3433 - “Pi’ - how can 3.14.….go on forever?

  -  3433  -  “Pi’  -  how can 3.14.….go on forever?   “Pi“, the ratio of a circle's circumference to its diameter, is one of the best-loved and most interesting numbers in math. Like "e," it seems to suddenly arise in a huge number of math and physics formulas. What Makes Pi so special?

-------------  3433  -    “Pi’  -  how can 3.14.….go on forever?

-  Mathematics is one of the only areas of knowledge that can objectively be described as "true," because its theorems are derived from pure logic. And yet, at the same time, those theorems are often extremely strange and counter-intuitive.  Politics is the latter but not the former.

-  

-  Random numbers are hard to come by.  Random data isn't actually all that random. In a given list of numbers representing anything from stock prices to city populations to the heights of buildings to the lengths of rivers, about 30 percent of the numbers will begin with the digit 1.

-

-   Less of them will begin with 2, even less with 3, and so on, until only one number in twenty will begin with a 9. The bigger the data set, and the more orders of magnitude it spans, the more strongly this pattern emerges.  What’s with this?

-

-  Because prime numbers are indivisible (except by 1 and themselves), and because all other numbers can be written as multiples of them, prime numbers are often regarded as the "atoms" of the math world.

-

-   Despite their importance, the “distribution” of prime numbers among the integers is still a mystery. There is no pattern dictating which numbers will be prime or how far apart successive primes will be.

-

-   In 1963, the mathematician Stanislaw Ulam noticed an odd pattern while doodling in his notebook during a presentation: When integers are written in a spiral, prime numbers always seem to fall along diagonal lines. This in itself wasn't so surprising, because all prime numbers except for the number 2 are odd, and diagonal lines in integer spirals are alternately odd and even.

-

-   Much more startling was the tendency of prime numbers to lie on some diagonals more than others and this happens regardless of whether you start with 1 in the middle, or any other number.

-

-  Even when you zoom out to a much larger scale, as in the plot of hundreds of numbers , you can see clear diagonal lines of primes , with some lines stronger than others. There are mathematical conjectures as to why this prime pattern emerges, but nothing has been proven.  Something for you to work on!

-

-  In an important field of mathematics is called “topology“.  Two objects are considered to be equivalent, or "homeomorphic," if one can be morphed into the other by simply twisting and stretching its surface; they are different if you have to cut or crease the surface of one to reshape it into the form of the other.

-

-  Consider a torus, the dougnut-shape object. If you turn it upright, widen one side and indent the top of that side, you then have a cylindrical object with a handle. Thus, a classic math joke is to say that topologists can't tell their doughnuts from their coffee cups.

-

-  On the other hand, “Moebius bands“, are loops with a single twist in them, and are not homeomorphic with twist-free loops (cylinders), because you can't take the twist out of a Moebius band without cutting it, flipping over one of the edges, and reattaching.

-

-  Topologists long wondered: Is a sphere homeomorphic with the inside-out version of itself? In other words, can you turn a sphere inside out? At first it seems impossible, because you aren't allowed to poke a hole in the sphere and pull out the inside. But in fact, "sphere eversion," as it's called, is possible. 

-

-  There's just a finite number of distinct geometric patterns. All Escher paintings, wallpapers, tile designs and indeed all two-dimensional, repeating arrangements of shapes can be identified as belonging to one or another of the so-called "wallpaper groups." And how many wallpaper groups are there? Exactly 17.   How can that e, exactly 17?

-

-  The letter "e" represents an irrational number (with unending digits) that begins 2.71828... Discovered in the context of continuously compounded interest, it governs the rate of exponential growth, from that of insect populations to the accumulation of interest to radioactive decay. 

-

-  In math, the number exhibits some very surprising properties, such as being equal to the sum of the inverse of all factorials from 0 to infinity. Indeed, the constant "e" pervades math, appearing seemingly from nowhere in a vast number of important equations.

-

-  Next, "i" represents the so-called "imaginary number": the square root of negative 1. It is thus called because, in reality, there is no number which can be multiplied by itself to produce a negative number (and so negative numbers have no real square roots).

-

-   But in math, there are many situations where one is forced to take the square root of a negative. The letter "i" is therefore used as a sort of stand-in to mark places where this was done.

-

-  “Pi“, the ratio of a circle's circumference to its diameter, is one of the best-loved and most interesting numbers in math. Like "e," it seems to suddenly arise in a huge number of math and physics formulas. What Makes Pi so special?

-

-  Putting it all together, the constant "e" raised to the power of the imaginary "i" multiplied by pi equals -1. And, as seen in Euler's equation, adding 1 to that gives 0. It seems almost unbelievable that all these strange numbers, and even one that isn't real would combine so simply. But it's a proven fact.

-

----------------------------------                 e^ix + 1 = 0

-

-  I am sure one of my readers will make sense of this and give us an explanation.

-

January 25, 2022            “Pi’  -  how can 3.14.….go on forever?                         3422                                                                                                                                               

----------------------------------------------------------------------------------------

-----  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”  -----------

-----------------------------  Thursday, January 27, 2022  ---------------------------

3431 - SPACETIME - a concept from General Relativity?

  -  3431   -  SPACETIME  -   a concept from General Relativity?   Space-time is a conceptual model combining the three dimensions of space with the fourth dimension of time. According to the best of current physical theories, space-time explains the unusual relativistic effects that arise from traveling near the speed of light as well as the motion of massive objects in the universe.

-------------  3431  - SPACETIME  -   a concept from General Relativity?

-  The famous physicist Albert Einstein helped develop the idea of space-time as part of his theory of relativity. Prior to his pioneering work, scientists had two separate theories to explain observed physical phenomena:

-

------------------------- Isaac Newton's laws of physics described the motion of massive objects,

-

------------------------ James Clerk Maxwell's electromagnetic models explained the properties of light.

-

-  Experiments conducted at the end of the 19th century suggested that there was something special about light. Measurements showed that light always traveled at the same speed, no matter what. 

-

-  Back in 1898, the French physicist and mathematician Henri Poincaré speculated that the velocity of light might be an unsurpassable limit. Around that same time, other researchers were considering the possibility that objects changed in size and mass, depending on their speed.  This seems weird?

-

-  Einstein pulled all of these ideas together in his 1905 theory of special relativity, which postulated that the speed of light was a “constant“. For this to be true, space and time had to be combined into a single framework that conspired to keep light's speed the same for all observers. After all “velocity” is space distance  / time.

-

-  A person in a superfast rocket will measure time to be moving slower and the lengths of objects to be shorter compared with a person traveling at a much slower speed. That's because space and time are relative, they depend on an observer's speed. But the speed of light is more fundamental and remains constant.   186,000 miles per second.

-

-  That space-time is a single fabric wasn't one that Einstein reached by himself. That idea came from German mathematician Hermann Minkowski, who said in a 1908 colloquium, "Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."

-

-  The space-time Minkowski described is still known as Minkowski space-time and serves as the backdrop of calculations in both relativity and quantum-field theory. The latter describes the dynamics of subatomic particles as fields.

-

-   Einstein realized as he developed his theory of general relativity that the force of “gravity” was due to “curves in the fabric of space-time“.   Massive object’s gravity create distortions in space-time that cause it to spacetime to bend. 

-

-  These curves, in turn, constrict the ways in which everything in the universe moves, because objects have to follow paths along this warped curvature. Motion due to gravity is actually motion along the twists and turns of space-time.

-

-  Despite its intricacy, relativity remains the best way to account for the physical phenomena we know about. Yet scientists know that their models are incomplete because relativity is still not fully reconciled with “quantum mechanics“, which explains the properties of subatomic particles with extreme precision but does not incorporate the force of gravity.   General Relativity covers gravity but can not handle subatomic particles.

-

-  Quantum Mechanics rests on the fact that the tiny bits making up the universe are discrete, or quantized. So photons, the particles that make up light, are like little chunks of light that come in distinct packets. Yet, they are massless?

-

-  Perhaps space-time itself also comes in these quantized chunks, helping to bridge relativity and quantum mechanics. Researchers at the European Space Agency have proposed the “Gamma-ray Astronomy International Laboratory for Quantum Exploration of Space-Time” (GrailQuest) mission, which would fly around our planet and make ultra-accurate measurements of distant, powerful explosions called gamma-ray bursts that could reveal the nature of space-time. 

-

-  The theory of gravity is General Relativity.  It took Albert Einstein in a magnificent feat taking  seven years to complete and providing amazing insights into how the world works.  It's easy enough to state the bare essence of the theory in a couple pithy statements: "Matter and energy tell space-time how to bend, and the bending of space-time tells matter how to move."

-

-   But the actual mechanics take a whopping 10 equations to describe, with each one very difficult and highly interconnected with the others. 

-

-   Einstein’s equations have the ability to explain the details of the orbit of Mercury. That innermost planet has a slightly elliptical orbit, and that ellipse ever-so-slowly rotates around the sun. In other words, the place where Mercury is farthest from the sun slowly changes with time.  Lower gravity, slower time

-

-  If you apply simple Newtonian gravity to the sun-Mercury system, this change over time, called “precession“, doesn't show up.   Isaac Newton's view is incomplete. Once you add in the gentle gravitational nudging and tweaking due to the other planets, “almost all” of the precession can be explained , but,  not all. 

-

-  By the early 1900s, it was a well-known problem in solar system dynamics, but not one that caused much controversy. Most folks just added it to the ever-growing list of "slightly weird things we can't explain about the universe" and assumed that we would find a mundane solution some day.

-

-   Einstein thought Mercury was giving him a clue into Releaivity. When, after years of attempts, he was able to flex his general relativistic muscles and explain precisely the orbital oddities of Mercury, he knew he had finally cracked the gravitational code.

-

-  Before Einstein put the finishing touches on the big General Relativity, he came to some startling realizations about the nature of gravity:

-

-   If you're isolated on a rocket ship that accelerates at a smooth and constant 1g , providing the same acceleration as Earth's gravity does , everything in your laboratory will behave exactly as it would on the planet's surface, Einstein reasoned. Objects will fall to the ground at the same speed as on Earth; your feet will stay firmly planted on the floor, etc.

-

-  This equivalence between gravity (as experienced on Earth) and acceleration (as experienced in the rocket) propelled (pun intended) Einstein forward to develop his theory.

-

- Hidden in that scenario is a surprising insight. Imagine a beam of light entering a window on the left side of the spaceship. By the time the light crosses the spaceship to exit, where will it be?

-

-  From the perspective of an outside observer, the answer is obvious. The light travels in a perfectly straight line, perpendicular to the path of the rocket. During the time the light was passing through, the rocket pushed itself forward. The light will then enter the rocket at one window near the tip and exit near the bottom, close to the engines. 

-

-  From the inside the spacecraft, though, things seem strange. In order for the light to enter a window near the tip and exit near the engines, the beam's path has to be curved. Indeed, that's exactly what you see.  And since gravity is exactly the same as acceleration, light must follow curved paths around massive objects.

-

-  It's difficult to observe this experimentally, because you need a lot of mass and some light that passes close to the surface to get a detectable effect. But the 1919 solar eclipse proved just the right opportunity, and an expedition led by Sir Arthur Eddington found the exact shifting of distant starlight that Einstein's nascent theory had predicted.

-

-  Another interesting result pops out of creative thought experiments surrounding general relativity. This conclusion relies on the good old-fashioned Doppler effect, but it's applied to an unfamiliar scenario.

-

-  If something is moving away from you, the sound it produces will get stretched out, shifting down to lower frequencies.  That's the Doppler effect. The same is true of light: A car moving away from you appears ever-so-slightly redder than it would be if the vehicle were stationary. The redder light, the lower the frequency. 

-

-  Cops can take advantage of this shift by bouncing a light off your car to catch you speeding. The next time you're pulled over, you can use the opportunity to reflect on the nature of gravity, and explain this theory to the cop.

-

-  If movement shifts light's wavelength, then acceleration can too.   A bit of light traveling from the bottom to the top of an accelerating rocket will experience a redshift. And under General Relativity, what goes for acceleration goes for gravity. That's right: Light emitted from the surface of the Earth will shift down into redder frequencies the farther upward it travels.

-

-  It took a few decades to conclusively demonstrate this prediction, because the effect is so tiny. But in 1959, Robert Pound and Glen Rebka proposed, designed, built and executed an experiment that enabled them to measure the redshift of light as it traveled a few stories up the Jefferson Laboratory at Harvard University.

-

-  Even with all that evidence, we continue to put general relativity to the test. Any sign of a crack in Einstein's magnificent work would spark the development of a new theory of gravity, perhaps paving the way to uncovering the full quantum nature of that force. That's something we currently don't understand at all. 

-

-  But in all regards, General Relativity passes with flying colors; from sensitive satellites to gravitational lensing, from the orbits of stars around giant blackholes to ripples of gravitational waves and the evolution of the universe itself.

-

-  Einstein's legacy is likely to persist for quite some time.

-

January 25, 2022    SPACETIME  -   a concept from General Relativity?        3431                                                                                                                                               

----------------------------------------------------------------------------------------

-----  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, January 26, 2022  ---------------------------

3430 - PHYSICS - energy and massless particles?

  -  3430  -  PHYSICS  -  energy and massless particles?   There could be a lot of massless things out there that either there’s no way to look for them, or rather we haven’t figured out how to look for them.   It could be that there’s this whole other world out there?

-------------  3430  -  PHYSICS  -  energy and massless particles?

-   In the field of physics we have waves and we have particles.   Imagine the particle. What comes to mind? If you aren’t a theoretical particle physicist, chances are you picture a tiny ball, bobbing in space.

-

-  But that’s not quite correct. One way to prove it: Try to imagine that tiny ball as a particle with no mass.  How can a particle not have mass?

-

-  Sometimes the word “mass” is used interchangeably with the word “weight.” That’s not entirely wrong. The mass of an object is measured by its resistance to a force. When you pick something up to test its weight, it is resisting the Earth’s gravity, so an everyday object’s weight on Earth is indeed one measurement of its mass.

-

-  But there’s more to mass than just a resistance to gravity, especially on the scale of the smallest pieces of matter. So physicists’ definition of mass gets a little more complicated.

-

-  Most fundamental matter particles, such as electrons, muons and quarks, that are present in all atoms get their mass from their resistance to a field that permeates the universe called the Higgs field. The more the Higgs field pulls on a particle, the more mass it has. 

-

-  When it comes to composite particles like protons and neutrons, which are made up of quarks, most of their mass comes from the pull of the “strong force” that holds the quarks together. 

-

-  Photons and gluons, two force-carrying particles, are fundamental, so they don’t host the internal tug-of-war of a composite particle. They are also unaffected by the Higgs field. Indeed, they seem to be without mass.  Massless force carriers.  And they always travel  at the speed of light, 186,000 miles per second.

-

-  Massless particles are pure energy.   These quanta of energy don’t have edges, and they don't have surfaces.

-

-  A better way to think of particles is as ripples on a “quantum field“. A quantum field has vibration modes like the harmonics on a guitar string. Pluck it with the right frequency and you get a particle.

-

-  The two particles physicists know to be massless—photons and gluons—are both force-carrying particles, also known as “gauge bosons“. Photons are associated with the electromagnetic force, and gluons are associated with the strong force.  Tey are force carriers. 

-

-   The graviton, a gauge boson associated with gravity, is also expected be massless, but its existence hasn’t been confirmed yet.  We are still working on gravity.

-

-  These massless particles have some unique properties. They are completely stable, so unlike some particles, they do not lose their energy decaying into pairs of less massive particles. 

-

-  Because all their energy is “kinetic“, they always travel at the speed of light. And thanks to special relativity, things traveling at the speed of light don't actually age.  So a photon is actually not aging relative to us. It’s timeless, in that sense.

-

-  Gravity affects anything with energy, even a particle that has no mass at all. That’s why the gravitational attraction of objects like galaxies and clumps of dark matter curves the path of light passing by them in space.  This is called “gravitational lensing“.  

-

-  It could be that the photon and the gluon are not the only massless particles in the universe. Scientists could one day find the aforementioned “graviton“. Or it could turn out that the lightest of the three types of neutrinos has zero mass. 

-

-  There could be a lot of massless things out there that either there’s no way to look for them, or rather we haven’t figured out how to look for them.   It could be that there’s this whole other world out there.

-

-  There is Dark Energy and Dark Matter that makeup 95% of the mass/energy in the Universe.  Everything we know and understand is a mere 5%.  Hardly even the tip of an iceberg of unknowns.  

-

January 24, 2022         PHYSICS  -  energy and massless particles?            3430                                                                                                                                               

----------------------------------------------------------------------------------------

-----  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, January 26, 2022  ---------------------------

3429 - STAR DUST - older than Earth?

  -  3429   -  STAR DUST  -  older than Earth.  That dust from supernova explosions is  prone to evaporate more quickly since its smaller. So there’s less of it in the inner Solar System, and on Earth.  This allows us to explain why the Earth has the largest enrichment of stardust from red giant stars compared to other bodies in the solar system.

-----------------------------  3429  -  STAR DUST  -  older than Earth?

-  When you drink a glass of water, that water has already been through a bunch of other people’s digestive tracts. Maybe Attila the Hun’s or Vlad the Impaler’s; maybe even a Tyrannosaurus Rex’s.

-

-  The same thing is true of stars and matter. All the matter we see around us here on Earth, even our own bodies, has gone through at least one cycle of stellar birth and death, maybe more. 

-

-  The story of our Solar System started about 4.5 billion years ago when a molecular cloud collapsed. At the center of that collapsed cloud the Sun came to life in a burst of fusion, and a disc of gas and dust formed around it. Eventually, all of the planets in our Solar System formed from that proto-planetary disc.

-

-  Within that disc of material were dust grains that had formed around certain other stars. These special grains were distributed unevenly throughout the disc. As the planets of the Solar System formed, each one contained its own mixture of gas and dust, and of those special grains.

-

-  Planets coalesce out of the remaining molecular cloud the star formed out of. Within this accretion disk lay the fundamental elements necessary for planet formation and potential life. 

-

-  Proto-planetary disk coalesce out of the remaining molecular cloud the star formed out of. Within this accretion disk lay the fundamental elements necessary for planet formation and potential life.

- 

-  Advances in measuring techniques allow scientists to detect the material the planets formed from, and to determine its origin. It all comes down to “isotopes“. An isotope is an atom of a given element with the same number of protons in its nucleus, but a different number of neutrons.

-

-   For example, there are different isotopes of carbon, like C13 and C14. While all carbon isotopes have 6 protons, C13 has 7 neutrons while C14 has 8 neutrons.  The mixture of different isotopes in a plane, not just of carbon, is like a fingerprint. And that fingerprint can tell scientists about a body’s origins.

-

-   Scientists have been studying these fingerprints on Earth and in meteorites. Comparisons between the two reveal how long-dead red giant stars have contributed matter to the formation of Earth and everything on it. Including us.

-

-   Scientists have been able to compare these isotopic anomalies between the Earth and meteorites for more and more elements.   They have examined isotope ratios for ruthenium and molybdenum, which are palladium’s neighbors on the periodic table. 

-

-  The meteorites contained far smaller palladium anomalies than expected.  Even though everything in our Solar System was created from stardust, one type of star contributed most to Earth: “red giants“, or asymptotic giant branch (AGB) stars. 

-

-  These are stars in the same mass range as our Sun which expand into red giants when they deplete their hydrogen. Our own Sun will become one of these in about 4 or 5 billion years.

-

-  As part of their end-state, these stars synthesize elements in what’s called the s-process. The s-process, or “slow neutron capture process“, creates elements like palladium, and its neighbors on the periodic table, ruthenium and molybdenum.  The s-process creates these elements with seeds of iron nuclei, which themselves were created in supernovae in previous generations of stars.

-

-  Palladium is slightly more volatile than the other elements measured. As a result, less of it condensed into dust around these stars, and therefore there is less palladium from stardust in the meteorites.

-

-  There is a greater abundance of material from red giants in Earth’s makeup than there is in Mars, or in asteroids like Vesta further out in our Solar System. The outer region contains more material from supernovae. 

-

-  In our young Solar System, dust from red giants resisted evaporation or destruction from the Sun better than dust from supernovae. That's why Earth contains more matter from red giants than bodies further out. 

-

-   When the planets formed, temperatures closer to the Sun were very high. Some of the dust grains were more unstable than others, including ones with icy crusts. That type was destroyed in the inner Solar System, close to the Sun. But stardust from red giants was more stable and resisted destruction, so it’s more concentrated close to the Sun. 

-

-  That dust from supernova explosions is  prone to evaporate more quickly since its smaller. So there’s less of it in the inner Solar System, and on Earth.  This allows us to explain why the Earth has the largest enrichment of stardust from red giant stars compared to other bodies in the solar system.

-

January 26, 2022       STAR DUST  -  older than Earth ?                    3429                                                                                                                                               

----------------------------------------------------------------------------------------

-----  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, January 26, 2022  ---------------------------

3428 - STARDUST - older than the Earth.

  -  3428   -  STARDUST  -  older than the Earth?   Scientists have discovered the oldest solid material on Earth: 7-billion-year-old stardust trapped inside a meteorite. This stardust provides evidence for a 'baby boom' of new stars that formed 7 billion years ago, contrary to thinking that star formation happens at a steady, constant rate.

-------------  3428  -  STARDUST  -  older than the Earth.

-  It is great to study stuff that is older than your are.  But, it keeps getting harder to find.  I had to look to the stars.  Stars have life cycles. They're born when bits of dust and gas floating through space find each other and collapse in on each other and heat up. They burn for millions to billions of years, and then they die. 

-

-  When they die, they pitch the particles that formed in their winds out into space, and those bits of stardust eventually form new stars, along with new planets and moons and meteorites. And in a meteorite that fell fifty years ago in Australia, scientists have now discovered stardust that formed 5 to 7 billion years ago, the oldest solid material ever found on Earth.

-

-  These are the oldest solid materials ever found, and they tell us about how stars formed in our galaxy.  The materials are called “presolar grains-minerals” formed before the Sun was born. They're solid samples of stars, real stardust. These bits of stardust became trapped in meteorites where they remained unchanged for billions of years, making them time capsules of the time before the solar system..

-

-  Presolar grains are rare, found only in about five percent of meteorites that have fallen to Earth, and they're tiny-a hundred of the biggest ones would fit on the period at the end of this sentence. 

-

-   The largest portion of this “Murchison meteorite”  has  a treasure trove of presolar grains that fell in Australia in 1969.   Once the presolar grains were isolated, the researchers figured out from what types of stars they came and how old they were.

-

-   Using exposure age data, which basically measures their exposure to cosmic rays, which are high-energy particles that fly through our galaxy and penetrate solid matter.  Some of these cosmic rays interact with the matter and form new elements. And the longer they get exposed, the more those new elements form.

-

-   By measuring how many of these new cosmic-ray produced elements are present in a presolar grain, we can tell how long it was exposed to cosmic rays, which tells us how old it is.

-

-  The researchers learned that some of the presolar grains in their sample were the oldest ever discovered-based on how many cosmic rays they'd soaked up, most of the grains had to be 4.6 to 4.9 billion years old, and some grains were even older than 5.5 billion years. 

-

-  Our Sun is 4.6 billion years old, and Earth is 4.5 billion.

-

-  But the age of the presolar grains wasn't the end of the discovery. Since presolar grains are formed when a star dies, they can tell us about the history of stars. And 7 billion years ago, there was apparently a bumper crop of new stars forming-a sort of astral baby boom.

-

-   This finding contributes to a debate between scientists about whether or not new stars form at a steady rate, or if there are highs and lows in the number of new stars over time.  This is direct evidence of a period of enhanced star formation in our galaxy seven billion years ago with samples from meteorites. 

-

-  By examining the way that the minerals in the grains interacted with cosmic rays, the researchers also learned that presolar grains often float through space stuck together in large clusters. 

-

-  Doing  astronomy with geological samples you can hold in your hand looking at the history of our galaxy. Stardust is the oldest material to reach Earth, and from it, we can learn about our parent stars, the origin of the carbon in our bodies, the origin of the oxygen we breathe. With stardust, we can trace that material back to the time before the Sun.

-

-  January 24, 2022          STARDUST  -  older than the Earth?              3428                                                                                                                                               

----------------------------------------------------------------------------------------

-----  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, January 26, 2022  ---------------------------

3427 - UNIVERSE - what is its lifetime like?

  -  3427   -  UNIVERSE  -  what is its lifetime like?  It may be a long journey to the very end, but if what we think about the Universe today is correct, even empty space, as far into the future as we care to go, can never be completely empty.  

-------------  3427  -  UNIVERSE  -  what is its lifetime like?

-  By probing the thermal history of the universe over the last 10 billion years astronomer found that the mean temperature of gas across the universe has increased more than 10 times over that time period and reached about 2,000,000 degrees Kelvin today, approximately 4,000,000 degrees Fahrenheit.

-

-  The large-scale structure of the universe refers to the global patterns of galaxies and galaxy clusters on scales beyond individual galaxies. It is formed by the gravitational collapse of dark matter and gas.  As the universe evolves, gravity pulls dark matter and gas in space together into galaxies and clusters of galaxies.  The drag is so violent that more and more gas is shocked and heated up.

-

-  Scientists can clock the progress of cosmic structure formation by “checking the temperature” of the universe.  The researchers used a new method that allowed them to estimate the temperature of gas farther away from Earth, which means further back in time, and compare them to gases closer to Earth and near the present time.

-

-   They have confirmed that the universe is getting hotter over time due to the gravitational collapse of cosmic structure, and the heating will likely continue.

-

-  To understand how the temperature of the universe has changed over time, researchers used data on light throughout space collected by two missions, Planck and the Sloan Digital Sky Survey. “Planck” is the European Space Agency mission that operates with heavy involvement from NASA; “Sloan” collects detailed images and light spectra from the universe.

-

-  They combined data from the two missions and evaluated the distances of the hot gases near and far via measuring redshift, a notion that astrophysicists use to estimate the cosmic age at which distant objects are observed. 

-

-  “Redshift” gets its name from the way wavelengths of light lengthen. The farther away something is in the universe, the longer its wavelength of light. Scientists who study the cosmos call that lengthening the redshift effect.

-

-  The concept of redshift works because the light we see from objects farther away from Earth is older than the light we see from objects closer to Earth, the light from distant objects has traveled a longer journey to reach us. 

-

-  That fact, together with a method to estimate temperature from light, allowed the researchers to measure the mean temperature of gases in the early universe, gases that surround objects farther away, and compare that mean with the mean temperature of gases closer to Earth, gases today.

-

-  Those gases in the universe today, the researchers found, reach temperatures of about

 2 million degrees Kelvin,  approximately 4 million degrees Fahrenheit, around objects closer to Earth. That is about 10 times the temperature of the gases around objects farther away and further back in time.

-

-  The universe is warming because of the natural process of galaxy and structure formation. It is unrelated to the warming on Earth.  At the very end of the Universe the stars — past, present, and future — have all burned out. 

-

-  Stellar corpses like neutron stars and white dwarfs have radiated the last of their remnant energy away, fading to black in color and ceasing to emit any radiation at all. The great gravitational dance of masses within galaxies has come to an end, as every mass has either spiraled into a blackhole or been ejected into the intergalactic medium.

-

-   These last remaining structures themselves will decay away, as blackholes evaporate due to “Hawking radiation“, while dark energy drives every unbound structure apart from every other such structure that it isn’t bound to.

-

-  At this stage, we’ll have a cold, empty Universe, where the density of matter and radiation has effectively dropped to zero. But our Universe also contains dark energy: an energy inherent to the fabric of space itself.

-

-   According to our best measurements, it appears that dark energy doesn’t decay, meaning that even as the Universe relentless expands forever and ever, this form of energy density will remain constant. 

-

-  Surprisingly, this fact alone will keep our Universe’s temperature from dropping to absolute zero, no matter how long we wait. 

-

-  Matter-and-radiation-filled Universes governed by General Relativity cannot remain static.  The story goes back to the early days of modern cosmology: when Einstein’s General Relativity was first published. 

-

-  A Universe governed by Einstein’s rules couldn’t, as was commonly thought to be the case, be filled with roughly equal amounts of material everywhere and still be stable and remain the same size. 

-

-  For generations, it was widely believed that the Universe was static and eternal, providing an unchanging “stage” upon which the matter in the Universe would engage in its cosmic performance. But as Einstein’s new theory of gravitation grew to prominence, many realized that this assumption was a physical impossibility.

-

-  If General Relativity governs your Universe, and your Universe is filled with a roughly equal density of “stuff” everywhere, where “stuff” can encompass any and every form of energy that’s possible, including normal matter, blackholes, dark matter, radiation, neutrinos, cosmic strings, field energy, dark energy, etc.,  there are only two options for what your Universe can do: expand or contract.

-

-   Every other solution is unstable, and after even an infinitesimal amount of time, will begin expanding or contracting, depending on what your initial conditions were.

-

-  In the 1920s, we began measuring individual stars in other galaxies, confirming their location outside of the Milky Way and their enormous, multi-million light-year distances from Earth. 

-

-  By measuring the spectrum of the light coming from those galaxies,  breaking the light up into individual wavelengths and identifying absorption and emission lines from atoms, molecules, and ions, we could also measure the redshift of that light: by what multiplicative factor every individually identifiable line was shifted by.

-

-  When we put that data together in the late 1920s, a feat independently accomplished first by Georges Lemaître, then Howard Robertson, and finally by Edwin Hubble, it pointed towards an unambiguous conclusion: “the Universe was expanding“. 

-

-  Subsequently, this was put together into a framework that became the modern Big Bang, with the discovery of the cosmic microwave background (a leftover bath of radiation from the hot, dense, early stages of the Universe).

-

-  From the 1960s through the 1990s, the science of physical cosmology had two major measurement goals.

-

------------------------------  To measure what we called the Hubble constant, H0, which would tell us how quickly the Universe is expanding today.

-

-----------------------------  To measure what we called the deceleration parameter, q0, which would tell us the rate at which a distant galaxy would appear to recede more slowly from us as time went on.

-

-  The idea is simple: the equations that govern the Universe dictate a relationship between the matter-and-energy present within it and how the expansion rate will change over time. If we can measure the expansion rate today and how quickly the expansion rate is changing, we can not only determine what makes up the Universe, but we can know its past history as well as its future fate. 

-

-  As the decades went on, new telescopes and observatories were built, and enormous advances in instrumentation occurred, our answers got both more accurate and also more precise.  Distances versus redshifts in the expanding Universe, along with best-fit cosmologies.

-

-  In a Universe filled with matter and radiation, there’s a key relationship between our Universe’s expansion rate and its fate. You can imagine the Big Bang as the starting gun of the ultimate cosmic race: between gravity, on the one hand, that works to recollapse the Universe and pull everything back together, and the initial rate of expansion, which works to drive everything apart. You can imagine multiple different fates:

-

---------------------------  One where gravity wins, and overcomes the expansion, causing the Universe to recollapse and end in a Big Crunch,

-

--------------------------  One where the expansion wins, where gravity is insufficient, and the Universe expands forever, with its density eventually dropping to zero,

-

--------------------------  One right on the border between those two, a “Goldilocks” case, where the expansion rate asymptotes to zero but never quite reverses.

-

-  But when the data came in, it pointed to none of these. Instead, gravitation fought the initial expansion, causing distant galaxies to recede from us at a slower and slower rate, and then something strange happened. About 6 billion years ago, these distant, receding galaxies began moving away from us at faster and faster rates. Somehow, the Universe’s expansion was accelerating.

-

-   Today, 13.8 billion years after the Big Bang, it’s apparent that the Universe not only contains many different forms of matter and radiation, but also an unexpected component: dark energy. 

-

-  When we look at the modern Universe, we’re seeing it in perhaps its most interesting state: after an enormous amount of interesting, luminous, large-and-small-scale structures have formed, but before dark energy has driven them all away from us to practically imperceptible distances.

-

-  In today’s Universe, we see stars forming, living, and dying; we see galaxies and galaxy clusters colliding and merging; we see new planets being formed; but we also see these distant objects speeding farther and farther away from one another. After enough time passes:

-

--------------------------  Stars will only form from the rare, occasional merger of failed or extinct stars,

-

-------------------------  All the shining stars will burn through their fuel,

-

-------------------------  Stellar remnants will radiate their energy away,

-

-------------------------  Blackholes will swallow a significant fraction of masses,

-

-------------------------  Galaxies will gravitationally kick out all of the remaining individual masses,

-

------------------------  Leftover radiation from the Big Bang will redshift to arbitrarily low energies,

-

------------------------  Every single black hole will eventually evaporate,

-

-----------------------    All while the Universe continues to relentlessly expand due to dark energy.

-

-  On the levels of individual particles, there may be some incredibly long-term effects that happen far beyond our means to measure them. Protons may decay, although modern experiments have constrained the proton’s lifetime to be longer than 10^25 times the present age of the Universe. 

-

-  Atomic nuclei may undergo quantum tunneling to arrive at a more stable configuration: iron-56 or nickel-60, for example. And improbable but not forbidden events, like the ionization of matter due to a stray, energetic photon, may eventually kick all of the electrons off of atoms and ions.

-

-  But, at some point, any arbitrarily large region of the Universe will be completely empty: devoid of all forms of normal matter, dark matter, neutrinos, or any of the radiation permeating the Universe today. 

-

-  Even that great thermal bath of photons created from the Big Bang will shift to long wavelengths, low densities, and energies that asymptote to zero. All that will remain will be the energy inherent to space itself, dark energy, and the consequences that it brings.

-

-  One of those consequences of a Universe with a cosmological constant, the form of dark energy that is best supported by the data, where the energy density of dark energy remains constant over time and throughout all of space, is that the temperature of the Universe does not go completely to zero. 

-

-  Instead, the Universe will be filled with a bath of extraordinarily low-energy radiation that will appear everywhere, but at an utterly minuscule temperature: 10^-30 K.  Compare that to the cosmic microwave background today, which is more like 3 K, or some 10^30 times hotter.

-

-  To understand why, we can start by thinking about blackholes. The reason blackholes evaporate is because they radiate energy, owing to the fact that observers close to the event horizon and observers farther from the event horizon disagree as to what the ground state of the quantum vacuum is. 

-

-  The more severely space is curved near the event horizon of a blackhole, the greater the difference an observer there versus far away will experience for the quantum vacuum.

-

-  But quantum fields are continuous throughout all of space, and there exist possible light paths that take you from anyplace outside the event horizon to anywhere else outside the event horizon. 

-

-  The difference in the zero-point energy of space between those two locations tells us, as first derived in Hawking’s landmark 1974 paper, that radiation will be emitted from the region around the blackhole, with the blackhole’s event horizon playing a key role. That radiation will have its temperature set by the mass of the blackhole, with lower-mass blackholes having higher temperatures, and will have a perfect blackbody spectrum.

-

-  We don’t have an “event horizon” in a Universe with a cosmological constant, but we have a different type of horizon: a “cosmological horizon“. Two observers in different locations will be able to communicate at the speed of light, but only for a finite amount of time.

-

-   Eventually, they’ll recede from one another fast enough that an emitted light signal from one will never reach the other, similar to how a signal emitted by us today could only reach an observer 18 billion light-years distant. Beyond that, they can only receive “older” signals from us, just as we can only receive “old light” from them.

-

-  The key that unlocks this entire puzzle is Einstein’s equivalence principle: the idea that observers cannot tell the difference between gravitational accelerations and any other form of acceleration of equal magnitude. 

-

-  If you’re in an enclosed rocket ship and you feel yourself pulled down towards one end, you cannot know whether you’re pulled down because the rocket is at rest on Earth or because the rocket is accelerating in the “up” direction.

-

-  Similarly, the Universe doesn’t care whether you’ve got an “event horizon” or a “cosmological horizon“; it doesn’t matter whether a point mass (like a blackhole) or dark energy (like a cosmological constant) is accelerating two observers relative to one another.

-

-   In either case, the physics is the same: a continuous amount of thermal radiation gets emitted. Based on the value of the cosmological constant we infer today, that means a blackbody spectrum of radiation with a temperature of 10^-30 K will always permeate all of space, no matter how far into the future we go.

-

-  Even at its very end, no matter how far into the future we go, the Universe will always continue to produce radiation, ensuring that it will never reach absolute zero. However, this final-state bath of photons should be tremendously difficult to ever observe. With a temperature of 10^-30 K, this cosmic radiation should have a wavelength of 10^28 meters, or about 30 times the size of the observable Universe today.

-

- It may be a long journey to the very end, but if what we think about the Universe today is correct, even empty space, as far into the future as we care to go, can never be completely empty.  That’s good to know.

-

January 26, 2022        UNIVERSE  -  what is its lifetime like?               3422                                                                                                                                               

----------------------------------------------------------------------------------------

-----  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, January 26, 2022  ---------------------------

3432 - PHYSICS - the way I learned it?

 -  3432   -  PHYSICS  -  the way I learned it?To get the famous equation  E = mc^2 we have to take the square root of   E^2 = m^2 * c^4.  When you take a square root you always get two answers because a square of a negative is a positive.  Therefore, mathematically a negative energy does exist.( E=mc^2)

-------------  3432  -  PHYSICS  -  the way I learned it?

-  Physics is the science of nature.  It is the study of the Universe’s matter, energy, motion and force.  Matter and Energy are the same thing ,  Energy = 90,000,000,000,000,000 * mass. ( E=mc^2).   

-

-   Motion and Force are related as:  Force = mass * acceleration. (F=m*a).  Acceleration is a change in a change in distance with time.  ( In calculus it is called the 2nd derivative) .  Distance can be called space, it can also be called length.  Physics boils down to:

-

--------------  velocity  =  length / time

-

--------------  acceleration  =  length / time^2

-

-------------- momentum  =  mass * length / time,        Momentum  =  mass* velocity

-

-------------  Energy  =  mass * length^2  / time^2,      Energy = Force * length

-

-------------  Force  =   mass * length / time^2 ,            Force  =  Momentum /  time

-

------------- Power  =  mass * length^2 / time^3,         Power  =  Energy / time

-

------------  Action  =  mass * length^2 / time,           Action  =  Energy * time

-

-------------  Frequency  =  1 / time                               Frequency  =  (time)^-1

-

-------------  Pressure  =  mass /  length * time^2,         Mass  =  Pressure * acceleration

-

-------------  Work  =  Torque  =  Energy  =   Heat Flow  =  mass * length^2  / time^2

-

-  If we replace these fundamental physic’s concepts with units of measurement  it all boils down to kilograms, meters and seconds.. :

-

-------------  Velocity  =  meters / second

-

-------------  Acceleration  =  meters / second / second

-

-------------- Momentum  =  kilograms * meters / second

-

-------------  Energy  =  kilograms * meters^2 / second ^2,   called  joules

-

-------------  Force  =   kilograms * meters / second^2,  called  Newton’s

-

------------- Power  =  kilograms * meters^2 / time^3 , called  watts =  joules / second

-

------------  Action  =  kilograms * meters^2 / second

-

------------  Frequency  =  1 / seconds, called  hertz

-

------------  Pressure  =  kilograms /  meters * seconds^2

-

------------  Work  =  Torque  =  Energy  =   Heat Flow  =  kilograms * meters^2 / second ^2  =  joules  =   electron volts  =  kilowatt hours

-

-  So, you can see that physics is simply kilograms, meters and seconds.  Mass, space and time.  Or, Energy, and  Space-time. That is pretty simple.  You only have 2 things to remember.   It gets even simpler. 

-

-   There are only 20 or so particles that make up all mass and all the forces that affect mass.  In our everyday lives this boils down to 3 particles:   Quarks , electrons,  and photons ( called Fermions, Leptons, and Boson , if you are a physicists).  

-

-    Up and Down Quarks and electrons make up ordinary matter, or mass.   Photons are the carriers of the forces that carry light and all electric and magnetic energy.  Chemistry and Biological are really only electric forces, so physics has live covered as well as the stars and planets.

-

-  If we list all the particles that make up the Universe we can see only 4.5% of the total Universe.  Hydrogen gas throughout space and the intergalactic medium is 4% so that leaves only 0.5% that is the Ordinary Matter for all the stars, planets, and life that we know of.  We see and know only 1 part in 200 of what is out there.

-

----------------------  0.5 %  stars, planets, and all the elements in the Periodic Table

-

---------------------    4  %   hydrogen gas

-

---------------------  22%  Dark Matter

-

---------------------   71.5 %  Dark Energy.

-

-  95% of the Universe is outside the physics that we understand.  We are dealing with only 5 % .  Are there many more particles that are unknown?    Or, are there more fundamental particles that these particles are made?  Maybe all the fundamental particles are made up of vibrating strings.  Then there would be only one fundamental particle.

-

-  When we study Particle Physics we use two branches of mathematics, Quantum Mechanics and Relativity.  These two math’s do not get the same answers, the math is not consistent.  There must be another theory out there that needs to bring these two together because Quantum Mechanics works perfectly on small things and Relatively works perfectly on big things, but not vice versa.

-

-  There are four particles that exchange or carry all four forces (called Bosons).  Photons carry the electromagnetic forces.  Gluons carry the Strong Nuclear forces that hold protons and neutrons inside the nucleus of atoms.  Bosons carry the Weak Force that causes radioactivity and atomic decay.  Gravitons carry the force of gravity, although no one has discovered this particle to date. 

-

-   Quantum Mechanics says Gravitons exist, yet Relativity says that gravity is not a force at all but a bending of space-time.  The pull of gravity is the path of least resistance through space-time.  Like centripetal force is not a force at all it is just an object resisting its normal motion to go in a straight line at a constant speed.

-

-    Some physicists believe these three forces can be combined into one fundamental force. Gravity, Electro weak, and Strong Nuclear force would combine at 10^25 electron volts.

-

-   In the 1860s the electric force and the magnetic force were thought to be two separate forces.  Now, we know it is carried by photons and only one electromagnetic force.  This force carried by photons and the Weak Nuclear force carried by Bosons may also be a single force.  The “Electroweak” force.

-

-  Because space has 3 dimensions forces radiate as a sphere with a surface are of 4*pi*r^2.   Therefore the forces decay is proportional to 1/ (radius)^2 , or,  (radius)^-2.  Gravitons and photons act over infinite distances.  Gluons and Weak Bosons only act over less than the diameter of the atom, 10^-10 meters.    The range of the Boson’s Weak Nuclear Force is only 10^-18 meters. 

-

-  Gravity is extremely weak compared to the other forces.  2 electrons repel each other with like negative polarities with a force 10^42 times greater than the force of gravity pulling them together.  Gravity is always an attractive force.  There is no negative gravity as far as we know. 

-

-   However, electric and magnetic forces come in opposite polarities to cancel each other out.  Quarks carry positive charges and electrons carry negative charges.  Add all the charges up in the Universe and it sums to zero.  Magnetic forces come with north and south polarities.  The same is true, these magnetic forces sum to zero.

-

-  The energy of any particle is a function of its mass and its motion.  E=mc^2 and        K.E.  = 1/2*m*v^2.  Kinetic Energy is the energy of motion.  It is equal to 1/2 times mass * (velocity)^2. 

-

-   Energy can be expresses in joules or electron volts, or kilowatt-hours.  One electron volt is the energy change of one electron moving across the electric potential of 1 volt.  1 eV  =  1.602*10^-19 joules.  

-

-  Since mass and energy are the same thing, mass too can be expressed as electron volts.  m =  E/c^2 .  However, the c^2 , speed of light squared is always assumed for  mass, expressed in electron volts.  It is never shown,  but it is there.  The mass of an electron is 511,000 eV / c^2,  but the c^2 is always assumed.  The mass of a proton is 938,000,000 eV.

-

-  Particles are often described as waves.  The wave is nothing more than description of the way in which particles convey energy.  Remember, mass and energy are the same thing.  Waves are not characterized by positions.  Waves are characterized as having wavelength, frequency, amplitude and phase.

-

-  The frequency of visible light is a range from 400,000,000,000,000 wavelengths/ second to 800,000,000,000,000 wavelengths / second.  Frequency is sometimes referred to as cycles / second.  The wavelengths of visible light ranges from 750 nanometers for red light to 375 nanometers for blue light. 

-

-   The velocity of light is always constant, the same, 299,792,458 meters / second  (3*10^8 m/sec).  Sometimes light appears slower in another medium but the speed is actually slower because light is being absorbed and remitted by atoms of the medium. Between atoms it is still light speed.  The product of frequency and wavelength is 

3*10^8  (f * w  =  c)

-

-  The energy of an electromagnetic wave is proportional to the frequency of the wave and inversely proportional to the wavelength of the wave.  The higher the frequency the higher the energy.  The smaller the wavelength the higher the energy.  X-Rays have higher energy than radio waves.  Gamma Rays have smaller wavelengths than visible light waves.

-

--------------------  E  --- proportional --- f

-

-  Any time one variable is proportional to another variable the expression can be turned into an equality if the appropriate Constant of Proportionality is a multiplier. “h” is Planck’s Constant of Action which is equal to 10^-34 

-

--------------------  E  =  h * f

-

---------------------  E  =  10^-34 * f

-

-  Momentum is inversely proportional to wavelength.  Frequency* Wavelength  =  Speed of light, f  * w = c,  f * w  = 3*10^8

-

------------------  Momentum  =  10^-34 / w

-

------------------  Energy  =  10^-34 * c / w   =   10^-26 / w

-

-  These energy and momentum numbers seem awfully small.  But, it is not small to an electron.  If the wavelength of an electron is accelerated through an electric potential of 50 volts, that is 50 eV,  its wavelength is 2 * 10^-10 meters,  which is roughly the spacing between atoms in a crystal.  (20 nanometers).

-

-    A wave is simply the way a particle distributes its energy.  Normally a particle has a mass, but, a photon is massless, yet, it still has wavelength, energy, and momentum.  An electron has a little mass and a wave of energy the length of which is the diameter of an atom, 10^-10 meters.  A proton has a mass 1,800 times that of an electron and a much smaller wavelength for distribution of its energy.

-

-  To observe a sub-atomic particle it must interact with something from the system of the observer.  Some physical quantities are waves with positions expressed as uncertainties (or, probabilities, or statistics).  

-

-    Some quantity uncertainties are linked together as “conjugates“.  The product of their uncertainties is always less than 10^-34.  If one uncertainty is very high than the other uncertainty is very low.  Energy and time are conjugate quantities.  The certainty you can determine the energy the less certainty you can measure the time it takes to measure the energy.  Position and momentum are two other conjugate quantities.  Momentum is mass * velocity.

-

----------  probability of position * probability of velocity  <  10^-34

-

----------------  dx  *   dv  <   10^-34 

-

-    If you measure the position of an electron  with greater certainty,( a larger probability for delta x) than you can not know its velocity with certainty ( a smaller probability for delta v) because the product of the two probabilities must be less than 10^-34. 

-

-   If you measure the velocity with greater certainty you can  know its position with less certainty.  The same trade off happens with Energy and time.

-

----------------  dE  *  dt  < 10^-34  

-

-  Mass is a gravitational charge.  It generates a gravitational field.  Much the same as an electrical charge generates an electric field, or a magnetic charge generates a magnetic field.

-

-------------  Force of Gravity  =  G *M * m / r^2

-

-------------  Force of Gravity  =  10^-11 *M * m / r^2

-

-------------  where:  “M” and “m” are the masses, “r” is the distance between them and “G” is the Constant of Proportionality. 

-

-------------  Force of Electric Charge  =  K * Q * q / r^2  

-

---------------Force of Electric Charge  =  10^9 * Q * q / r^2  

-

------------  where:  “Q” and “q” is the two electric charges, “r” is the distance between them and “K” is the Constant of Proportionality.   Note that the electric force is much larger than the force of gravity.

-

-  Symmetry requires there be laws of Conservation for Energy and Charges.  The conservations laws came from the fact that there is Symmetry in the Universe where things remain unchanged regardless of the frame of reference.  If something stays constant with changes in space and time it is “invariant“.

-

-    Emmy Noether (1882-1935) developed the theory that for every global invariant there is a physical quantity that is conserved.  Energy is conserved, Charge is conserved.  Momentum is conserved.  Neither can be created or destroyed, they can only change from one form to another. 

-

-   From space-time Symmetry we can conclude the Conservation of Energy.   Energy can have many forms, however, all can be boiled down to Kinetic Energy, the energy of motion, or Potential Energy, the potential energy of mass and fields.  Energy is the product of Force and distance. 

-

-   A theory is that all 3 forces can be combined into one unified force.  Gravity, electro weak, and the Strong Nuclear forces unify at 10^16 billion electron volts.  The 4 forces come from Gauge Symmetry.  Relativity comes from the Symmetry of space and time.  Rotational Symmetry is the Conservation of Angular Momentum.  Parity is mirror Symmetry.

-

-  Angular Momentum, or spin, is always an integer or half integer of “h”, 

Planck’s Constant, 10^-34.

-

--------------------------  0,   h/2,   h,   3h/2,   2h,   5h/2,   3h............  etc.

-

-------------------------- Fermions are the 1/2 integer spins and Bosons are the integer spins.

-

-  Matter is made from Fermions, Light is made from Bosons.  Quarks and electrons are Fermions and photons are Bosons.  Fermions can not occupy the same space.  Bosons can.  

-

-  Two flashlight beams can face each other and overlap easily.  Two electrons can not occupy the same space inside an atom.  However, if the light beams were made more powerful sending Gamma Rays at each other the photons energy can change into matter.(E=mc^2).  Photons can collide and electron and anti-electrons are produced.  Anti-electrons and all anti-matter are negative energy particles traveling backwards in time.

-

-  As you add more energy to matter new generations of particles are created.  Most decay rapidly as all particles seek the lowest energy level.  Ordinary matter is at the lower energy level.  That is what makes it stable:

-

----------------------  Quark  Up --------- 3,000,000 eV

-

---------------------           Down ---------  7,000,000 eV

-

----------------------  Electrons    ---------    511,000 eV

-

---------------------    Neutrino   ---------            0.13 eV

-

-  Now add more energy and the next generation of 4 particles are formed:

-

----------------------  Quark  Charm --------- 1,200,000,000 eV

-

----------------------  Strange -----------  120,000,000 eV

-

----------------------  Muon    ----------------------    200,000 eV

-

---------------------    Muon Neutrino   ------------------ 0.13 eV

-

-  Add even more energy and the 3rd generation of 4 particles are created:

-

----------------------  Quark  Top --------- 175,000,000,000 eV

-

---------------------    Bottom ---------  4,200,000,000 eV

-

----------------------  Tau    ------------------   1,800,000,000 eV

-

---------------------    Tau Neutrino   -------------------- 0.14 eV

-

-  For the force carriers the mass-energy of photons, gluons and gravitons is zero.  However, the mass of bosons that carry the Weak Nuclear force range from 80,420,000,000 eV to 91,190,000,000 eV. 

-

-   You can see why particle physicists need to use high energy cyclotrons and beam colliders to study these particles.  But, the amazing thing is that there are only 12 particles of matter and 4 force carriers.  That is the whole Universe that we know of.  The other 95% we are still working on.  Physics just got started.

-

-  Relativity comes from symmetry in space-time.  Physics is the laws of nature and the laws remain the same regardless of where you are, which direction you are going, or how fast you are moving.   That is space-time symmetry.   

-

-  Light is the communicator of motion.   Communication can only move at 3*10^8 meters / second.  Holding this speed constant in all frames of reference requires that as a object approaches the speed of light, v = d /t , time must slow down, distance must shorten, mass must increase.

-

-    The equation for Relativity  where “o” stands for the observer, where T, Time, L, length, and c+ 3*10^8.  ( 1 / ( 1-v^2 / c^2) is called “ Gamma” or the Lorentz Factor.)

-

-------------------  To^2  -  Lo / c  =  T^2  -  (L / c)^2

-

-------------------  To^2  =  T^2  /  ( 1 - v^2 / c^2)

-

----------------  Lo =  [ 1 / (1 - v^2 /c^2)] ( L - v * T)

-

-  If an observer is traveling at 87%  the speed of light than in 1 second we would observe 2 seconds, because time has slowed down.  It the spaceship was 100 feet long we would observe it at 50 long and flattened like a pancake.  Mass approaches infinity and it would take an infinite amount of energy to accelerate it further.

-

-  Relativity’s equation for  Energy.  Energy is proportional to Time.    Momentum is proportional to Space, where E, energy, p, momentum, p=m*v  =  mass * velocity. 

-

-------------  E o^2  -  p * c^2  =  E  -  p * c^2

-

-  If a particle is at rest than momentum, p, = zero. And the equations are reduced to:

-

----------------  E^2  =  m^2 c^4

-

-  To get the famous equation  E = mc^2 we have to take the square root of 

E^2 = m^2 * c^4.  When you take a square root you always get two answers because a square of a negative is a positive.  Therefore, mathematically a negative energy does exist.( E=mc^2)

-

-  Maybe Dark Energy has something to do with negative energy.  The vacuum of space may be filled with particles in the Negative Energy state.  Anti-matter may be negative energy going backwards in time.

-

-  E = mc^2 is for particles at rest.  If a particle is moving we have to add Kinetic Energy in order to get Total Energy.

-

---------------------  E  =  mc^2  + p^2 / 2m

-

--------------------    p  =  m * v

-

---------------------  E  =  mc^2 + m*v^2 / 2

-

-   Getting used to big and small numbers.  2.2 pounds, or one mole of material has 602,000,000,000,000,000,000,000 molecules. 

 The mass of an electron = 0.000000000000000000000000000000911 kilograms 

 There numbers are more easily expressed as 6.02*10^23 molecules and 9.11*10^-31 kilograms.

-

-    Whenever things are proportional the expression can be turned into an equality by multiplying by a Constant of Proportional.  E = h * f.   10^-34 is Planck’s Constant of Action actually equal to 6.6260755*10^-34 joule * seconds, or,

 4.1356692*10^-15 electron volt * seconds,  or,

  h/2*pi, the wavelength of one 2*pi cycle, 1.0545727*10^-34 joule* seconds.  

We will just use 10^-34 for our constant of proportionality and keep the units in kilogram*meters^2/ second.

-

-  G is the Gravitational Constant  =  6.67259 * 10^-11 meters^3 / (kilogram * second^2)  “K” is the Coulomb Constant  =  8.987552*10^9 kilogram* Meters^3 / (seconds^2 * coulombs^2)

-  

January 25, 2022          PHYSICS  -  the way I learned it?         1074     3432                                                                                                                                               

----------------------------------------------------------------------------------------

-----  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, January 25, 2022  ---------------------------