3445 - WAVE FUNCTIONS - the electron’s behavior?

  -  3445  -  WAVE FUNCTIONS  -    the electron’s behavior?    In water waves, the quantity that varies periodically is the height of the water surface. In sound waves, it is pressure. In light waves, electric and magnetic fields vary. What is it that varies in the case of matter waves? 

-------------  3445  -   WAVE FUNCTIONS  -    the electron’s behavior?

-  The quantity whose variations make up “matter waves” is called the wave function 𝞧, (the Greek letter psi). The value of the wave function associated with a moving body at the particular point x, y, z in space at the time t is related to the probability of finding the body there at the time. 

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-  The wave function itself has no direct physical significance. There is a simple reason why the wave function cannot interpreted in terms of an experiment. The probability that something be in a certain place at a given time must lie between 0 (the object is definitely not there) and 1 (the object is definitely there).

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-   An intermediate probability, say 0.2, means that there is a 20% chance of finding the object. But the amplitude of a wave can be negative as well as positive, and a negative probability, say 0.2, is meaningless. 

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-  Hence the wavefunction cannot be an observable quantity. This objection does not apply to the square of the absolute value of the wave function, which is known as “probability density“. 

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-  A large value wavefunction square means the strong possibility of the body's presence, while a small value means the slight possibility of its presence. As long as wavefunction square is not actually 0 somewhere, however, there is a definite chance, however small, of detecting it there. 

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-  This interpretation was first made by Max Born in 1926.  There is a big difference between the probability of an event and the event itself. Although we can speak of the wave function that describes a particle as being spread out in space, this does not mean that the particle itself is thus spread out. 

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-  When an experiment is performed to detect electrons a whole electron is either found at a certain time and place or it is not; there is no such thing as a 20 percent of an electron. However, it is entirely possible for there to be a 20 percent chance that the electron be found at that time and place, and it is this likelihood that is specified by wavefunction square.

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-   If an experiment involves a great many identical objects all described by the same wave function, the actual density (number per unit volume) of objects at x, y, z at the time t is proportional to the corresponding value of wavefunction square. 

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-  It is instructive to compare the connection between the wavefunction and the density of particles it describes. To understand this connection consider the formation of a double-slit interference by photons. 

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-  In the wave model, the light intensity at a place on the screen depends on E^² the average over a complete cycle of the square of the instantaneous magnitude E of the em wave's electric field. 

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-  The intensity depends instead on N * h * f, where N is the number of photons per second per unit area that reach the same place on the screen. Both descriptions must give the same value for the intensity, so N is proportional to E². 

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-  If N is large enough, somebody looking at the screen would see the usual double-slit interference pattern and would have no reason to doubt the wave model. If N is small perhaps so small that only one photon at a time reaches the screen the observer would find a series of apparently random flashes and would assume that he or she is watching quantum behavior. 

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-  If the observer keeps track of the flashes for long enough, though, the pattern they form will be the same as when N is large. The probability of finding a photon at a certain place and time depends on the value of E² there.

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-   If we regard each photon as somehow having a wave associated with it, the intensity of this wave at a given place on the screen determines the likelihood that a photon will arrive there. When it passes through the slits, light is behaving as a wave does. When it strikes the screen, light is behaving as a particle does. 

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-  The linear momentum, angular momentum, and energy of the body are other quantities that can be established from the wavefunction. The problem of quantum mechanics is to determine the wavefunction for a body when its freedom of motion is limited by the action of external forces.

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-   Wave functions are usually complex with both real and imaginary parts. A probability, however, must be a positive real quantity. The probability density (wavefunction square) for a complex wavefunction is therefore taken as the product wavefunction with its complex conjugate. 

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-  The complex conjugate of any function is obtained by replacing i(√-1) by -i wherever it appears in the function. Every complex function can be written in the form: 

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-----------------  wavefunction= A+iB, where A and B are real functions. 

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-----------------  Wavefunction*= A-iB. Wavefunction square = A²-i²B² = A²+ B². 

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-  Wavefunction square is always a positive real quantity.  Even before we consider the actual calculation of the wavefunction, we can establish certain requirements it must always fulfill. For one thing, since wavefunction square is proportional to the probability density P of finding the body, the integral of wavefunction over all space must be finite ,the body is somewhere.

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-   If the integral is zero, the particle does not exist, and the integral obviously cannot be infinity and still mean anything . Furthermore, wavefunction square cannot be negative or complex because of the way it is defined. 

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-  The only possibility left is that the integral be a finite quantity if the wavefunction is to describe properly a real body. It is usually convenient to have wavefunction square be equal to the probability density P of finding the particle described by the wavefunction, rather than merely be proportional to P.

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-   If the wavefunction square is equal to P, then it must be true that the integral of the wavefunction square from - ∞ to + ∞ equal to 1, since if the particle exists somewhere at all times. This wavefunction is said to be normalized. Every acceptable wave function can be normalized by multiplying it by an appropriate constant.

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-  This gets more complicated as we introduce more dimensions, but we will only consider an electron traveling in a line, in one dimension. The definite integral from a to b gives us the probability that the electron is in between points a and b.

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-  Given the wave function, the electron is most likely to be found at its tallest peak or its lowest trough, depending on which one is deeper. But how does this wave function define superposition? 

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-  The wave function can be broken down into many states. Say an electron can have only two states: spin up, and spin down, they're two completely independent states of being. 

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-  When the electron is in superposition, an interesting thing happens when the electron is observed. One of the probabilities drops to zero, and the other jumps up to one. This is called the "collapse" of the superposition. This is not only for this case.

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-  In a scenario where the particle is in a superposition of 15 states, all other probabilities drop to zero except for a single one, which jumps to one. The wave function becomes something called a “delta function“, where it has a peak at the measured value, this is why after you take a single measurement of the state of a quantum particle, it will continue to show that same state if you measure it again and again and again. 

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-  If you let the wave function settle back into its original waveform after a long time, it may give a different point. This means by measuring the particle, you directly alter the wave function. 

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-  Something else important about the wave function: the wavelength of the function is the momentum of the particle. A longer wavelength implies a smaller momentum. The important thing to understand here is that for a particle where we know the momentum, the wavefunction square will be the same everywhere, and we will no longer have any idea as to where the particle is. 

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-  When we know the position, the wavelength will always be different, and we will have no idea what the momentum is. This is called the “Heisenberg uncertainty principle“. 

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-   Heisenberg uncertainty principle is inextricably linked to the wavefunction. But what is the function itself? Nobody knows. This is a mystery that's been unsolved for nearly a century.

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-   Nobody really knows what this function is, but we use it, nonetheless. This function has evaded understanding and there are definitely some theories out there as to what the function could be, but at the end of the day, nobody knows what this function is.

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February 3, 2022      WAVE FUNCTIONS  -    the electron’s behavior?            3445                                                                                                                                               

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-----------------------------  Friday, February 4, 2022  ---------------------------

3444 - SOLAR CYCLES - storms on the Sun?

  -  3444  -  SOLAR  CYCLES  -  storms on the Sun?    While no one can predict exactly when the next big solar super storm or long-lasting storm will hit.   The Sun might be 93 million miles away, but that doesn't mean it doesn't have a huge impact on Earth with it’s sunspots.

-------------  3444  -   SOLAR  CYCLES  -   storms on the Sun? 

-   An extremely powerful solar storm pummeled our planet 9,200 years ago, leaving permanent scars on the ice buried deep below Greenland and Antarctica.  Ancient ice samples were found that this previously unknown storm is one of the strongest outbursts of solar weather ever detected and would have crippled modern communications systems if it had hit Earth today.

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-   The massive storm appears to have hit during a solar minimum, the point during the sun's 11-year cycle when solar outbursts are typically much less common.  Because of this unexpected discovery, researchers are concerned that devastating solar storms could hit when we least expect them, and,  that Earth might not be prepared when the next big one arrives.

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-  These enormous storms are currently not sufficiently included in our risk assessments.  It is  important to analyze what these events could mean for today's technology and how we can protect ourselves.

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-  Solar storms occur when magnetic field lines on the sun's corona (the outermost part of the sun's atmosphere) become tangled up and then violently snap back into place. This sudden magnetic reconnection can release huge amounts of plasma and magnetic field known as coronal mass ejections (CMEs), which surf across space on the sun's ever-gusting solar wind.

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-  If a powerful CME passes over Earth, it can compress the planet's magnetic shield, causing what's known as a geomagnetic storm.  Mild geomagnetic storms can damage satellites and interrupt radio transmissions; severe storms, like the "Halloween storms" of 2003, can cause widespread power outages across the world and permanently damage electrical infrastructure, such as power transformers. 

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-   A sufficiently large solar storm could also ravage the world's undersea internet cables, resulting in an "internet apocalypse" that leaves huge chunks of the world population disconnected for months.

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-  CME outbursts typically peak every 11 years or so, when the sun enters the part of its natural activity cycle known as the solar maximum, the time when magnetic activity in the corona is  high.

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-  Today, satellites can monitor solar outbursts directly. But finding evidence of ancient storms requires some atomic detective work.  A study looked for evidence of special particles known as “cosmogenic radionuclides“, radioactive isotopes (versions of elements) created when charged solar particles collide with elements in Earth's atmosphere.

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-  These radioactive particles can appear in natural records, like tree rings and ice cores.  Analyzing several cores drilled in Antarctica and Greenland where both locations showed a remarkable spike in the radionuclides beryllium-10 and chlorine-36 around 9,200 years ago, indicating that a powerful solar storm swept across Earth at that time.

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-  Further analysis of the cores showed that the storm was particularly powerful perhaps on a par with the most powerful solar storm ever detected, which occurred during a solar maximum between the years 775 B.C. and 774 B.C.

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-  The newly discovered storm's occurrence during a solar minimum, when magnetic activity on the sun should be low, left the study authors puzzled and alarmed.  This storm further pushes the magnitude of a potential worst-case scenario for solar storm events.  

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-  Researchers now need to detect more ancient, extreme storms in the ice-core and tree-ring records, to determine if there is some sort of pattern beyond the sun's 11-year cycle that dictates when the most extreme storms will occur.   

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-  How the Sun affects satellites?  At the edge of space, the ever-growing fleet of satellites in low-Earth orbit are locked in a constant, precarious battle with friction.

These satellites orbit in a normally quiet region hundreds of miles above the surface, at the edge of Earth's atmosphere.

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-   Usually, the satellites only feel a gentle push due to the headwinds of the rarified air there, but extreme storms from the Sun can change Earth's atmosphere enough to pull a satellite farther off orbit in one day than they'd normally experience in a year.

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-  These orbital deviations don't cause satellites to fall out of the sky, but they can disrupt their communication with Earth, shorten their lifespan, and can even increase the chances of a terminal collision in space.

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-  This effect, known as “orbital drag“,  is evidence that less intense, but longer-lasting storms surprisingly have bigger effects on satellites' orbits than the shorter, more severe events.

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-  Low-Earth orbit satellites provide the backbone to Earth and weather observations and telecommunications systems. The new research looked at rare extreme historic storms to will help satellite operators better understand satellite lifetimes and dynamics, making the near-Earth space environment safer when the next big super storm hits.

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-  This new result highlights the fact that even during less extreme space weather events, orbital drag of satellites is of greater impact than we anticipated. And it is becoming more and more of an issue, simply because we've got more and more and more spacecraft up there.

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-  The Solar Dynamics Observatory caught a glimpse of a huge coronal mass ejection, or CME, leaving the Sun on July 23, 2012. If such a CME had hit Earth, it could have caused trillions of dollars in damage to telecommunications and infrastructure. 

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- The Sun provides the light to nurture life on Earth, but , it also spews dangerous particles and radiation that can affect astronauts and technology in space.  High-energy particles and radiation from the Sun can heat Earth's atmosphere as they collide with common molecules, like nitrogen and oxygen. 

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-  The heated air rises and causes the atmosphere to expand like a balloon. If a storm is strong enough, it will cause the atmosphere to expand so much that it engulfs the orbits of low-Earth orbit satellites that would otherwise fly through areas with little to no atmosphere.

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-   Increased atmosphere is like running in a headwind, it slows you down. For a satellite, this resistance causes it to slow and drop down in altitude. During an extreme magnetic storm event, a satellite could drop nearly a third of a mile in elevation in one day. That's as much as a satellite would typically lose in a year.

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-  Scientists are finding that the effects of weaker, but longer-lasting storms might be just as impactful as extreme storm events.  Super storms from the Sun are rare, only one has occurred since the dawn of the space age, and it was only half as powerful as the 1921 event. However, in the same period there have been dozens of lesser magnetic storms from the Sun, not all of which have reached Earth.

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-  The strongest storms don't necessarily produce the most drag. The effects of a longer, less intense storm can build up over time, ultimately causing more orbital drag than a short, powerful storm. 

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-  Solar storms disproportionately affect low-Earth orbit satellites, which live within the first 375 miles of space above Earth's surface, which can be enveloped by a swelling atmosphere. The vast majority of new satellites call this region home, including the quickly growing constellations of communications satellites launched by private industries.

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-  Once a satellite is knocked out of orbit, the effects only worsen, since at lower altitudes there is more atmosphere and thus more drag, even in calm conditions. The lower a satellite is dragged, the amount of drag it experiences only increases.

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-  Orbital drag is bad for a satellite that wants to stay at a working altitude, but it's also bad for nearby satellites that might collide with a satellite that's been dragged off-course.  Even tiny pieces of space debris pose a huge risk for satellites, so minimizing collisions is key to keeping the near-Earth environment a functional space for satellites.

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-   The new results are just one aspect of space weather and the field of “helophytic“, in which scientists try to understand how activity on the Sun ripples across the solar system and affects Earth.

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-  In the 1970s solar activity led to increased drag on NASA's Skylab mission, causing it to deorbit earlier than expected. Improved models over the years have helped scientists better understand the effects of normal solar activity on orbital drag. However, the rarity of extreme events has made it difficult to know exactly how they might affect current satellites.

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-  Heliophysics mission is to monitor the Sun's activity. Missions like the Solar Dynamics Observatory and the Solar and Heliophysics Observatory keep a constant eye on the Sun, while other missions like the Ionospheric Connection Explorer, Space Environment Testbeds, and the upcoming Atmospheric Waves Experiment study how space weather and solar variability affect Earth's upper atmosphere and satellites and other technology. 

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-  While no one can predict exactly when the next big solar super storm or long-lasting storm will hit.   The Sun might be 93 million miles away, but that doesn't mean it doesn't have a huge impact on Earth..

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February 3, 2022      SOLAR  CYCLES  -   storms on the Sun              3444                                                                                                                                               

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-----  Comments appreciated and Pass it on to whomever is interested. ---

---   Some reviews are at:  --------------     http://jdetrick.blogspot.com -----  

--  email feedback, corrections, request for copies or Index of all reviews 

---  to:  ------    jamesdetrick@comcast.net  ------  “Jim Detrick”  -----------

-----------------------------  Friday, February 4, 2022  ---------------------------

3443 - UNIVERSE - history over 14 billion years

  -  3443   -  UNIVERSE  -   history over 14 billion years.    The history of the universe and how it evolved is accepted as the “Big Bang model“, which states that the universe began as an incredibly hot, dense point roughly 13.7 billion years ago. So, how did the universe go from being fractions of an inch across to what it is today?

-------------  3443  - UNIVERSE  -   history over 14 billion years. 

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-  The Big Bang was not an explosion in space. Instead, it was the appearance of space everywhere in the universe all at once.. According to the Big Bang theory, the universe was born as a very hot, very dense, single point in space.  A very small space packed full of universe.

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-  Cosmologists are unsure what happened before this moment, but with sophisticated space missions, ground-based telescopes and complicated calculations, scientists have been working to paint a clearer picture of the early universe and its formation.

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-  A key part of this comes from observations of the “cosmic microwave background“, which contains the afterglow of light and radiation left over from the Big Bang. This relic of the Big Bang pervades the universe and is visible to microwave detectors.

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-  In 2001, NASA launched the “Wilkinson Microwave Anisotropy Probe” (WMAP) mission to study the conditions as they existed in the early universe by measuring radiation from the cosmic microwave background. Among other discoveries, WMAP was able to determine the age of the universe to be about 13.7 billion years old.

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-  When the universe was very young, like a hundredth of a billionth of a trillionth of a trillionth of a second, it underwent an incredible growth spurt. During this burst of expansion, which is known as “cosmic inflation“, the universe grew exponentially and doubled in size at least 90 times.

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-  The universe was expanding, and as it expanded, it got cooler and less dense. After cosmic inflation, the universe continued to grow, but at a slower rate.   As space expanded, the universe cooled and matter formed.

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-  Light chemical elements were created within the first three minutes of the universe's formation. As the universe expanded, temperatures cooled and protons and neutrons collided to make deuterium, which is an isotope of hydrogen. Much of this deuterium combined to make helium.

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-    For the first 380,000 years after the Big Bang the intense heat from the universe's creation made it essentially too hot for light to shine. Atoms crashed together with enough force to break up into a dense, opaque plasma of protons, neutrons and electrons that scattered light like fog.

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-  About 380,000 years after the Big Bang, matter cooled enough for electrons to combine with nuclei to form neutral atoms. This phase is known as "recombination," and the absorption of free electrons caused the universe to become transparent. 

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-  The light that was unleashed at this time is detectable today in the form of radiation from the cosmic microwave background.  This era of recombination was followed by a period of darkness before stars and other bright objects were formed.

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-   400,000,000 years after the Big Bang, the universe began to come out of its dark ages. This period in the universe's evolution is called the age of “re-ionization“.  This dynamic phase was thought to have lasted more than a half-billion years, but based on new observations, scientists think re-ionization may have occurred more rapidly than previously thought.

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-  During this time, clumps of gas collapsed enough to form the very first stars and galaxies. The emitted ultraviolet light from these energetic events cleared out and destroyed most of the surrounding neutral hydrogen gas. The process of re-ionization, plus the clearing of foggy hydrogen gas, caused the universe to become transparent to ultraviolet light for the first time.

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-  Astronomers comb the universe looking for the most far-flung and oldest galaxies to help them understand the properties of the early universe. Similarly, by studying the cosmic microwave background, astronomers can work backwards to piece together the events that came before.

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-  Data from older missions like WMAP and the “Cosmic Background Explorer” (COBE), which launched in 1989, and missions still in operation, like the Hubble Space Telescope, which launched in 1990, all help scientists try to solve the most enduring mysteries and answer the most debated questions in cosmology.

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-  Our solar system is estimated to have been born a little after 9 billion years after the Big Bang, making it about 4.6 billion years old. According to current estimates, the sun is one of more than 100 billion stars in our Milky Way galaxy alone, and orbits roughly 25,000 light-years from the galactic core.

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-    The sun and the rest of our solar system was formed from a giant, rotating cloud of gas and dust known as the solar nebula. As gravity caused the nebula to collapse, it spun faster and flattened into a disk. During this phase, most of the material was pulled toward the center to form the sun.

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-  In the 1960s and 1970s, astronomers began thinking that there might be more mass in the universe than what is visible. Vera Rubin, an astronomer at the Carnegie Institution of Washington, observed the speeds of stars at various locations in galaxies.

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-  Basic Newtonian physics implies that stars on the outskirts of a galaxy would orbit more slowly than stars at the center, but Rubin found no difference in the velocities of stars farther out. In fact, she found that all stars in a galaxy seem to circle the center at more or less the same speed.

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-  This mysterious and invisible mass became known as “dark matter“. Dark matter is inferred because of the gravitational pull it exerts on regular matter. One hypothesis states the mysterious stuff could be formed by exotic particles that don't interact with light or regular matter, which is why it has been so difficult to detect. 

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-  In the 1920s, astronomer Edwin Hubble made a revolutionary discovery about the universe. Using a newly constructed telescope at the Mount Wilson Observatory in Los Angeles, Hubble observed that the universe is not static, but rather is expanding.

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-  Decades later, in 1998, the space telescope named after the famous astronomer, the Hubble Space Telescope, studied very distant supernovas and found that, a long time ago, the universe was expanding more slowly than it is today. This discovery was surprising because it was long thought that the gravity of matter in the universe would slow its expansion, or even cause it to contract.  The opposite was happening.

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-  “Dark energy” is thought to be the strange force that is pulling the cosmos apart at ever-increasing speeds, but it remains undetected and shrouded in mystery. The existence of this elusive energy, which is thought to make up 80% of the universe, is one of the most hotly debated topics in cosmology.

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-  While much has been discovered about the creation and evolution of the universe, there are enduring questions that remain unanswered. Dark matter and dark energy remain two of the biggest mysteries, but cosmologists continue to probe the universe in hopes of better understanding how it all began.

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-  The James Webb Space Telescope (JWST), launched in 2021, will continue the hunt for the elusive dark matter, as well as peering back to the beginning of time and the evolution of the universe using its infrared instruments.

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-  For more information about the evolution of the universe check out:

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-------------------- "The History of the Universe" by David H. Lyth 

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-------------------- "A Brief History of Time" by Stephen Hawking.

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--------------------  You can also keep up to date with the discoveries of JWST, visit NASA's dedicated webpage or the European Space Agency's dedicated webpage.

 Also see:

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-------------------  Scientific American, "The Evolution of the Universe", October 1994. 

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-------------------  Walter Perry, "Origin and Evolution of the Universe", Journal of Modern Physics, Volume 12, November 2021.

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-------------------  Bharat Ratra and Michael S. Vogeley, "The Beginning and Evolution of the Universe", Publications of the Astronomical Society of the Pacific, Volume 120, March 2008, 

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--------------------  NASA, "Brief History of the Universe", December 2006. 

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February 2, 2022     UNIVERSE  -   history over 14 billion years.                3443                                                                                                                                               

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-----  Comments appreciated and Pass it on to whomever is interested. ---

---   Some reviews are at:  --------------     http://jdetrick.blogspot.com -----  

--  email feedback, corrections, request for copies or Index of all reviews 

---  to:  ------    jamesdetrick@comcast.net  ------  “Jim Detrick”  -----------

-----------------------------  Friday, February 4, 2022  ---------------------------

3442 - PLANETS - how many out there?

  -  3442   - PLANETS  -  how many out there?  Today astronomers have many planet-finding methods like “stellar wobble“, the “transit method“, “direct imaging“, and “microlensing“.  They have discovered  thousands of planets beyond our Solar System. Over 5,000 as of January 2022.

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-------------  3442  -    PLANETS  -  how many out there?

-  Astronomers expect there are “trillions” of planets in the Milky Way alone. With an estimated 2 trillion galaxies in our observable Universe, we can finally make an accurate estimate of the total number of planets. The enormity of cosmic "chances" for life is beyond coprehension.

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-   Each star within each galaxy contains its own stellar system, and potentially, its own set of planets. For a long time, we didn’t know how many of these stars actually possessed planets or what the likelihood of planets of different masses were. Today, more than 30 years after the first exoplanet was discovered, we are closer than ever to understanding just how many planets populate our Universe.

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-  In the early 1990s, the first planetary detections around other stars arrived.  To know how many planets there are in the Universe, one way to make such an estimate is to detect planets to the limits of an observatory’s capabilities, and then to extrapolate how many planets there would be if we viewed it with a limitless observatory.  The average number of planets-per-star is greater than 1. 

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-  As planets orbit their stars, those stars orbit their mutual center-of-mass, creating “wobbles” in their motion.  When a massive planet orbits its parent star, the star and planet will both orbit their mutual center of mass. 

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-  Even if the planet is not directly observable, its presence, orbital period, and mass (multiplied by an uncertain angle-of-orbital-inclination) can be extracted simply by measuring the periodic motion of the parent star with the method of Doppler Effect. 

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-  This stellar wobble, or radial velocity, reveals planetary masses and orbital periods, up to an uncertain inclination angle.  Exoplanets that cannot be directly seen or imaged can still be detected through their gravitational influence on their parent star, which causes a periodic spectral shift

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-  Meanwhile, transiting planets obscure a portion of their parent star’s light.  When planets pass in front of their parent star, they block a portion of the star’s light: “a transit event“.

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-   By measuring the magnitude and periodicity of transits, we can infer the orbital parameters and physical sizes of exoplanets. When transit timing varies and is followed (or preceded) by a smaller-magnitude transit, it may indicate an exomoon as well, such as in the system “Kepler-1625“.  This periodic dimming reveals a planet’s radius and period; it’s responsible for most presently discovered planets.

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-  The candidate rogue planet “CFBDSIR2149“,  imaged in the infrared, is a gas giant world that emits infrared light but has no star or other gravitational mass that it orbits. It is one of the only rogue planets known, and was only discoverable because its large-enough mass emits its own infrared radiation. 

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-  Direct imaging and microlensing also reveal exoplanets; their numbers may skyrocket in coming decades.  When a gravitational microlensing event occurs, the background light from a star gets distorted and magnified as an intervening mass travels across or near the line-of-sight to the star. 

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-  The effect of the intervening gravity bends the space between the light and our eyes, creating a specific signal that reveals the mass and speed of the planet in question. 

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-  With 400,000,000,000  Milky Way stars, we estimate they contain 1-to-10 trillion orbiting planets, total.  Although the Milky Way is full of stars, the stellar density map of the sky, constructed with data from the ESA’s space-based “Gaia” mission, is only accurate to the extent that visible light gives us accurate information.

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-   The ultraviolet and visible light emitted by the Milky Way’s stars is obscured by the light-blocking dust in our galaxy, requiring longer-wavelength views to reveal them. Through a combination of multi-wavelength observations and inferences about the low-mass stars in our galaxy, we now estimate that there are 400,000,000,000  stars within the Milky Way, and 80% of those are M-class red dwarfs. 

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-  Rogue / orphan planets , those ejected and formed without parent stars, could be 10-to-10,000 times as numerous.  “Rogue planets” may have a variety of exotic origins, such as arising from shredded stars or other material, or from ejected planets from solar systems, but the majority should arise from star-forming nebula, as simply gravitational clumps that never made it to star-sized objects. When a microlensing event occurs, we can use the light to reconstruct the intervening planet’s mass. 

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-  With 2 trillion galaxies within our observable Universe, we can extrapolate our Universe’s planetary total.

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-  The “Hubble eXtreme Deep Field”  may have observed a region of sky just 1/32,000,000 th of the total, but was able to uncover a whopping 5,500 galaxies within it: an estimated 10% of the total number of galaxies actually contained in this pencil-beam-style slice. 

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-  The remaining 90% of galaxies are either too faint, or too red, or too obscured for Hubble to reveal, but when we extrapolate over the entire observable Universe, we expect to obtain a total of 2 trillion galaxies within the visible Universe. 

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-  There are 10^25 planets that orbit stars, with some 10^26  to  10^30 additional starless planets.

-

-  When starlight passes through a transiting exoplanet’s atmosphere, signatures are imprinted. Depending on the wavelength and intensity of both emission and absorption features, the presence or absence of various atomic and molecular species within an exoplanet’s atmosphere can be revealed through the technique of “transit spectroscopy“. 

-

-  Will we find the first extra-solar planet housing extraterrestrial life.  The “Drake equation” is one way to arrive at an estimate of the number of spacefaring, technologically advanced civilizations in the galaxy or Universe today. However, it relies on a number of assumptions that are not necessarily very good, and contains many unknowns that we lack the necessary information to provide meaningful estimates for. 

-

-  So, study astronomy.  There are a lot more discoveries out there, somewhere.  

-

February 2, 2022          PLANETS  -  how many out there?               3422                                                                                                                                               

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-----  Comments appreciated and Pass it on to whomever is interested. ---

---   Some reviews are at:  --------------     http://jdetrick.blogspot.com -----  

--  email feedback, corrections, request for copies or Index of all reviews 

---  to:  ------    jamesdetrick@comcast.net  ------  “Jim Detrick”  -----------

-----------------------------  Wednesday, February 2, 2022  ---------------------------

3440 - QUANTUM GRAVITY - more we know stranger it gets?

  -  3440   -  QUANTUM  GRAVITY  -  more we know stranger it gets?     By demonstrating that particles display the “Aharonov-Bohm effect” for gravitational forces, previously only seen with electromagnetic ones, we might have our first clue to gravity's quantum nature.       

          

-------  3440  -   QUANTUM  GRAVITY  -  more we know stranger it gets?    

-

-     See Review 3435 -  “Quantum Gravity  -  have we demonstrated it”  for more on this subject.

-

-  Three of our fundamental forces of nature, the electromagnetic and strong and weak nuclear forces, are known to be “quantum’ in nature. Quantum meaning the forces are carried by particles.  However, the oldest known fundamental force, gravity, has only been shown to exhibit behavior described by Einstein's general relativity: a classical and continuous theory. 

-

-  If you were to break down the matter in our Universe to its smallest and most fundamental subatomic constituents, you’d find that everything was made up of individual “quanta“, each of which possesses both wave and particle properties simultaneously.

-

-   If you pass one of these quantum particles through a double-slit and don’t observe which slit it passes through, the quantum will behave as a “wave“, interfering with itself  and leaving us with only a probabilistic set of outcomes to describe its ultimate trajectory. Only by observing it can we determine precisely where it is at any moment in time.

-

-  This bizarre, “indeterminate probabilistic” behavior has been thoroughly observed, studied, and characterized for three of our fundamental forces: the electromagnetic force and the strong and weak nuclear forces.

-

-   However, it’s never been tested for gravitational forces, which remains the one remaining force that only has a classical description in the form of Einstein’s general relativity. Although many clever experiments have attempted to reveal whether a quantum description of gravity is required to account for the behavior of these fundamental particles, none has ever been performed decisively.

-

-  The “Aharonov-Bohm effect“, has just been discovered to occur for gravity as well as electromagnetism.  It could be our first clue that gravity is truly quantum in nature.

-

-  In general relativity, the presence of matter and energy determine the curvature of space. In quantum gravity, there will be quantum field theoretic contributions that lead to the same net effect. So far, no experiment has been able to establish whether gravity is quantum in nature or not.

-

-  In the world of quantum physics, few experiments are more demonstrative of the bizarre nature of reality than the double-slit experiment. Originally performed with photons more than 200 years ago, shining light through two thin, closely-spaced slits resulted not in two illuminated images on the screen behind the slits, but rather in an interference pattern. The light that went through each of the two slits must be interacting before they reach the screen, creating a pattern that displays light’s inherent wave-like behavior.

-

-  This same interference pattern was shown to be generated with electrons as well as photons; for single photons, even as you passed them through the slits one at a time; and for single electrons, again even as you passed them through the slits one at a time. 

-

-  As long as you don’t measure which slit the quantum particles go through, the wave-like behavior is easily observable. It is evidence of the counterintuitive, but very real, quantum mechanical nature of the system.   Somehow, an individual quantum is capable of going through “two slits at once” where it must interfere with itself.

-

-   And, if you do measure which slit these quanta pass through, you see no interference pattern at all. Instead, you just get two “clumps” on the far side of the screen, which correspond to the set of quanta that went through slit 1 and slit 2, respectively.

-

-   You cannot simply ascribe definite quantities like a “position” and a “momentum” to each particle, as you would in a classical, pre-quantum treatment of those quantities. Instead, you have to treat position and momentum as quantum mechanical operators, mathematical functions that “operate” on a quantum wave function of probabilities.

-

-  When you “operate” on a wave function, you get a probabilistic set of outcomes for what is possible to observe. When you actually make that key observation, when you cause the quantum you’re “observing” to interact with another quantum whose effects you then detect, you recover only a “single collapsed value“.

-

-   You can perform this experiment with electrons, particles with a fundamental, negative electric charge, and you send them through these slits one at a time. If you measure which slit the electron goes through, it’s easy to describe the electric field generated by the electron as it goes through that slit. But even if you don’t make that critical measurement  you can still describe the electric field that it generates. 

-

-  The reason you can do this is because it isn’t just the individual particles or waves that are quantum in nature, but the physical fields that permeate all of space are quantum in nature as well.   Yhey obey the rules of “quantum field theory“.

-

-  For the electromagnetic interaction, as well as the strong and weak nuclear interactions, science has verified and validated the predictions of quantum field theory many times over. The agreement between theoretical predictions and the results of experiments, measurements, and observations is spectacular, agreeing in many cases to better than 1-part-in-a-billion precision.

-

-    What happens to the gravitational field of an electron as it goes through a double slit?  Theoretically, without a working quantum theory of gravity, we cannot make a robust prediction, while experimentally, detecting such an effect goes far beyond our current capabilities.

-

-   At present, we do not know whether gravity is an inherently quantum force or not, as no experiment or observation has been able to make such a critical measurement.

-

-  If you have a charged particle in motion, it can be affected by both the presence of electric fields and magnetic fields.  The electric field will accelerate the charged particle along the direction of the field, in direct proportion to the strength of the field and proportional to the charge of the particle, causing it to either speed up or slow down in the process.

-

-  The magnetic field accelerates the charged particle perpendicular to both the magnetic field and the direction of motion of the particle, causing it to bend but not to increase or decrease its speed.

-

-  If your electric and magnetic fields are both zero, your electron won’t accelerate; it will just continue along in constant motion.

-

-  But in the quantum Universe, there’s another effect that comes into play that can change the behavior of your quantum particle, even when the electric and magnetic fields are both zero,  the “Aharonov-Bohm effect“.

-

-  Electric potential is more commonly known as “voltage“. Changes in voltage, from one region to another, are what creates electric fields and compels electric currents to flow. You can get the electric field from the “electric potential” simply by taking the gradient, which details how the field changes, directionally, throughout space.

-

-  “Magnetic potential” is a little more complicated because it doesn’t have a common analog like voltage, and also because the magnetic field itself doesn’t come about from a simple gradient, but rather from a mathematical operation known as the “curl” of the magnetic potential.

-

-  You can have a non-zero electric or magnetic potential in a region even where the electric and magnetic fields are both zero.   The potential couples to the phase of a charged particle’s wave function, and if you measure the phase of that charged particle you’ll find that it does depend on the electromagnetic potential, not just on the electric and magnetic fields.

-

-  The Aharonov-Bohm effect states that a particle’s phase will change as it moves around a region containing a magnetic field, even if the field itself is zero everywhere the particle is present. The phase shift has been robustly detected for decades now, leading many to pursue extensions of the original physics, which applied only to the electromagnetic force. 

-

-  The way we typically measure the Aharonov-Bohm effect is to set up a cylindrical region of space that contains a substantial but highly confined magnetic field: something that’s easy to create with a long coil of wire, like a solenoid. You then set up a charged particle in motion around that magnetic field, but carefully, so that the particle itself doesn’t pass through the region containing the field.

-

-  The wave function will still experience a phase shift that can be observed experimentally. This is true even though the electric and magnetic fields are negligible outside the confined region containing the field, and the probability of finding the particle within the field-containing region is also negligible.

-

-  The same effect that’s been observed for the magnetic potential should be observable for any force that arises as a consequence of a potential. This includes not only the electric force and the other known quantum forces, but also the gravitational force.

-

-   When you want to experiment with the gravitational force, the biggest problem is always that gravitational effects are so small. Although people have been designing experiments for many decades with a view toward detecting this effect, an enormous breakthrough came in 2012.

-

-  The idea was that you can create ultra-cold atoms and control their motion by pulsing a laser beam, including into a region where the gravitational potential, but not the field, is different from other locations. Even in regions where the gravitational force is zero, which can be arranged by a careful setup, the non-zero potential could still have an effect.

-

-  If you can then split a single atom into two matter waves, move them into areas with different potentials, and then bring them back together, you could observe an interference pattern, measuring their phase and quantifying the gravitational Aharonov-Bohm effect.

-

-   January, 2022,  a team took multiple ultra-cold rubidium atoms, put them into quantum superpositions with one another, and compelled them to trace two different paths inside a vertical vacuum chamber. Because there was a heavy mass at the top of the chamber, but one that was axially symmetric and completely outside of the chamber itself, it only changed the gravitational potential of the atoms, with the atom that reached a higher trajectory experiencing a greater change in potential.

-

-  Then, the atoms are brought back together, and from the interference pattern that is produced, a phase shift emerges. The amount of the phase shift that’s measured should correspond to:

-

--------------------------  How separated the two atoms are from one another,

-

--------------------------  How close they each come to the top of the chamber

-

-------------------------  The external mass which alters the gravitational potential is present or not.

-

-  Measure the phase shifts of these atoms and compare them with the theoretical predictions for the gravitational Aharonov-Bohm effect the match is dead on.

-

-   This is a remarkable achievement. But the analysis could be applied to any force or field that’s derivable from a potential, both quantum and classical. It’s a tremendous triumph for quantum mechanics under the influence of gravity, but it isn’t quite enough to demonstrate the quantum nature of gravity itself. 

-

-  When you “operate” on a wave function, you get a probabilistic set of outcomes for what is possible to observe. When you actually make that key observation, when you cause the quantum you’re “observing” to interact with another quantum whose effects you then detect, you recover only a single value.  How does all this happen?

-

January 31, 2022      QUANTUM  GRAVITY  -   stranger it gets?                 3440                                                                                                                                               

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-----  Comments appreciated and Pass it on to whomever is interested. ---

---   Some reviews are at:  --------------     http://jdetrick.blogspot.com -----  

--  email feedback, corrections, request for copies or Index of all reviews 

---  to:  ------    jamesdetrick@comcast.net  ------  “Jim Detrick”  -----------

-----------------------------  Tuesday, February 1, 2022  ---------------------------

3436 - BLACKHOLES - new discoveries to study?

 -  3436   -  BLACKHOLES  -  new discoveries to study?    In  2021 there were many exciting new results regarding  strange gravitational beasts we call “blackholes:.  In February  physicists revised their estimates of the properties of the cosmic monster sitting in the heart of the Cygnus X-1 system, which also happens to be the first blackhole ever confirmed to exist. 

-------------  3436  -    BLACKHOLES  -  new discoveries to study?

-  Discovered nearly 60 years ago, the “Cygnus X-1” blackhole was found to be 50% more massive than previously thought, making it 21 times the sun's  mass, and spinning very close to the speed of light, setting a new record for blackhole rotation. 

-

- The blackhole Cygnus X-1 is located about 7,200 light-years away and is slowly consuming a blue supergiant companion star.  When a star wanders too close to the edge of a blackhole, gravitational forces will pull it apart into long strands that get sucked down the blackhole's center. 

-

-  This process, known as "spaghettification," produces light as the stellar material heats up via friction, allowing astronomers to see it. 

-

-  In May, 2021, researchers for the first time spotted another star being shredded and devoured in this way by this blackhole weighing an astounding 30 million times the mass of the sun and located in the center of a galaxy 750 million light-years from Earth. 

-

-  In June, 2021,  researchers with the “Laser Interferometer Gravitational-Wave Observatory” (LIGO) watched two gigantic blackholes merge into a single entity and analyzed the ripples in the fabric of space-time called ‘“gravitational waves” created as the blackholes spiraled toward each other at high speed.

-

-   The resulting blackhole's surface area was larger than the first two combined. In addition to providing amazing data, the findings help prove a 1971 conjecture from British astrophysicist Stephen Hawking known as the “blackhole area theorem“. 

-

-  The Hawking theorem states that it is impossible for the surface area of a blackhole to decrease over time, a law Hawking derived using both Einstein's theory of general relativity as well as his understanding of entropy. 

-

-   According to quantum mechanics, blackholes should be able to shrink and evaporate, and so it's unclear how to square that with Hawking's law that their surface area must also always increase. 

-

-  LIGO had many of blackhole findings to deliver in June, 2021, when researchers working with the facility announced that, for the first time, they were confident that they'd seen blackholes merging with compact entities called neutron stars.

-

-   Along with blackholes, neutron stars are one potential end result of a massive star's death, when the star explodes as a supernova and leaves behind a remnant. While LIGO had previously seen hints of potential blackhole-neutron star mergers, it wasn't until, 2020, that two signals conclusively proved such mergers were happening.

-

-   Both detections occurred in January, 2020, roughly 10 days apart. The first involved a blackhole with about six times the sun's mass devouring a neutron star one and a half times the sun's mass, while the second involved a blackhole about nine times the mass of the sun and a neutron star about twice as massive as the sun.

-

-    Almost every known galaxy has a supermassive blackhole in its center, suggesting that there is a tight relationship between the two. But scientists still don't understand how a blackhole affects its galactic host. 

-

-  Research released in June, 2020, showed high-speed winds being blown from a 13 billion-year-old galaxy, one nearly as old as the universe itself. This is the earliest detected example of “galactic wind“, which is burped out of supermassive blackholes as they consume surrounding gas and dust.

-

-   The powerful winds were traveling at  1.1 million mph.  They were moving fast enough to propel material all over the galaxy and likely hinder star formation.  

-

-   In July, 2021, astronomers captured X-rays flaring from a supermassive blackhole in the center of a spiral galaxy called Zwicky, which is 1.8 billion light-years away. The researchers not only detected light coming from the front of the blackhole, but they also managed to find strange echoes of light that they initially couldn't place.

-

-   These turned out to originate from the “back of the blackhole“, meaning that the mammoth entity was warping the fabric of space-time so much that light was being pulled from one side of the blackhole to the other. This process is exactly what would be expected from Einstein's theory of general relativity but, until now, hadn't been definitively detected.

-

-  12 enormous invisible black holes could be lurking on the outskirts of the Milky Way. The results from a new simulation of galaxy collisions show that gravitational forces could cause supermassive blackholes, weighing millions or billions of times that of the sun, to go flying and wander the inky depths of the universe.  

-

-  In December, 2021,  telescopes captured evidence of the closest blackhole pair to our own planet, a duo spinning around one another some 89 million light-years away from Earth in the constellation Aquarius. 

-

-  The previous record-holding blackhole pair is located five times farther away than this one, meaning scientists have the opportunity to study such systems in greater detail than before. 

-

-  Both members of the duo are heavyweights, the larger has a mass of almost 154 million suns, while the smaller is 6.3 million times more massive than our star. They orbit one another with a separation of 1,600 light-years indicating that they will merge into one giant blackhole 250 million years from now.

-

-  A tiny galaxy orbiting our own at a distance of about 820,000 light-years appears to contain an oddity. The “Leo I” dwarf galaxy, which is 50 times smaller than the Milky Way, hosts an outsized blackhole, one with almost the same mass as the blackhole in the Milky Way's center. 

-

-  Astronomers are baffled as to how such a large blackhole came to reside in such a small galaxy.  Figuring out precisely what this means for both blackhole and galactic evolution will have to wait for the coming years.

-

-  Astronomers study stars that shine.  Now we are studying blackholes that take away that light.  We need new instruments to see in these new “light” dimensions.  

-

January 31, 2022       BLACKHOLES  -  new discoveries to study?           3436                                                                                                                                               

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-----  Comments appreciated and Pass it on to whomever is interested. ---

---   Some reviews are at:  --------------     http://jdetrick.blogspot.com -----  

--  email feedback, corrections, request for copies or Index of all reviews 

---  to:  ------    jamesdetrick@comcast.net  ------  “Jim Detrick”  -----------

-----------------------------  Tuesday, February 1, 2022  ---------------------------

3439 - UNIVERSE - Expanding in all directions.

  -  3439   -  UNIVERSE  -   Expanding in all directions.   -  Earth’s motion through space isn’t just defined by our axial rotation or our motion around the Sun, but the Solar System’s motion through the galaxy, the Milky Way’s motion through the Local Group, and the Local Group’s motion through intergalactic space.

-------------  3439  -  UNIVERSE  -   Expanding in all directions. 

-   Only with all the motions combined, and by comparing to the Big Bang’s leftover glow, can we arrive at a meaningful answer of how the Earth and you are moving through the Universe.  

-

-  The Earth spins on its axis, orbits the Sun, and travels through the Milky Way, which itself is in motion relative to all the other galaxies around us. By measuring the objects around us and the light left over from the Big Bang, maybe we can determine our cumulative cosmic motion. 

-

-  The Earth rotates on its axis, spinning a full 360° with each passing day.  You are moving east at 700 miles per hour.  The pendulum takes two full rotations of Earth in order to make a single, complete rotation at this particular latitude; the rotation angle, just like the speed at Earth’s surface, is latitude-dependent

-

-  That translates into an equatorial speed of 1000 miles / hour, dropping lower with increasing latitudes.   At my latitude it is down to 700 miles per hour.  At the north pole you just turn in little circles.

-

-  The Earth, moving in its orbit around the Sun and spinning on its axis, appears to make a closed, unchanging, elliptical orbit.  Our planet is actually spiraling away from the Sun by about 1.5 centimeters per year, and “precesses” in its orbit on timescales of tens of thousands of years. 

-

-  Meanwhile, the Earth revolves around the Sun, at speeds ranging from 67,000 miles per hour.

-

-  Just 800 years ago, perihelion and the winter solstice aligned. Due to the precession of Earth’s orbit, they are slowly drifting apart, completing a full cycle every 21,000 years.   Over time, the Earth drifts slightly farther from the Sun, the precession period increases, and the eccentricity varies as well. 

-

-  Early January’s perihelion causes the fastest motions, while July’s aphelion yields the slowest.

-

-   All of the major planets orbit the Sun in ellipses that are nearly circles, with only a few percent deviation among even the most eccentric planets. The rotational speed of any planet is tiny compared to its orbital speed, but the orbital speeds of the planets are small compared to the Solar System’s motion through the galaxy. 

-

-  The entire Solar System travels around the Milky Way.  The Sun, like all the stars in our galaxy, orbits around the galactic center at speeds of thousands of miles per second. In our neighborhood, the speed of the Sun and the other stars around the galactic center have an uncertainty of around 10%, on 44,739 mph, which is the largest factor of uncertainty when it comes to calculating our cumulative motion. 

-

-  Our heliocentric speed of 469,757 mph is inclined 60° to the plane of the planets.

-

-  Although the Sun orbits within the plane of the Milky Way some 25,000  to 27,000 light years from the center, the orbital directions of the planets in our Solar System do not align with the galaxy at all.

-

-   The orbital planes of the planets occur randomly within a stellar system, often aligned with the central star’s rotational plane but randomly aligned with the plane of the Milky Way. 

-

-  However, our motion isn’t vortical, but a simple sum of these velocities. Vortical means whirling around a vortex.   An accurate model of how the planets orbit the Sun, which then moves through the galaxy in a different direction-of-motion. 

-

-  The speeds of the planets around the Sun are only a small fraction of the Solar System’s motion through the Milky Way galaxy, with even Mercury’s revolution around the Sun contributing only 20% of its total motion through our galaxy. 

-

-  The Milky Way and Andromeda travel toward each other at 244,000 miles per hour.   When two galaxies merge, their supermassive blackholes are fully expected to merge together as well.

-

-  Attractive clumps and repulsive underdense regions both tug on our Local Group of Galaxies. The Virgo supercluster, spans more than 100 million light-years and contains our Local Group, which has the Milky Way, Andromeda, Triangulum, and about 60 smaller galaxies. The overdense regions gravitationally attract us, while the regions of below-average density effectively repel us relative to the average cosmic attraction. 

-

-  Combined, we move 1,402,560 miles per hour relative to the cosmic average.

-

-  Because matter is distributed roughly uniformly throughout the Universe, it isn’t just the overdense regions that gravitationally influence our motions, but the underdense regions as well. A feature known as the “dipole repeller” was discovered only recently, and may explain our Local Group’s peculiar motion relative to the other objects in the Universe. 

-

-  However, the Big Bang’s leftover photons offer a cosmically unique rest frame.  At any epoch in our cosmic history, any observer will experience a uniform “bath” of Omni-directional radiation that originated back at the Big Bang. Today, from our perspective, it’s just 2.725 K above absolute zero, and hence is observed as the “cosmic microwave background“, peaking in microwave frequencies.

-

-   The Sun moves at a cumulative 823,200 mph relative to the Cosmic Microwave Background (CMB).  Although the cosmic microwave background is the same rough temperature in all directions, there are 1-part-in-800 deviations in one particular direction: consistent with this being our motion through the Universe.

-

-   At 1-part-in-800 the overall magnitude of the CMB’s amplitude itself, this corresponds to a motion of about 1-part-in-800 the speed of light, or 823,200 mph. 

-

-  An inherent uncertainty of ± 4,500 mph comes from not knowing the intrinsic CMB dipole’s magnitude.

-

-  Although we can measure the temperature variations all across the sky, on all angular scales, we cannot disentangle whatever the intrinsic dipole in the cosmic microwave background is, as the dipole we observe, from our motion through the Universe, is more than a factor of 100 larger than whatever the primordial value is.

-

-   With only one location to measure the value of this parameter , we cannot disentangle which part is due to our motion and which part is inherent; it would take tens of thousands of such measurements to reduce the uncertainties here below their current values.  Being confined to the Milky Way, we can only dream of making such measurements.

-

-  The initial fluctuations that were imprinted on our observable universe during inflation may only come into play at the 0.003% level, but those tiny imperfections lead to the temperature and density fluctuations that appear in the cosmic microwave background and that seed the large-scale structure that exists today. 

-

-   Measuring the CMB at a variety of cosmic locations would be the only feasible way to disentangle the intrinsic dipole of the CMB from that induced by our motion through the Universe. 

-

-  One hundred years ago, a Russian cosmologist named Alexander Friedmann proposed the idea that the Universe expands from a singular point. A true visionary, he also found that the Universe could oscillate in time, with alternating periods of expansion and contraction. We now call the equations that describe the temporal evolution of the Universe the “Friedmann equations.” 

-

-  The expansion of the Universe is one of the most remarkable scientific findings of all time. It is also widely misunderstood, both conceptually and historically.

-

-  Expansion is not like a bomb.  Expansion means cooling.  When we say the universe is “expanding,” it is hard to avoid the image of a bomb that detonated a long time ago. The Big Bang is the “explosion,” and the galaxies that fly away from the exploding point are like shrapnel spreading outward in all directions from that central point. 

-

-  But that is not what the cosmic expansion means at all. If this image was accurate, space would be a static background, and the Universe would have a very special point, the center where the explosion originated. But there is no special point in the Universe. Cosmic geometry is very democratic, with all points being equal in the eyes of space.

-

-  The usual way this is explained is by picturing a balloon with coins glued to its surface. The balloon’s surface represents space (in two dimensions, which is easier to see), and the coins represent galaxies. 

-

-  As the balloon expands, the coins stay the same size but move away from one another. If you were a being in one galaxy, you would see all other galaxies moving away from you. But so would your neighbors as well as observers in any of the other galaxies.

-

-   This is what is meant by the Universe not having a center. All points on the balloon are stretching away from one another. The expansion of space carries the galaxies (coins) away.

-

-   This is an example of an expanding “closed” geometry, since the surface of the balloon is closed: if you start moving in one direction, you would get back to your starting point.

-

-   Now play the movie backward for both examples. The balloon shrinks, the classroom shrinks. At some moment in the past, all the coins and desks would be on top of one another, a big bundle of stuff. That is the point of maximum compression that, extrapolated to its ultimate mathematical limit, would be a point of infinite mass-energy density. 

-

-  In 1917, Einstein found the first solution for the geometry of the Universe, using his brand new theory of general relativity, the theory that attributes gravity to the curvature of space around a massive body. Einstein’s result was quickly followed by another solution by the Dutch Willem de Sitter, also from 1917.

-

-  Einstein’s solution pictured a static spherical universe with radius and a “cosmological constant,” a parameter he put in by hand to find a static solution. How remarkable is it that with paper and pen in hand a human could devise a theory for the Universe as a whole? 

-

-  De Sitter’s solution was different. His universe was empty, that is, it had no matter, only the cosmological constant. It was later shown that de Sitter’s solution was equivalent to a Universe filled with the cosmological constant expanding exponentially fast. This was of interest because observations were showing that the light from distant “nebulae” (later shown to be galaxies) was redshifted, stretched toward the red end of the color spectrum (which goes from violet to red, like the rainbow). 

-

-    De Sitter and others suggested that this redshift was possibly due to the moving of the nebulae away from us, like the Doppler shift from car horns that change as they move away (lower pitch) or approach (higher pitch).

-

-  The Friedmann equations dated June 29, 1922, discovers that one doesn’t need either to impose a static Universe (Einstein) or an empty one (de Sitter) to find solutions with expanding geometry.

-

-   So, he takes the radius to change in time, and solves for R(t), with the time variable denoting “the time that passed since Creation”.    Friedmann discovered different solutions that depend on the relative value of the cosmological constant and other parameters.

-

-   In the “Monotone World of the First Kind,” the Universe starts at a singularity at t =0 and expands in a rate that first decelerates and then accelerates in time forever.

-

-   In the “Monotone World of the Second Kind,” expansion starts from a finite radius and goes on exponentially fast forever. 

-

-  Friedmann found what he called the “Periodic World,” where the Universe starts from a singularity at t = 0 and expands and contracts periodically in time.

-

-  In 1923, Friedmann published his book “World as Space and Time“, where he makes a connection between his periodic Universe and Hindu mythology, while making an estimate for the age of the Universe expanding from “nothingness”.

-

-  A non-static Universe represents a variety of cases.  It is possible that the radius of curvature constantly increases from a certain initial value; it is also possible that the radius changes periodically. The Universe compresses into a point (into nothingness), then increases its radius to a certain value, and then again compresses into a point. 

-

-    In 1929, Edwin Hubble confirmed Vesto Slipher’s previous data on receding nebulae, since then correctly understood as galaxies in an expanding universe. We now call the cosmological constant, or something very similar to it, “dark energy.”

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February 1, 2022         UNIVERSE  -   Expanding in all directions.           3422                                                                                                                                               

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-----------------------------  Tuesday, February 1, 2022  ---------------------------