/when-25000-little-dice-are-ag.html

How Do Hurricanes Form?

Hurricanes are the most violent storms on Earth. People call these storms by other names, such as typhoons or cyclones, depending on where they occur.

The scientific term for ALL of these storms is tropical cyclone. Only tropical cyclones that form over the Atlantic Ocean or eastern and central Pacific Ocean are called “hurricanes.”

Whatever they are called, tropical cyclones all form the same way.

Tropical cyclones are like giant engines that use warm, moist air as fuel. That is why they form only over warm ocean waters near the equator. This warm, moist air rises and condenses to form clouds and storms.

As this warmer, moister air rises, there’s less air left near the Earth’s surface. Essentially, as this warm air rises, this causes an area of lower air pressure below.

This starts the ‘engine’ of the storm. To fill in the low pressure area, air from surrounding areas with higher air pressure pushes in. That “new” air near the Earth’s surface also gets heated by the warm ocean water so it also gets warmer and moister and then it rises.

As the warm air continues to rise, the surrounding air swirls in to take its place. The whole system of clouds and wind spins and grows, fed by the ocean’s heat and water evaporating from the surface.

As the storm system rotates faster and faster, an eye forms in the center. It is vey calm and clear in the eye, with very low air pressure.

Tropical cyclones usually weaken when they hit land, because they are no longer being “fed” by the energy from the warm ocean waters. However, when they move inland, they can drop many inches of rain causing flooding as well as wind damage before they die out completely. 

There are five types, or categories, of hurricanes. The scale of categories is called the Saffir-Simpson Hurricane Scale and they are based on wind speed.

How Does NASA Study Hurricanes?

Our satellites gather information from space that are made into pictures. Some satellite instruments measure cloud and ocean temperatures. Others measure the height of clouds and how fast rain is falling. Still others measure the speed and direction of winds.

We also fly airplanes into and above hurricanes. The instruments aboard planes gather details about the storm. Some parts are too dangerous for people to fly into. To study these parts, we use airplanes that operate without people. 

Learn more about this and other questions by exploring NASA Space Place and the NASA/NOAA SciJinks that offer explanations of science topics for school kids.

Make sure to follow us on Tumblr for your regular dose of space: http://nasa.tumblr.com.

Credits: NASA Space Place & NASA/NOAA SciJinks

We Need Your Help to Find STEVE

Glowing in mostly purple and green colors, a newly discovered celestial phenomenon is sparking the interest of scientists, photographers and astronauts. The display was initially discovered by a group of citizen scientists who took pictures of the unusual lights and playfully named them “Steve.”

When scientists got involved and learned more about these purples and greens, they wanted to keep the name as an homage to its initial name and citizen science discoverers. Now it is STEVE, short for Strong Thermal Emission Velocity Enhancement.

Credit: ©Megan Hoffman

STEVE occurs closer to the equator than where most aurora appear – for example, Southern Canada – in areas known as the sub-auroral zone. Because auroral activity in this zone is not well researched, studying STEVE will help scientists learn about the chemical and physical processes going on there. This helps us paint a better picture of how Earth’s magnetic fields function and interact with charged particles in space. Ultimately, scientists can use this information to better understand the space weather near Earth, which can interfere with satellites and communications signals.

Want to become a citizen scientist and help us learn more about STEVE? You can submit your photos to a citizen science project called Aurorasaurus, funded by NASA and the National Science Foundation. Aurorasaurus tracks appearances of auroras – and now STEVE – around the world through reports and photographs submitted via a mobile app and on aurorasaurus.org.

Here are six tips from what we have learned so far to help you spot STEVE:

1. STEVE is a very narrow arc, aligned East-West, and extends for hundreds or thousands of miles.

Credit: ©Megan Hoffman 

2. STEVE mostly emits light in purple hues. Sometimes the phenomenon is accompanied by a short-lived, rapidly evolving green picket fence structure (example below).

Credit: ©Megan Hoffman 

3. STEVE can last 20 minutes to an hour.

4. STEVE appears closer to the equator than where normal – often green – auroras appear. It appears approximately 5-10° further south in the Northern hemisphere. This means it could appear overhead at latitudes similar to Calgary, Canada. The phenomenon has been reported from the United Kingdom, Canada, Alaska, northern US states, and New Zealand.

5. STEVE has only been spotted so far in the presence of an aurora (but auroras often occur without STEVE). Scientists are investigating to learn more about how the two phenomena are connected. 

6. STEVE may only appear in certain seasons. It was not observed from October 2016 to February 2017. It also was not seen from October 2017 to February 2018.

Credit: ©Megan Hoffman 

STEVE (and aurora) sightings can be reported at www.aurorasaurus.org or with the Aurorasaurus free mobile apps on Android and iOS. Anyone can sign up, receive alerts, and submit reports for free.

Make sure to follow us on Tumblr for your regular dose of space: http://nasa.tumblr.com.

Six stages of debugging

Cassini Spacecraft: Top Discoveries

Our Cassini spacecraft has been exploring Saturn, its stunning rings and its strange and beautiful moons for more than a decade.

Having expended almost every bit of the rocket propellant it carried to Saturn, operators are deliberately plunging Cassini into the planet to ensure Saturn’s moons will remain pristine for future exploration – in particular, the ice-covered, ocean-bearing moon Enceladus, but also Titan, with its intriguing pre-biotic chemistry.

Let’s take a look back at some of Cassini’s top discoveries:  

Titan

Under its shroud of haze, Saturn’s planet-sized moon Titan hides dunes, mountains of water ice and rivers and seas of liquid methane. Of the hundreds of moons in our solar system, Titan is the only one with a dense atmosphere and large liquid reservoirs on its surface, making it in some ways more like a terrestrial planet.

Both Earth and Titan have nitrogen-dominated atmospheres – over 95% nitrogen in Titan’s case. However, unlike Earth, Titan has very little oxygen; the rest of the atmosphere is mostly methane and traced amounts of other gases, including ethane.

There are three large seas, all located close to the moon’s north pole, surrounded by numerous smaller lakes in the northern hemisphere. Just one large lake has been found in the southern hemisphere.

Enceladus

The moon Enceladus conceals a global ocean of salty liquid water beneath its icy surface. Some of that water even shoots out into space, creating an immense plume!

For decades, scientists didn’t know why Enceladus was the brightest world in the solar system, or how it related to Saturn’s E ring. Cassini found that both the fresh coating on its surface, and icy material in the E ring originate from vents connected to a global subsurface saltwater ocean that might host hydrothermal vents.

With its global ocean, unique chemistry and internal heat, Enceladus has become a promising lead in our search for worlds where life could exist.

Iapetus

Saturn’s two-toned moon Iapetus gets its odd coloring from reddish dust in its orbital path that is swept up and lands on the leading face of the moon.

The most unique, and perhaps most remarkable feature discovered on Iapetus in Cassini images is a topographic ridge that coincides almost exactly with the geographic equator. The physical origin of the ridge has yet to be explained…

It is not yet year whether the ridge is a mountain belt that has folded upward, or an extensional crack in the surface through which material from inside Iapetus erupted onto the surface and accumulated locally.

Saturn’s Rings

Saturn’s rings are made of countless particles of ice and dust, which Saturn’s moons push and tug, creating gaps and waves.

Scientists have never before studied the size, temperature, composition and distribution of Saturn’s rings from Saturn obit. Cassini has captured extraordinary ring-moon interactions, observed the lowest ring-temperature ever recorded at Saturn, discovered that the moon Enceladus is the source for Saturn’s E ring, and viewed the rings at equinox when sunlight strikes the rings edge-on, revealing never-before-seen ring features and details.

Cassini also studied features in Saturn’s rings called “spokes,” which can be longer than the diameter of Earth. Scientists think they’re made of thin icy particles that are lifted by an electrostatic charge and only last a few hours.  

Auroras

The powerful magnetic field that permeates Saturn is strange because it lines up with the planet’s poles. But just like Earth’s field, it all creates shimmering auroras.

Auroras on Saturn occur in a process similar to Earth’s northern and southern lights. Particles from the solar wind are channeled by Saturn’s magnetic field toward the planet’s poles, where they interact with electrically charged gas (plasma) in the upper atmosphere and emit light.  

Turbulent Atmosphere

Saturn’s turbulent atmosphere churns with immense storms and a striking, six-sided jet stream near its north pole.

Saturn’s north and south poles are also each beautifully (and violently) decorated by a colossal swirling storm. Cassini got an up-close look at the north polar storm and scientists found that the storm’s eye was about 50 times wider than an Earth hurricane’s eye.

Unlike the Earth hurricanes that are driven by warm ocean waters, Saturn’s polar vortexes aren’t actually hurricanes. They’re hurricane-like though, and even contain lightning. Cassini’s instruments have ‘heard’ lightning ever since entering Saturn orbit in 2004, in the form of radio waves. But it wasn’t until 2009 that Cassini’s cameras captured images of Saturnian lighting for the first time.

Cassini scientists assembled a short video of it, the first video of lightning discharging on a planet other than Earth.

Cassini’s adventure will end soon because it’s almost out of fuel. So to avoid possibly ever contaminating moons like Enceladus or Titan, on Sept. 15 it will intentionally dive into Saturn’s atmosphere.

The spacecraft is expected to lose radio contact with Earth within about one to two minutes after beginning its decent into Saturn’s upper atmosphere. But on the way down, before contact is lost, eight of Cassini’s 12 science instruments will be operating! More details on the spacecraft’s final decent can be found HERE.

Make sure to follow us on Tumblr for your regular dose of space: http://nasa.tumblr.com

Jupiter’s Great Red Spot

Jupiter’s Great Red Spot (GRS) is an atmospheric storm that has been raging in Jupiter’s southern Hemisphere for at least 400 years.

About 100 years ago, the storm covered over 40,000 km of the surface. It is currently about one half of that size and seems to be shrinking. 

At the present rate that it is shrinking it could become circular by 2040. The GRS rotates counter-clockwise(anti-cyclonic) and makes a full rotation every six Earth days. 

It is not known exactly what causes the Great Red Spot’s reddish color. The most popular theory, which is supported by laboratory experiments, holds that the color may be caused by complex organic molecules, red phosphorus, or other sulfur compounds. 

The GRS is about two to three times larger than Earth. Winds at its oval edges can reach up to 425 mph (680 km/h) 

Infrared data has indicated that the Great Red Spot is colder (and thus, higher in altitude) than most of the other clouds on the planet

Sources: http://www.universetoday.com/15163/jupiters-great-red-spot/ http://www.space.com/23708-jupiter-great-red-spot-longevity.html

New Research Heading to Earth’s Orbiting Laboratory

It’s a bird! It’s a plane! It’s a…dragon? A SpaceX Dragon spacecraft is set to launch into orbit atop the Falcon 9 rocket toward the International Space Station for its 12th commercial resupply (CRS-12) mission August 14 from our Kennedy Space Center in Florida.

It won’t breathe fire, but it will carry science that studies cosmic rays, protein crystal growth, bioengineered lung tissue.

Here are some highlights of research that will be delivered:

I scream, you scream, we all scream for ISS-CREAM! 

Cosmic Rays, Energetics and Mass, that is! Cosmic rays reach Earth from far outside the solar system with energies well beyond what man-made accelerators can achieve. The Cosmic Ray Energetics and Mass (ISS-CREAM) instrument measures the charges of cosmic rays ranging from hydrogen to iron nuclei. Cosmic rays are pieces of atoms that move through space at nearly the speed of light

The data collected from the instrument will help address fundamental science questions such as:

Do supernovae supply the bulk of cosmic rays?

What is the history of cosmic rays in the galaxy?

Can the energy spectra of cosmic rays result from a single mechanism?

ISS-CREAM’s three-year mission will help the scientific community to build a stronger understanding of the fundamental structure of the universe.

Space-grown crystals aid in understanding of Parkinson’s disease

The microgravity environment of the space station allows protein crystals to grow larger and in more perfect shapes than earth-grown crystals, allowing them to be better analyzed on Earth. 

Developed by the Michael J. Fox Foundation, Anatrace and Com-Pac International, the Crystallization of Leucine-rich repeat kinase 2 (LRRK2) under Microgravity Conditions (CASIS PCG 7) investigation will utilize the orbiting laboratory’s microgravity environment to grow larger versions of this important protein, implicated in Parkinson’s disease.

Defining the exact shape and morphology of LRRK2 would help scientists to better understand the pathology of Parkinson’s and could aid in the development of therapies against this target.

Mice Help Us Keep an Eye on Long-term Health Impacts of Spaceflight

Our eyes have a whole network of blood vessels, like the ones in the image below, in the retina—the back part of the eye that transforms light into information for your brain. We are sending mice to the space station (RR-9) to study how the fluids that move through these vessels shift their flow in microgravity, which can lead to impaired vision in astronauts.

By looking at how spaceflight affects not only the eyes, but other parts of the body such as joints, like hips and knees, in mice over a short period of time, we can develop countermeasures to protect astronauts over longer periods of space exploration, and help humans with visual impairments or arthritis on Earth.

Telescope-hosting nanosatellite tests new concept

The Kestrel Eye (NanoRacks-KE IIM) investigation is a microsatellite carrying an optical imaging system payload, including an off-the-shelf telescope. This investigation validates the concept of using microsatellites in low-Earth orbit to support critical operations, such as providing lower-cost Earth imagery in time-sensitive situations, such as tracking severe weather and detecting natural disasters.

Sponsored by the ISS National Laboratory, the overall mission goal for this investigation is to demonstrate that small satellites are viable platforms for providing critical path support to operations and hosting advanced payloads.

Growth of lung tissue in space could provide information about diseases

The Effect of Microgravity on Stem Cell Mediated Recellularization (Lung Tissue) uses the microgravity environment of space to test strategies for growing new lung tissue. The cells are grown in a specialized framework that supplies them with critical growth factors so that scientists can observe how gravity affects growth and specialization as cells become new lung tissue.

The goal of this investigation is to produce bioengineered human lung tissue that can be used as a predictive model of human responses allowing for the study of lung development, lung physiology or disease pathology.

These crazy-cool investigations and others launching aboard the next SpaceX #Dragon cargo spacecraft on August 14. They will join many other investigations currently happening aboard the space station. Follow @ISS_Research on Twitter for more information about the science happening on 250 miles above Earth on the space station.  

Watch the launch live HERE starting at 12:20 p.m. EDT on Monday, Aug. 14!

Make sure to follow us on Tumblr for your regular dose of space: http://nasa.tumblr.com

The simple harmonic oscillator

Anonymous asked: Please explain the intuition of solving the SHM equation.

Okay Anon! Here you go, this is my rendition.

The problem

You have a mass suspended on a spring. We want to know where the mass will be at any instant of time.

Describe the motion of the mass

The physical solution

Now before we get on to the math, let us first visualize the motion by attaching a spray paint bottle as the mass.

Oh, wait that seems like a function that we are familiar with - The sinusoid.

Without even having to write down a single equation, we have found out the solution to our problem. The motion that is traced  by the mass is a sinusoid.

But what do I mean by a sinusoid ?

If you took the plotted paper and tried to create that function with the help of sum of polynomials i.e x, x2, x3 … Now you this what it would like :

By taking an infinite of these polynomial sums you get the function Since this series of polynomial occurs a lot, its given the name - sine.

I hope this shed some light on the intuition of the SHM equation. Have fun!

Big math news! It’s been thirty years since mathematicians last found a convex pentagon that could “tile the plane.” The latest discovery (by Jennifer McLoud-Mann, Casey Mann, and David Von Derau) was published earlier this month. Full story.