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physics

Jupiter: King of Planets or Failed Star

Image credit NASA

As you probably know Jupiter is the largest planet in our solar system. The mass of Jupiter is approximately 2.5 times the mass of all of the other planets combined. Approximately 1,300 Earth’s could fit inside of the Jovian planet. Jupiter is the fifth planet from our sun and is classified as gas giant. Mercury, Venus, Earth, and Mars are rocky terrestrial planets. Jupiter and Saturn are gas giants while Uranus and Neptune are considered ice giants.

So just what is a gas giant you may ask. According to NASA “A gas giant is a large planet mostly composed of helium and/or hydrogen. These planets, like Jupiter and Saturn in our solar system, don’t have hard surfaces and instead have swirling gases above a solid core. Gas giant exoplanets can be much larger than Jupiter, and much closer to their stars than anything found in our solar system.”… ice giants by comparison “are mostly water, probably in the form of a supercritical fluid; the visible clouds likely consist of ice crystals with different compositions.” (planetary society)” Terrestrial of inner planets are described by Nasa as “… planets (Earth sized and smaller) are rocky worlds, composed of rock, silicate, water and/or carbon.”

So What’s in a Name?

Credit: Britannica.com This image is often used to depict both Jupiter and Zeus

“Jupiter was a sky-god who Romans believed oversaw all aspects of life; he is thought to have originated from the Greek god Zeus.” (national geographic) Jupiter was also known as Jove, and in Latin was referred to as Iuppiter, Iovis, and Diespitter according to Britannica.com. Jupiter is known as god of the sky in Roman mythology. He was believed to be king of the gods and the protector of the Roman people. “He granted supremacy to the Romans over other human being in return for all the respect he got from them. In the Roman Empire, the kings and other ministers swore in his name when they took the oath of office. (DifferenceBetween.com)

Image Credit National Geographic. Ruins of a Roman temple to the god Jupiter

For every DC comic book superhero there is an equivalent Marvel superhero. Think Green Arrow in DC comics and Hawkeye in the Marvel Universe. Zeus is the counterpart to Jupiter in Greek mythology. Zeus is also seen as the god of the sky and king of all the other Greek gods as well as the king of humans. Jupiter and Zeus are both thought to have their names derived from terms meaning bright in the respective cultures of the Romans and Greeks. This is in all likelihood due to the bright appearance of Jupiter in the night sky. Jupiter has an apparent magnitude of -2.2 which makes it the third brightest object in the sky behind Venus and the moon. Many people believe that Jupiter and Zeus are the same god having simply having different names in Roman and Greek mythology.

Just the Facts

Let’s check out some facts about the King of Planets The average distance between Jupiter and the sun is 778 million kilometers or 5.2 astronomical units (AU). One astronomical unit is the average distance between the Earth and Sun, this distance is roughly 93 million miles or 150 million kilometers.

Credit Space.com

Why is a day on Earth 24 hours and a year 365 days? The Earth rotates about its axis once every 24 hours and the it revolves around the sun approximately once every 365 days. So what would a day and a year be on Jupiter? A Jovian day is about 10 hours long. This is the shortest day of any planet in our solar system. Jupiter is much farther from the sun than is the Earth so as you might expect a “year” on Jupiter is much longer than an Earth year. A Jovian year is equivalent to roughly 12 Earth years. Interestingly enough, Jupiter is so large that it doesn’t actually orbit the Sun in the same way other planets do. The Sun and Jupiter actually orbit a common center of gravity. Jupiter “pulls the center of mass between it and the sun, also known as the barycenter, some 1.07 solar radii from the star’s center which is about 30,000 miles above the sun’s surface.” (businessinsider.com)

The Earth has an axial tilt of 23.5 degrees which accounts for the seasons on our home planet. Jupiter has a tilt of only 3 degrees which means there is very little variation in the planets seasons. That certainly does not mean that there is not a complex weather pattern on this behemoth of a planet.

Measuring the rotational speed was a challenge for scientists because the gas giant does not have surface features to use as a frame of reference. Eventually radio emissions from the magnetic field were used to calculate the rotational speed and period. Different parts of the Jupiter’s atmosphere rotate at different speeds. The speed at the equator rotates faster than at the poles.

Credit NASA In this image you can see different parts of the Jovian atmosphere rotating at different velocities. Also visible is the Great Red Spot.

Jupiter has 53 named moons and and additional 26 moons waiting to be named (nasa.gov) The four largest of the named moons are Io, Ganymede, Callisto, and Europa. These are referred to as Galilean satellites as they were discovered by Galileo Galilei in the year 1610. Each of the Galilean satellites are tidally locked meaning one side of the moon is always facing the giant planet. The Earth’s moon is also tidally locked to our home planet.

Credit NASA Image of the Galilean moons shown from left to right: Io, Europa, Ganymede, and Callisto.

The Great Red Spot

Jupiter’s “Great Red Spot” is a massive storm roughly 10,000 miles wide. This storm has been observed for over 200 years and scientists believe that it has been around for much longer. The Hubble Space Telescope (HST) allowed scientists to determine that the outer ring of the storm is rotating counter clockwise and that wind speeds have increased by 8 percent between 2009-2020. The speeds in this “high speed ring” region of the storm top out at over 400 miles per hour. (EarthSky.org) It appears that the “Great Red Spot” is shrinking and changing in shape according to a study in journal Geophysical Research. Scientists are still trying to determine what is causing the wind speed of the storm to increase on the outside of the storm while decreasing its speed inside. According to planetary.org “Measuring the depth of the GRS would provide some context, but even our best estimates from spacecraft are ambiguous; in 2017 NASA’s Juno found that the Spot is “50 to 100 times deeper than Earth’s oceans,” but we still don’t know exactly where the storm ends.” It appears to be anyone’s best guess as to when or if the Great Red Spot. The storm has been decreasing in size for nearly 150 years but scientists are still not certain as to the fate of the solar system’s most famous storm.

The Composition of Jupiter

Jupiter is 93% hydrogen, 7% helium and contains very small quantities of methane, ammonia, and water vapor. It is believed that Jupiter may posses a rocky core that is more than 12 times the mass of the Earth. This core is surrounded by a large body of liquid metallic hydrogen which is surrounded by gaseous hydrogen.

The King of Planets has a large make up of cloud bands that move up to 240 miles per hour. The differing colors of the cloud bands indicate varying chemical composition within the bands. The temperature of the planet increases as you travel below the clouds toward the core of the Jupiter.

Credit Britannica.com

It may surprise you to learn that Saturn is not the only planet in our solar system that has rings. In fact, all of the outer planets have their own set of rings. It is believed that Jupiter has a set of four rings around the planet. The rings were first discovered by the Voyager 1 in 1979. According to nasa.gov the rings are difficult to view because the rings “are so faint and tenuous, they are only visible when viewed from behind Jupiter and are lit by the Sun, or directly viewed in the infrared where they faintly glow.” The rings of Saturn are composed of large ice chunks and rock while Jupiter’s rings are composed of small dust particles. Nasa.gov reports that “Jupiter’s rings are formed from dust particles hurled up by micro-meteor impacts on Jupiter’s small inner moons and captured into orbit” In order for the rings to continue to exist the dust and particles must constantly be replenished with dust from the moons.

How was Jupiter Formed and Why is it Called a Failed Star?

Jupiter was formed the same time as the rest of the solar system some 4.5 billion years ago. Gravity caused swirling gas and dust to coalesce and collapse on itself to form a the planet we now know as Jupiter. Most of the mass and debris left over after the formation of the Sun was taken up by the formation of Jupiter. “Giant planets form really fast, in a few million years,” Kevin Walsh, a researcher at the Southwest Research Institute in Boulder, Colorado.

“Jupiter is often lauded as a shield for Earth, but that may not have always been the case. Recent studies suggest that gas giants speed up the timescale of impacts. Early in the life of the solar system, Jupiter tossed material helter-skelter, raining some of it on the terrestrial planets while hurling some of it completely out of the solar system. In systems without Jupiters, however, the impacts are weaker but continue through a planet’s lifetime. That’s because most of the rocks are stuck in orbit around the sun without a giant planet to boot it aside” (space.com).

According to Scientific American Jupiter is a called a failed star because Jupiter “…is made of the same elements (hydrogen and helium) as is the Sun, but it is not massive enough to have the internal pressure and temperature necessary to cause hydrogen to fuse to helium, the energy source that powers the sun and most other stars.” Jupiter only has about .001 times the mass of the our sun which scientists speculate is the result of the Sun obtaining most of the mass during the formation of our solar system. According to Astronomy.com Jupiter would need to be about 75 times its current mass to be able to ignite nuclear fusion in its core and become a star.

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physics

The Ultraviolet Catastrophe

Courtesy of assignmentpoint.com

So what comes to mind when you hear the term catastrophe? It certainly sounds ominous and dreadful. According to merriam-webster.com a catastrophe is: a momentous tragic event ranging from extreme misfortune to utter overthrow or ruin and/or utter failure. It is the “utter failure” description that more accurately describes this particular catastrophe. So just what is the ultraviolet catastrophe and what was its significance to the birth of quantum mechanics? Keep reading to find out.

As the 19th century drew to a close, there was among the scientific community, an belief that most of the physical phenomena could be described and explained through classical physics. Nature, however, had other ideas. A series of discoveries would usher in a new branch of physics that classical or Newtonian physics was not able to describe. The photoelectric effect was one of these discoveries. This phenomena was accurately described by Albert Einstein which demonstrated that light travels as a wave and interacts with matter as particles. This is often described as the dual nature of light. The double slit experiment showed that particles, such as electrons, could produce interference patterns by interfering with themselves as they traveled through a narrow set of slits. This remarkable experiment showed that the behavior of individual particles could travel as particles and still demonstrate wave like behavior. Oddly enough, when scientists attempted to determine which slit the particle traveled through the interference pattern collapsed. The result of this collapse is what would be expected from a series of single particles being fired though one slit or another. Both of these topics have been discussed in earlier blog posts on my site. Feel free to go read those posts if you haven’t already.

So both of the above experiments helped describe discrete amounts of fundamental units. These units were considered to be quantized that is containing the smallest whole number amount of a specific material. For example, a quanta of light is a photon. So let’s see how the ultraviolet catastrophe relates to all this.

Blackbody and Blackbody Radiation

It will be helpful to be familiar with some of the vocabulary associated with this phenomenon. A blackbody is an idealized or theoretical object that absorbs all electromagnetic radiation that falls on it. A blackbody, according to Kirchoff, is a body that is able to “…completely absorb all incident rays, and neither reflects nor transmit any.” A blackbody emits blackbody radiation which is also known as thermal radiation. Many objects such as people, heating elements, flames, and the sun approximate blackbodies.

So you may be wondering how would a person experimentally measure blackbody radiation? You could set up a hollow container with a small hole in it. This cavity allows incident radiation to get in while the design makes it unlikely that much radiation will escape.

A blackbody cavity courtesy of https://phys.libretexts.org/

A small amount of emitted radiation will pass back out through the cavity opening where it can be measured. Thermal equilibrium occurs when two objects are in direct contact or close contact with each other but no net energy is transferred between them. They may gain energy from one another but no net energy is transferred. The amount of emitted radiation is small enough that it will not disturb the thermal equilibrium inside the cavity. As it turns out, the radiation a blackbody emits depends upon the temperature of the body.

Catastrophe

In science a theory and the mathematical representation of the theory must match the experimental results in order for the theory to be valid. Using classical physics, Lord Rayleigh and Sir James Jeans, working independently developed a law to predict the amount of radiation intensity emitted at a given wavelength. They were trying to come up with a rule that would allow them to accurately predict the color a blackbody would radiate based on temperature. The Rayleigh-Jeans Law predicted that the intensity of radiation was proportional to the wavelength so as the intensity increased the wavelength should decrease.

Courtesy of researchgate.net

In the graph above you can see that as the temperature in Kelvin increases the peak of the curve is shifted to the left. At 5000 K the peak of the curve is in the red portion of the spectrum and at 6000 K the peak is in the yellow portion of the spectrum. The catastrophe occurred in the ultraviolet portion of the spectrum and it stated that at low wavelengths the intensity should become infinite. This obviously was a violation of the law of conservation and because this occurred in the ultraviolet portion of the spectrum it was named the ultraviolet catastrophe.

Courtesy of Professor Dave Explains You Tube channel

The graph above shows the experimental results versus the classical theory predictions regarding the intensity of radiation versus wavelength. You can see that at higher wavelengths the classical theory closely matches experimental results but at lower wavelengths there is no agreement.

A Quantum Way Out of Catastrophe

Max Planck solved the ultraviolet catastrophe in 1900. Planck developed a model in which the electromagnetic radiation in the cavity is absorbed by simple harmonic oscillators or resonators. These oscillators were merely a description and he didn’t argue that they actually exist in the walls of the cavity. Planck determined that the energy absorbed by these resonators needed to be in discrete packets or quantized. These discrete packets of energy became known as quanta of energy. This idea of quanta of energy was the birth of quantum theory. He developed a formula to relate the energy absorbed to the frequency of oscillation: E = hv where E is the energy absorbed, v is the frequency of oscillation and h is Planck’s constant 6.626 x 10^-34 J s

Max Planck derived his blackbody radiation law working backward from Wein’s distribution law. Planck realized that Wein’s distribution did not agree with experimental data at long wavelengths, that is wavelengths in the infared portion of the spectrum. The results from Planck’s blackbody radiation law are in agreement with experimental data.

Courtesy of physicsforums.com

The above equation was derived from Wein’s distribution law. Planck’s equation differs in that it allows the units of measure to be derived entirley based on the universal physical constants or the four fundamental constants of nature, Planck’s constant (h), Boltzman’s constant (kB), speed of light (C), and the universal gravitational constant (G).

 Planck’s theoretical result (continuous curve) and the experimental blackbody radiation curve (dots). Courtesy of https://phys.libretexts.org/

Max Planck was able to work through the ultraviolet catastrophe and develop an theory that matched the experimental results. His realization that the radiation in the cavity must be absorbed in discrete quantities ushered in a brand new branch of physics called quantum mechanics. Here is a short video describing Planck’s discovery of light being quantized and the birth of quantum mechanis: https://youtu.be/i1TVZIBj7UA Ironically, many physics students probably refer to this as the quantum catastrophe!

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physics

The Andromeda Galaxy!!!

Image Credit: scifinews.com

If you are lucky enough to live in an area free from light pollution you may have glimpsed the Milky Way Galaxy on a dark cloud-free night. So, what other galaxies might you be able to see from your favorite sky gazing site? It used to be thought that the Large and Small Magellanic clouds (LMC, SMC) were the galaxies closest to our own at 179,000 light years away and 210,000 light years away respectively. In 1994, however Sagittarius Dwarf Elliptical Galaxy was discovered and found to be closer than either the LMC or the SMC at approximately 70,000 light years away. In 2003 the Canis Major Dwarf Galaxy was discovered and is currently the nearest known galaxy to us, about 25,000 light years from our sun.  

There are three major galaxies which comprise the local group galaxies. According to earthsky.org, these are galaxies that reside “within 5 million light years of space around us.” The three major galaxies making up the local group are the Milky Way, the Triangulum, and the Andromeda galaxy. Also included in the local group are about 50 dwarf galaxies. According to esahubble.org a dwarf galaxy is a small galaxy containing a few billion stars whereas larger galaxies may contain hundreds of billions of stars. These dwarf galaxies “are thought to have been created by gravitational forces in the initial stages of the creation of these larger galaxies, or as a result of collisions between galaxies, forming from streams of material and dark matter ejected from the parent galaxies.” 

The largest of the major galaxies in the local group is the Andromeda Galaxy (Messier 31 or M31 also New General Catalog 224 or NGC 224 and this also happens to be the closest non-dwarf galaxy to us at 2.5 million light years away. As a refresher a light year is the distance light can travel in one year and is not a measure of time but of distance. This distance equates to about six trillion miles or 9.7 trillion kilometers.  

Andromeda according to Greek mythology was the daughter of King Cepheus and Queen Cassiopeia. In an effort to save the kingdom the king and queen chained Andromeda to a rock as a sacrifice to the sea god Poseidon. According to the legend, Perseus, who was riding the sky on his winged equine Pegasus rescued and married Andromeda.  

How Big is the Andromeda Galaxy 

Our home galaxy, the Milky Way, is approximately 100,000 light years across and contains an estimated 100-400 billion stars. A light year is equivalent to 5.88 trillion miles or 9.46 trillion kilometers, so our galaxy is ridiculously large when you compare it to our everyday experiences with distance. You may be wondering how big the Andromeda Galaxy is? M31 is about twice as large as the Milky Way at 200,000 light years across and according to astronomy.com, the Andromeda Galaxy may contain as many as 1-trillion stars.  

When and Where to Find M31 

It becomes easiest to see the Andromeda Galaxy beginning in August when it is high enough in the sky to be seen all from dusk to dawn. M31 has an apparent magnitude of 3.1 which means it is bright enough to be seen with the naked eye. According to earthsky.org “The easiest way is to use the constellation Cassiopeia the Queen. You can also use the Great Square of Pegasus.” To locate Cassiopeia in the night sky, look at stars that make a “W” or “M” pattern. Once you have found the constellation, find the star named Schedar and follow an imaginary line to M31. 

Image Credit: earthsky.org

Another way to find the Andromeda Galaxy is a bit trickier and more involved. The Great Square of Pegasus contains “three of the brightest stars (Markab, Scheat, Algenib) in the Pegasus constellation, and Alpheratz (Alpha Andromedae), the brightest star in the constellation of Andromeda (astronomytrek.com).” You will need to find the Great Square of Pegasus. It will be oriented like a diamond. Think of it as a baseball diamond and then draw an imaginary line from first base, which is the star Markab to third base which is the star Alpheratz. Look for a smudge or what appears to be clouds and you have found the Andromeda Galaxy.  

Image Credit:nj.com

Interesting Facts about Andromeda

German astronomer, Simon Marius, was the first person to observe the Andromeda Galaxy through a telescope. Marius was not the first person to discover the galaxy, however. According to nasa.gov “Persian astronomer Abd al-rahman al-Sufi’s The Book of Fixed Stars from the year 964 contains the first known report of the object.” Until the 1920s M31 was thought to be a nebula or star forming region. In 1917 a 100-inch (254 cm) telescope was completed at the Mt. Wilson Observatory. Edwin Hubble studied images of stars taken from the new telescope and was able to conclusively determine M31 was in fact a galaxy rather than a nebula (britannica.com). 

The Andromeda Galaxy is a barred spiral galaxy. According to schoolobservatory.org a barred spiral galaxy is ” 

A barred spiral galaxy is a spiral galaxy with a central bar-shaped structure made of stars. Bars are found in up to 65% of spiral galaxies. They affect the motions of stars, dust, and gas. It is believed that bars act a bit like a funnel, pulling matter into the bulge from the disk. This leads to stars forming in bursts within the center”. 

Image Credit: nasa/hst

At the center of the Andromeda Galaxy, as with the Milky Way, there is a supermassive black hole. This blackhole at the center of M31 is 100-140 million solar masses. According to esahubble.org M31’s core “core is composed of a ring of old, red stars and a newly discovered disk of young, blue stars. The disk is trapped within a supermassive black hole’s gravitational field.” 

Image Credit: esahubble.org

The Andromeda Galaxy is traveling toward the Milky Way Galaxy at a rate of 110 kilometers per second or about 68 miles per hour. M31 will collide with our home galaxy in about 4 billion years. How do we know that the galaxies are going to collide? The stars in each galaxy are so far apart from each other that the likelihood of any stars colliding is quite small. According to theplanets.org “If two stars struck each other during a collision, the impact would cause both stars to break apart. The gases would dissolve at the same time that the gases evaporated. As the different gases interacted, it would create large shockwaves that spread across the universe. Those waves could cause new stars to form from the dust and gases left behind.” What will happen some 4 billion years from now when the Andromeda Galaxy and the Milky Way collide? According to astronomy.com the “…end result will convert the two spiral galaxies into one spheroidal elliptical galaxy, empty of almost all of its star-forming gas. The supermassive black holes will spiral together, eventually becoming a single monster in the heart of the new galaxy. 

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physics

All About Our Sun!

Image Credit: forbes.com

You may have heard people describe our sun as ordinary or not special. In comparison to other stars in the universe that may be true, but I submit that to those of us in our solar system the sun is quite special. Let us take a closer look at our sun and then decide if you think it is special or not. Our sun is the only star in our solar system. Eight major planets orbit the sun which is at the center of our solar system. The average distance between the earth and sun is 149,668,992 km or 93 million miles. Astronomers use this average distance as a unit of distance called astronomical units or AU. The distances in our solar system, galaxy, and beyond are so vast that it is easier to calculate distances using astronomical units than it is to use miles or kilometers. The sun sits at the center of our solar system and makes up more than 99% of the mass of the entire solar system. The diameter of our sun is 1.4 million kilometers (865 thousand miles), over one million earths could fit inside the sun. The sun produces heat and light which is needed for life on Earth. Without the sun the planet would freeze and life as we know it, would not exist.

What is Our Sun Made of and What Makes it a Star

Our sun is a G-class star that was formed some 4.6 billion years ago and is expected to last another 5 billion years. Stars form in a stellar nursery known as a nebula. A nebula is “… an enormous cloud of dust and gas occupying the space between stars and acting as a nursery for new stars (spacecenter.org) The sun, like all stars, is a hot ball of ionized gas. Our sun does not have a solid surface nor a solid core. The sun is 73.4% hydrogen and 25% helium by mass. The sun also contains trace amounts of carbon, nitrogen, oxygen, neon, magnesium, silicon, sulfur, and iron (ucf.edu). 

What makes our sun, or any other star a star? The object must be massive enough that nuclear fusion of elements can occur in the core due to the immense pressure inside the object. The smallest stars that exist are approximately 10 percent the mass of our sun while “high mass” stars are classified as stars having more than three times the mass of our sun. UY Scuti is the largest star ever observed and it has a radius that is 1700 times larger than our sun and it has a mass 7-10 times the mass of our star. 5 billion suns could fit into a sphere with the volume of UY Scuti.

The Layers of the Sun 

Image Credit: nasa.gov

The structure of the sun contains several different layers. The core of the sun is where nuclear fusion occurs as the sun fuses hydrogen into helium through a process called the proton-proton chain. This is a three-step process that results in fusing of hydrogen to produce helium. According to NASA “In the first step two protons collide to produce deuterium, a positron, and a neutrino. In the second step a proton collides with the deuterium to produce a helium-3 nucleus and a gamma ray. In the third step two helium-3s collide to produce a normal helium-4 nucleus with the release of two protons.” A byproduct of the nuclear reactions that occur in the core is the production of elementary particles called neutrinos. Neutrinos, according to scientificamerican.com are subatomic particles that is remarkably similar to an electron but has no electrical charge and a ridiculously small mass, which might even be zero. Neutrinos are one of the most abundant particles in the universe. These reactions are what produce the heat and light that we receive on Earth. The core of the sun extends about a quarter of the distance from the center of our star. The temperature within the core is over 15 million Kelvin.

The radiative zone is the next layer after the core. This region is where energy is carried outwards via radiation. The energy is carried through the radiative zone by photons. These photons, which travel at the speed of light, collide with other particles during their journey to the surface. According to suntoday.org, it takes “several hundred thousand years for radiation to make its way from the core to the top of the radiative zone.”

The convection zone is the outer most layer of the interior of the sun. This zone is much cooler than the core with temperatures of 2,000,000 C at the base of this zone while it is only 5,700 C at the top of the zone. This large temperature difference results in a phenomenon called convection. By definition, convection is “the movement caused within a fluid by the tendency of hotter and therefore less dense material to rise, and colder, denser material to sink under the influence of gravity, which consequently results in transfer of heat.” The convective motion in this zone results in “the generation of electric currents and solar magnetic fields (cora.nwra.com)

The photosphere is the first layer of the sun we can directly observe. This layer is 100 km thick and has a temperature range of 6500 K at the bottom and 4000 K at the top of the photosphere. This region is where sunspots, faculae, and granules are observed.  

The chromosphere is an irregular area located above the photosphere. Temperatures range from 6000 C to 20,000 C. In the chromosphere activity such as prominences, solar flares, filament eruptions can be observed. The reddish color seen in prominences is a result of the light given off from hydrogen at the higher temperatures.  

The outermost layer of the sun, often called the solar atmosphere, is the corona. This portion of the sun is visible during solar eclipses as the whitish edge of the sun. The corona features things such as loops, streamers and plumes that may be visible during a solar eclipse. The temperature of the corona is 1 million C. This is 1000 times hotter than the photosphere despite it being further from the core of the sun. In 1942 Swedish scientist Hannes Alfvén proposed a theory to explain this temperature anomaly. According to earthsky.org he “theorized that magnetized waves of plasma could carry huge amounts of energy along the sun’s magnetic field from its interior to the corona. The energy bypasses the photosphere before exploding with heat in the sun’s upper atmosphere.” 

The Death of Our Star 

Image Credit: schoolobservatory.org

The ultimate fate of a star depends on the star’s mass. High mass stars end their lives by going supernova and becoming a blackhole or a neutron star. Our sun is not massive enough to end its life in such spectacular fashion. When the sun exhausts its fuel, it will “expand into a red giant star, becoming so large that it will engulf Mercury and Venus, and possibly Earth as well (solarsystem.nasa.gov). According to an article published in Nature Astronomy the sun will “… produce a visible, though faint, planetary nebula” (earthsky.org). A planetary nebula is a bit of a misnomer as it is not related to planets. The term was coined by “… William Herschel, who also compiled an astronomical catalog. Herschel had recently discovered the planet Uranus, which has a blue-green tint, and he thought that the new objects resembled the gas giant” (space.com). A planetary nebula, according to Oxford languages is “a ring-shaped nebula formed by an expanding shell of gas around an aging star.” This phase of stellar evolution may last for tens of thousands of years which is a brief period astronomically speaking. Over time the faint planetary nebula will fade, and the sun will cease to shine, and its temperature and pressure will drop. The sun will become a white dwarf about the size of the earth. Is that the end of the cycle? Perhaps not. Astronomers believe that the white dwarf will continue to cool down to a point where it no longer emits light or heat. At this point it will no longer be visible and will be called a black dwarf. This cooling period is thought to take trillions of years so no black dwarfs exist. See my earlier post if you want to learn more about these fascinating objects.

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physics

Say Hello to Maxwell’s Demon

Image Credit: Phys.org

You likely took chemistry and or physics in high school. and some of you make have taken these courses in college as well. One topic that is covered in both classes is thermodynamics. As a refresher thermodynamics at its most basic level is the study of the heat and how it interacts with energy. There are four laws of thermodynamics that describe how thermal energy interacts with matter. Let’s take a closer look at the laws of thermodynamics. You can find these laws in any high school chemistry or physics textbook. I am using the laws of thermodynamics as found at chem.libretexts.org.

The Law of Thermodynamics

Image credit: sciencenotes.org

The Zeroth Law of thermodynamics “states that if two systems are in thermodynamic equilibrium with a third system, the two original systems are in thermal equilibrium with each other. Basically, if system A is in thermal equilibrium with system C and system B is also in thermal equilibrium with system C, system A and system B are in thermal equilibrium with each other.” You may be curious as to why this law is called the zeroth law rather than the first law. The first and second law had already been established before the zeroth law was developed. Scientists believed that the zeroth law was a more fundamental law than the first and second law. They named it the zeroth law so it would appear first in the numeric listing of the laws.

The first Law states that “…energy can be converted from one form to another with the interaction of heat, work and internal energy, but it cannot be created nor destroyed, under any circumstances.” This is basically a restatement of the Law of Conservation of Energy.

The second Law of thermodynamics states that “… the state of entropy of the entire universe, as an isolated system, will always increase over time. The second law also states that the changes in the entropy in the universe can never be negative.” According to chem.libretexts.org “entropy is simply a measure how much the energy of atoms and molecules become more spread out in a process and can be defined in terms of statistical probabilities of a system or in terms of the other thermodynamic quantities.” You can find a much more in depth description of entropy in one of my earlier posts. The second law also describes the direction of the flow of heat. If two objects of differing temperatures are brought together in an isolated system the heat will flow from the warmer object to the cooler object until both objects reach thermal equilibrium which simply means they reach the same temperature. Another point to be made here is that the temperature of an object is a measure of the average kinetic energy of the object’s particles. So the higher the kinetic energy the higher the temperature. Faster moving particles are hotter than slower moving particles. This will be a key factor later in the discussion.

The third law of thermodynamics “… essentially allow us to quantify the absolute amplitude of entropies. It says that when we are considering a totally perfect (100% pure) crystalline structure, at absolute zero (0 Kelvin), it will have no entropy (S). Note that if the structure in question were not totally crystalline, then although it would only have an extremely small disorder (entropy) in space, we could not precisely say it had no entropy. One more thing, we all know that at zero Kelvin, there will still be some atomic motion present, but to continue making sense of this world, we have to assume that at absolute Kelvin there is no entropy whatsoever.

Gedankenexperiment

Physicists often use gedankenexperiment or thought experiments to describe scientific phenomena when testing the idea may not be practical or possible. One example of a thought experiment is one Albert Einstein had of a person trying to chase a beam of light. He tried to imagine what would happen if a person were able to catch up to the wave and ride it like a surfer riding on a water wave. This idea played a pivotal role in the development of his special theory of relativity. Perhaps the most famous thought experiment was one developed by Erwin Schrodinger known as Schrodinger’s cat. According to wtamu.edu ” Schrodinger’s Cat was simply a teaching tool that Schrodinger used to illustrate how some people were misinterpreting quantum theory. Schrodinger constructed his imaginary experiment with the cat to demonstrate that simple misinterpretations of quantum theory can lead to absurd results which do not match the real world.”

Maxwell’s Demon and the Second Law

James Clerk Maxwell was a Scottish scientist who lived from 1831-1879. He developed the theory of electromagnetism which unified light, electricity, and magnetism into one central theory. He derived a set of four equations that describe electromagnetism. Maxwell is generally regarded on equal footing as Isaac Newton and Albert Einstein. His ideas helped in the derivation of Einstein’s theory of special relativity as well as contribute to quantum theory.

Image credit: thunderbolts.info

Now that we have some of the background information out of the way let’s take a look at Maxwell’s demon and how in pertains to the second law of thermodynamics. Maxwell’s demon is a thought experiment created by James Clerk Maxwell in 1871 to see if it would be possible to violate the second law of thermodynamics. In this thought experiment Maxwell envisioned a container separated in half by a partition which has a small door on it. The air is the same temperature on both sides of the container that is to say both sides of the box are in thermal equilibrium with each other. A demon sits on top of the partition and is able to observe the path and velocity of all the individual particles and this demon has the ability to open the door and let particle pass from one side of the container to the other.

In his thought experiment the demon would open the door to allow high speed particles to pass from the right side of the container to the left. The demon would also open the door to allow slow moving particles from the left side to the right. Eventually the left side of the box would contain all the high moving particles while the right side would contain all the slow moving particles. Remember, the particles on the left side of the box are hotter than those on the right because they are moving faster and because temperature is a measure of the average kinetic energy of the particles. The two sides of the container are no longer in thermal equilibrium with one another. At this point the entropy is lower than it was before the demon began separating particles. Recall that the second law of thermodynamics states that the entropy of an isolated system will always increase over time.

So is that the end of the story? Did James Clerk Maxwell determine that the second law of thermodynamics can be violated by a demon capable of separating high speed particles from low speed particles? If so does our current technology have the ability to do the same thing? Scientists and physicists wrestled with this idea for more than a hundred years as the thought experiment was seen as a threat to the second law of thermodynamics.

The Resolution to Maxwell’s Demon and the Preservation of the 2nd Law of Thermodynamics

In 1961 Rolf Landauer came up with an idea to solve the paradox of Maxwell’s demon and the violation of the 2nd law of thermodynamics. Landauer came up with an idea, now called the Landauer principle which states “any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase in non-information-bearing degrees of freedom of the information-processing apparatus or its environment.” Great, so what does that actually mean and how does that solve this conundrum? Well, the demon must learn about the particles if he is to do his job. There is an inherent randomness to the particles before the demon starts his task. As he separates the particles the randomness of the particles decreases while the randomness of the demon’s memory increases. Be it a demon or a technological device there is a finite amount of memory available. Eventually the memory must be reset in order for the task to continue. According to an article in cacm.acm.org: “physicists resolved the paradox by noting that Maxwell’s demon eventually would need to erase the information it had gleaned about the molecules, and that this erasure would create enough entropy to preserve the Second Law.” The deletion of information creates heat which is radiated into the box or out to the universe ultimately increasing entropy of the system thus preserving the 2nd law of thermodynamics. Here is a good video describing both the thought experiment as well as the resolution: https://youtu.be/8Uilw9t-syQ

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physics

The Orion Nebula

Image Credit: Forbes.com

If you look up at the constellation Orion you can find some fascinating objects to observe. You can easily find Mintaka, Alnilam, and Alnitak, the three stars that make up Orion’s belt. The star that marks the shoulder of Orion the hunter, up and to the left of Orion’s belt is Betelgeuse and the star to the lower right of the belt is Rigel.

The Orion constellation is a favorite of backyard astronomers as it contains two of the ten brightest stars in the sky. Astronomers use different terms when discussing luminosity or brightness of an astronomical object. The Apparent magnitude of an object is how bright the star appears from Earth. There are two reasons why a star may appear bright to us. The first reason is that the star may be very close to us. The second reason is that the star may actually be highly luminous. Of course a star could be close to us and be intrinsically bright. Absolute magnitude is the magnitude a star would have if it was at a distance of 10 parsecs from the Earth. If all the stars were at the same distance from Earth, 10 parsecs, then it would be obvious which stars were actually brighter. Absolute magnitude is a measure of how bright the star actually is regardless of its distance from an observer. 1 order of magnitude is equal to 2.512 time brighter. Lower magnitude values translate to brighter stars. Betelgeuse is easily recognizable by it’s reddish color. It has an apparent magnitude of .45 and an absolute magnitude of -5.14. Rigel has a bluish color and has an apparent magnitude of .18 and an absolute magnitude of -6.69. The fact that Rigel has a lower magnitude indicates that it is brighter or more luminous than Betelgeuse.

Image Credit: AstroBackyard

So are there other interesting objects besides stars in the Orion constellation? Actually yes. The closest stellar nursery to Earth can be found in this constellation. Nebula, according to NASA “are enormous clouds of dust and gas occupying the space between the stars.” So how does a star form out of a nebula? According to Hubblesit.org. when regions of mass and dust within the nebula are sufficient enough so “that the gas and dust can begin to collapse from gravitational attraction. As it collapses, pressure from gravity causes the material at the center to heat up, creating a protostar. One day, this core becomes hot enough to ignite fusion and a star is born.”

The Orion Nebula is the closest star forming region to us at a distance of 1,350 light years away and is believed to be 2 million years old. The nebula is more than 30 light years in diameter. As a refresher a light year is a measure of distance and not time. A light year is the distance light can travel in one year which is approximately 6 trillion miles or 9.7 trillion kilometers. The Orion Nebula or Messier 42 (M42) has an apparent magnitude of 4.

It’s easy to locate the Nebula according to Science Focus “…look below the three stars of Orion’s Belt (or above, if viewing from the southern hemisphere). You will see a faint line of stars, which make up Orion’s sword. The nebula is halfway down the sword and will appear as a fuzzy-looking star”

Image Credit: Science Focus

Four stars are visible from an open cluster in the central region of the nebula. An open cluster is a loosely bound collection of several thousand stars which are relatively young. This cluster is known as the Trapezium based on their trapezoidal configuration. The Orion Nebula is part of a larger stellar network called the Orion complex. According to Astronomy.com the complex contains “. ..a mixture of cold hydrogen and dust grains. M42 is known as an emission nebula. The hydrogen is excited by the hot stars buried within. Excitation is a process by which hydrogen atoms absorb energy (from nearby stars). The atoms can’t hold the energy for long, however, and quickly release it as light.”

M42 contains “… contains hundreds of very young stars, less than a million years old, and also protostars still embedded in dense gas cocoons. The nebula is home to about 700 stars in different stages of formation. The youngest and brightest members are believed to be less than 300,000 years old, and the brightest of these may be as young as 10,000 years old.” (messier-objects.com) Feel free to take a tour through the Orion Nebula in infrared and visible light: https://youtu.be/fkWrjrdT3Zg

The best time of year to view the Orion constellation including the Orion Nebula is in December and January when the constellation is at its highest point in the sky for the Northern Hemisphere. The Orion Nebula is a bit unusual in that it can be observed with the naked eye in areas with very dark skies. Most nebula are not visible without the aid of a binoculars or a telescope. Now that you know a little about Orion go find a dark sky location and have a look for yourself I promise you won’t be disappointed.

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physics

Introducing the Black Dwarf Star

Credit: OSR.org A conceptual depiction of a black dwarf star

The ultimate fate of a star once it is has died is dependent upon the mass of the star during its lifetime. A star in general falls into one of the following mass categories: low mass, medium mass, or high mass. The determination of a star’s mass occurs at birth as the star is forming. Stars do not acquire mass throughout their lives and do not grow from low mass star to high mass star for example.

You may be familiar with the what happens to a star once its fuel has run out and it is nuclear fusion is no longer occurring in its core. High mass stars generally have the most spectacular death as they transition to a red supergiant before going supernova and eventually reaching their final fate.

Credit Nasa Image of Supernova 1987A.

A high mass star’s eventual fate will either be as a neutron star if it has a mass of 1.4 to 3 times the mass of the sun or as a blackhole if the star has a mass larger than 3 times the sun. An average star will end its life as a red giant shedding its layers to become a planetary nebula. The red giant core will settle in as a white dwarf. This may not seem like a new revelation but there is a theory that takes the white dwarf to one final stage. We have discussed the life cycle of stars and the death of stars in other posts. Today we want to talk about a very specific and theoretical star known as a black dwarf. Have you ever heard of one? No? Well don’t worry most people haven’t heard of them and absolutely nobody has seen one and no one in our lifetime ever will.

Credit Britannica.com

What is a Black Dwarf?

A black dwarf is a theoretical result of a white dwarf cooling down to a point where it no longer emits light or heat. The object still retains its mass in this phase but does not emit any radiation. You may be thinking to yourself that if it emits no light or heat that is why no one has ever seen one. This might appear to be similar to a black hole which had never been observed until the Hubble Space Telescope (HST) produced the first ever image in 2019. It is true that we would not be able to directly observe a black dwarf but the lack of light or heat is not why we haven’t observed one of these objects yet.

Credit: Science News for Students First image of a black hole from galaxy M87

It turns out it takes a long time for a white dwarf to cool down enough to enter the black dwarf phase. A really long time. Scientists believe it takes trillions of years for a white dwarf to become a black dwarf. According to Scientific American, it takes “few billion years” for a white dwarf to cool down to the surface temperature as our sun. What that means is that not one black dwarf exists at this moment in time. There simply hasn’t been enough time for one to form. If you take the age of the universe to be around 15 billion years old you can understand why no black dwarfs exist yet. Here is a short video that describes what will eventually happen to our sun as it becomes a black dwarf: https://youtu.be/1mXueDqxvFs

One theory suggests that black dwarf stars eventually “break down and disperse into space” according to Universe Guide. Another idea is that very massive black dwarfs, those between 1.2 to 1.4 solar masses may result in a supernova. According to the article “Fusion can still occur at very cold temperatures – it just takes an incredibly long time and requires some help from quantum mechanics. Eventually, those fusion products should build up enough to choke the black dwarf into a supernova, in a similar way to more massive stars. This explosive fate awaits as many as one percent of all stars shining today,” So if you’d like to wait around and see when the last black dwarf is projected to go supernova you’ll be waiting for a while. How long? Try 10^32,000 in the future according to the article.

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physics

The Life Cycle of Stars

Credit: npr.org

If you have ever found yourself awe struck by the beauty and mystery of stars in the night sky you are not alone. The night sky and stars in particular have fascinated and inspired people since the dawn of man. Stars have been used to help sailors navigate the ocean, been used to predict the harvest, and even for religious purposes. Science fiction and pop culture are full of ideas about traveling to the stars or “shooting for the stars” and you can even find registries online that will let you name a star. So a logical set of questions you may have asked yourself are how are stars created, how long do they live, and how do they die?

Fun Facts about Stars

Before we dive into answering those question let’s discuss some facts about stars. Some of these you may know and others may be news to you. There is only one star, our sun, in the our solar system but there are over 100 billion stars in the Milky Way galaxy. The Alpha Centauri system contains the three closest stars, other than the sun to Earth. The stars in this system are Alpha Centauri A, Alpha Centauri B, and Proxima Centauri. Alpha Centauri A & B are a binary pair of stars with an average distance of 4.3 light years from Earth while Proxima Centauri is roughly 4.22 light years from Earth.

Let’s describe some of the terms discussed above. A binary pair can be defind as “… two stars orbiting a common center of mass. The brighter star is officially classified as the primary star, while the dimmer of the two is the secondary (classified as A and B respectively).” (https://www.space.com/22509-binary-stars.html) Despite the term year appearing in the word, a light year is not a measure of time but rather a measure of distance. A light year is the distance that light can travel in one year. Light travels at an incredibly high rate of speed, how fast you ask? Try 300,000 kilometers per second or 186,000 miles per second. So a light year is approximately 9 trillion kilometers or 6 trillion miles. So if we could travel a 186,000 miles per second it would take us 4.3 years to reach Alpha Centauri A & B.

light year Archives - Universe Today
Credit:universetoday.com

How are Stars Formed

With over 100 billion stars in our Milky Way galaxy alone an obvious question is where did these stars come from and how are they formed? Well I’m glad you asked. Stars are formed in stellar nurseries called nebula. According to https://spacecenter.org/what-is-a-nebula/ a nebula is “an enormous cloud of dust and gas occupying the space between stars and acting as a nursery for new stars.” These regions can be formed from the death of other stars via a supernova or from interstellar dust and gas found in the universe. The nebula can be some of the most breath taking features in the night sky.

Horse Head Nebula Credit: noirlab.edu

The life cycle of a star is determined by the mass of the star itself. Stars with a greater mass end up having a shorter lifetime than other stars. So what determines the mass of a star? As it turns out, the mass of a given star is a result of the amount of matter available to it in the stellar nursery or nebula where it is being formed. Nebula provide gas and dust which slowly begins to collapse under its own gravity. As the amount of matter begins to increase the temperature and pressure also increase and the cloud begins to spin about the center of mass. This is the birth of a protostar. (also known as a T Tauri star) According to science.nasa.gov a protostar is the “hot core at the heart of the collapsing cloud that will one day become a star.” As the protostar continues to heat up it reaches a temperature of 15,000,000 K at which time nuclear fusion begins converting hydrogen to helium. When these atoms of gas are fused together the result is the release of an extremely large quantity of energy. This release of energy is a consequence of Einstein’s famous theory E=mc^2 which states that the amount of energy obtained from an object is equal to the mass of the object multiplied by the speed of light squared, an incredibly high number. Here is a short video clip from the Science Channel’s How the Universe Works “A Star is Born” episode. It can take close to 50 million years for an average star, such as our sun to form!

In order for the nuclear fusion to occur a star candidate must have a minimum mass of .08 the mass of the sun. Objects that have a mass that is between 15 and 75 times the mass of Jupiter are known as Brown dwarfs. Often called failed stars, Brown dwarfs are too large to be a planet and too small to be a star. It is believed that brown dwarfs form in the same way as stars do but these objects don’t have enough mass to allow for nuclear fusion to occur.

Giant Gas Planet or Brown Dwarf – Where Does One Draw the Line?
Image credit: astromart.com

The Life and Death of a Star

The lifetime of a star is directly related to the mass of the star. Very low mass stars burn their fuel slowly and have a much longer life than high mass stars. The standard classification of stars uses mass and temperature to distinguish between types of stars. Stars are classified as one of the following types: O, B, A, F, G, K, and M. O type stars are the most massive and hottest stars with temperatures around 40 000 K while M type stars have temperatures of 3000 K. Our sun is a type G star with a surface temperature of 6000 K.

Image credit: quora.com

The lower mass (lower temperature) stars burn their fuel more slowly while the higher mass (higher temperature) stars burn through their fuel more rapidly. It is believed that almost all of the low mass M type stars that were ever formed still exist and nearly all the high mass O and B type no longer exist.

Hertzsprung-Russell Diagram

The Herzsprung-Russel of H-R diagram is “… a scatter graph of stars, a plot of stellar absolute magnitude or luminosity versus temperature or stellar classification. It is an important astronomical tool for understanding how stars evolve over time.” (https://science.nasa.gov/plotting-pulsating-variable-stars-hertzsprung-russell-h-r-diagram)

Gallery: Stars (article) | Khan Academy
Image credit: Khan Academy

The image above shows where stars fall based on the temperature and luminosity or brightness. Blue giants and supergiants occupy the top left of the diagram. Our sun occupies a spot near the middle of the diagram while red dwarfs are located near the bottom right of the chart. Stars spend 90 % of their lives on the main sequence portion of the diagram. While on the main sequence stars are actively fusing hydrogen in their cores. As a star begins to exhaust its fuel supply the star may move off of the main sequence portion of the H-R diagram. This occurs when hydrogen becomes depleted at the center of the star’s core.

The Death of an Ordinary Star

When a star such as our sun begins to fuse elements other than helium in its core the star will enter the red giant phase. The star will expand to more than 400 times its normal size. In the case of our sun, this would mean that it expanded to the orbit of Mars. Over time the core of the star shrinks and the core begins to fuse helium into carbon-12. A star with a 10 solar mass will enter the red supergiant phase rather than a red giant phase when it begins fusing carbon. The initial mass of the star determines if it eventually becomes a red giant or a red super giant. A red super giant will expand beyond the orbit of Jupiter. Helium flash occurs as the star fuses the helium to carbon as described above. This phase will last approximately 100 million years at which point the helium is exhausted. The helium flash is a runaway nuclear reaction caused by the sudden ignition of helium. “About 6% of the electron-degenerate helium core, which by now weighs in at about 40% of a solar mass, is fused into carbon within a few minutes.  (This corresponds to burning roughly ten Earth masses of helium per second, if you are keeping score.) time.”(https://faculty.wcas.northwestern.edu/~infocom/The%20Website/end.html)

Helium+Flash+He+core+H+layer+Envelope.jp
Image credit: science forums

A low mass star eventually “will lose all of the mass in its envelope and leave behind a hot core of carbon embedded in a nebula of expelled gas.” (https://map.gsfc.nasa.gov/universe/rel_stars.html) The planetary nebula left behind will eventually be used in the creation of other stars. What once was a sun like star is now nothing more than a carbon core called a “white dwarf” surrounded by a planetary nebula.

The Death of High Mass Stars

A supernova
Supernova 1987A Courtesy of NASA

https://www.nasa.gov/audience/forstudents/5-8/features/nasa-knows/what-is-a-supernova.htmlLet’s talk briefly about the death of stars larger than our sun. If a star is roughly 8 times the mass of our sun (8 solar masses it likely will undergo a spectacular death. The death of this sized star is called a Type II supernova. A supernova is “…. the explosion of a star. It is the largest explosion that takes place in space.” (https://www.nasa.gov/audience/forstudents/5-8/features/nasa-knows/what-is-a-supernova.html)

When a star goes supernova it becomes the brightest object in the sky and can be seen even in daylight. One result of a star of a massive star (8-18 solar masses) that has gone supernova is a neutron star. A neutron star is an incredibly dense remnants of a supernova explosion. They are 1.4-3.2 solar masses condensed down to the size of approximately 20 kilometers. According to EarthSky.org a tablespoon of a neutron star would weigh more than 1 billion tons! They are called neutron stars because all of the electrons and protons are compressed and combined to form neutrons. Some neutron stars spin very rapidly and emit radio waves from the poles. These are called pulsars and have extremely powerful magnetic fields. Here is a cool video about pulsars. https://youtu.be/VxVlwAvi6Zo

Supernova remnant Cassiopeia A (Cas A),
The remains of a supernova called Cassiopeia A, located in our galaxy about 11,000 light-years from Earth. Credit NASA

Black Holes

Stars with a very high mass, approximately 18 solar masses or greater, end their lives by becoming a black hole. Most people are aware that black holes are a region in space where the gravitational force is so strong that not even light can escape it. The reason the gravity is so strong is because the entire mass of the star is compressed down to an incredibly small size relative to the stars size prior to it going supernova.

Stellar black holes can be up to twenty solar masses or 20 times the mass of the sun. A new class of black holes were coined as intermediate black holes. These black holes are in between the stellar black holes and super massive black holes. In 2014 an intermediate black hole was found in the arm of a spiral galaxy according to space.com. Supermassive black holes may be 1 million times the mass of the sun or more. These are often found at the center of galaxies.

Sagittarius A is a supermassive blackhole at the center of the Milky Way galaxy and it has a mass of about 4 million solar masses. Black holes were predicted by Einstein in 1916 but not observed directly because it does not emit any light. All that changed on April 10th 2019 when the first image of a black hole was presented to the world. This black hole is from the center of galaxy M87 which is about 55 million light years from Earth.

Credit: sciencenewsforstudents.org

Here is one last video giving a quick description of how a dying star becomes a white dwarf, a neutron star, or a black hole. Spoiler, it is due to the mass of the star. https://youtu.be/NucdlR9EGbA

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physics

The Science of Time Dilation and Time Travel

Courtesy of bbc.co.uk

This will be the first in a series of posts describing the science behind time travel. Today’s post will focus on time dilation and we will tie this into time travel in the post next week. Movies such as Interstellar, Back to the Future https://youtu.be/2sLnnjHjDgE, the Terminator series, and The Final Countdown have captured the imagination of fans by building their blockbuster films around the topic of time travel. H.G. Wells authored what may be the most famous work of fiction on the topic with his 1895 book appropriately titled “The Time Machine”.

Who, among us, hasn’t wished we could go back in time to change a decision we made or wanted to go into the future to see how our lives or the world around us will look in 10, 25 or even 100 years? Surely these idea are just fantasy right? We all know that time travel isn’t real, the very idea of it must violate some law of physics right? As it turns our, physics does not rule out the possibility of time travel and you may be surprised to learn that time travel is an active an ongoing area of research in physics today. There is experimental proof of time dilation as well as real life practical applications that we use in our daily lives. Let’s take a look at what science tells us about the possibility of time travel and the problems associated with it.

Is Time an Absolute?

What time is it? A deceivingly simple question. Just look at your watch or your phone and you can answer that question. So does that mean that time flows at the same rate for everyone anywhere in the universe? As it turns out, time is not the absolute or constant quantity you may think it is. Under certain circumstances the arrow of time may run differently than we experience in our everyday lives.

Einstein was able to prove this with his two theories on relativity. This idea of time running differently is called time dilation. Merriam-Webster.com defines time dilation as “a slowing of time in accordance with the theory of relativity that occurs in a system in motion relative to an outside observer and that becomes apparent especially as the speed of the system approaches that of light.” So what does that mean?

Relativity

In 1905 Albert Einstein published his theory of special relativity. One of the consequences of this ground breaking theory is that as an object’s speed increases time slows down as compared to an observer in another inertial frame of reference. Before we get more into this let’s describe some of the terminology associated with this phenomenon. According to https://www.space.com/36273-theory-special-relativity.html, the theory of special relativity “explains how space and time are linked for objects that are moving at a consistent speed in a straight line.” Einstein described two postulates for special relativity, the first is that all inertial frames of reference are equally valid and the second is that the speed of light in a vacuum is a constant.

A frame of reference can be described as “a set of criteria or stated values in relation to which measurements or judgments can be made.” (Oxford dictionary) Simply put a frame of reference is the point of view an individual uses to relate the motion of another object. For example, if I am standing on the sidewalk and a car drives by me at 20 miles per hour and throws a ball at a rate of five miles per hour, in the same direction as the vehicle is moving, from my frame of reference I would judge the ball being thrown at 25 miles per hour. From my frame of reference I would conclude that I am at rest and the car is moving. The occupants of the car would deem themselves at rest as I pass them by at 20 miles an hour and they would see the rate of the ball being thrown at five miles per hour. An inertial frame of reference is a frame of reference that is moving at a constant velocity.

So what does this all have to do with time travel and how does it change the flow of time? Einstein was able to show that because the speed of light is constant than something else much change when looking at speed, time, and distance. As it turns out it is time that changes. The faster an object moves through space the slower it moves through time. Distances also contract when an object travels at a significant percentage of the speed of light but we will not consider that consequence in our discussion. The effects in everyday life are negligible but if you can accelerate an object to a significant percentage of the speed of light the effects become remarkable. You may be tempted into thinking this is merely a mathematical trick but this has been proven experimentally.

This image has an empty alt attribute; its file name is 050318mathew_time_dilation.gif

The above equation can be used to calculate time dilation due to differences in velocity. t’ represents the amount of time viewed from the rest frame, for example if we wanted to know how much time would elapse on Earth as a rocket traveled at close to the speed of light, t’ would be how much time elapsed back on Earth. t is the amount of time the traveler experiences while traveling at a significant percentage of the speed of light. the v^2 represents the speed of the rocket and c^2 represents the speed of light squared. For ease of calculations we set c^=1 and v^2 = to the percentage of the speed of light the rocket is going. For example is a traveler on a spaceship was gone for 10 years according to his clock and was traveling at 90% the speed of light, by using the above equation we can see that 22.9 years back on earth have passed while only 10 years have passed for the astronaut.

If you have watched the movie Interstellar you saw a description of another type of time dilation relying not on velocity but on a strong gravitational field. Gravitational time dilation is supported by Einstein’s theory of general relativity which describes how massive objects distort the fabric of space-time. https://youtu.be/lznM-fygfqo It has been experimentally verified that clocks run more slowly in the presence of a strong gravitational field. The results have been verified in distances as small as one meter apart.

The above equation can be used to calculate the time dilation due to a massive non-rotating spherical object. t’ represents time at a distance far away from the gravitational field. t is the amount of time passing in the gravitational field created by the massive object. G is the universal gravitational constant (6.67E-11 N m^2/kg^2). M is the mass of the object causing the time dilation, r is the separation distance from the center of the massive object to the observer within the gravitational field, and c^2 is the speed of light squared. There are approximations of this equation for smaller distances that we will ignore for now.

Experimental Examples of Time Dilation

“In October 1971, Hafele and Keating flew cesium-beam atomic clocks, initially synchronized with the atomic clock at the US Naval Observatory in Washington, D.C., around the world both eastward and westward. After each flight, they compared the time on the clocks in the aircraft to the time on the clock at the Observatory. Their experimental data agreed within error to the predicted effects of time dilation. Of course, the effects were quite small since the planes were flying nowhere near the speed of light.” (physicslink.com)

All of have utilized the global positioning system (GPS) on our phones at one time or another. So how do they relate to time dilation? “GPS has a small correction for time dilation between the surface of the earth and up in space. A satellite in space experiences 0.6 nanoseconds more for every second on Earth. This is actually how GPS works – by knowing what time each satellite the receiver is getting data from thinks it is, it can use the time dilation to calculate the distance from the receiver to each satellite, which can be used to triangulate the receiver’s position.” (https://tvtropes.org/)

“Particle accelerators, such as the Large Hadron Collider, are able to accelerate subatomic particles near the speed of light, and time dilation is a measurable effect. (Del Monte, Louis A.. How to Time Travel: Explore the Science, Paradoxes, and Evidence (p. 52)

Speaking of particles, muons which are subatomic particles that are 200 times more massive than electrons, also demonstrate time dilation. The life span of a muon is much shorter than an electron. “muons are produced naturally in the upper atmosphere by cosmic ray impacts. The fast ones are generated at a high enough altitude that few should reach the surface before decaying, but many do – and the Rossi-Hall and Frisch-Smith experiments confirmed they arrived in numbers that agreed with their lifespans being elongated by time dilation.” (https://tvtropes.org/) Here is a short clip describing the muon time dilation: https://youtu.be/rVzDP8SMhPo

So now we have some of the experimentally verified science behind time dilation we can begin to look at how this can be used to travel in time. Next week we will consider some of the current ideas on how to make the idea of time travel a reality and the obstacles that stand in the way of making this happen. The following week we will discuss some of the paradoxes that would seem to prevent time travel.

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physics

The Uncertainty Principle

Courtesy of cartoonstock.com

Heisenberg’s uncertainty principle is of those topics where people feel confident that they understand it but many people only understand a portion of it. The uncertainty principle is likely the first thing people will mention if you ask them about quantum mechanics. As with many things in science there is actually a much deeper and richer explanation of this phenomenon than you might be aware of. So let’s jump in and learn about the history and applications of one of the most famous and misunderstood topics in physics.

Werner Karl Heisenberg was born on December 5th, 1901 in the city Wurzburg, Germany. Heisenberg displayed an aptitude for mathematics from an early age and it wasn’t until he attended the University of Munich in 1920 that he began his study of physics in earnest. At the tender age of 25 he was appointed professor of theoretical physics in Leipzig. During this time Heisenberg worked with Max Born, Neils Bohr, Arnold Sommerfeld and others to develop and refine the field of quantum mechanics.

In 1925 Werner Heisenberg submitted a paper that in his words “seeks to establish a basis for theoretical quantum mechanics founded exclusively on relationships between quantities which in principle are observable.” This paper helped describe quantum mechanics using the mathematical principles of matrices. This method of calculating the quantum behavior of particles was a tremendous breakthrough in the emerging field of quantum mechanics.

History of the Uncertainty Principle

Before we describe exactly what the uncertainty principle states and describe its applications let’s take a moment to discuss how Heisenberg arrived at this monumental insight. In 1926 a debate was raging between those that held to Heisenberg’s matrix version of quantum theory and Erwin Schrodinger who believed in the wave theory of quantum mechanics. Most scientists of the day preferred the wave theory due in, no small part, to the ease and familiarity with the mathematical equations presented by Schrodinger.

Erwin Schrodinger presented his findings that the wave theory and the matrix theory gave identical mathematical results. As a result of this finding Paul Dirac and Pascual Jordan developed a set of unified equations collectively known as transformation theory which became the foundation for quantum mechanics. While Heisenberg studied how to measure the variables in the unified equations, and with input from Wolfgang Pauli, Heisenberg detected a problem with trying to measure the variables.

Heisenberg noticed that in trying to determine the precise position and momentum of a particle, at the same time, imprecisions appeared. These imprecisions occurred when trying to measure the time and energy variables at the same moment as well. Heisenberg presented his results in a paper to Pauli dated February 23rd, 1927. Upon receiving positive and encouraging feedback from Pauli, Heisenberg formalized and submitted his findings for publication.

What Does the Uncertainty Principle Mean?

Werner Heisenberg attempted to use his matrix mechanics, in a thought experiment to describe the path of an electron in a cloud chamber. He realized that the path the electron traversed was made visible by the condensation of droplets of water that were actually larger than the electrons they were trying to detect. (J Baggott, The Quantum Story p91). The consequence of this meant that the instantaneous position and velocity of the electron can only be approximately known. We will come back to the electron and cloud chamber thought experiment later.

Let’s discuss a few terms that we will need in our explanation of the uncertainty principle. Planck’s constant represented by the letter h and has a value of 6.6262E -34 Joule-second. “Planck’s constant defines the amount of energy that a photon can carry, according to the frequency of the wave in which it travels.” (https://science.howstuffworks.com/dictionary/physics-terms/plancks-constant.htm) Next is momentum which is the product of mass multiplied by velocity. This is important because you will see momentum used in some descriptions of the uncertainty principle and in others you will see velocity. It is more common to use momentum as all particles such as electrons, have a mass associated with them.

Heisenberg had discovered a fundamental property of nature which states “the uncertaintites is position and momentum cannot be smaller than Planck’s constant.” (J Baggott, The Quantum Story p91) This results in a limit to the amount of precision we can simultaneously have regarding the position and momentum of a particle. This fundamental limit does not hold true in our everyday experiences of classical mechanics.

Courtesy of clutchprep.com

The image above is the equation for the uncertainty principle where x represents position, p represents momentum and the triangle represents the uncertainty. The equation states the product of the uncertainty of the position and momentum must be greater than or equal to the Planck’s constant divide by 4pi. This equation can be rewritten to include the uncertainty of time and energy in addition to position and momentum.

Recall the electron and cloud chamber thought experiment from earlier. One way to measure the position and momentum would be to use a microscope. An issue here is that every time a photon bounces off the electron the momentum and position of the electron is changed. One might be able to determine the electrons instantaneous position, however the large interaction between the electron and the device we are using to measure its position means we are unable to determine its momentum. You may be asking yourself can we use a device with lower energy photons, that is those with a lower frequency or longer wavelength ? This would allow us to calculate the electron’s momentum but we would not be able to accurately measure its position. This thought experiment is useful to give you a conceptual understanding of the uncertainty principle but it is more useful than truthful.

What is really happening here is that because of the wave particle duality it is impossible to know the exact location and momentum of an object. The reason for this is because “what we can measure is limited by the fact that position and momentum are undefined until we measure them in the quantum realm. In the thought experiment with the electron and the cloud chamber the electron has a definite position and momentum prior to making a measurement. In the quantum world, due to the wave-particle duality the precise position and momentum do not exist. (C Orzel, How to Teach Quantum Physics to Your Dog p44). Here is a quick conceptual explanation of the uncertainty principle: https://youtu.be/m8VQue1Nffw

Misconceptions of the Uncertainty Principle

One of the most common misconceptions of the uncertainty principle is that it is caused by the act of measurement. The idea here is that the act of measuring the object causes a change in the position or speed of the object as in the thought experiment. The reality is that the principle is a result of the dual nature of quantum objects.

A second misconception is that current technology limits our ability to determine both the position and momentum of a quantum object. It turns out that the uncertainty principle is a fundamental limit set by nature rather than a technological or observational limit.

What it All Means

The point of all this is that the uncertainty principle, also known as the indeterminacy principle, is a fundamental limit of nature and is due to the wave-particle nature of quantum particles. The concept of an exact position and exact momentum of a quantum particle is meaningless. “Any attempt to measure precisely the velocity of a subatomic particle, such as an electron, will knock it about in an unpredictable way, so that a simultaneous measurement of its position has no validity. This result has nothing to do with inadequacies in the measuring instruments, the technique, or the observer; it arises out of the intimate connection in nature between particles and waves in the realm of subatomic dimensions. (https://www.britannica.com/science/uncertainty-principle) As stated earlier this applies not just to position and momentum but to energy and time as well. Well, I certainly hope you enjoyed this post.

Categories
astronomy physics solar system

The Alpha Centauri System

Planets at Alpha Centauri?
Courtesy of Physics.org

If you ask someone what the nearest star is, other than the sun, the likely reply will be Alpha Centauri. As it turns out, Alpha Centauri is actually a system of three stars discovered in 1915. The two main stars are a pair of binary stars Alpha Centauri A and Alpha Centauri B. They are termed binary stars because they orbit a common center of gravity (space.com). The third star in the system is named Proxima Centauri. So why then do people say that Alpha Centauri is the closest star to our sun? As it turns out when you look up at the night sky you see this three star system as a single star.

What Do We Know about the Physical Structure of Alpha Centauri?

Courtesy of gravitywarpdrive.com

Let’s talk about the characteristics of each of the stars in this system. Centauri A has a surface temperature of 5770 K (10,000 F) which is similar to that or our own sun which has an average surface temperature of 5778 K according to evimage.org. According to earthsky.org Centauri A has a diameter 25 percent greater than our sun. The luminosity, or intrinsic brightness of Centauri A is 1.6 times the luminosity of our own sun

Centauri B has a surface temperature of 5300 K (9,000F) and a luminosity which is equal to one half the luminosity of the sun. Centauri is 90 percent the mass of the the sun. If Centauri B were not part of this binary system it would rank as the 21st brightest star in the night sky. (earthsky.org)

Proxima Centauri is a red drawf star which orbits the Centauri A&B pair. Proxima has a mass that is about 12 percent or ouf sun and a radius that is 14 percent the size of our sun (solarsystemquick.com) and is 20 thousand times fainter than our sun. (nineplanets.org)Proxima has a relatively cool surface temperature of 3500 K (5840 F).

Centauri A and Centauri B orbit a common center of mass with an orbital period of 80 years. The average distance between them is 23 AU or astronomical units which is the distance from the Earth to the sun. The distance between Centrauri A&B and Proxima Centauri is about 13,000 AU and it takes almost a half a billion years for Proxima to orbit Centauri A&B. (nineplanets.org)

How Far Away is Alpha Centauri?

Distance Alpha Centauri measured in astronomical units. Courtesy of futurism.com

We have stated that the three star system Alpha Centauri is the closest star to our sun but just how far away is it? Alpha Centauri A and Alpha Centauri B are an average distance of 4.3 light years from earth according to space.com and Proxima Centauri is 4.22 light years from earth. This may not sound like a large difference but it means that Proxima Centauri is 620 billion miles closer than Centauri A and Centauri B. (earthsky.org) Let’s take a moment to discuss the term light year. This is a measure of distance and not of time. A light year is the distance light can travel in a year. This distance is roughly 6 trillion miles or 9.5 trillion kilometers. In order for us to reach Proxima Centauri, the closest of the three stars, we would need to travel at the speed of light for 4.22 years. As a refresher, the speed of light is roughly 670,616,629 miles per hour, stated another nearly 671 million miles per hour. Even if we could somehow travel at that rate it would still take over four years to reach it.

Is Alpha Centauri a Planetary System?

Courtesy of phl.upr.edu

You may be thinking about our star, the sun, and the planets that orbit it. We know this is our solar system and you may be asking yourself if the Alpha Centauri system has any planets orbiting it? The answer is yes, astronomers discovered a planet orbiting Proxima Centauri in 2016. The fact that this star has a planet orbiting it makes this a planetary system. A planetary system is simply a star with a planet or planets orbiting the star. You may ask how is that different than a solar system. The solar system is simply our planetary system which we named the solar system. The planetary system of this planet has three suns, Centauri A, Centauri B, and Proxima Centauri.

The planet orbiting Proxima Centauri is named Proxima b. The planet is 1.3 times as massive as Earth according to space.com and resides in the habitable or Goldilocks zone of the Proxima Centauri. The term habitable zone is a bit misleading as it does not necessarily mean that any planet in this zone can support life. What it does mean is that it is at an appropriate distance that if the planet has water it won’t freeze or boil off the surface. NASA defines the habitable zone as “is the range of distance with the right temperatures for water to remain liquid.”

Proxima Centauri b is is classified as a super Earth planet. Livescience.com defines a super Earth planet as “a planet with a mass between 1 and 10 times that of Earth. The super-Earth classification refers only to the mass of the planet, and does not imply anything about its surface conditions or habitability.” The exoplanet of the Alpha Centauri system has a radius that is 1.08 times the radius of the Earth. (exoplanets.nasa.gov) Proxima Centauri b has an orbital period of 11.2 days which means it takes 11.2 days to orbit Proxima Centauri and is only 4.7 million miles from Proxima Centauri which is about one half of an astronomical unit AU. By way of comparison the Earth is roughly 93 million miles from our own sun which is one AU.

Could Alpha Centauri Host Other Exoplanets?

In 2019 astronomers detected a second potential exoplanet orbiting Proxima Centauri. The object has tentatively been named Proxima c pending verification that the object is indeed a planet. This potential planet appears to reside in the habitable zone which sounds like an exciting prospect. According to space.com “the candidate world, which has a minimum mass about six times that of Earth, orbits 1.5 astronomical units (AU) from Proxima Centauri and is therefore probably very cold. Its equilibrium temperature hovers around minus 390 degrees Fahrenheit (minus 234 degrees Celsius).” Proxima c is 1.5 AU from Proxima Centauri which is a bit of a problem for astronomers. Scientists measure the gravitational effects of an orbiting planet or other object on the star. The effects are minor at on a smaller star at such a great distance.

How to View Alpha Centauri

As mentioned earlier Alpha Centauri appears to be a single star to the naked eye. This star system form the brightest star in the Southern constellation called Centaurus. Only the stars Sirius and Canopus appear brighter making Alpha Centauri the third brightest star in the night sky. Unfortunately for most of us in the northern hemisphere we are unable to see Alpha Centauri. Anyone north of 29 degrees latitude will not be able to view this bright star. Stargazers in portions of the southern hemisphere, including Australia, will note that the star is cirumpolar which means it never sets. If you are lucky enough to be in an area where you can view Alpha Centauri take advantage of it. Some of may never get to gaze directly at the third brightest star in the night sky. Here is a quick video tour of the Alpha Centauri system: Alpha Centauri Virtual Tour